Author: Doni, Giovanni Battista
Title: Treatise on the Genera and on the Modes of Music, second book
Source: Bologna, Museo internazionale e Biblioteca della Musica, MS D.143, <224>- <496>

[-<224>-] On the Modes, second Book On the seven Species of the Diapason. It is something recognised by everyone that some difference between the Modes derives from the species of the Diapason, albeit the modality of this was not agreed universally, as well as the issue of whether something else is required to differentiate one from the other. It is necessary to explain what these species are before anything else. Therefore, Ptolemy says [[then he adds that these differences in the Diapente and in the Diapason are found through the Disjunction, but in the Diatessaron Therefore, it is certain that a System will have as many intervals as species.]] Therefore, every System will be distinguished according to the different position of the interval which is found in it only once, and, because such interval can change position as many times as the intervals are, it follows that the System of four notes, namely, the Diatessaron, cannot have but three species, because [-<225>-] it is composed of just three intervals. The System of five notes, or Diapente, has four and the Diapason seven, but the divisions of the species of the octave derive from the combinations of the species of the fourth and of the fifth, which, since they regulate the melodies and the first division of the Diapason, the differences are derived from these and not from other smaller intervals, rather than from the fact that the ancients did not know any other smaller consonance, as Salina says in the first chapter of the fourth book. Because the intervals also vary according to the different genera, since each genus has a particular one which is the third one going upwards, as the Tone in the Diatonic, the Trihemitone in the Chromatic and the Ditone in the Enharmonic, one should derive the difference between the fourths from this, but, for greater eas, and because there is also another tone in the diatonic fourth, the habit of considering the position of the Semitone in the diatonic fourth has prevailed, albeit Ptolemy adopts the third interval in every genus. However, everything turns out the same because the Greeks begin from the top, while the Latin writers from the lower end, therefore the first species of those is also the first species of these, and so are the other ones. Therefore, the first species of the Diatonic fourth is the one which has the Semitone in the first place towards the low register, the second the one that has it in the second one and the third one in the third place. However, in the case of the Diapente as well as in the Diapason, since they have the tone of the Disjunction, it is more convenient to base the different of the species on it, albeit one should note already that it is not true, as Salinas says, that there is a discrepancy [-<226>-] between Ptolemy and Cleonides (whom he called Euclides) in counting the species, because both of them and all the Greeks maintain the same order ascending from the low register to the high one in counting the species of the Diatessaron and of the Diapente, either considering the high interval of each of them which is the tone or the low one, or Semitone (which one must bear in mind to avoid the misunderstandings that cloud the minds of many). The Greeks begin the first species from the Hypate hypaton [sqb] mi to the Paramese [sqb] and then the second one from the Parhypate Hypaton [ [C sol fa ut add. supra lin.] to the C sol fa ut, and thus the others in sequence, assigning the first species (the lowest) to the highest Tone, the second one to the following one, and so on, if we consider the disposition from the low to the high register, but, if we consider the order of the Tones, we should progress from the high to the low register. This has to be considered well because it is not something which is understood so well, and it has made many make some strange statements since they believed that there are contrasting opinion among the Greeks themselves, while Boethius counted as first species of the octave the one which occurs between Proslambanomenos A re and the mese a la mi re, as the second one This distribution was followed by modern writers up to Zarlino, who - considering that the new Scale or System called Gamma because it starts from [gamma] rather than from A re - wanted the order of the seven species to start from [-<227>-] that or from C fa ut, which is the same according to modern modes, since there is everywhere the same deduction, namely, Ut re mi fa. Consequently, since Boethius had to alter the sequence of the fourth and of the fifths, if he wanted them to correspond to his species of octave which is formed by them, equally, Zarlino was bound to alter the sequence of the species in his fourths and fifths. From this there followed that what was the first species of the fourth according to the Greeks, it became the second according to the followers of Boethius and the third one according to more modern theorists or followers of Zarlino, and thus all the others are disrupted in the same way, as well as the fifth which depend on those and those of the octaves which are based on both. Hence, one can see manifestly that everything is disrupted in time and that music, begets always some new monster, such as Africa does. One will be able to ascertain from what follows whether the followers of Boethius improved much their profession or rather added to its disruption by moving away from the Greeks, and whether modern writers have done so by moving away from the Greeks and from the followers of Boethius. One can see from the example that I placed here what correspondence have with each other these different ways of counting the consonances. [-<228>-] Second chapter [Doni, Treatise of the Genera and of the Modes, second book, 228, 1; text: secondo i Greci, Boetiani, ut, re, mi, fa, sol, la, a, G, F, E, D, C, [sqb], A, [gamma], prima specie, seconda, terza] [[Doni, Treatise of the Genera and of the Modes, second book, 228, 2; text: ordine de Greci, Boetiani, ut, re, mi, fa, sol, la, a, G, F, E, D, C, [sqb], A, [gamma], prima specie, seconda, terza, aa, g, f, e, d, c]] One must consider a number of matters. Firstly, in our present System of nine notes (which we have placed here because it contained the first Diapason of the ancient System with the note added by Guidone from which modern theorist start their deductions) the Greeks could not start the first species from [sqb] mi but from e la mi, if they wanted that the other should follow in order, namely, that [-<229>-] the first one should have the Semitone in the first place from the bottom, the second in the second and the third in the third. Conversely, modern theorist can start their first species, which says ut re mi fa, both on Gamma ut on C fa ut. Secondly, the Greeks would not have elected to start from [sqb] mi in particular, had they followed the practice to place the [gamma], called by some Hypoproslambanomeons for this reason, ut under A re or Proslambanomenos, because they could count the species from these three notes. However, modern theorists starts more readily from C fa ut than from gamma ut and the followers of Boethius from D sol re than from A re, because they distinguish Authentic and plagal modes, and consider those the most noble and first. We shall see late what this means. However, the ancient Greeks did not consider this difference. Thirdly, the fact that Cleonides begins (in the two genera, Enharmonic and Chromatic) the first species form [sqb] to E and follows it with the one from C to F, rather than from E to a, as Ptolemy does, suggests to Salinas that he followed a different sequence. This is not true, because a little further on he says that the first Species in the Diatonic has the semitone in the first place, the second in the second and the third in the third, therefore it does correspond to Ptolemy’s sequence and to the one of the other Greeks. However, we shall see later why this difference occurs in the two other genera. Fourthly, this distribution is much clearer and easier than the others, as Salinas also confirms following the natural sequence of the disposition of the Tetrachords which have the Semitone in the first place in all genera (albeit there is no uncompounded Semitone in the Enharmonic). Therefore, [-<230>-] since it would not be attractive not to place in the sequence of the tetrachords the one that follows their natural disposition within the System, thus, they placed the species that has the Semitone in its lowest part as the first species with good reason. This proved practical as well for them as such species suits the Dorian, which is the most highly regarded of the modes and the one in the middle of them all, as well as the Mixolydian and Hypodorian, which are the first and last of the seven ones and they are almost subordinate and plagal in relation to the Dorian, as we shall see later. Fifthly, one must note that only the first of the three species of fourth occurs between stable notes, since it has the same first and last note as those of the Tetrachords which occur naturally in the System, while the other two occur between the mobile notes, which are the two middle ones, as one can see in these tetrachords [sqb] c d E. .E F G a. where the stable ones are [sqb]. E a. and the other four are mobile. We can consider the different way of numbering the species of the fifth adopted by the Greeks, by Boethius’ followers and my the more modern theorists in a similar way, because the first of the Greeks is the second of Boethius’ followers and the third of the modern theorists, the second of the Greeks is the third of the Boethius’ followers and the fourth of modern writers, the third of the Greeks is the fourth of Boethius’ followers and the second of modern theorists, the fourth of the Greeks is the first of Boethius’ followers and the second of modern writers and the fifth of the Greeks is the first of Boethius followers and the of modern theorists. Nevertheless, the Greeks have considered the different position of the tone in differentiating them, namely of the third one which is found in all genera, and this produces a much better result because the same disposition works for all the genera, while the others have considered the position of the Semitone. [-<231>-] [Doni, Treatise on the Genera and on the Modes, second book, 231; text: [gamma] A re, [sqb] mi, C fa, D sol re, E la mi, F fa ut, G sol re, a la mi, [sqb] fa, c ordine de Boetiani, di Iacopo fabro secondo i, del Zarlino moderni, prima specie, seconda, terza, quarta, noi, nostro] [-<232>-] However, one must note here that Boethius placed the first species from a to E, the second from [sqb] to F, the third one from C to G and the fourth one from D to a, while in the second one there is not a true fifth but a Semidiapente, since it has a Seemitone instead of a tone, since he considered not so much the consonance of the note, but their order. He was not followed in this, and quite reasonably so, since in this way he establishes only three species and instead of the fourth one he places a false fifth, which it is something that he must have been very aware of, but that he disregarded. Not also that we have placed the disposition of the diapente according to the Greeks following the way in which Ptolemy and Cleonides are interpreted commonly. However, since one cannot gather from Ptolemy’s words if he understood as first species the one which has the tone of the disjunction in the first place from the bottom and the fourth in the first place above, or the other way round, since he does not name the notes, but says only that the first and the fourth species are contained by stable notes and the other two among the mobile ones (which occurs in one way and in the other) and also because Cleonides departs from this somewhat (if there text is correct) by placing the tone in the first species the tone in the high one but in the second place upwards in the second, we still consider much better to place the tone in the first place from the bottom in the first species, in the second place from the bottom in the second going upwards, in the third place in the third species and in the fourth one in the fourth species. These are the reasons, namely, because it is convenient to distinguish the fourths according to the position of the Semitone and the fifths from the position of the tone of the disjunction, but much more because the three principal modes, Dorian, Phrygian and Lydian, are distinguished according to the three species of fourths, as we shall see, and the four which are less principal from the four species of fifth, apart from the fact that Boethius himself followed the middle disposition for the most part, [-<233>-] nor, in my opinion, it is possible to find a disposition which is more attractive than this one, or one which is easier to remember. As to Fabro’s disposition, it is not worth discussing, because it is not very rational as it does not follow the order of the Semitone or of the Tone and it does not place its fifths among the notes, the first and the second at the distance of a semiditone and the second and the third at the distance of a ditone. For this reason it has not been followed by anyone, as far as I know. Moreover, albeit he was a follower of Boethius, he has deviated more than any other from his order and sequence because of the difficulty, I believe, that he met in the second species of the fifth that occurred between [sqb] and F, which is a false fifth. [-<234>-][Doni, Treatise on the Genera and on the Modes, second book, 234; text: 7 Spezie della Diapason ordine del Zarlino [[moderni]], de Greci, di Boetio, Boetiani, [gamma], A, [sbq], C, D, E, F, G, a, c, d, e, f, g, aa, [sbq][sbq], ut, re, mi, fa, sol, la, [alpha], [beta], [delta], [epsilon], [zeta], [eta], 1, 2, 3, 4, 5, 6, prima, seconda, terza, quarta, quinta, sesta, settima] [-<235>-] [[This table illustrates that the first species of the octave is formed of the first of the fourth and of the fourth, the second of the third of the fourth and the second of the fifth, the third from the second from the fourth and the third of the fifth.]] Perhaps one will be better able to learn how the species of the Diapason are composed of the Diatessarona and of the Diapente from the table drawn below, where we have placed each species in two ways, as it occurs within the octave, as well as these signs S and T, which indicate tones and semitones. [Doni, Treatise on the Genera and on the Modes, second book, 235-236; text: Specie della Diatessaron, S, T, prima secondo i Greci, seconda de Boetiani, terza de moderni, del fabro, 1, 2, 3, 4] [-<237>-] [Doni, Treatise on the Genera and on the Modes, second book, 237; text: 7 Specie della Diapason secondo i Boetiani] [-<238>-] On the Species of the Diatessaron and of the Diapason in the Chromatic and in the Enharmonic. In order to understand correctly how the species of the first consonances occur in the two genera Chromatic and Enharmonic, we must remember what is Thick or Dense in the tetrachords, because it is clear that the three sorts of Diatessaron are distinguished by its varying position, as the three sorts of Diatessaron and of the Diapente are distinguished in the Diatonic by the simple Semitone and from its different position. Denso o piu comunemente dal Sito deel tuono (che in questi due generi [[si t]] non se ne troua più di uno nelle quinte) come [[ci inseg]] si caua manifestamente da Equally, one must know that the first and lowest notes of each Tetrachord are called Barypycne, which means low and dense or low and thick from the word [barys], which means low and [pyknos], which means dense. They are called in this way because towards the Dense extremity, because the Dense is placed in the lowest part of each tetrachord. Therefore all the two Hypate shall be Barypycne, as well as the paramese and the Nete Diezeugmenon, since each is the first note from the bottom of the four Tetrachords of the Disjunct System. [-<239>-] Moreover, the second note of each tetrachord is Mesopycne, because mesos means middle and they are called thus because they divided the Dense and separate the first and lower interval from the second and higher one. These are the two Parhypate of the two lowest tetrachords and the two Trite of the two high ones, which correspond to those. Oxypycne, or high and thick because [oxys] means high, are called the ones which contain the dense towards the high part of the tetrachord and separate it from the second interval, which is the Trihemitone in the Chromatic and the Ditone in the Enharmonic. These are the two lychani of the lowest tetrachords and the two Paranete of the higher ones which correspond to them. Also, since the barypycne are the extreme notes of the Tetrachords, they are all stable, while the Mesopycne and oxypycne are all mobile, because they change according to the genera, as it was said above and the illustration shows. Besides these, there are the Apycne, or not dense or far-removed from the Dense, because a is a particle which indicates deprivation. The ones that mark the low boundary of the two separate tones of the Tetrachords, namely the Proslambanomenos, the Nete and the last of all or nete Hyperboleon, are called thus. It is very true that the Mese is not Apycna all the time because it is not Apycna any more when one uses the tetrachord of the conjunct notes or when one sings with the b flat, but it becomes Barypycna because, in that case [-<240>-] it is the first and lowest of said Conjunct Tetrachord, the second of which, namely, the Trite, is Mesopycna, as the other Trite, and, equally, the Paranete is oxypycna, as the paranete of the other tetrachords. However, the Mese of this Tetrachord is Apycna, because, since this conjunct Tetrachord is divided in the Tone of the Disjunction, said tone occurs a tone higher and it divides the Synemmenon and the Hyperboleon, hence the nete Hyperboleon cannot be Barypycna any longer, because it has not the Dense above itself but said Tone. Therefore, it becomes Apycna instead of the Mese, since all that is adjacent to said Tetrachord, on the contrary turns out to be Barypycnon, as we said. Therefore, the Apycne are three, namely, the Proslambanomenon, the Nete Synemmenon and the Nete Hyperboleon, while the Barypycne are four in number, namely, the Hypate Hypaton, the Hypate Meson, the Paramese and the Nete Hyperboleon. The Mesopycne are five, namely, the two Parhypate of the hypaton Tetrachord and of the meson, the three Trite, Synemmenon, Diezeugmenon and Hyperboleon. The oxypycne are also five, namely, the two Lichanos, Hypaton and Meson, and the three Paranete, Synemmenon, Diezeugmenon and Hyperboleon. Finally there is a variable one, since it can be either Apycna or Barypycna, which is the Mese, although, as I said above, only a note (which is the trite b ga) of the Synemmenon Tetrachord has a different sound from the other ones, at least in the participated System. If we take all this as our basis, the first Species of the Diatessaron in these two genera is Barypycna or among the Barypycne, the second one is among the the Mesopycne and the third one among the mesopycne, so that, the three [-<241>-] Diatonic Species correspond exactly to these and they occur among notes of the same name, and the, moreover, the Barypycna species corresponds also in its extreme intervals, as we can see here. [Doni, Treatise on the Genera and on the Modes, second book, 241; text: Prima Specie della Diatessaron, Diatonica, Cromatica, Enarmonica, Tuono, Semituono, diesi, ditono Trihemiuono, A, E, F. [sqb], Barypycna, Hypate Meson, Mese, lichanos hypaton, Parhypate, Hypate, Diatonica, Seconda, D, F, G, C, Mesopycna, Proslambanomenon] [-<242>-] [Doni, Treatise on the Genera and on the Modes, second book, 242; text: Terza Specie della Diatessaron, Diatonica, Cromatica, Enarmonica, oxypycna, Tuono Semituono, Triheemituono, Ditono, diesis, lichanos meson, Parhypate Hypaton, Hypate, Mese, Diatoniche, Mese] [-<243>-] Explanation of these illustrations, Chapter Since it is possible that who reads these illustrations might find something not so easy to understand at first sight, it will be appropriate that we move on and illustrate them. First of all we shall explain why the chromatic and Enharmonic notes of the Tetrachord correspond to the Diatonic in the first species, but not in the others. To explain this, we must remember that in every Diapason, which is a perfect System, there are no more than two intervals which belong to the Chromatic (leaving aside the compounded Tetrachord for now) and also two Enharmonic notes, which are the two lichani, in the lower tetrachord where we place our examples, as the Paramese above, because the Parypate correspond in sound and name to the Diatonic ones. These two intervals are the second semitone of each tetrachord, and they have as their lower note C and F, according to modern practice, and, as to their higher note, we do not change the letter, but we distinguish them with these special signs # #, which denote them and, albeit they do not change the note, we must imagine that they are higher (since they are called raised) just as their interval is enlarged by a Semitone. Equally, in the Enharmonic, one does not add anything than a note for each tetrachord, which divides the first interval of the tetrachord, just as the Chromatic divides the second one, namely, the first tone. However, since this does not correspond in its place or in its tone to any chromatic note, since it is a specifically Enharmonic one, it is called simply Enharmonic Parhypate and it should have its own figure as the chromatic lichanos does, as it had in ancient times. However, we accommodate [-<244>-] this by using the very same notes of the Hypate which are common and mobile simply by adding this sign [signum] or this one [signum] (which seems to us easier because it expresses better the three common ones of the five which the larger Semitone then contains) and by imagining also that such note is an Enharmonic diesis higher, just as the sound that it represents. Now, therefore, since the first species follows the natural order of the Tetrachords and it is contained among the stable notes, the two extreme ones are necessarily the same in each genus. This however does not happen in the other two species, because, since they have as their extremes some mobile notes, which are different as to their sound and their tone when genera vary, therefore, it follows that they cannot have the same extreme notes, and that the diatonic fourth in the second species starts on D la sol re or a la mi re up to G sol re ut or D la sol re, according to the selected tetrachord, while in the Chromatic it starts from C sol fa ut or F fa ut up to F fa ut and b fa, according to the conjunct tetrachord. However, in the Enharmonic the same species of fourth starts on E la mi or [sqb] mi with the enharmonic diesis and goes up to E la mi with the diesis and also to A la mi re with the same diesis, were it to proceed through b flat or by conjunct tetrachord. The same would occur if one wanted to play the Chromatic and the Diatonic on an instrument, for instance a Harp with the span of two or three octaves and with all the necessary notes of all the genera. In fact, in the species contained within stable notes his melodies in all the genera according to their extreme notes would be successful, but in the species based on mobile notes this would not occur, therefore, if one played within the species of E la mi [sqb] mi or a la mi re [-<245>-] one would start and finish one’s melodies in one of these notes, but if one wanted to play in the species of D la sol re or G sol re, which contains the third species of fourth, he would not start nor stay in unison when one moves from a genus to the other, as one can see from the illustration. One must pay close attention to it, because without it is not possible to understand how the Seven modes are organised according to the last two genera. We must also note that the highest and the lowest note of the tetrachords in the third species are marked, according to our practice, in the same notes, except for the fact there is the added accidental sign in the chromatic, which demonstrates that they are in unison in the Diatonic and in the Enharmonic, but not in the Chromatic. This derives from the fact that the Enharmonic lichani are in unison with the Diatonic and Chromatic Parhypate, but the Chromatic lichani are particular to it and have a different sound. [[This disruption did not occur in the ancient tablatures]] One must also be aware that our way of writing music was very different from the ancient one, which was more logical and easy, because, whereas we, for instance, would mark the eight notes of an Enharmonic octave in this way: E E# F A [sqb] [sqb]# C e, because we place in the same note and Diatonic line the Enharmonic and Chromatic particular voice adding this sign [signum], hence there follows this draw-back, namely that one cannot see the eight letters and that the Ditone and Semiditone do not appear otherwise uncompounded, since they are in a simple genus, the ancients followed another method, ascribing certain signs only to the particular chromatic and Diatonic notes, as for instance [sqb] C [signum] D E F G [signum] A [sqb] where the dot is added only to the two which are specifically Enharmonic. Therefore, it follows that an octave has all its eight letters, as it has the same eight names of the notes in all the genera, with the addition of the adjective Chromatic or Enharmonic to the particular notes, namely Hypate, Parhypate, Lichanos, Hypate Lichanos Hypaton Paripate Lichanos Meson Paramese. This distribution was really more [-<246>-] wellstructured and adapted to their use in the three genera than our own. It follows from here that where we change the note beneath when we change genus, we would have to do the same with the one above. I will explain this more clearly because, starting from the first note of the perfect System A re, I move on to the second one which is itself common to all the genera and stable as well as the interval that it produces. If then I move on to the next Diatonic note, I proceed to the C which is mobile and it is a Semitone removed from B. However, if I want to ascend Enharmonically rather than Diatonically, it is necessary that I should choose the Enharmonic Parhypate, which produces such interval and which it should have been marked with a C with the added sign that I shall use to indicate the Enharmonic, rather than with a B, which is a stable note, and, consequently, it has always the same Sound and it should not be raised as a figure. I say that this is only brought about by the fact that nowadays there is no distinction between stable and mobile notes, which is something that creates a great deal of confusion and difficulty in understanding the theory and in applying it in practice in these genera. [[For this reason we have wanted to produce here the illustration of the perfect system with all the notes and the names and with the difference between the stable and mobile notes, and those which complete and do not complete the]] [-<248>-] One must also be aware that, in the second and third species of Diatessaron of the Diatonic, the first notes of the Tetrachord have a different name, because in the first one there is only one lichanos, while in the place of the second one there is the Proslambanomenos or the Mese, because the deduction of a Tone, Semitone and Tone, or Re mi fa sol begins only from those two notes, while from the Lichanos Meson one finds the deduction of three tones, namely, fa, sol, re, mi, which occurs because of the Tone of the Disjunction which occurs towards the high register. In the second example one places the Parhypate Hypaton and the Lichanos Meson instead of the Parhypate Meson, because the deduction of three tones fa sol re mi, which is not a species of diatessaron, but a Tritone begins from the Parhypate Meson. Hence one notices the difference between the lay-out of the species of the Diatessaron in the Diatonic from the one which occurs in the two other genera. For this reason the ancients, who were marvellous and incredibly diligent in these matters, considered very rightly that one could not produce a mutation in the thick genera and in the non thick one through the same interval of a Semitone, albeit it is found everywhere accompanied by another one in the Chromatic and divided in the Enharmonic [-<249>-] Demonstration that there can be no more than three species of Diatessaron and four of Diapente, Chapter Therefore, considering with great care the different Position of the Thick in the Chromatic and the Enarmonic, which, if we think carefully, we shall find that it cannot produce other structures or varieties, since, either it is found all toghether towards the low register, as in the Barypycna, or towards the high register as in the Oxypycnna, or half towards the high register and half towards the low one, when the large interval occurs in the middle, as in the Mesopycna, but it cannot occur in the middle, should we not divide the large interval and if we made it compounded from uncompounded by adding another note. However, in that case the Tetrachord would not be simple and it would require five notes. Since I said earlier that the Species of the Diapente in the last two genera progressed in the same way and that they could not be more than four, it will be best to explain this more clearly. Therefore, ne must be aware that, just as one can see that in any of its dispositions the large interval is placed always above the thick, consequently, the Tone of the Division (which makes up the Diapente with the other three intervals) will always be the large interval and below the Thick, as, for instance, in the Barypycne: [Doni, Treatise on the Genera and on the Modes, second book, 249; text: E, F, A, [sqb], Denso, Interuallo grande, ditono, Tuono]. Cleonides places the first species of fifth [-<250>-] in the Mesopycna, which is the second Species in his writings, [Doni, Treatise on the Genera and on the Modes, second book, 250, 1; text: diesi, Ditono, Tuono, medesimo, E [signum] F A [sqb]] in the oxypycna, which is the third Species: [Doni, Treatise on the Genera and on the Modes, second book, 250, 2; text: [[Ditono, E, F]] Ditono, Tuono, Denso, F, A, [sqb], [sqb] [signum], C], and again in the Barypycne with the tone in the first place, which si the fourth species [Doni, Treatise on the Genera and on the Modes, second book, 250, 3; text: Tuono, Denso, Ditono, A, diesi, [sqb] [signum], E] One must note that where the tone is not actually above the large interval, as in this last species, it is so at least virtually, because if one continues the Series of the notes towards the low register, one will have to place the Ditone beneath and the note F beneath the A. The same follows respectively in the Chromatic, by changing the Ditone into a Semiditone and the Semitone divided into dieses into a Tone divided into Semitones. Hence one can see that the four species are determined by the varied positions of the tone of the division, which it is in the first place towards the high register in the first species, in the second place in the second species, in the third in the third species and in the fourth in the fourth one. This fourth species could also have been called Apycna because it starts from a note which is Apycna. Here we are not obliged, but it appears the right thing to do to follow the ancients who considered that in this fourth species one returs to the first species of Diatessaron which starts from the Pycne, and therefore they called the Diapente as well Barypycnon. [-<251>-] As to the fact that this disposition to place a Thick and a large interval alternatively and a Tone of the disjunction (which has the large interval beneath itself and the thick one above) between every two fourths must be always observed, this is confirmed not only from these species, which nobody has enlarged in number, but from the entire lay-out of the perfect System and from the Aristoxenus very words, who discusses this at length in the third book of his Elements, where he often often states that [pyknon pros pykno ou melodeitai oute holon oute meros autou], which means that “the Dense is not sung after the Dense, either whole or in part,” that [touton d'outos ekhonto anagkaion enallax tote pyknon cai to ditonon keisthai.], which means that “the matter laying in this way, it is inevitable that the Dense and the Ditone should be placed alternatively,” that [duo de ditona exes ou tithesetai], namely, that “two ditones cannot be placed one after the other”, then that [peri de ton anison nyn lekteon; pyknon men oun pros ditonou kai epi to bary kai epi to oxy tithetai. dedeiktai gar ei the synaphe enallax tithemena tauta te diastemata;], a little later that [tonos de pros to ditono epi to oxy monon tithetai], a little further that [Tonos de pros pykno epi to bary monon titheto], a little further [en diatono de, tono eph'ekatera hemitonion ou melodeitai [[duo]] a little further that [duo de tonon e trion hemitoniou eph'ekatera melodeitai], a little further that [duo de ditona exes ouketi tithetai.], a little further that [duo de pykna exes ou tithetai], and a little further that [homoios d'hexei kai epi ton khrematon plen [-<252>-] to ge meses kai likhanou diastema metalambanetai anti ditonou to ginomenon kath'ekasten chroan kai to tou pyknou megethos; homoios d'hexei kai epi ton diatonon; apo gar tou koinou tonou ton genon mia estai ep'hekatera hodos; epi men to bary epi meses kai likhanou diastema ho, ti an pote tugkhane hon kath'ehasten khroan ton diatonon. Epi [[de]] to oxy, epi to parameses kai trites.], which mean: “However, now we must discuss the unequal intervals. Firstly, the Dense is placed near the Ditone towards the low register and towards the high one (namely, above and below it) because it has been proven that these two intervals are placed alternatively in the conjunction;” “The tone is placed only near the high part of the Ditone; the tone is placed only near the low part in the Dense; in the Diatonic one does not sing a Semitone below the tone, and also above it; the Semitone is placed before and after two or three Tones; one cannot place two Ditones one after the other; two Dieses cannot be placed one after the other; the matter is the same in the Chromatic genus, except that between the Mese and the Lichanos one takes, instead of the Ditone, the interval which belongs to each species and division and also the Dense. The same will happen in the Diatonic, because from the common Tone of the genera one will make a progress (namely, interval) towards both ways, namely, downwards towards the interval between the Mese and the Lichanos which is specific of each Diatonic species and upwards towards the interval of the Paramese and the Trite,” and other statements which he adds along the same lines. [-<253>-] However, if we consider three different sorts of intervals which the Diatessaron has in the perfect System of the Syntonic Diatonic, namely, larger Tone, smaller Tone and larger semitone, from the difference exchange of position of those, which can occur in six ways, one could define as many species of Diatessaron. However, because the difference between the two tones is so very small, one would only hear a very small difference, if any, in the melody. For this reason, neither modern composers or ancient composers and theorists did not take it up, if any are left. Moreover, they adopt the Syntonic of Aristoxenus or the Diatonic Diatoniaus which have no difference of Tones, and, consequently, it will be fruitless to observe the two species of Ditone, one of which has the larger tone first and then the smaller one, and the other one the opposite. But not only the two species of the Ditone, the two of the semiditone and the three of the two hexachords are not useful in anything and are part of the Diapente or are composed of the Diatessaron, where the species of these two, which govern the melodies, produce the differences of the ones of the Diapente, so, consequently, it is even more redundant to consider the species of the Seventh, which is a dissonant interval. [-<254>-] Explanation of the perfect System according to the three genera with the names of the notes, Chapter However, before we explain the Seven species of the Diapason (which is one of the most important matters of music and it is most relevant to our aim) it will be appropriate to consider well the order and disposition of the largest and perfect System of the ancients with all its parts and terms, so that what we shall say next will may be understood without any difficulty, since this is why we have placed it here. Perfect System of the Ancients according to the three Genera After I considered above what Tetrachords are, the reason behind their sounds as well as their application, especially in the case of the Conjunct which is added on the side, and the names of each note which are the same in all genera, now we shall consider what is left over. We have divided the whole system into 48 Enharmonic Dieses following the practice of the ancients which comports much clarity and usefulness without considering, for now, the larger and smaller Tones. Therefore, it is enough to know that each octave contains six tones twelve semitones and twenty-four dieses, hence the Heroic verse corresponds to it by excellence, which is almost the model and the basis of all of them, which also contains six feet, twelve syllables (since two short are taken as a long one) and twenty-four tempora. Each Diapente [-<255->] comprises three tones and a Semitone, namely, seven Semitones and fourteen dieses, while each Diatessaron contains two Tones and a Semitone, or five semitones, and, consequently, ten dieses. First of all, note the boundaries of the tetrachords marked by us with two lines, and then the notes which represent a particular sound, which have their lines extended outwards, because these are the notes which are considered in the perfect System according to all the genera, and they do not exceed the number of twenty-five in all, if we do not consider the ones in unison in the conjunct tetrachord. Who understands well their disposition and application, understands the whole of Harmonics. One can see from here which ones have the stable notes and which one the mobile ones, which the Apycne, the Mesopycne and the Oxypycne. I have also added two types of Notes, one according to modern practice and the other one according to the practice of the ancients. The latter ones differ in the fact that they allow us to see all the seven letters in every octave of each genus with this difference, namely, that one adds just a dot in the Enharmonic ones, which shows the small difference in sound, while the chromatic ones are altered also in this way. [Doni, Treatise on the Genera and on the Modes, second book, 255; text: [[Diat]] Sette uoci Diatoniche A, B, C, D, E, F, G, cromatiche, [Delta], enarmoniche [signum]] The same letters are adopted n the second diapason towards the high register, but written in lower case. The fact that the Chromatic genus has only two [-<256>-] notes different from the others within each octave, and four the Enharmonic derives from the fact that it has, as we said, two notes in common with the Diatonic. These signs would be very useful to intabulate the three genera without confusion, albeit nobody is forced to accept them, nor being our intention in this treatise to show the way which could be adopted to intabulate the music in a much better way that the one used nowadays, not only in the melodic part but also in they rhythmic one. However, with God’s help, we could do this another time. I also marked with semicircles the places of the Tones and the notes which show the species of the modes to avoid repeating them afterwards. [-<257>-] How many are the species of the Diapente according to the good and ancient authors, Chapter After having considered the above mentioned System, we must understand now that Ptolemy (book 2, chapter 9) shows that the perfect System is the one that contains all the consonances with their every species, since, in short, perfect is what is complete of all of its parts, and that, albeit the System of the Diapason is perfect in some way (as Salina also maintains) and the ancient concentrated on this for this reason, namely that it contains all the consonances, since the ones which exceed the Diapason are simply repeated, nevertheless, only the Disdiapason System of fifteen notes is the truly perfect one, because it contains non only all of the consonances, but all the species of each one of them. Therefore, he does not class the Diapason Diatessaron System of eleven notes as perfect because it does not contain all of the seven species of the Diapason, [[and not only the four of the Diapente, but only when two conjunct tetrachords are below the tone of the disjunction and the same number above it and in the middle of four Tetrachords]] albeit they did not use the larger System at the time when the three modes Dorian, Phrygian and Lydian were used, and the reason for this will be explained later. However, it must be known that Ptolemy starts from the high register to the low one in counting the seven species, as the other Greeks do, but in the order of the species he goes from the low register to the high one. This must be considered to avoid any misunderstanding. We shall start from the low register for greater clarity, as this is the practice of our day. Therefore, he places the first species between the Hypate Hypaton [-<258>-] Hypaton and Paramese (namely between B and [sqb]) the second specie between the parhypate Hypaton C fa ut and the Trite Diezeugmenon C sol fa ut, the third one between the Lichanos Hypaton D sol re and the Paranete Diezeugmenon d la sol re, the fourth one between the Hypate Meson E la mi and the Nete Diezeugmenon e la mi, the fifth between the parhypate Meson F fa ut adn the Trite Hyperboleon f fa ut, the sixth between the Lichanos Meson g sol re ut and the Paranete Hyperboleon g sol re ut, and the seventh and last one between the Mese a la mi re and teh Nete Hyperboleon a a la mi re, which is the last note of the System. Now it is necessary that we know why it is really the best System of all. The first reason is so that the first species of the octave would match the first of the Diatessaron and of the Diapason, which both start with the Semitone. The second reason is so that the order of the species would match the one of the seven Tones which had been accepted and organised one with the other in that way much earlier. Thirdly, because, if one started from the high register, it was more convenient to leave out the first note from the bottom (proslambanomenos) than the first from the top (Nete Hyperboleon), apart from the fact that the latter is also more ancient and more important because it is part of a Tetrachord, while the former has been invented only so that the Mese should have its correspondent at the octave. [[For which reason nobody should have ever abandoned this disposition.]] Therefore, as Girolamo Mei observed acutely, the species proceed in a tidy and organised way in the distribution of Ptolemy and of the other Greeks, who agree with him, and not in the ones by Latin writers, since Boethius started from the low register and did not leave out the note which is the first one in that order from [-<259>-] Proslambanomenos to Mese. Therefore, one can see that if one wants to follow the order as an uninterrupted sequence, the seventh species must be taken from the Mese to the Nete Hyperboleon, rather than from the Proslambanomenos to the Mese, although in practice this is the same. Therefore, in the first species the Tone of the Disjunction occurs in the first place towards the high register, or in the last one starting from the bottom; in the second in the second place, in the third in the third place, in the fourth in the fourth place, in the fifth in the fifth place, in the sixth in the sixth place and in the seventh in the seventh place. In this way the species are distinguished orderly according to the position of this tone, as Cleonides does. As to the position of the two Semitones, for greater clarity we shall start from the bottom. The first species has the Semitone in the first and in the fourth place [[and it is composed of the first species of the fourth and of the first species of the fifth.]], the second has it in the third and seventh place, the third in the second and sixth, the fourth in the first and fifth, the fifth in the fourth and seventh, the sixth in the third and sixth and the seventh in the second and fifth. The first species is composed of the first of fourth and fifth, or of the Semidiapente and of the Tritone; the second one is composed of the third of the fourth and of the second of the fourth, or of the third of the fifth and of the fourth; the third one is composed of the second of the fourth and of the third of the fifth, or from the fourth of the fifth and of the second of the fourth; the fourth Species is composed of the first of the fourth and of the fourth of the fifth, or of the first of the fifth and of the fourth, while the fifth species is composed of the second of the fourth and of the third of the fourth or of the Tritone and of the Semidiapente, and he sixth species is composed o the third of the fourth and of the fifth or of the third of the fifth and of the second of the fourth; finally, the seventh species is composed of the second of the fourth and of the fourth of the fifth, or of the fourth of the fifth and of the first of the fourth [-<260>-] Here one must note that of those seven species, four can have the fourth under the fifth and the other way round, while the other two can only occur in a way, and instead of the second way they have the semidiapente underneath the tritone, or the other way round. However, in our modern modes it is a different matter, because they distinguish this different position of the fourth and of the fifth and for this reason they become twelve, because the five species, with two different lay-outs, turn out to be ten. [-<261>-] On the Seven ancient Modes or Tones, chapter The aforesaid seven species of the Diapason are called Modes, or rather they are the ones that constitute and determine the modes, which are called Tropes [tropoi] in Greek, a term that has the same meaning and it derives from [trepo] which means turned and changed, and denotes different changes and ways to combine the sequence of the small and large intervals in the System used in singing and in the Diatonic, especially in relation to Tones and Semitones. Franchino called them Manieras in Latin, using a non-classical term. These are the ones that have given much to write and quibble to the ancient musicians and to the modern ones, because of the contrasting opinions held around them. Now, it has to be known that when one talks about the Seven Modes, every theorist, ancient of modern, means these: Hypodorian, Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian and Mixolydian. Ptolemy assigns one of the seven species of octave to each of these, and these are called Ptolemy’s modes, not because he invented them, either one or all of them, or because he ordered them in the way they are ordered, or because he assigned to them those species. In fact, this was done much before him and he found them to be accepted and established by the ancient musicians already form many centuries, with those fundamental rules which we shall see, and they were also practised by singers and instrumentalists just as they would be for a long time after him, until the invasion of the barbarians, when everything was turned upside down. Therefore, they are called Ptolemaic either because none of the authors that we have deals with them better than he does (hence Boethius took from Ptolemy what he says about them) or to distinguish them from [-<262>-] those of Aristoxenus, which are thirteen, as we shall see. The same modes are called more often Tones ([tonoi]), which is a word taken to mean the same, albeit there are some differences, because Tone has the specific meaning of a System or a melody which is higher or lower, even if one progresses through the same species and variation, while Mode has the specific meaning of that or another variation or style, although Mode and Tone are used in both those meanings, albeit Tone is used more often. Therefore, one must know that the meanings of the word Tone are several, but four are the main ones used by the ancients, as Cleonides notes, Salinas after him, although he interprets it in his own way, and Zarlino and others. Firstly, it is interpreted as [they called Heptatona the Lyre with seven strings, that had but seven notes in marg.] voice or sound, as when Terpander and other ancient poets used it. Secondly, it is interpreted as the measured interval called Tone, which is the difference between the fifth and the fourth and it is represented by the sesquiottava proportion. Thirdly, it is taken to mean the place of the voice, because when someone sings more acutely, we say that he sings higher, as if the voice walked up to a higher place and towards the higher part of the System, or within the lower part, when it sings low. Fourthly, it is taken to mean the span of a voice compared to others, when we mean that someone has a high tone, as the Soprano, or a middling one, such as the tenor, or a low one, such as a Baritone. The word [tonos] comes from the verb [teinein], which means to extend. I will add a fifth meaning to this least, which occurs when we say to sing high, low or in a middling manner, not in terms of high or low [[as Zarlino understood it]] [Supplementi book 6, first chapter in marg.], but at high, low or middle volume. Of all these meanings, the third one is more suited to our purpose, because in that case it is taken to mean Mode, although, in a more precise way Mode and Tone means only the manner of the octave. Cleonides defines it in this way according to this meaning: [Tonos de esti topos tou tes phones dektikos suste matos, aplates.], which means “Tone is a certain place of the voice which can accept a System and one which is without width.” [-<263>-] In order to explain this, let us suppose that someone could not rise higher or descend lower than two octaves or a Bisdiapason. It will be possible to organise a varying numeber of Systems of octave according to their distance from each other. In fact, the smaller their intervals are, the larger the number of them that will be contained therein. Therefore, if we imagine this span of two octaves as divided into twelve Tones or equal parts, we establish the System of a Diapason and we want to fit it to the extension and height of that pan of two octaves, we shall find that it will occupy half of it. For instance, if we place it first in the lowest part, or from the deepest part of the voice to the middle one, and then we raise it little by little with the notes through each tone until we have placed it in the highest part, we shall find that space, namely, from the middle voice to the highest, will have changed seven positions. This means that that place of the human voice contains a System, which will be explained even more clearly. If we take seven small Harps or seven small lyres built in the ancient style with eight strings, each divided into octaves, which each will be as many systems, but so that those systems are separated each from the other by a tone, namely, that the second Harp is tuned a tone higher than the first one, and the third a tone higher than the second et cetera, and, if we have a singer match his eight lower intervals [-<264>-] to the strings of the first and lowest little Harp, sing the extreme notes in unison and if we have him do the same with the third one and with the others, we shall find that he will always raise his voice until he arrives to the highest sound of that Disdiapason. Then, his highest notes will correspond to the notes and to the strings of the sixth and highest little Harp. However, if we imagine this diapason divided into 224 Semitones or places and we take seven little harps tuned in such a way that two of them are at the interval of a Semitone, while we leave the tone in the other spaces, we shall find that the voice of the singers makes as many change of position, moving across seven systems corresponding to those of the little harps. This occurs because, having divided an interval into tow, an interval was left over, and if, for every interval of a semitone which we have made, we apply to the voice of the singer as many systems of however many voices artfully disposed within boundaries of the octave, the same voice and the same System will be able to change position higher or lower thirteen times. If we divide the same Disdiapason into quartertones or dieses and we raise or lower the System through each step one would have the number of variations. This can be also gathered from the neck of a string instrument with a string divided proportionally into the same parts of Tones, semitones or Dieses through the span of two octaves. Starting from the first note or fret towards the high or low register we shall build a System with its corresponding octave, and then we shall raise or lower it gradually. One can understand this also from a ruler divided into twelve equal parts. We measure a span divided into ounces, [-<265>-] according to both ancient and modern practice. If we take a small ruler or a little stick measuring half a span divided in the same way, I will apply its extremities to each division of the entire span until I change its position six times. Also, since we have to conceive the Disdiapason System, to which we adjust all of the other Systems of octaves, as fixed and stable, for this reason it has to be understood as the System specifically called Immobile, which represents the series of the fifteen notes of a man with an ordinary voice who sings in the Tenor range, which are ordered as we saw above, because ancient musicians became accustomed to compare all the species and varieties of the Tones and of the Modes to it. This could be represented ordinarily as an organ of as many pipes, leaving aside the strings which are of variable intonation, or by a flute divided into as many notes. However, to go back to Cleonides’ definition, it is not easy to understand what word [aplates] or without width means. Zarlino interpreted as meaning that the voice, when it rises by degrees through the sounds of a Tone and then descends in the same way step by step, it has to go through the same steps or produce the same intervals. Were this true, if ascend through the eight diatonic notes and descend through the eight which are Chromatic or Enharmonic, I would change Tone, but this is not so, since the genera have nothing to do with the Tones. [Doni, Treatise on the Genera and on the Modes, second book, 265; text: Sistema d'una Diapason mobile, Immobile disdiapason] [-<266>-] That the difference between Mode and Tone is not well understood nowadays and of the seven Modes of Ptolemy and of the thirteen of Aristoxenus Since modern theorists did not understand well this difference, they have fallen into many errors, while, those who have strived to restore the ancient modes have sweated in vain in their toil. [book 4, chapter 12 in marg.] Salinas as well made copious mistakes, as well as others, and it has extracted a very different meaning from the intention of the authors and from certain passages of Ptolemy and Boethius. For this reason he was wrong to reprehend Gaffurio and Glareano because they ascribed the same meaning to Mode and Tone. Glareano was also rebuked wrongly by Maillard, Master of the chapel of the church of Tournai in France, whose only aim in a very prolix book of his written in French is to prove that Tones and Modes are different and that the former are eight and are used for the plainchant, and the latter are twelve and are used in figured music. However, we shall see later how we this difference between Tones and Modes can be squared. Now I shall quote Boethius’ words firstly, and then Ptolomy’s (but in Greek) although Salinas quotes him in Latin, to check if he has understood them correctly. Boethius says this at chapter fourteen of the fourth book: “Therefore, the consonances of the Diapason consist of species which are called Modes, which some equally call Tropes or Tones.” He clearly states in this passage that the words Mode, Trope and Tone have the same meaning and are the same, as it is really true, albeit Tone and Mode differ as well [-<267>-] in the way that has been illustrated. Ptolemy, however, says this at chapter six of the second book: This means: “However, two sorts of changes occur with regard to the Tone, as it is called: one is when we proceed through all the melody with a higher or lower tension of voice while we keep the appropriate proportion throughout the specie; the other one, instead, occurs when the tension of the voice is not changed throughout all the melody, but only within a part of it corresponding to its beginning. For this reason it is called change of melody than of tone, because the change of the tone does not affect the melody but the tension of the voice, while harmony is altered through the change of the melody.” Here Ptolemy means that a melody can be changed in two ways, either singing the same air higher or lower, or by changing just a section of that melody without raising or lowering the voice, namely, by altering the intervals and by placing a tone instead of a semitone or a Semitone instead of a tone, as one can see in these examples.[-<268>-] On the names of the seven modes according to Ptolemy and the other Greeks Therefore, since the Modes are specifically seven, as we have seen, a species of the Diapason as assigned to each of them by Ptolemy, who only teaches us which lay-out they have one in relation to the other, which is this one. The first one or Myxolydian is the highest of all and has the first species. The Lydian is the second and has the second species, and so on, the Phrygian has the third one, the Dorian the fourth one, the Hypodorian the fifth one, the Hypophrygian the sixth one and the Hypodorioan the seventh one. [[All the ancient Greek and Latin writer agree in this]] Thus, the lowest species, or, to be more precise, the one which occurs in the notes of the lowest Diapason of the perfect immobile System, except the one from the Proslambanomenos to the Mese, is ascribed to the highest Mode or Tone. The second species (going towards the high register) is assigned to the second Mode (towards the low register) and thus the others follow with the same order. One must be certain that all the ancient writers agree in this. Moreover, Boethius himself, except that he starts firstly from the Hypodorian in the opposite way, he assigns the species from A re to a la mi re instead from a la mi re to a a la mi re, and he concludes with the Myxolydian. Also, although many of them made a grave mistake at the beginning, let us see how well Cleonides [-<269>-] agrees with Ptolemy. He also says that the first species of the octave is contained within the notes Barypycne, that it has the Tone in the first place towards the high register, which is between the Hypate Hypaton and the Paramese and that the ancients called it Myxolydian. He says that the second species is contained within the notes Mesopycne, that it has the tone in the second place going from the high to the low register, that it is contained between the notes Parhypate Hypaton and Trite Diezeugmenon and that it was called Lydian. As to the third one, he says that it is contained within the notes oxypycne with the tone in the third place, that it occurs between the Lichanos hypaton and the Paranete Diezeugmenon and that it is the Phrygian. He states that the fourth species is contained among the notes Barypycne, that it has the tone in the fourth place, that it spans from Hypate Meson to Nete Diezeugmenon and that it corresponds to the Dorian mode. The fifth one, he says, is contained within the notes Mesopycne, that it has the Tone in the fifth place, that it spans from the parhypate Meson to the Trite Hyperboleon and that it corresponds to the Hypolydian. The sixth one is contained within the notes oxypycne, it has the tone in the seventh place, it spans from the Meson to the Paranete Hyperboleon and it corresponds to the Hypophrygian. Finally, the seventh one is contained within the notes Barypycne, it has the Tone in the seventh place or the first one towards the low register, it corresponds to the Hypodorian and it is contained within the Mese and the Nete Hyperboleon or from Proslambanomenos to Mese, and it was also called Hypodorian, Common Mode and Locrian. He also states that the first species of the diatonic has the Semitone in the first and in the fourth place, while the second one has it in the third and in the seventh, and so on the others, as I told you earlier on. [-<270>-] On the Distance from one Tone to the other, Chapter However, when we deal with the distance from a Tone and another one we do not use the word Mode, but the word Tone, although they do not differ substantially. In fact, the word tone means, principally and in Recto, as the Scholastics say, the tension or place of the voice, whether it is higher or deeper, while, less principally and in obliquo, it means the species of the Diapason and the Mode, contrary to what Ptolemy says. Therefore, if one supposes that the three most ancient and principal tones, Dorian, Phrygian and Lydian are separated from each other by a Tone, as I confirmed, in that the Phrygian is a tone higher than the Dorian and the Lydian is a tone higher than the Phrygian, he says that the Myxolydian was created by ascending a fourth above the Dorian, and that four tones were established in this way. Also, in order that the other two corresponded by fourth in the low register, as the Myxolydian corresponds to the Dorian, they placed the Hypolydian under the Lydian and the Hypophrygian under the Phrygian and they added the Hypodorian under the Dorian, by adding the prefix [hypo] which means under. They called Hypermxolydian tone that corresponded at an octave above the Hypodorian, using the prefix [hyper] which means above. This one caused an infinite number of mistakes and it has been the origin of this misunderstanding, as they say, and as we shall demonstrate further on. Moreover, he states that it follows from this consonant interval that a tone is separated from the other by a tone, a semitone or a limma (which is interpreted as the same) and that it is better to proceed in this way rather than from the interval that two next to each other form collecting the one which the ones which are further removed create, since the intervals and [-<272>-] the notes that can be sung are extracted from the differences between consonant intervals, and it does not happen the other way round, namely, that consonances are formed from the addition of those intervals. Therefore, he says that the Hypophrygian rests a Tone above the Hypodorian, just the Phrygian above the Dorian and the Hypolydian above the Hypophrygian. Moreover, the Dorian is a semitone above the Hypolydian, as the Myxolydian, its correspondent, above the Lydian. Then, the Phrygian, as we said, has a tone higher as the Lydian has, while the Myxolydian is placed a semitone above this one. For this reason it was called in this way, namely, almost mixed with the Lydian because of its proximity to it, in such a way that it turns out to be two fourths or a minor seventh or a Disdiatessaron above the hypodorian, since it is half-way between one and the other Dorian. This exact distance is confirmed by others as well as by Cleonides, where he says, when he mentions the distance of a Tone not only from the one next ot it but from the second, third and so one, as that the Myxolydian is a semitone higher than the Lydian, a Threhemitone than the Phrygian, a Diatessaron than the Dorian and so on, which I omit in order to be concise. Also, so that nobody may doubt , Boethius himself has held the same opinion and agrees punctually with Ptolemy and with the other Greek writers. I shall quote here his exact words, so that, at last, everyone may agree that there is not among them that contradiction of which they have dreamt, nor there is an error in the text as good Glareano believed or pretended to believe, because, had this not been the case, his calculations would have matched his ideas. Therefore, Boethius says at chapter of his book: Has igitur constitutiones si quis totas faciat acutiores uel in graues remittat: secundum supradictas diapason consonantiae species [-<272>-] efficiet modos septem. quorum nomina sunt haec. Hypodorius Hypophrygius Hypolydius Dorius Phygius, Lydius, Mixolydius. Horum uero sic ordo procedit. Sit in Diatonico genere uocum ordo dispositus a Proslambanomeno in Neten Hyperboleon atque hic sit Hypodorius modus. Si quis proslambanomenon in acumen intendit tono Hypatenque Hypaton eodem tono attenuet, caeterasque omnes tono faciat acutiores, acutior totus ordo proueniat quam fuit prius quam toni susciperet intensionem. Erit igitur tota constitutio acutior effecta hypofrigius modus. Quodsi in Hypophrygio toni rursus intensionem uoces acceperint. Hypolydij modulatio nascitur. At si Hypolydium quis semitonio intendat Dorium faciet et in aliis quidem similis est in acumen intensionemque processus. This is the translation: “Therefore, if one raises these Constitutions or Systems, or if he lowers them according to the aforesaid species of the consonance Diapason, one shall create the seven Modes. These are their names: Hypodorian, Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian and Mixolydian. Their order proceeds in this way. Order the series of the notes from A re to a a la mi re in the Diatonic genus, and this be the Hypodorian. If one raises the note from A re by a semitone, and if he raises B mi and all the others, the entire series of notes shall be higher that it was before it was raised by a Tone. Therefore, the entire raised constitution will be the Hyphrygian mode. However, if the notes of the Hypophrygian will be raised by a tone again, the Hypolydian melody shall be born, and it one [- <273>-] raises the Hypolydian by a Semitone, the result shall be the Dorian. One proceeds similarly in the same way in the others, by raising the voice towards the high register. How said extract from Boethius must be understood. Here one must consider (and here almost the knab of all this difficulty) that, although Boethius says that, for instance, one must raise the System of the Hypodorian by a tone starting from A re to create the Hypophrygian, and that then, one must also raise B mi and all of the others by a tone until the entire System is a tone higher than the one of the of the Hypodorian, he does not mean by saying this that the Hypophrygian then proceeds in his melody in the same way as the Hypodorian. Therefore, we must rebember what he said a little earlier, namely, that, if someone raises these constitutions or systems, or lowers them according to the aforesaid species of the consonance Diapason, one will create the seven modes. Hence, after we have established two systems, each from A re to a a la mi re, but the second a tone higher than the first one, if we want to create the melody of the Hypophrygian we shall have to imagine again that the note ut (Lichanos Meson), which creates that Hypophrygian species, should be placed on A re or Proslamanomenos and the a la mi re (Mese) on B mi (Hypate Hypaton), and other ones should follow in order until one arrives to the Nete Hyperboleon, [-<274>-] although one must maintain the difference that these transposed notes have from them, rather than the notes that receive them, which will be at the same distance as in the Hypodorian Tone. One must make this intellectual adjustment in order to harmonise the Modes with the Tones, or the species of the Diapason with the raising of the voice which each Tone requires in relation to the first one, and Boethius should not have been silent about it, if he wanted to be understood. However, this was ascribed not to any kind of negligence on his part, but to the succinctness to which he aspired to the fact that this work was left unfinished, as everyone knows and to the fact that this matter pertains more to practice than Theory, which was his only subject in this work. In fact, had modern theorists been aware of this, they would not have highlighted those differences on the disposition of the Tones between Boethius and Ptolemy, as Gallilei does, who makes all of Boethius modes start from A re and end on a a la mi, and Ptolemy’s ones each on different notes, because, although perhaps the ancient laid out the Modes in their illustrations of them so that they all started from A re and end on a a la mi re, as they are here, [-<275>-] nevertheless this was done only to highlight the distance between a Mode and another one and to pick up the tone, as we say, because, if, for instance, one wants to sing the Hypophrygian from its lowest note, one would take its Proslambanomenos or A re by producing the note re, which was a tone higher than the lowest of the Hypodorian. Then, as to the Species, one would take the Lichanos meson or G sol re ut pitcing the note ut at the same height as the said re, by placing said G sol re ut on A re in his mind, if he wanted, and a la mi re on B mi, or ascending continuously with that same note taken from the beginning to the last one. After this one, if one wanted to continue with the other notes, he would have gone back to B mi in the lower register, leaving aside A re if he had sung a a la mi re, and so on until he would arrived to the last note of the fifteenth which is a a la mi re (Nete Hyperboleon) in the System which we define as stable or g g sol re ut or G sol re ut in the mobile System, which is the one formed by this specific species of the Hypophrygian placed within its notes. Equally, if one wanted to sing the entire Hypolydian System, one would take its A re or Proslambanomenos and to pitch it a ditone higher than the one of the Hypodorian, or one would take the F fa ut (Lichanos Meson), which is its initial note, and pitch the ut with a tone taken as Proslambanomenos, proceeding with the same sequence of the notes up to the fifteenth or beyond (by starting again with the notes of the low register once the high ones ran out) according to the notes provided by the voice and following the illustration given here. [-<277>-] [Doni, Treatise on the Genera and on the Modes, second book, 277; text: Modo Ipofrigio, a a G sol, g F fa, f E mi, e D re, d c fa, c B mi, [sqb] A re, [signum], ut, Ipolidio] In order that nobody should think that I dreamt up this by myself, here is Gaudentius (who is qualified as philosopher and to whom is ascribed a Brief Introduction to Greek Music already translated and published by Valla) who says it expressly with these words, which I have copied from a book in the Vatican Library: [Ekhresanto de palaioi onomasi pros thn semasian ton [[..]] oktokaideka phtoggon kai [[grma]] grammasi tois kaloumenois semeiois mousikois peri hon vyn rheteon; hopos me ta onomata kath'ekaston graphoito; kai eni de semeio dunaito tis epiginoskein kai aposemeiusthai phthoggon; epei de hoi phtoggoi diaphoro tasei kinountai kai ouk epi tou autou tote pantos menousin, oush enos de pouthen semeiou kath'ekastonton phtoggon; alla diaphoron edeesan hoste kai ten [this author was translated into Latin by a certain Mutianus, as Cassiodorus states, but I do not believe that this translation corresponds to the text that we have, as it is a mere compendium add. infra lin.] [- <278>-] diaphoron tasin autou semainein; kath'hecason gar tropon he tonon diapherontes te tasei tantes panton hoi phthoggoi ginontai; hoion pote men ton physei barytaton phthoggon proslambanomenon hos en to hypodorio tropo tithemetha; kai meson ten pros touton antiphonon cai tous allous cata ton pros aoutous ocheon onomazomen; pote de aouton meson ton nun antiphonon to proslambanomeno en taxei proslambamenou demenoi; kai ten tautes antiphonon meson [[.]] hypothemenoi kai tous allous toutois analogon, houto khrometha to panti systemati; pollakis de kai ton metaxy proslambanomenou kai meses en tina paralabountes eis arkhen tou sustematos proslambanomeno tauto chrometha, kai ten tasin tou pantos systematos pros touton armozomen; anagke de eph'hekastou systematos pleionon protidentos systemato hes he mese pros ton meson ekhei he hos ho proslambanomenos houtos hontinoun ton homonymon ekhei pros to homonymon; kai hapan to systema pros hapan to systema;], which means: “However, the ancients used certain words to indicate the eighteen notes of the System and of some letters which are called musical figures and which we shall discuss now. The application of musical figures was invented to signify the notes [-<279>-] so that one should not have to write the entire word for each note and so that anyone may recognise and indicate a certain note with a simple sign. However, since these notes or sounds move with different degrees of tension and are not all fixed in the same place, a single sign was not at all sufficient for each note, but several were required to indicate their different tension, because all the notes vary in tension according to each Mode or Tone. For instance, sometimes we place the sound which is naturally the lowest, the Proslambanomenos, in the Hypodorian Mode. Similarly, we indicate the Mese, which is equivalent to it in sound, and the other notes according to the distance or relationship that they have with it. On other occasion, we place the Mese (which now responds to the Proslambanomenos at the distance of an octave) in the position of the Proslambanomenos itself. We place a Mese corresponding at the octave and all the other notes according to their distance under this note and thus we use the entire System. Moreover, very often we take any note contained between Proslambanomenos and Mese and we employ it as the first note of the System instead of the Proslambanomenos and we adjust to this the tension of the entire System. Therefore, it follows as a consequence that, having placed other Systems in each system, each note or figure will have the same relationship to any note or figure which corresponds in name to its own as a Mese has to another Mese or to the Proslambanomenos and an entire System to another one.” Gaudentius explained to us very clearly with these words [-<280>-] how that intellectual process mentioned by me above occurs. This explanation is very similar to what Ptolemy explains at chapter five of the second book. Explanation of what was said, Chapter However, in order that one may understand more clearly that the ancients Modes had each a particular tension of the voice and that they deserved the name of Tone unlike our own, which do not, one must be aware that each of them had a particular System or scale, as it was mentioned, which, nevertheless, had the same number of notes called with the same names. However the notes were represented by different signs and each Tone had several which were specific to it, as we shall see later. In this the main difference between their modes and our own consists, because ours are all contained within a single System ordered in the same way. Therefore our tones are parts of a System or smaller different Systems contained by a lager one, rather than separate Tones, and for this reason one can move easily from one to another, one because that Series and consecutive conjunction of tones and Semitones which make up a fifth, then a fourth and then a fourth and thus ad infinitum is not interrupted, [- <281>-] while those were so different that one could not move from one to the other one without interrupting the previous sequence by entering a series and disposition of notes which was very different. This is what produced so much variety and beauty in their melodies, because, when one moved from one tone to another one, not only one changed the species of the octave, but the tension of the melody changed greatly. This can be heard nowadays as well when one uses the sign of the Diesis # in many notes close to each other as the best composers do, such as the Prince of Venosa, Tommaso Pecci other of that ilk, because one moves really from mode to mode or from Tone to Tone, which is the same, and one hears a great variety in the melody, which produces incredible pleasure in the listener. Nevertheless, this cannot be sustained long with the same perfection achieved by the ancients, not so much because our way to write music is insufficient (since this could be remedied) but because they did not have modes as interconnected as ours are. Hence, when we place a diesis on a note, albeit we change the Tone, we change it blindly, as they say, without knowing the tone that we are entering and with what reason, hence we cannot continue into this second mode and make its cadences, and even less can we move from this tone to another one orderly, but the greatest secret [-<282>-] of the ancient modes and the greatest mystery of this doctrine consists in this. We can gather rom this how mistaken all modern musicians are when they believe that all the melodies where these accidental signs occur are chromatic and they baptise them in this way without realising that they do not proceed chromatically, those signs denote a change of Mode or Tone, but not of genus, and that, although there may be some chromatic note such as the C or the F with the diesis, nevertheless those very notes express also the notes which arise by moving from a Tone to another one and do not constitute the chromatic way of proceeding. [-<283>-] Further explanation of the difference between Mode and Tone Although I believe to have explained sufficiently this matter with regard to those who have a profound understanding of music, nevertheless, in order to be better understood also by simpler and less perceptive persons, I want to explain the difference that exists between the mode taken simply and the Tone equally simply considered separately from the mode with other examples and illustrations, as well as the difference between the Tone and mode considered together in the manner of the ancients and the modern Modes, which can be better described as Systems because in a span divided into some larger segments, which we call tones, and other smaller one which we call semitones. If we take another equal span, divided according to the same order, and we place it one, two, three tones or a semitones higher and so on, the result shall be a change of tone (take in the meaning of , rather than of term mode) as in this example. However, if we change the sequence and the disposition of the large and small parts, namely tones and semitones, within the same span, namely, if we make it start with a Semitone instead of a tone, without raising it or lowering it in position, this will correspond to a change of Mode, rather than of tone. If then we mix one and the other taking another span or System of equal length but differently ordered in its parts and placed in a higher or lower position, we shall represent the variety of the ancient Tones in the best possible way. However, if we take equal portion from one [-<284>-] limit or division (which represents a note or sound) up to another which corresponds to it, within the same span and disposition of great and small quantities, which is something that one does with the octaves in the musical System, whether moving them higher or lower, in this way we shall represent the modes according to modern practice: [Doni, Treatise on the Genera and on the Modes, second book, 284; text: I, 2, 3, 4, Diuersità di tensione di uoce, o Tuono solo, specie Modo solo, Tuoni, Modi antichi, de moderni, a, G, F, E, D, C, B, A, [sqb], a a, g, f, e, d, c] [-<285>-] In order that purely practical musicians, who understand the notes better from staff notation, may be satisfied, I shall place here the following examples. [-<286>-] How the distance from a Tone to an other one should be understood, Chapter Therefore, we can understand how the ancient Modes differ from ours toto caelo and that we are left only with a shadow of them. However, in order to ascertain the distance between one mode and another one, a certain rule consists in look at the Mese (this follows if one looks at the Proslambanomeons and Nete Hyperboleon as well) as the aforementioned Gaudentius and Ptolemy himself teache us. In fact, the distance between the Mese of a mode and the Mese of another one (the same goes also for the other two notes) will be the same as the distance between one whole System and the other, as we can understand from two equal span one wider than the other, because the distance that has the middle measurements or the extremes of two lengths will be the same as the distance between the two lengths. However, the method of looking at the middle of the other span is not so accurate, because, if the fifteen notes of each System are laid out according to the sequence of the species, in a Proslambanomenos System the second notes will be at the distance of a smaller Semitone from the first one, and in another System it will be at the distance of a larger tone. Therefore the interval that is contained between the first note (Proslambanomenos) of a System to the first of another one will not occur between the second note of the former one and the second of the latter one, as one can see here, where the Proslambanomenos of the Dorian is in unison with the Hypate Meson of the Hypodorian [Doni, Treatise on the Genera and on the Modes, second book, 286; text: a, f, F, E, D, C, A, g, d, c, Proslambanomenos, Hypodorio] [-<287>-] and at the distance of a Diatessaron from the Proslambanomenos of the Hypodorian Mode, which is the real distance between these two modes. However, the Hypate Hypaton of the Dorian is separated from the one of the Hypodorian by a just a Ditone, as one can see, and for this reason one must believe that the ancients used to place the Systems with the same disposition of intervals of the Hypodorian Mode, which is, so to speak, the basis of all of them and it is the one which has the same species as the Immobile System which is the foundation of the others because the notes are placed on it in the various ways that I have described above. For this reason, said Hypodorian mode had to be called also common, although I believe that the tension of the voice of the Dorian mode (which is the one that occurs in the middle and therefore more apt to connect with the other mobile systems, higher or lower) is ascribed more correctly to the stable System. This is what Ptolemy does in the table the follows after the eleventh chapter of the second book. I have based the following illustration, in which I adjust to the Immobile Dorian the other six Modes, on this table. I have marked the Mese of each of them as well as the first species of the Diapason, but I have avoided distinguishing the Tones and semitones in individual boxes, as Gallilei does, because the Mese are not represented at the extremities with the due distance which pertains to one and the there. In fact, Ptolemy did not intend to show the precise distances in this table, but he aimed instead to illustrate the variety of the seven species placed in a System through one that was equidistant and in unison with the ones in the middle of the Dorian and between them. Perhaps he did not have much consideration for the fact that only the part of the six modes which corresponded to the Dorian was sung. For instance in the Hypodorian one started from D sol re (lichanos Hypate) as it is in unison with the Proslambanomenos of the Dorian, and continued up to the Nete Hyperboleon of the same Hypodorian, while in the Myxolydian one started from A re Proslambanomenos, which is also marked a a la mi re in this connection, up to E Nete diezeugmenon: [-<288>-] [Doni, Treatise on the Genera and on the Modes, second book, 289; text: Connessione de Sette Modi, Hypodorio, Hypophrygio, Hypolydio, Dorio Stabile, Phrygio. Lydio. Missolydio, D, C, B, a a. A, g, f, e d, c, [sqb], a, G, F, E, D, Nete Hyperboleon, Paranete, Trite, Diezeugmenon, Paramese Mese, Lichanos Meson, Parhypate, Hhypate, Proslambanomenos, [signum]], [-<289>-] as Greek anonymous theorist says in a work preserved in the Vatican Library, whose precise words I quote here: However, it is true that this has to be understood (as I shall demonstrate elsewhere) as referring to the common notes. Therefore, a deep Bass was able to sing the entire Hypodorian System appropriately as well as, possibly, a few lower notes besides. Conversely, a very high voice was able to sing the entire Myxolydian tone and a few more notes. This is how we must interpret Aristides Quintilianus where he says that nobody can sing the entire System of two Diapasons, except than in the Dorian Tone. However, if we have to make some considerations based on this illustration, we can say that we can see here all the seven species placed in a similar tension of voice, as I said. Of these, the one of the lowest Tone has the Mese in the same position, the second one in second place and the seventh in seventh place. The eighth tone would have it in the eighth place, but we shall discuss it later on. However, the following illustration seems to me very appropriate in order to understand the structure and order of the ancient modes, because one can find in it the complete sequence of the fifteen notes of each mode with the appropriate distances of Tones and Semitones and with the equivalence to the notes that would be used in each of them according to modern practice. The sixth modes are adjusted to the Hypodorian rather than to the Dorian, as we believe that it was the case commonly, because of the above stated reasons, although everyone will be free to imagine in this case that all the notes are mobile, so that the first of each is the Proslambanomenos, the second the Hypate et cetera or [-<290>] [Doni, Treatise on the Genera and on the Modes, second book, 291; text: Sistema Immobile, Modo Ipodorio, Ipofrigio, Ipolidio, aa., g, f, e, d, [sqb], a, G, F, E, D, C, B, la, sol, fa, mi, re] That the Mobile System starts from the Proslambanomenos, the Hypodorian from the Mese, the Hypophrygian from the Lichanos Mese, the Hypolydian from the Parhypate Mese and similarly the others from the note which is marked from the initial letters of each. [[One learns from here to which notes of the Dorian the Mese of each of the others corresponds or is in unison with, noting that the Mese of the Hypodorian corresponds to the Hypate meson E la mi quella D.]] However, if one wants to know to which notes of the Dorian the Mese of each of the six tones corresponds or is in unison with, it will be necessary to connect them according to the degrees of tension, as the ancients were used to doing and according to the lay-out of Boethius’ illustration. Therefore, we shal find that the Mese of the Hypodorian corresponds to the Hypate Meson E la mi of the Dorian, and the one of the Hypophrygian to the Parypte Meson F fa ut, the one of the Hypolydian . [-<291>-] of the [-<292>-] [Doni, Treatise on the Genera and on the Modes, second book, 292; text: Tauola de gli otto modi secondo Manuel Brienni, Hypomisolydio, Misolydio, lydio, Phrygio, Dorio, Hypolydio, Hypophrygio, Hypodorio, Hypate, Proslambanomenos, Nete Hyperboleon, Paranete, Trite, Diazeugmenon, Paramese, Mese, Lichanos, Parhypate, Tono, Semitono, stabile, Mobile, Sistema Immobile de la Diapason] [-<293>-] SYSTEM OF THE MODES according to the tension of the voice. [-<294>-] How wrongly modern musicians have understood the lay-out of the ancient Modes One cannot believe the variety of contrasting opinions and the confusion found in the writings of modern theorists about the order and lay-out of the ancient modes. In fact, since they supposed that those were connected together within a single system as ours are, since they did not understand the meaning of those words of Boethius that begin “Therefore, these constitutions, and being influenced also by the fact that Boethius locates the Hypodorian indifferently between A re and a la mi re as well as between a la mi re and a a la mi re, which is the lowest one and the first of all the modes, they have convinced themselves that the following mode, which is the Hypophrygian has its species between B and [sqb], and, equally, the Hypolydian between F and f, the Dorian between E and e, the Phrygian between D and d, the Lydian between C and c and the Myxolydian between G and g, considering that these notes follow the same sequence after A r towards the high register. On the other hand, since they realised that this did not agree with the distance that Boethius, Ptolemy and the other greeks place between each two them, because, for instance, they believe that there is a Semitone between the B, which they consider the starting note of the Hypophrygian and C, which they ascribe to the Hypolydian, rather than a tone, as there should be between those two modes, they [-<295>-] have wondered and asked themselves, producing the most strange explanations in the world, such as that Boethius’ text is corrupted, that there is a great contradiction between him and Ptolemy, and that Cleonides or Euclid does not agree with him che se lo dichiara and other similarly silly statements of this sort. Gaffurio (who then was followed in this by Glareano, a man himself believed by many but not very versed in Greek texts) among these, seeing that the distance ascribed to the interval between the tones did not correspond to the order according to which he laid them out, convinced himself that Boethius’ text was incorrect. Glareano himself, noting that Cleonides account did not agree at all with his foundations and principles, had no problem in rejecting it openly. In short, as our Mei states, since they started to read the ancient authors worrying in his heart because he believed and wanted to believe that our Modes corresponded to ones of the ancients, they have disrupted everything and they made this subject, which was already obscure, utterly impossible to understand and completely unfathomable, to such an extent that one can barely find anyone who has enough patience to read the long and baffling discourses that they write on this matter. Moreover, although they have worked hard on this and they have racked their brains for a long time, nevertheless they have admitted that they still have many doubts and that they did not understand these modes. This drove Glareano to say that the disposition of the Modes was almost something arbitrary: “However, we shall not discuss these matters employing all our strength arguing with anyone because it is something almost [- <296>-] arbitrary.” In the following chapter he states: “The opposing views of modern writers are a very obnoxious question, and one that it is fruitless to investigate, in my opinion.” Therefore, Maillard came to state that he appears to be the most indecisive man in the world, and that, therefore, it is a miracle that he has so many followers. However, this has to be ascribed to the times when he lived, that so much less refined were they than ours, so much more cultured men were regarded and so much less envious were they of each other. Maillard, a man otherwise of sound judgment and culture, reprehends Boethius because he started from the Hypodorian, saying that this and the other two, Hypophrygian and Hypolydian, since they are subordinate and inferior, should not have been preferred to the others, as it would have been a good lay-out had he started from one in the middle and then moved on to the ones at each end. Glareano himself, who had taken Boethius as his lead and guiding start in the order of the species was forced to abandon him, explaining himself with these words: “And now, the last person whom I thought that would do this, Boethius himself comes back to me, our Helice and our Cynosura, and, having pushed our ship almost backwards, prevented me from continuing on the route on which I set off. In fact, at chapter thirteen of the fourth book, he lays out the species of the diatessaron and of the diapente in a completely different way from the sequence in which I ordered them, since I set the first one as sol re, the second one as mi la, the third as ut fa, while he ordered the species of the diatessaron in this way, namely, mi la, ut fa and re sol, and this is the way followed by most of the ancients. Similarly we place the Diapente et cetera.” Then he states: “But, what upsets me the most and stopped me from continuing on my route almost as if my sails were directed towards the opposite direction, is the fact that in the same book, in the chapter straight after this one, he says of the starting points of the Modes that the Hypolydian is a tone higher than the Hypophrygian, while we only placed a semitone higher. But, if [-<297>-] my statements are false and Bouethius’ text is correct, we must abandon any dithering, turn our pen and re-write most of this commentary which we have constructed with great effort.” Also, in order to solve that difficulty regarding the ordering of the species, he states that Boethius put as first species Mi la, since it occurs between stable notes, as if starting from stable or mobile ones made a big difference. You shall see what interesting Dilemma he adduces to justify that both the Hypophrygian, which he places on B and the Hypolydian, which he places on C, must be at the distance of a semitone instead of a tone, as Boethius says. “In fact, in this place either Boethius text is wrong or he called proslambanomene the lowest string of the Cithara and then he ordered the strings in the way that one can see that they are ordered still nowadays, from C to c or from F to f in the Synemmena, as one can see.” Then he states without any foundation of sorts that Boethius’ division of the Monochord in the Lydian mode makes more sense if applied to the Hypolydian or Hyporodorian, and for this reason he considers it suspect because of the copyists’ mistakes or incomplete. Then, he states: “All this aims at showing us plainly that this change occurred also at the time of the ancients, but that the majesty of the seven species of the diapason remained always unchanged, regardless of the way the others fell. The right of giving something a name changes easily and Cleonides, who starts his modes from the Hypate Hypaton and places the Mixolydian from that note to the paramese, can testify to this effect.” This should have made Glareano realise his mistake, had he disposed himself to believe what the ancients were teaching him unanimously, instead of adjusting the authorities of the ancients to his statements, as the Heretics of our day do by interpreting the Sacred Scripture in their own way. Had he done son, he would never have had the idea of criticising Poliziano, who had an intellect very different from his, as “a [-<298>-] collector of facts that he does not understand” and he would have strived to read Aristoxenus, Briennius and the other authors quoted by Giorgio Valla, instead of mocking him by stating that he quoted authors that he or nobody else ever saw in order to increase the reputation of his own works. Even Zarlino himself, although he treats the matter soundly and with good foundations for the most part, he is wrong when he hazards these conclusions from his noticing that Cleonides (or Euclid, [Institutioni, part four, chapter seven in marg.] as he calls him) and Gaudentius besides Boethius place the first species called Mixolydian from Hypate Hypaton to Paramese: “ One can see the reason for this openly, and it consists in the fact that he does one of two things, namely, either he places the Mixolydian mode in the lower part of His Monochord (where it is really) and the Hypodorian and the Locrian in the higher part, or he places the strings on that Instrument in a way which is different from the practice of the other ancient theorists.” In this conjecture of his he agrees with Glareano, whom, however, he names on very few occasions. [-<299>-] That one sees no less uncertainty of opinion in authors more recent than Glareano with regard to the Ancient modes. From what has been told, one learns that Glareano must have had a really good stomach to be able to digest his opinions on the modes against so many objections and doubts that were raised against him. Therefore, Salinas, as someone extremely clever and intelligent, realised easily that the matter could not stand in that way and he said at chapter thirteen of his fourth book. “Hence one can easily understand how mistaken are those who believe the Dorian to be the first tone of the ancient ones or rather one more recent, and the Phrygian the third one, the Lydian the fourth one and the Myxolydian the seventh. In fact, according to Ptolemy’s doctrine it was said that the Lydian is a tone higher than the Phrygian and the Myxolydian a semitone higher than the Lydian, while it is necessary for the opposite to be true in the disposition of the Tones. In fact, the fifth of them, which spans from F to f, is a Semitone removed from the third one which spans from E to e and the seventh, from G to g, is a tone removed from the fifth which spans from F to f, as every one knows, even practical musicians. Therefore the Mixolydian mode cannot be the seventh of the more recent ones, but, either the Dorian has to be located between C and c and the Phrygian and Lydian on C and E, which species is removed by a tone, and the Myxolydian on F, which is at the distance of a semitone from E, or they could not have had anything to do with them.” He opposed this particular position but not the rest. Zarlino, although he mostly discusses the matter sensibly and judiciously, nevertheless he blunders a lot on this matter of [-<300>-] [Institutioni, part 4, chapter 7 in marg.] the ancient Modes, for instance when he points out that Cleonides (or Euclid, as he calls him) and Gaudentius, beside Boethius, place the first species called Mixolydian from Hypate Hypaton to Paramese and draws these conclusions: “ One can see the reason for this openly, and it consists in the fact that he does one of two things, namely, either he places the Mixolydian mode in the lower part of His Monochord (where it is really) and the Hypodorian and the Locrian in the higher part, or he places the strings on that Instrument in a way which is different from the practice of the other ancient theorists.” Here I point out two things: firstly, that he agrees with Glareano in this conjecture, although he names him on very few occasions; secondly, that I cannot see how one may gather from this that Cleonides lays out the strings on his Instrument (namely, in his System0 in a different way from the one adopted by the other ancient theorists, because he states that Boethius and Gaudentius agree [Demostationi Harmoniche, Ragionamento 5. Institutioni, book 6, chapter 3 in marg.] and he could have seen that in Ptolemy’s work there is no contradiction with what these authors state. Zarlino himself, seeing that he could not adjust the distances of the tones by placing them within the notes in which the authors place them because he had not understood this transposition of the whole System (since one who has got it into his head that the ancient modes correspond to ours and that each does not exceed the distance of a Diapason can hardly imagine it) in order to preserve their distances bases some on notes which are different from those on which the ancients placed them. Therefore, he places the Hypodorian on G, the Hypophrygian on A, the Hypolydian on B, the Dorian on C, the Phrygian on D (which is the only one which turns out correctly) the Lydian on E and the Myxolydian on F, which is its exact opposite. He seems to concur in this with Salinas’ opinion and with the one of Ponto di Tiard in his Solitario. [-<301>-] [[If these, who have been the most learned and judicious thinkers in the field of music understood the subject of the ancient modes so badly, we should not be surprised]] Now we shall say something about Gallilei, who, partly because of his beautiful mind, partly because of his strict connection with Mei (who worked on this matter more than anyone else) and also because of his familiar relationship with Signor Giovanni de Bardi of the Counts of Vernio, a most gifted Nobleman and promoter and learned scholar of the music of the ancients, achieved a greater understanding than anyone else and he was able to distinguish correctly what is false from what is true, as he did when he recognised that the sequence of the consonances according to the ancient Greek and the Latin writers is not different, but the same. Nevertheless, he made several mistakes, such as when he states that the first species of the Diapason which occurs between [sqb] mi and [sqb] mi, which is taken by the Greeks as the first one and which is used in the Myxolydian tone, corresponds to the one which was applied to the Dorian by Latin theorists, without considering the difference that occurs in the position of the second Semitone, or when he says that the reason why the Greeks did not accept as first species of the Diapason and of the other consonances the one that start in the lowest note, Proslambanomenos, was because this note is outside the tetrachords and it is the last one and was added on after the others, or that the lowest note of the Diapason can be used in the high Tone, or, equally where he believes it was more probable that the second species of the Diapente was placed between Hypate Hypaton B and that it should respond with the Trite Synemmenon or b fa, because there is no true Diapente between B and F, not realising that that he and the ancients place it more readily between low F fa ut and high [sqb] both to avoid that obstacle of the false Diapente which occurs on B mi, as well as to place the basis of the three Species of te Diatessaron in the three notes from B to E exclusive and the basis of the four species of the Diapente on four other notes from E to e inclusive, which is a very beautiful order. Thus, placing the figures of the Tones as they must be raised one above the other according to the Boethius’ thought, he lets himself be swayed by the current of common blundering when he lays out the Tones according to Ptolemy’s thought, although he marks the species correctly in the middle of the Systems and places them also between the cardinal notes of the Modes, as we shall illustrate further on. Nevertheless, this Description of his does not correspond to Ptolemy’s intention, but he is justified greatly because [-302-] Ptolemy is an writer very difficult to understand, especially because of the inaccurate translation at chapter five of the second book where he wants to show how Therefore, Zarlino, who tranlsates his words into Italian, does this in a way that one can see well that he translates the words, but not their meaning, which he only understood in a confused way, since it is abundantly clear that the modes must be connected in one of the three way mentioned above, if they have to be laid out well. Nevertheless, this way adopted by Gallilei should not have been discarded, had correspondence between the distances from a tone and another been preserved, which he tries to salvage with intellectual device similar to the one which he adopts by ordering all the modes from A re to a la mi re. In fact, had this been done, that simple connection would have been more successful, although in this disposition by Gallilei their distance is not preserved without mental transportation and the proper species does not appear between the lowest notes of the Systems [-<303>] Ordine de Tuoni come gli pone il Gallilei secondo la mente di Tolomeo [Doni, Treatise on the Genera and on the Modes, second book, 303; text: Hypodorio, Hypofrigio, Settima Specie del Diapason, Sesta, Media, D. d, c, [sqb], a, g, f, e, d, A, G, F, E, c c, C] [-<304>-] Therefore, if these were the most subtle and intelligent writers of musical matters and they have explained the subject of the ancient modes so badly, it will not come as a great surprise that Artuso and the other second-rate writers, who follow mainly the lead of the former, found themselves deviating from the straight path. Hence it follows that poor Artuso blunders and believes that the Modes of Euclid and Cleonides proceed in inverted order compared to those of Ptolemy from the Phrygian onwards and accomodates the seven modes in their notes well according to Cleonides, but not according to their order, because his Mixolydian is lower and the Hypodorian is higher. As to Ptolemy’s order, he agrees with Zarlino, basing the Hypodorian on G, the Hypophrygian on A and so on the others one after the other, and he makes him say that it is not possible to observe the order of the Modes and the one of the Species. However, I shall stop listing all the contradictions of opinion and the blunders of modern writers on the seven species in their adjustment to the modes, since perhaps I have said too much, let us see now what is the consequence of the addition of the eighth Mode, which has given so much to say and write to Music theorists and was the second reason of malpractice on the subject of the modes. [-<305>-] On the Hypermixolydian, the eighth mode mentioned but not accepted by Ptolemy. The fact that Ptolemy mentioned another tone, called Hypermyxolydian by those who added it, besides the original seven, because it follows the Myxolydian in highness of pitch, has been the cause of several clamorous blunders and confusions in music, or, to put it better, this has proceeded from the fact that Boethius believed that Ptolemy accepted it, or rather, from the fact that Boethius was interpreted in a way which was different from what was appropriate. Therefore, since we want to erase any doubt from the mind of the reader, we shall tell briefly how this occurred. Some considered that the seven modes do not complete the diapason, or, to be more precise, that the Disdiapason or the whole System, and that either its lowest or its highest note could not be included in it. They considered this a fault and for this reason they added another tone, the eighth, which, for the reason mentioned above, was calle Hypermyxolydian, which corresponds to the Hypodorian, as they used to say, to the Hypodorian. However, this opinion is refuted openly with excellent arguments by Ptolemy. In fact he says that, since the highest and lowest sounds of the Diapason are considered as one sound and, therefore, the consonances added to the Diapason are the same as if they were simple, because, for instance a Tenth is equivalent to a third, an eleventh to a fourth, a twelfth to an fifth, thus, equally, the melody of a single voice can start from an octave [-<306>-] higher or lower, but it will produce always the same air and melody. Hence, since the eighth note corresponds to the first one, thus the eighth mode will differ from the first one. Therefore, just one cannot ascribe more or less than eight notes to a mode, conversely one can only lay out seven tones if they have to be all different, as, if it is the first tone is allowed to have its correspondent at the octave once, why should the second, the third and the others not be allowed? Thus, one would continue ad infinitum. Hence, for this reason one must not define the number of the Tones or the terms of the octave, but the intervals, which, being only seven, and since the species or varieties that can be produced by starting from the first, second note et cetera are also only seven, as many components of the octave must be established. This is what Ptolemy says in substance against those who introduced the eighth mode. Nevertheless, one can see that, although these reasons are very plausible and adequate, the prevalent practice of both modern and ancient theorist headed towards the opposite direction, since they not only reached the octave, but they exceeded it by a tone, since it is possible that this eighth mode was somehow the invention of practical musicians, who believed that one could produce some variety by maintaining the same species, albeit it is more probable that it was introduced through malpractice and that it had no difference from the first one, except for its pitch. In fact, Athenaeus, of its own initiative or on the basis of some more ancient writer and music professor, berates the invention of the eighth tone, and for the same reason modern theorists have enclosed the circle of their Modes within an octave, if they refer to the bases or terms of each system, and of two octaves, if they meant the whole Systems. Therefore, it appears that Boethius believed that Ptolemy was the author of this eighth Tone where he says: “And this is the eighth Tone which Ptolemy superannexuit,” although it seems to me that [-<307>-] one may interpret this word in this way: “And this is the eighth Tone which Ptolemy added to them on top,” namely, “that he mentioned after the others,” rather than “that he considered among the legitimate and reasonable ones.” This seems to me to be more probable than to believe that a great scholar such as Severinus Boethius was, to which that title of last of the Romans, which ascribed to him, was well suited and which cost him his life, and who was endowed which such great knowledge and judgment, had been responsible for a blunder of such kind, since Ptolemy’s words in this passage are so clear and precise that no doubt arises. Moreover, Ptolemy does not let himself be understood in any other passage better than in this one. It is also possible that some musician who lived after Ptolemy (acting like someone who goes and commit a sin having learned of it from a book of moral dilemmas) took the chance to introduce the eighth mode from the fact that Ptolemy mentioned (although he disapproved of it in effect) thus he wrote something about it ascribing to it some individual feature to distinguish it from the others, called Hypermixylydian and in some way he attributed it to Ptolemy. Boethius might have remembered this and attributed it to Ptolemy, not on the basis of Ptolemy’s own words, who did not accept it, but rejected it. It is known widely, in fact, that even great men are not exempt from memory lapses, and that those who read widely are more subject to them. This seems to me so much more probable since before Ptolemy the fifteen or at least thirteen tones of Aristoxenus were accepted and practised commonly, but the Hypermixolydian is not one of them. [-<308>-] Consequences of the addition of the Eighth Mode, chapter Mei is surprised with good reason that Franchino, who, despite rating highly the Greek writers, having read something of them and saying that he commissioned somebody to translate them, nevertheless, he trusted these simple words of Boethius’, did not compare them with Ptolemy’s, attributed the discovery of this eighth mode to Ptolemy himself, accepted it as legitimate and approved and introduced with that difference of the Harmonic and Arithmetic division which I shall explain further on. Now, one must know that ancient Ecclesiastical writers, as Guidone andAbbot Oddo, who lived a little before Guidone, state, did not know but four modes, which they used to called Protos, which means first, Deuteros, which means second, Tritos, which means third and Tetartos, in the previous centuries. The first was considered to be the Dorian, the second the Phrygian, the third the Lydian and the fourth the Mixolydian, although the first one occupied the species of the Phrygian, since it is based on D, the second the one of the Dorian, being based on E, the third one of the Hypolydian, which is based on F, and the fourth of the Hypophrygian, being based on G. With really mature judgment the ancient Primates and Saintly Pontiffs Gelasius and Gregory the Great (although Franchino ascribes to the latter the addition of four other tones) appear to have satisfied with only four modes, firstly, because none of the four species of the Diapente, to which it was more convenient to attain more than to those of the Diapason, because the Psalms, which were the main reason why they were introduced [-<309>-] (since only Hymns used to be sung in the early Church, and the the Gospels, the Homilies, the Prefaces and similar, as Glareano and Maillard observed) rarely exceed the span of the fifth, as Maillard says, part 2, chapter 1. Secondly, because he judged wisely that matters connected with the Church required a certain unaffected simplicity and and a style of singing which was more pious and devout, rather than secular. Had Ecclesiastical music continued within this boundaries, as perhaps it would have been better, it would not have required eight or twelve modes, which then would be subdivided into several types, namely, Authentic, Plagal or Collateral, Harmonically or Arithmetically divided, Whole, Superfluous, Diminished, Regular, Irregular, Simple, Mixed, Commixed, perfect, Imperfect and More then perfect, and others that can be called in different ways which confuse the mind of practical musicians, waste theorists’ time fruitlessly and move many to despise this observance of the modes. So that nobody may believe that they are figments of my imagination, I invite everyone to see that Glareano’s Dodecachordon, the Fiore angelico by , the Tesoro by Illuminato and other books of this kind which bear so great and flashy names on their title pages are full of them. However, to go bac to the Ecclesiastical Tones, since Odone mentions only four, one must believe that the other four were added by Guidone of its own invention, who took them always from the badly interpreted text of Boethius, unless he took them from the Greeks of his time, who used four authentic modes and four plagal ones, as they do still in the present day. It is enough what he states in the Micrologo, namely, [-<310>-] Now, so that one may note how a mistake begets another one, consider that from the fact that Boethius forgot Ptolemy’s doctrine regarding the eighth mode, there follow the fact that he appears to be writing about it in such a way as he ascribed it to him. Then, from the fact that Boethius had been interpreted wrongly, there followed that the uncivilised men who lived in the early modern times created eight tones, although there are some authors of that time who say that this had been done in imitation of the eight parts of the speeches, which are as similar to the tone as the moon resembles grains of sand. Franchino, explaining the sort of music that came before his time, so rusty and rendered totally uncivilised, was prompted by this to maintain the same number of modes and to differentiate the eighth from the first one by adopting two sorts of division. This prompted Glareano to do the same in other four, thus raising their number up to twelve. After him, Zarlino, who maintained the same number, but changed their order, improved little or nothing their understanding but authenticated them in the eyes of the composers perpetuating a great lie, [[but this will be shown now in more detail, if briefly.]] Finally, Maillard, in his ambition to prove that Tones and Modes are two different things, confirmed the old malpractice instead of erasing it. However, this will be shown here now in more detail, but briefly. [-<311>-] Meaning of the Harmonic and Arithmetic division of the octave, Chapter In order to understand this proposed matter correctly it is necessarily firstly to know what Proportionality is. Therefore, Proportionality is what the Greeks call [analogia] and it is called more appropriately in Latin Proportio [Progression of similar Ratios add. supra lin.] than proportionalitas. It is a continuation of two or more similar proportion which are called [logoi] and Rationes in Latin. The main species of them are three, as Boethius, Giordano and other writers show. The first and simpler one is called Arithmetic and is contained between the second and the third, and so on, in sequence, in the others, as in this case 1, 2, 3, 4, 5, 6 or 2, 4, 6, et cetera. Its property is to have equal differences but unequal proportions, as one can see [, Treatise on the Genera and on the Modes, second book, 311, 1; text: 2 differenza, I., IV., VI., progressione Aritmetica, 2/3 Proportione add. in marg.] questi tre 2. [2 add. supra lin.] 4. [2 add. supra lin.] a 6. [[et]], since the difference is two in one and in the other interval, and the subdupla proportion occurs between the first and the second and the subsesquialtera between the second and the third. Geometric Proportionality is called the one in which the numbers are ordered in such a way that the first with the second, the second with the third, and similarly the others shall have unequal differences, as one can see here [[I. [1 add. supra lin.] 2. [2 add. supra lin.] 4.]] [Doni, Treatise on the Genera and on the Modes, second book, 311, 2; text: 2, differenza, I., II., IV., Progressione Geometrica, ½ Proportione add. in marg.] However, the one that is called Harmonic Proportionality or Progression is the one where the proportion between the first and the third one occurs also between the difference between and the second and the difference [-<312>-] between the second and the third. In this one, not only the differences but also the proportions are different, as in this case: [Doni, Treatise on the Genera and on the Modes, second book, 312, 1; text: 2, 1, VI. IV. III, 3/2, 4/3, differenza, Proportionalità Harmonica Proportionali]. One can see there that just as the first number, which is six is in dupla proportion with the third one, which is three, thus two, which is the difference between six and four has the same proportion with one, which is the difference between four and three. This proportion occurs in the opposite way to the arithmetic proportion, where the larger proportion occurs between the larger numbers and the smaller between the smaller ones. Although this proportion is different from the other two, nevertheless it is composed by them coming closer now to one now to the other. This proportionality is called harmonic because the median number which is called the divisor divides the proportion which lays between the first one and the third one into two proportions next to each other and orderly laid out which produce the first and most perfect consonances within the number six, and outside of that number produce other dissonant Harmonic intervals but all the more perfect, all being the same, caeteris paribus, the closest they are to the number six, as one can see here: [Doni, Treatise on the Genera and on the Modes, second book, 312, 2; text: terza minore, maggiore, VI. V. IV. III, II, I, sesquiquinta, sesquiquarta sesquiterza Diatessaron, Sesquialtera Diapente, Dupla Diapason, Sesquialtera 6/4], [-<313>-] where one can see that, just as the Dupla and the Diapason are divided harmonically into the sesquialtera, which represents the Diapente, and into the Sesquitertia, which represents the Diatessaron, thus the Diapente, which is the principal consonance after the Diapason is divided harmonically into the Sesquiquarta, which represents the Ditone, and the Sesquiquinta, which represents the Semiditone. Also, since larger numbers are assigned to lower sounds and smaller numbers to higher sounds, because they are compensated virtually by those, as Aristotle teaches us in the Musical Problems and experience confirms in the division of the Monochord, and because the Arithmetic proportion is achieved by adding parts to part or number to number, while the Harmonic is produced by dividing a proportion with smaller proportion, which consists in dividing the parts into smaller particles, for this reason one keeps growing the more one moves away from the number one, while in the Harmonic proportion one decreases the further one approaches the number one. Therefore, I would say that Harmonic proportionality is the symbol of divine unity and of the human soul approaching God, who is Supreme and first Number One, while the Arithmetic symbolises Division and worldly and physical Imperfection. Therefore, it follows from here that in the Harmonic, as opposed to the Harmonic, one places the largest numbers first, which occur in the double combinations of sounds, namely, when two consonants are placed one above the other so that the most perfect, which is represented usually by a larger proportion, is placed underneath or in the lower register, which represents the larger number and the first number of the proportionality, while the less perfect is placed above and towards the high register, thus producing a much sweeter than in the opposite way. In fact, the fifth under the fourth [-<314>-] and the Ditone under the semiditone produce such beautiful an effect, which is greatly superior to the one achieved when the fourth is placed under the fifth and the Semiditone under the Ditone. We note that this precise order is observed also in Painting and in Architecture, which I would define as the Harmony of the visible quantities of the bodies, in the same way as music is the harmony of the audible quantities or sounds. In fact, nobody would praise an Architect who would place the longest and largest columns above and the shorter and slender ones underneath in a portico composed of several orders, nor the painter who placed the smaller figures at the bottom of a canvass and the largest above. Where the enlargement of the number of the twelve modern Modes originated. From what was said everyone can gather what a Diapason Harmonically divided or partitioned is and what is a Diapason Harmonically divided, since the first one is understood to take place when the Diapente is placed in the bottom register and the Diatessaron in the high register, and the second one when they are placed in inverted sequence. One must also know that these modern theorists, following the custom of the Greeks as it was [-<315>-] fashionable at the time, added ti each if those four Ecclesiastical modes, First, second, third and fourth, which we shall name thus instead with their Greek names, added another one at the distance of a fourth in the low register in imitation of the ancients who had added the Hypodorian, the Hypophrygian and the Hypolydian under the three main ones, Dorian, Phrygian and Lydian at the same distance but with a different artifice. Following the Greek style, as it was very popular in several professions, they called the first four Authentic, which in not-soancient Greek translates as main ones or principal ones, while they called the other four plagal, as to mean oblique and subordinate. They called the first of those Plagius Proti, the second Plagius Deuteri, the third one Plagius Terti and the fourth one Plagius Tetarti. Later theorists called them differently, calling the first Authentic simply First, the first plagal Second, the second Authentic simply Third and the second Plagal Fourth, the third authentic equally just Fifth, the third plagal Sixth, the fourth authentic Seventh and the fifth plagal Eighth. Thus the authentic and higher in pitch ones turn out to be the odd one and the plagal and lower in pitch the odd ones. Also, because they are all considered as belonging to the same System, it follows that every Plagal shares the Diapente with its Authentic as one can see here, and who introduced these other four Modes left the first four in their original form without bothering to add one to [Gamma], the noted added by Guidone to avoid altering the ones that were universally accepted in the Ecclesiastical chant, as the majority of modern theorists did later on.: [-<316>-] [Doni, Treatise on the Genera and on the Modes, second book, 316, 1; text: I, III, [[[III]] V, 2, 4, 6, [signum]] as one can see here [signum], but for the figured chant. [Doni, Treatise on the Genera and on the Modes, second book, 316, 2; text: Otto Tuoni de gl’Ecclesiastici, Autentici, plagali, I, III, V, VII, 1, 2, 3, 4, 6, 8]. One can see here that the white notes are the extreme and final ones of the Authentic Modes, the middle ones are the extreme and final notes of the Plagal Tones. The compositions for several voices usually end on them. However, the black ones are the the extreme of the plagal Modes and Modern composers do not usually build their final cadences on these. The numbers placed in the positions of the fifths and of the fourths indicate the species of each according to the order of Boethius’ followers, who have claimed to have been the theorists who introduced these eighth modes. [-<317>-] Therefore, Franchino observed this eighth tone, which he believed with certainty to be the Hypermixolydian attributed, as he believes by Boethius to Ptolemy. However, not only he was mistaken in this, as it has been said, but also in believing that it was the same as the ancient Hypermixolydian. Glareano, Zarlino and Mei proved against him that this was not true, because one can see clearly that this eighth Ecclesiastical Mode has the same species of the pre-ordereded Dorian D d, while the ancient one had it in common with the Hypodorian. Thereore, Glareano was happier to call it Hypomyxolydian, although he vario’’ assai in this, that Hypermixolydian, because it is the plagal of the plagal of the pre-ordered Myxolidian G g, since that ancient one, had the Hypodorian had this distinction, namely, to be described as different only because it has the fourth below and the fourth on top, which it did not have otherwise, he would have been divided differently, namely with the fourth above and the fifth beneath, and it would have been authentic rather than plagal, as Mei learnedly discusses. Therefore, Glareano realised that the eighth Tone does not differ from the first one except in the transposition of the fourth and the fifth, since the first one the fifth lays beneath the fourth, and that the fact that a species was divided Harmonically or Harmonically consisted in this (which was a definition introduced by Franchino, because mathematics was evolved enough before him). Glareano regarded it as a good invention, and, since it served its purpose very well which was to restore the thirteen Modes of Aristoxenus or at least twelve, because he was not able to restore all thirteen starting from these elements, he embraced it enthusiastically and he was very pleased with it. Therefore, [-<318>-] he observed that only five of the seven species of the Diapason allow both the division, namely, Harmonic and Arithmetic, because the other two can be divided only in one way into a fifth and a fourth, since they are divided by the other median note into a tritone or Distrihemitone, also called Semidiapente, he realised that five species produced ten Modes, which with the other two produced from the other two Species reached the number of twelve. So he had to be contented with twelve, because a thirteenth tone did not fit, and he added four, Ionic, Aeolic, Hypoionic and Hypoaeolic to the other eight which were thought to be the Hypodorian, Hypophrygian, Hypolydian, Dorian, Phrygian, Lydian, Myxolydian and Hypermyxolydian of the ancients, and he mentioned not only these twelve in the first-page of his book, but also the two Hyperphrygian and Hyperaeolian, although he rejects them afterwards as illegitimate. These are the ones which lay between the notes [sqb] and F, when their octaves are divided with the false fifth above and the tritone beneath or with the tritone above and the false fifth beneath, almost meaning that, since he had not been able to find the middle one between the number twelve and fourteen to re-discover all the ones of Aristoxenus, he awaited some celestial spirit to enlighten him so that he may find the thirteenth which had lost itself along the way. However, these modes of Glareano have as much to do with those of Aristoxenus as the Moon has with crabs. [-<319>-] On Glareano’s Twelve Modes and on the Twelve of more recent Musicians and on many mistakes contained in his Dodecacordo Nevertheless, Glareano’s authority was so great, since he matched uncommon knowledge with some understanding of musical practice, that, as I was saying, his twelve Tones were accepted and there was even somebody who compendio’ his very prolix Dodecacordo, so that it may be read more easily. Zarlino came after him, who thought it best to start the lowest mode from [Gamma] ut, so that the first note of the modern system may not be let wanting. Therefore he established the first species on C fa ut and placed there the first authentic Mode, considering also that it was good, for the same reason, that the species should start from Ut rather from Re, because the deductions called by [sqb] square, by nature and by b flat start from there. He called the Modes, rather than Tones, to distinguish them from the eight Ecclesiastical Tones, of which the eight and the first are equivalent. Hence Zarlino, followed afterwards by all the composers of counterpoint, simply organised the number of the species, or, to be more precise, the number of the twelve Tones which he found already introduced. [-<320>-] [Doni, Treatise on the Genera and the Modes, second book, 320; text: Tuoni del Glareano [[le altre maniere egli segna cosi con tre chiaui per comprenderli tutti in cinque linee e ne loro spatij,1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, Aritmetica, Harmonica, [signum], Hypodorio, Aeolio, Hypophrygio, Hyperaeolio, Hypolydio, Ionico, Hypermissolydio, Hyperionico, Dorio, Hypoaeolio, Phrygio, Lydio, Hypoionico, Missolidio] One must note that the ones that are marked with a start are the four added to the eight Ecclesiastical ones, while the two with the darkened notes are the two that would originate beside the twelve if the division of the Diapason [sqb] [sqb] into Semidiapente and Tritone and of the diapason F f into tritone and semidiapente were to be accepted. However, in order not to leave behind any of those of Aristoxenus, named one of these Hyperaeolian and the other one Hyperphrygian, despite calling them bastardised, and he did not hesitate to call the first one Harmonically divided and the second one Arithmetically divided. Now, one would struggle to believe how little success he had in this and into how many vile pitfalls he fell. I will be content with mentioning a few of them, so that, those who consider him a great Salomon in the subject of the Modes may know what an expert he is. The first one, namely, his claim of wanting to restore Aristoxenus’ modes, to apply their names at his own whim and to put their order and their distance between each other into disarray, this cannot be justified in any way. I leave aside his placing the Hypodorian and the Aeolian [- <321>-] at the same degree of tension, because, since he had some reason to mention them as completely equal, one can forgive him this. However, one cannot forgive him the fact that he placed the Ionic or Iastian under the Dorian and the Hypoaeolian above it, confusing, as one says, sky with the earth, and the prefix hypo with the prefix hyper. Equally, one cannot approve his placing the Hypoionian above the Lydian or his calling the same Mode now Hypomixolydian and now Hypermixolydian, as he does not do with the Hyperiastian, without considering that it is not a fourth above that from which they derive, as must be the ones with the prefix Hyper. Moreover, I cannot see on which masis he banishes the poor Hypophrygian, if not the fact that it is the last one of those of Aristoxenus might have counted against it, while, as to the Hyperaeolian, which was added by the followers of Aristoxenus at a later stage, this can be forgiven to him, if it has occurred in that way from his not accepting the Hypolydian, but he cannot be forgiven for criticising Poliziano and Franchino (the former of whom was much more learned than he was and the other a greater expert in the field of music theory) and for having counted the Hyperlydian among the others. In fact, since he [-<322>-] refused the Hyperaeolian because he could not find a place or a form for it, why should he have attempted that enterprise rather than say freely that to restore them was hopeless, as he said about the two genera, Chromatic and Enharmonic? Other indeed too serious errors, which appear, however, on the first-page of his book, are to say that the Hypoaeolian is the same as the Hyperdorian of Martianus, that the Lydian is the same as the Hyperphrygian and that the Myxolydian is the same as the Hyperlydian. I do not know if I have to call him simple or mad where he states that the System arrived up to fifteen notes or strings, “Nevertheless, the ancient division of the notes into tetrachords prevailed, since future generation appreciated so profoundly the simplicity of the System of the ancients.” What shall we say about the fact that he called the distinctive note [likhanos] adducing the authority of Suida, who derives it from [leikho], which means to lick, which is the ethymology of [likhanos] which means finger, from which the meaning of lichanos, the third note of those tetrachords, was derived at a later stage. What shall we say about the fact that he interpreted the word Phonascus as Melopoeus or inventor of a melody or a subject, rather as the person who exercised the voice, and Symphonetes as a composer, rather as one who sings consonances with others? Because of this, many have incurred this mistake after him. I also do not know where he found that the tone was accepted as a consonance, the unison was classed as consonance and the fourth among the consonances. Although this has little importance in practice according to our contemporary practice, it did not befit someone who professed to be a man of polished and exquisite letters, but he should have abandoned this manner of speaking. I am much more surprised that, despite setting himself to restore the ancient modes, he had such a poor understanding of the true meaning of Tone, Trope and mode, so that he was drawn to say that [-<323>-] the word Tone originated at the time of Boethius and it was not used by the Greeks. [book 1, chapter ii in marg.] Similarly he was mistaken, together with the others who followed him, when he believed that Arsis means the rising motion of a melody towards the high register, while Thesis is its descent towards the low one, while he also interpreted Prolepsis and Eclepsis in the same way. He rebuked Franchino without reason for comparing the four modes to the four complexions, thinking that he should not have the other three behind. However, had he known that four modes are more general than all the seven ones, he would not have stated that. He is mistaken where he says that Martianus Capella leaves out two of the modes of Aristoxenus, the Myxolydian and the Hypermyxolydian, because He is wrong when he states that Martianus did not understand Aristoxenus (in fact, how correct is Franchino in this!) and when he says that the Cassiodorus’ Constitution is opposed to Boethius’ one. He is wrong where he reprehends Franchino to have placed only four final keys, as it was common knowledge, saying that only the [sqb] mi has to be banned, because we shall show that this one has to be accepted as well as the others. He was wrong in criticising those who believed that the mode is not changed because the position of a Semitone is moved, as it happens in the case of b flat [book 2, chapter 6 in marg.], and he is also wrong in rebuking those composers who changed the form of the moved in certain compositions of theirs by adding this key. Nor the fact that some believe that he changed the mode by adding the b fa in the eight ancients should have been a good reason for him to believe this. On the contrary, instead of following them, he should have persuaded them to regret this mistake. [-<325>-] On the twelve Zarlino’s and other modern theorists’ twelve Modes The matter of the twelve tones was set in the terms which we have seen from Glareano’s time to Zarlino, which is less than twenty years. But Zarlino, as someone of perceptive mind and great expertise in music, noting many details in the sequence of the Tones of Glareano which did not satisfy the mind and helped memory, as the fact that the Scale starts from Gamma ut and the sequence of the Tones from A re, that the Hexachords and deductions begin from Ut and the species from Re, that the order of the Species of the Diapente and of the diatessaron does not progress continuously, he thought it much better to consider the species of the Diapente and of the Diatessaron in a different way, as we noted above. He placed the first from C fa ut, as well as the first Mode (but he called them Modes rather then Tones, to distinguish them from the eight Ecclesiastical Tones). He placed the second one on [Gamma] ut as te plagal of the preceding one, according to the order found before him, and thus the third one on E la mi, the fourth one on A re, the fifth one on E la mi, the sixth one on [sqb] mi, the seventh on F fa ut, the eighth one on C fa ut arithmetically divided (while the first, fourth and also the third, fifth, seventh and all the authentic or odd ones are divided Harmonically) the ninth on C c sol re Harmonically divided [- <326>-] (as the second one which has the same species is divided Arithmetically) the tenth on D la sol re Arithmetically divided, the eleventh on a la mi re Harmonically divided, and finally the twelfth on E la mi divided Arithmetically. He was prompted to place the first species on C sol fa ut from this fact, namely that the intervals that derive from the Harmonic Division of the Diapason into its parts follow the order of those of this species, and, since he believes that this was also the Dorian mode, the D la sol re the Phrygian, the E la mi the Lydian and the others in sequence, it worked very well, because he found between all of them the distance that he ancient modes had. However, since not even he understood that the ancient modes had each a particular System, he was not able to place them in their true species. [Doni, Treatise on the Genera and on the Modes, second book, 326; text: li XII Modi del Zarlino, Dorio, Phrygio, Lydio, Mixolidio, Hypodorio, Hypophrygio, Hypolydio, Hypomyxolydio, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] Hence one can see that the Modes of modern theorists are contained correctly within the terms of sixteen notes, namely the fifteen of the ancient System [-<327>-] and the one added by Guidone. It is also worth knowing that each mode can be transported a fourth higher or a fifth lower by changing the [sqb] mi to the b a, namely, by moving through the conjunct tetrachord instead of the disjunct. Therefore, since the species is changed with the addition of the b flat and the sequence of the fourths and of the fifths, their species is necessarily changed. [Doni, Treatise on the Genera and the Modes, second book, 327; text: Li XII Modi per b molle, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12] [-<328>-] On the cadential notes of the Modes The cadences which occur in the compositions, called by the Greeks [katalexeis] and [katalogai] are certain conclusions of the compositions or of sections of them which give a certain sense of conclusion corresponding to their beginning, according to the species of melody which was adopted. The cadence is like the full-stop in writing or that accent or that accentuation or turn of voice which occurs at the end of the phrase and in the others where the sense is complete. Moreover, just as the sections of the phrase are recognised not only by the completeness of the meaning and by the metre or Rhythm of the oratory, which it is often slower, measured and interrupted by some rests in that place, thus in the compositions, if the melodies are perfect and have the meaninful rests which the Greeks call [lexeis], they are recognised from the closes which complete the meaning. [-<329>-] The Seuouae or Euouae, as others write it, is interpreted as the end of the verse, which ascends normally as the Intonation ascends. This word is made up of the vowels of these two words, Seculorum amen, which are the conclusion of the last verse, namely, the Gloria patri, as one can see better from this example. [Doni, Treatise on the Genera and on the Modes, second book, 329, 1; text: Intonatione, Mediatione, Dixit Domnus Domino meo sede a dextris meis] However, there are two sorts of intonations. One is the simple one and the other is the solemn one. The simple is the one which sings almost all of the syllables on the same tone of voice and renders the chant very simple because it starts in the middle and from the dominant note and it moves not very far from. This sort of chant is used in the less solemn days to shorten the service and distinguish it from the one of the more solemn days. Here is an example: [Doni, Treatise on the Genera and the Modes, second book, 329, 2] The solemn intonation is the one used in the Psalms on solemn and feast days as well as in the Cantica, such as the Magnificat, the Benedictus and so on. Both species of chants are performed with the antiphon, so that from the last note of the antiphon one leaps to the Dominant (which in the above example is the la of a la mi re) which usually is a leap of a fourth or of a fifth. Theorists have devised the following rule on this, which we shall quote here without verse: [-<330>-] [Doni, Treatise on the Genera and the Modes, second book, 330; text: Prima Regola, 2. Re fa, 3 Mi, 4, 5, 6, la,ut sol, 8] This means that the first syllable is the same as the last note of the antiphon which precedes the Psalm, while the second one is the dominant note of the Psalm (I believe that this function is performed also by the notes which the Greeks call [aianes], [neanes] and so on) and the dominant note is the first of the EVOVAE because it concludes the intonation and begins the conclusion. However, because, as Maillard states, the last note of the antiphon is not always an essential note of the tone, it follows that one cannot gather from it alone to which tone or species of the seven the Psalm belongs. I am also sure that one will be able to gather to which of the four most principal and ancient Tones it belongs from the species which is found within that leap of a fourth or of a fifth. One must note also with Maillard that Glareano, Giorgio Raw and other German writers wanted to change some of those notes so that they may distinguish the tones, and that new device proved not only fruitless and useless but also destructive of the Psalmodies. One must also know that a note is often added in many Antiphons (when one sings the same syllable with two notes if the syllables are not enough) in order to facilitate pitching the note and render the leap easier, such as the one of the fourth, as in the case of the note ut of the example quoted here below, [- <331>-] in the antiphon of the first tone which is used to introduce the Psalm Dixit Dominus: [Doni, Treatise on the Genera and the Modes, second book, 331, 1; text: Vidi turbam magnam]. However the solemn Intonations of the Psalms are noted in this way: Ma le [la ante corr.] Intonationi [Intonationee ante corr.] solenni de Salmi sono notate in questo modo: [Doni, Treatise on the Genera and the Modes, second book, 331, 2; text: primo et sesto fa, sol, la, secondo, terzo, ottauo, ut, re, fa, quarto, quinto, settimo, Mi]. These indicate the intonation of the first three syllables of each verse, as in the first Dixit Do where one sings fa, sol, la or ut, re, mi, which is the same. One can recognise the Modes in the Introits, Responsoria, Hymns and similar chants by following the same rule. Maillard himself states that the last note of the SEVOVAE should be always the first of the antiphon because it shows the connection between one and the other one. However, since some tones have different EVOVAE which do not conclude all in the same form and these have been altered a lot, for this reason it is customary to add some added note beneath them which may distinguish the specific note of the tone. Therefore, said notes were called by the ancients Neumata with a Greek word, which corresponds to the Latin nutus, from the verb [neuo] which means to point at, because of their function in highlighting the note of the tone and the connection between the Antiphon and the Psalm. Also, because [-<332>-] these notes often lack their own syllable, they are sung under the last one of the verse and they are marked with two notes linked together, and because one has ha long stroke which comes between them, they are called tails. Therefore some think that the Neums and these notes are the same [Glareano as well incurred this error at chapter 25 of the second book in marg.], but they are mistaken because Neums are only the ones invented for the aforesaid reason, while tails are the ones which are sung in the middle and outside of the Psalms, some of which are very long, as when the Dean releases the congregation with these words “Go, the Mass is finished” (Ite Missa est) elongating the syllable the with a very large number of notes. [[If anyone requires further information,]] Saint Isidore describes what the Neuma is [-<333>-] On the use of the Ecclesiastical tones In the music of plainchant which is the real Ecclesiastical chant, since figured music has been used in churches only in the last two hundred years, more or less, as Glareano and Galilei point out) there is no mention of the twelve Modes, but only of the eight which are used mostly to intone the Psalms, which were sung by Christians since the most ancient times and were dressed with the most beautiful melodies, which were both sweet and modest, by those great men, Saint Gelasius, Saint Gregory the Great, Saint Ambrose and similar ones who were endowed with as much sanctity as judgment and knowledge. Hence those Psalmodies of theirs are sung all the time after so many centuries and still last, and one can see from experience that the ones that were composed in later times do not arrive to the majesty and excellence of those, or because of the lack of refinement of that age, because of the mixing of the blood and traditions of Italians and Barbarians, who wanted to compose all music as figured music. Also, despite the fact that the disregard for the rules typical of modern musicians and the corruption of the ancient pronunciation and language, which is the foundation of music, were a very important force, nevertheless the whole melody of the Psalms, Hymns and particularly Introits, which are small section of some Psalms which are sung in certain Masses with different intonations and more elaborate than those of the Psalms because they were sung exclusively by priests and singers, while the melodies of the Psalms were written for the people who used to sing them in antiquity, was preserved very well. Moreover, one reads that many kings and Emperors [-<334>-] did not distain to sing them in church, as Theodosius the younger, Charlemagne, Louis the Pious, and Hugo Capetus used to do. However, since this pertains more to a treatise on Ecclesiastical Music which I have sketched out than to the present subject, I shall say only a few things about the more general use of the eight tones, as far as it is necessary for one to know them for someone who wanted to have some knowledge of music. Therefore, I state that one can learn the Air and melody of the Psalm either from the Psalms themselves or from the Antiphons which are sung between a Psalm and another, and are extracted from the Psalm itself by ordination. However, leaving aside to research why they are called in this way, how they used to be sung and how they are used nowadays according to the Gregorian, Ambrosian, Isidorian and Greek tradition, it seems to me that they were invented principally to help in the intonation of the Salms and to distinguish their tones. In fact, since they required very few notes ordinarely, one would easily realise their species or tone. Therefore, we see that the Antiphons span at least a fourth, a fifth or a sixth and sometimes they are wider and that from its last note one can learn to which tone it belongs itself and the Psalm to which it is associated. Therefore, one must know that the psalm and each of its verses contain s three parts which are called Intonation, Mediation and Seuouae, which correspond to the beginning, the middle and the end. In fact the notes and syllables which precede the dominant note are called Intonantion, while the dominant note is the one on which several syllables are sung one after the other in the middle of the verse, hence that part is called Mediation. [-<337>-] Some of the most beautiful Ecclesastical melodies Now, so that one may see clearly that the most ancient melodies of the plain and Ecclesiastical chant are the most attractive, I shall mention some which, in my opinion, will be judged very beautiful by anyone of good taste. One of these is the one of the Hymn Te Deum, which is of the Tone or Mode and has a certain emotional majesty, as it is the one of the Aue Maris stella, which has something of the lively and very cheerful and reminds me anamente [[l'Aria di]] those orphic melodies and of those Paeans of the ancient Greeks and that is of the Tone. A very beautiful melody is also the Veni creator Spiritus, which is full of energy and, as I wrote oltre to a learned man, it appears to prompt the Holy Spirit to descend onto earth. Equally attractive is the melody of the psalm In exitu Israel de Aegypto which has something of the extraordinary and beyond human. Similarly beautiful is the melody o gloriosa Domina, which is full of a certain angelic jubilation. [-<338>-] The melodies of the lamentations of Jeremiah, which are sung during the Holy Week, are also very heartfelt. Bottrigari considers probable that the majority of these sacred melodies were taken by the ancient Fathers from those of the Greek populations, however, I believe that he is very mistaken in this. In fact, apart from the fact that those early Christians were wary of imitating the rites of the pagans, despite not being superstitious, and especially in the matter of chant, which it would have been necessary to extract in its entirety from those secular and pagan melodies full of the praises of those false gods, those compositions of theirs were full of artifice, mostly in the Enharmonic mode, as I mentioned earlier with regard to the Nomoi of Olympus, and always accompanied by instruments, while the Christian melodies were always Diatonic and not only not accompanied by any instrument, but instruments were prohibited expressly to be used until the times of Pope Vitaliano, who allowed the use of the organ, as history tells us. Moreover, I do not know how easy it would have been to translate into the Latin language chants originally written in Greek, which is a such a different language with regard to accents and turns of phrases, especially because they were not broken into small strophes or repeated sections, the way ours are, but woven with many variations and devised to a specific Rhythm, as I observed elsewhere. Therefore, they must consider certain that the Psalmodies and other ancient Ecclesiastical melodies have not been derived otherwise from the names and the Melodies of the ancient Greeks, but composed by the effort and industry of those most saintly Priests who excelled [- <339>-] in every field. Also, although they appear so beautiful that one does not believe that our contemporary musicians would have the ability to compose other ones similar to these, this must be ascribed mainly to the knowledge and to the judgment of the individual composer and secondly to the age in which they lived, because, although the Latin language had declined already very considerably, as all the noble arts had, it did not have yet another sound and another quality, which it acquired later on. Nobody must believe that this is said without foundation, because not only the sweetness of the languages is an extremely important basis of the excellence of music, but even more so the variety and gracefulness of the accents which says that they are a Musices seminarium [musical nursery] and one of the most important reason of the delicate nature of that ancient music of the Greeks. In fact, Latin writers themselves admitted that they remained much inferior to them. See Quintilian, book . The French nowadays resemble the Greeks very much, and for this reason we see how plentiful they are in finding new, beautiful and very varied melodies all the time. These would be even more abundant if they had their accents not only in the last and in the penultimate syllable, but also in the third from the last one. [-<341>-] from the lengthening of the last notes which are followed mostly by some rests, and particularly from the melody itself of the composition which is known by a certain action by which it shows that it wants to conclude it its particular and special notes, while where there words are not important, as when someone sings some simple melody to the accompaniment of the flute, it is known from the same features, except from the meaning of the words. These are the cadences of the melodic compositions, namely, those for a single voice, while the cadences of the compositions for several voices, which modern theorists could not distinguish from the others, with the resulting confusion as to the good method) are all the ones which occur between two or more voices singing in consonances, which once can identify on the basis of the features of the cadences occurring in compositions for a single melodic line, as in the Ecclesiastical chant and also from the consonances, as the most perfect are used usually in those cadences, because every conclusion must contain perfection, so those consonance allow the ear to remain content and not expecting any other conclusion. However, since our topic is not Melopoeia or [Symphonourgia], I shall not proceed to describe the species of one and of the other sort of cadences and what belongs to each of them, but I will confine myself to discussing what one observes about them with regard to the Modes. One must know, therefore, that modern theorist recognise the modes usually [-<342>-] from their last note, and that, in polyphonic pieces, of whatever number of parts, if all end on the same note (as it happens in compositions of two parts) although the System exceeds the octave, that composition will be called of a single Mode. However, if one or several end on a note and another one or several end on another note which is at the distance of a fourth towards the low register or a fifth towards the high register, then they say that the composition is of two Modes, one of which will be the authentic and the other one the plagal. Also, if there are other parts which conclude on the same notes (according to the faculty called [dynamin] by the Greeks) but in a different place, namely an octave higher or lower than those, then such compositions shall be called of four modes or more, even if the parts conclude on a larger number of notes which are typical and principal of the modes, which are the ones indicated in the previous examples and complete the fourth and the fifth of each mode. However, it is true that one looks principally at the cadence of the Bass, since, being the foundation of all the composition, so to speak, the note on which it ends is considered the principal of all and it is called, appropriately, the final note, which usually completes the fourth below and the fifth above, while they call confinalis the one of an internal part which concludes the fifth above or the fourth below. Therefore, if a part of a compositions ends on C fa ut and the other one an octave higher on G sol re ut, the Mode of all the piece will be judged from that one and it will be called [-<343>-] of the first Mode (although those who are most expert do not want that it should be judged from the last note alone but also from the cadences which occur most often in a particular piece) and of the second, or just of the first one, because the final note of both of them is the same C sol fa ut, according to the rule which states that the authentic and plagal mode have the final note in common, which is the one that concludes the fifth below. However, since in the pieces for several voices some parts will end on the octave above, others on the note that divides said fifth into two parts and other on higher or lower notes, it follows that a composition will embrace several modes, such as the first and the second, and also the fifth, ninth and tenth. Moreover, since some parts do not span the octave, and others exceed it, from this that confuse mass of modes (mixed, compound, mixed, perfect, imperfect et cetera) derives, which are of little use in practice that to occupy the memory of poor composers unduly, rather than to help them to use the modes more appropriately. Cadences are also mostly divided into Regular and Irregular. Regular are the ones which conclude on the specific notes of each mode, namely, one the first and last one of the Diapason and in the one that divides it into its Diapente and Diatessaron, while Irregular are the ones that ones that end on other notes. Also, since when theorists talk about cadences they always refer to polyphonic compositions, these other notes must be interpreted as the ones which divide the fifth into two thirds, which are also called Half-way cadences, while the Regular ones could be all so called cadences which occur in the extreme notes. [-<344>-] On the Syllables which mark the eight Tones and the twelve modes Now, since not only the modes, but also the eight tones are identified from the last note of the compositions, which occurs in one of the first of the eight notes of the octave when it is sung ascending with one of the six syllable of Guidone, certain rules were formulated to help beginners to know these Tone, and it was said that they would help memory. These are similar to those that one learns in logical formulae. However, since these are not necessary and elegant, I will not bother filling these pages with them nor to match these syllables to the twelve Tones of Glareano, [- <345>-] which have almost completely vanished, but only to the eight Ecclesiastical tones and to the twelve Modes of the Contrapuntists. I state first that the syllable Re is used in the first and second Tone, the Mi in the third and fourth, the fa in the fifth and sixth and the sol in the seventh and eight. Moreover, to match the six syllables to the twelve Modes, we can say that the Ut is used in the second, the Re in the third and fourth, the Mi in the fifth and sixth, the fa in the seventh and eighth, the sol in the ninth and tenth and the La in the eleventh and twelfth, taking the la in the high register, because no deduction starts from la in the low register. However, so that one may see the Division of the Diapason of every Tone and mode in its progress, it will be better to observe the middle syllable, which is the note that divides the diapason into a fourth and a fifth, thus: [Doni, Treatise on the Genera and the Modes, second book, 345; text: Primo, secondo, terzo, quarto, quinto sesto settimo ottauo Tuono, Re, Mi, fa, sol, la, D, E, [sqb], F, C, G, d, e, f, a]. [-<346>-] However, as to the fifth and sixth, one can also use the syllable ut instead of the syllable fa, and ascribe the syllable sol to the first instead of Re, or even to the seventh and eight, to distinguish one couple from the other. The twelve Modes may be marked in this way: [Doni, Treatise on the Genera and the Modes, second book, 346; text: Primo, secondo, terzo, quarto, quinto, 6, 7, 8, 9, 10, 11, 12, Modo, [Gamma], Ut, Re, Mi, fa, sol, la, D, E, [sqb], F, C, G, d, e, f, a] [-<347>-] On the 13 Tones of Aristoxenus Up to now we have told as best as we could the story of the change and corruption of the seven ancient modes of Ptolemy (which are called thus not because he is their inventor, but because he described them better than anyone else and stated that their number was not larger than it was) until our day. We have also demonstrated how seven became eight and how they were then reduced to four, how they reached the number of eight and finally they were increased up to the number of twelve, and how, because of the long passage of time, like a brook what changes the taste of its waters because it covers long spaces of ground of different quality, and finally it looses itself in the depth of the sand, thus the Modes changed their form completely and lost almost their entire substance. Now we must move to another side and pick up a new thread of discourse, since the school of Aristoxenus, which flourished for a long time across many centuries in the past, has disappeared entirely, so that almost every record of it was lost, while, the Ptolemy’s school, because of his three very learned books which have come down to us and to those of Boethius, at least some shadow of memory has lasted, although we can believe that in some of the most uncivilised centuries [-<348>-] (of which we lost all record, and, in particular, of their music and musicians) they were hardly read. Be this as it may, one must presume that, when one deals with the Tones of Aristoxenus, we must not take him as the author, as many of the good authors are convinced because of their ignorance. In fact, we know well that the most part of the thirteen and principal Tones were used before him and we do not know for sure whether he invented any. However, since he must have written about them in a better and more authoritative way that the others, just as he describes all the parts of music in minute detail, for this reason he is the only one named by Ptolemy and by the others, and modern theorists ascribe to him the thirteen Tones, although he does mention only some in his three books of the Harmonic Elements, not because those books are lacking in any respect, as they are, but because, according to the order of his doctrine, which proceeds very methodically in a similar way to Geometry, it was convenient for him to deal first with the parts of the Harmonics, such as the notes, the intervals, of the Systems and of the genera, of which he discusses in the three aforesaid books, but, as one can gather from the last words of the third book where he begins to discuss the species, one can see that in the following books he should have dealt with them specifically. Although, the damage of time deprived us of them, nevertheless this loss is restored partially by those who wrote about it, namely Aristides [-<349>-] Quintilianus, ancient and inquisitive writer, the very judicious Plutarch and others who have left us some compendium of music. However, before we move forward, one must notice already that those who think that Aristoxenus Tones did not differ one from the other except for their pitch are very much mistaken. In fact, as Zarlino says, that difference between a Tone and another one would be reduced to the difference between two ho sing the same melody, one higher or lower than the other one. However, Zarlino should not have criticised Gallilei [Supplementi, book six, chapter in marg.] for locating these tones of Aristoxenus one higher than the other, but with the same intervals between the notes, because the ancients described them in this way as well, although they started from the principal and particular notes of each one when they sung them, as I mentioned above. [For this reason Athenaeus derides those who were able to distinguish in the Tone only the difference in pitch [E per ciò Ateneo si arride di quelli che sapeuano discernere ne Tuoni altra differenza che di graue et acuto imaginandosi un'Armonia [[Hyp]] (cioè uono) Hypophrygio e qualche altra uuole: [[quat con]] anzi che nemmeno l'Ipofrigio (dice egli) uegga hauer propria harmonica, cioè differente maniera et modo add. in marg.] Now, the thirteen Tones of Aristoxenus area at a distance of a semitone one from the other, hence, since they contain twelve intervals of a semitone, consequently they complete the octave exactly, since the lowest from the highest is at the distance of an octave. The most principal of those and almost models for the others are the middle ones which take their names from the nations who introduced them and used them. These, apart from the three Dorian, Phrygian and Lydian, are the Iastian and the Aeolian, the first one of which is contained between the Dorian and the Phrygian and the second one between the Phrygian and the Lydian. After these, the Mixolydian and the Hypolydian remained in their places assigned above, because one was at the distance of a semitone from the Lydian and the other one from the Dorian, and for this reason they could [-<350>-] not be divided by any others, while the others were inserted in between with the addition of the prefix Hypo, if they occurred beneath, and two were added above the Myxolydian with the addition of the prefix Hyper, which means above, and retaining the relation of fourth with their principal Tone, as it happens in the seven tones. Moreover, since the interposed tones were closer to one than the other, as I shall demonstrate further on, or had more in common with the species of one than of another one, for this reason Aristoxenus ascribes to them the name of their collateral besides their specific name with the addition of the term lower. This is the way in which Aristides describes them. Their order and lay-out is this one, with the addition in the high of the two added by the followers of Aristoxenus, with the effect that the Aeolian and the Iastian had their correspondent above, as the other ones do, so that they would exceed the octave by a Tone, since that is the distance between the Hypolydian from the Hypodorian. Thus the number of fifteen was achieved, of which five are principal, five correspond to those in the low register with the prefix Hypo and as many in the high register with the prefix Hyper. It follows from this that, just as the Dorian is the middle one in the seven modes of Ptolemy, and the Iastian in the thirteen of Aristoxenus, thus in the fifteen modes of the followers of Aristoxenus the middle one of all is the Phrygian. [-<351>-] [Doni, Treatise on the Genera and the Modes, second book,, 351; text: Hyperlydio, Hyperaeolio, Hyperphrygio, Hyperiasio, Hyperdorio, lydio, Aeolio, Phrygio, Iastio Dorio, hypolydio, Hypoaeolio, Hypuphrygio, Hypoiastio, Hypodorio, ò, piu graue, Hypermixolydio, due Myxolydij] One must heed the fact that Aristoxenus names Hyperdorian the tone a fourth above the Dorian as well as the more ancient name of Mixolydian, and he is very right in doing this, which prevents the Dorian, which was more highly regarded by the Greeks, from lacking its corresponding tone in the high register, as the Phrygian and the others have. As to Hyperphrygian, although some call it also Hypermixolydian according to Arisoxenus, nevertheless I am inclined to think that Aristoxenus did not call it in this way, because its name shows in truth that he should have been a fourth above the Mixolydian, as the other ones are which have the prefix Hyper before the name of their principal tone. Hence, this name would be apt for a tone which would be added to the fifteen ones and which would correspond to the Mixolydian with the same interval with which the fifteenth, or Hyperlydian, corresponds to the Lydian. Therefore, [-<352>-] it is much more probable that it was called thus instead by who added the eighth tone to the seven of Ptolemy and for that reason it occurs in that position, and that for this reason those who accepted the thirteen or fifteen tones used the name of Hyperprhigiand and Hypermixolydian interchangeably, which is the same, but in one case with the term used by Aristoxenus, and in the other with a term used by somebody else who wanted to establish eight Modes. As to calling two Modes Mixolydian, namely, the true one which is also called Hyperdorian because it is a fourth above the Dorian and the Hyperiastian, it is possible that Aristoxenus used to do this because they had possibly the same species, but I do not think this should be done, in order to avoid confusion and to avoid giving the Hyperiastian three names, while two are more than enough. However, do let us consider the origin and the basis of these terms. Why the tones were called by the Ancients in this way. It is certain, as Ptolemy and the other good writers mention, that in the most ancient times of Greece only three Tones were known and used, the Dorian, the Phrygian and the Lydian and that they lasted in this way for a few tens of years. In fact, one cannot say in truth that only two existed in the most ancient times, namely the Dorian and the Phrygian, as some state, as this is gathered from the ancient proverb which says ‘To move from the Dorian to the Phrygian’ which means ‘to move on to something very different’, not even because the Phrygian and Lydian were discovered and imported into Greece at very different times, because not much time intervened and the proverb is very ancient indeed. [-<353>-] For this reason one shall not find any credible author who states that the ancient used just two Tones. Therefore, if the Tones used by the Greeks in Heroic times were one of their own and two foreign ones, (I call them foreign because Phrygians and Lydians were not Greek populations but barbarian and of Asian origin, while ancient Greece was all contained within Europe. Not that they were savage, uncivilised and crude population in the same sense as the Schytians and the Cannibals, but barbarians in the way in which the Greeks called barbarians all of those who were of different descent except the Greek one, as the Romans called barbarian all the population which were not of Greek or Italian origin) those two nations had their own languages, customs, and attire, in the way that in antiquity each population had particular and general differences from the others. These differences were erased then for the most part because of the expansion of the populations and of the monarchies which absorbed entire populations and reduced them under a single rule of law, language and name, as it is happening little by little in the America, where, in the provinces which continue to be discovered, one notices enormous differences from one population to another one. However, the Phrygian and Lydian population are among the most ancient and noble in the world. It is considered certain that the latter one descends from that Lud and that the Phrygian must have descended from another one of the descendents of who lived at the same time as Lud, albeit he is not named in the Sacred Scripture. These populations occupied two of the largest, most fertile and temperate provinces of Asia minor, which used to be considered the most attractive part of the world. They were rich and very devoted to pleasures and to music in particular. The Phrigians flourished around the time of the [-<354>-] Trojan war – the Trojans were Phrygians – and the Lydians two centuries after them, before the rise of the Persian monarchy. It is true that the Phrygians were more bellicose and sanguinary, therefore they were devoted to the sacrifices in honour of Bacchus and found of wine, hence they could be compared to the Germans. On the contrary, the Lydian were more effeminate and were particularly fonf of exquisite food and large banquets, [they were more fond of eating than of drinking, hence tells the story of Candaules, king of the Lydians, who was so hungry one night that he devoured his wife. in marg.] as Athenaeus and other ancient writers report. Therefore, we could compare them to the English and to the French, although these two people are more bellicose and fond of war, as the Europeans are in comparison with Asian populations. Their singing was not at all demure, and it was apt more to dances and wedding feasts rather than to manly subjects and those connected with war, as it was the one of the Phrygians which had something of the lively and possessed. However, the Greeks, who, attracted by the abundance and the resources of the land began to land in Asia in great numbers and to build many towns and colonies to the point that in those later times Greek was spoken almost everywhere, although at the beginning they owned little more than the ports, as it happens today in some colonies of the Portuguese in some part of the South America, nevertheless they absorbed those manners and customs quickly. Moreover, one can say that it is true that they learned the basics of music, as the learned the basics of all the other sciences from the nations which they called Barbarians, such as the Jews, the Chaldeans, the Assyrians, the Phrygians and the Lydians, but they developed them and reduced them to perfection. This is what happened in the matter of the Modes because, although the Greeks took from the Phrygians and [-<355-] the Lydians their style of singing and imitated their own tone, they turned it into an art form assigning to each System and to every note of it its dispositions and characters, after they observed [after observing the intervals and Tone of the flute in marg.] with their perceptiveness in what consisted that style of singing which expressed a great variety of traditions and feelings. Hence they found that it consisted mainly in the variety of the intervals and in the varied sequence of large and small intervals which mingle in the melodies and are ordered step by step in the Systems. Hence they created those three principal styles of singing, namely, the Dorian, the Phrygiand and the Lydian. It is true, however, that Heraclides Ponticus, erudite music writer quoted by Athaenaeus in book , maintains that the three main modes had to be these three, the Dorian, the Iastian and the Aeolian, substituting the Phrygian with the Iastian and the Lydian with the Aeolian, saying that, since those nations were barbaric and foreign, it was not appropriate to derive from them the variety of the styles, while one ought to take them from the three general Greek nations and people, which are the Dorians the Ionians and the Aeolians. One can believe that the latter two differed between each other in a way which was somewhat similar to the way in which Phrygians and Lydians differed, with whom they must have had a lot in common because Aristoxenus (if indeed it was him) called the Iastian mode also Phrygian, but in a lower form, and the Aeolian also Lydian, but in a lower form. However, Heraclides’ opinion [-<356>-] had no following. On the contrary the three modes Dorian, Phrygian and Lydian were always considered as principal and as the basis of the others, either because of their antiquity and because their names had been accepted by everyone, or because that difference between the Ionic and Aeolian style and between these two and the Dorian derived from their familiarity and their interbreeding between the Ionian and Aeolian nation with the Lydian and the Phrygian. [nevertheless Polymnestus and Sacada, ancient musicians quoted by Plutarch, recognised only these three Tones, namely, Dorian, Phrygian and Lydian. in marg.] Therefore, it is worth knowing that those two nations did not fuse together when they moved across to Asia, but that each one kept itself by itself, the Aeolians on one side more towards the strait of the Hellespont and on the coast of Phrygia and Mysia, occupying also the island of Lesbos, while the Ionians were located more towards the south in the costal part of the Lydia and on the island of Scio. Although many colonies of Dorians moved south towards Rhodes as well, the way that not only the Spanish, but also the French and the English have occupied some small part of North America, nevertheless they are not talked about as far as music is concerned, perhaps because they kept themselves more intact and preserved, as it is known, their own more European traditions and customs. Although these three nations are Greek in an equal way, nevertheless they differ from each other in their traditions, language, laws and customs and such like more than the Castilian, Portuguese and Catalan, which correspond in many ways to those three Greek nations. Consequently, music, [-<357>-] which expresses their character and individual complexions was differed very much in the case of each of them. Therefore, the singing style of the Aeolians was bloated, haughty and deep in tone, as it suited that people which was more proud and courageous that shrewd, generous in spending and in hosting guests, breed horses and organise sumptuous dinners and participating in banquets and love-making, characteristics which, in my opinion, are more typical of the Lombards than of other people of Italy, and of the Portuguese in the Iberian peninsula. Moreover, it is noticeable that the Aeolian dialect with that termination (– aon) which belongs to the plural genitive is very similar to the Portuguese language. However, the Dorian nation had more severe and serious and patrician character instead, which are qualities that match the character of the Castilians, especially those who are older and live on the mountains. The character of the ancient Ionians which survived very much in the one of the Athenians, since the ones who moved to Asia became unnerved and dissolute within a short space of time, was to be contentious and stubborn, not keen on foreigners, in the way that the Genoese are and the Ligurians in our country, and the Catalans in Spain. Therefore their harmony was equally very plain and rather dry and harsh, although it showed something of the magnificent, hence it was accepted within the tragedy. The more modern Ionian style, on the contrary, was attractive, graceful, cheerful and dissolute, and for this reason apt to dances, banquets and to falling in love. This stile nowadays would match the character of the inhabitant of Valencia in Spain, who are very warm-hearted. These are the natural reasons of the special differences [-<358>-] of the modes. Now, since the Greeks imitated the Phrygians and the Lydians in their style of singing more than the other nations that shared a border with them, since they must have had types of singing too different and removed from their own, so that they could not find them attractive, nevertheless one has to believe that they shared with the Greeks many features of their music, as they did with their language, not in the sense that they made their words, which were very different, similar to the Greeks, but as to many combinations of letters and similarities of accentuation and terminations, and in partaking very much with that graceful and beautiful pronunciation of the Greeks and other common features of this kind that one can notice in the words of those languages that we have left in the works of Greek writers. On two sorts of special differences of the most ancient Modes. With the accurate reflection which we have provided fo the ancient Modes and on the basis of the writers who talk about it we have observed that they had two sorts of differences and properties, some of them essential and inseparable and others accidental and that could be separated. The first consist of two elements, the first one is the different tension of the voices towards the low and high register, while the second is the variety of species of fourth, fifth and octave which they used, as it was explained in part further on. I shall call the other differences accidental and separable because one can maintain the specific substance and nature of the modes without them, but not in the degree of perfection that was achieved when individuals of the same nation sang or played on instruments, or sang and played then at the same time, or when others played them who could imitate them perfectly. [-<359>-] These accidental differences can be reduced to three point: Firstly, to some differences which I find that they had in the particular forms of the three genera which we call species (however the word species is used in a different meaning than when one refers to the species of consonance) and which the ancient called colours [khroas], because I find that certain modes produced small intervals or Semitones more or less intense or major or minor, and proportionately in the others, or at least in the Chromatic, as I shall point out further on. The second accidental difference should have consisted in the different way to produce accenti, passaggi (which were used in ancient times as well, but perhaps were not as long as ours) and other special singing special effects, which I call condiments and are also called graces. We must not doubt that Dorian style had very different ones from the ones of the Phrygian and Lydian style et cetera, because the same occurs in the different styles of singing which are adopted nowadays in the main nations of Europe, which are more mixed among each other than those were and, consequently, must not have such stark differences in their singing styles. Nevertheless, we see that the French hold the voice in a way, the Spanish in another one and the Italians in another one still. Among the Italians the Sicilians use the voice in a very different manner, since they are for the most part of foreign origin. These condiments are of two sorts, because some can be noted with some particular sign (and they usually are marked in this way) because they consist either in the melos or in the Rhythm. These are the accenti, the passaggi, the French trills [-<360>-] et cetera. [These could be notated and distinguished in detail if we had a collection of the most common and natural airs which are sung not only in different parts of Italy and in Sicily, but in France, Spain and England, and if they were intabulated very accurately and purely as they are sung in these provinces by those who have no musical instruction but who make them special and interesting through their mere good talent. Certain very attractive Piedmontese airs would be of this kind, as well as some sung by the populations of the Cava near Salerno, which have a very unusual character. A musical scholar could also extract some principle from them so that they may be altered and applied according to their quality to the main ancient modes. For instance, the ones which are cheerful in character could be adapted to the Lydian, the grave ones to the Dorian, the sad ones to the Mixolydian and the lively ones to the Phrygian. One could start from the songs of those people that are more remote and that mingled the least with the others, such as the Irish, who are very devoted to music otherwise, use the bagpipes in their battles and have employed the harp for many centuries up to this day, which is also the emblem of the Reign. in marg.] Other ornaments, instead, consist in the way the voice is held and they could not be expressed very well with their own signs. These are the tremblements used very widely by the French and the manner of using passaggi, now more separate, articulated and majestic, now more legato and slippery, in drawing out the breath in one go or little by little, and other similar circumstances. However, the third property, which is possible to separate from the Modes, consists in the variety of Rhythms and different movements which are applied accidentally more to one mode than to another one, since the fast and furious movements were often used in the Phrygian. It is not as if they were always used in that mode as such, but they were used in it very frequently, although it was not applied always to lively and furious subjects. In fact, as Athenaeus says: I wanted to say this because nowadays many are confined that the variety of the ancient modes consists more in their Rhythm than in anything else, but they are very much mistaken, as we shall see further on. [-<361>-] On the inventors of the modes. The seven principal modes are the ones of which we know the name of the inventor, albeit with some discrepancy. They Hypophrygian is the one of which we do not know the name of the inventor. Therefore, we shall progress to tell in brief the names of each according to the reports of Plutarch, Athenaeus, Clement of Alexandria, Pliny the elder and Apuleius. Therefore, the Dorian, to start with, is the most noble and ancient and it is ascribed to Thamyris of Thrace [[as Plutarch, Clement of Alexandria, Pliny and others state]]. This confirms what I was saying, namely, that music itself, although cultivated and perfected by the Greeks, had its beginnings elsewhere, not to speak of Iubal who was the first musician in the world, as the Sacred Scripture attests. They say, about this Thamyris or Thamira, whom is called with various names, that he excelled above everyone else of his age for his singing ability and beautiful voice, and for this reason they invented the legend that he participated in a contest with the Muses. After him there came the Phrygian Harmony, which was discovered by Hyagnis, Marsyas’ father, who was Phrygian or by Marsyas himself, according to Pliny. Pliny ascribes the Lydian harmony to Amphion, son of Geon, or as some others say, of Mercury and Anthiope, but it attributed by Clement of Alexandria to Olympus of Mysia, a flute player. This information was taken from a work by Aristoxenus who, quoted by Plutarch, stats that Olympus played a lugubrious melody according to the Lydian fashion on the death of Python. However, Pindar, in his Paeans, quoted by Plutarch himself, reports that that Harmony was used for the first time at the wedding of Niobe. Others name Torebus or Atoremus, as one wants to say, as the author, among whom a Dionysius nicknamed Iambus by Plutarch, [[while Pollux ascribes it to a certain Anthippus]]. [-362-] Anyway, from what one can gather, it is clear that the melodies of Olympus and Marsyas, which lasted for many centuries, were in the Phrygian and Lydian modes, as Pollux and Plutarch report. The most ancient after these is the Mixolydian, which is the Myxolydian which is ascribed commonly to the poet Sappho who, as a woman, had a higher voice than the Lydian Tone which up to that time was used in funeral chants and, having little lack in her lover relationship, composed many tearful and graceful poems on her misfortunes and sang them in this particular harmony which she discovered, which was a semitone higher than the Lydian and was called Mixolydian, namely mixed with the Lydian, because it was nearer to it than to the other three. This is what Aristoxenus reported in his writing. However, in the anonymous History of Music it was said that it had been discovered by the flutist Pythoclides, while Lysis, quoted by Plutarch, reported in his writings that its author was Lamopocles of Athens, who also recounts on which occasion this happened, namely, that he observed that the one of the Disjunction was not where it was seen commonly, namely in the middle, as it occurs in the Dorian, but towards the higher register, hence he established its System and species, as it is, between the note Paramese [sqb] mi and the Hypate Hypaton [sqb]. I make two deductions from this; firstly, that he confirms very strongly the form which Ptolemy and the other Greeks ascribe to this Tone, namely that the Myxolydian Mode derives from the Dorian Diapason laid out through b flat, as he says, namely, with the conjunct Tetrachord, because it is really nothing else but the Dorian System through b flat transposed by a fourth. There is also the third, and from this description one can gather that Lampocles was not its first inventor, [-<363>-] but the person who described it and who produced its illustration. In this way, one can recognise that the apparent contradiction which appears to exist in the invention of the modes is not really there, because sometimes the invention of something is attributed to the first person who laid its foundations, some other time to who communicated it to the world and sometimes to the person who improved it and increase it. The invention of the Hypolydian mode, as Plutarch reports, is ascribed to Damon of Atherns, whom I consider to be the person who taught Socrates music. Others ascribe it to Polymnestus or Polymnastus, which is the same, according to Plutarch. However, the inventor of the Hypodorian mode was Philoxenus of Cythera, a famous Dythirambic poet and excellent musician who introduced several innovations into this profession. This mode was also called Locric or Locrian, because he must have been used a lot by the Locri, a Greek population of Dorian origin. [The Locrian harmony was the same as the Mixolydian as Zarlino writes in the Institutioni, Part 4, Chapter 3 in marg.] The same was confirmed by Pollux. It was very popular, as Athaenaus writes, at the time of Pindar and Simonides, but then fell out of use almost completely. The last one to have been adopted seems to have been the Hypophrygian, although it is not the last one in the sequence. One can gather this from a passage in Athaenaeus, where he illustrates that this mode began to be used again at that time on the basis of the witness account of some earlier author. Nevertheless, one can be confident that the last one was the Hypodorian because, as Aristide Quintilianus states, as well as Briennius after him, the Hypophrygian tone was called also [barys], which means low, because, before the invention of the Hypodorian, it was the lowest of them all. However, it is possible that the Hypodorian Harmony was invented before the Hypophrygian, although [-<364>-] not in its own Tone, which is a fourth under the Dorian, but in some other one, and perhaps in the Aeolian, which according to Heraclides was the same as the Hypodorian. However, this must be understood in relation to the species rather than to the tone, which, as we have seen, was between the Phrygian and the Lydian. In fact, if Lasus of Hermione, who wrote about music before any other, called the Aeolian Mode [Aiolida barubroton harmonian], namely, “the Aeolian lowest Harmony”, perhaps he refers to the Hypoaeolian, which is tone lower than the true Aeolian. However, Pratinas, in a certain poem of his, hints to the fact that the Aeolian mode was neither too high or too low: [Me syntono dioke met'aneimenon Iasti ousan alla tan mesan neon Arouran aiolize to mele], which means: “Do not follow the intense and high Lydian Nor the relaxed and too languid Ionian, but choosing your path in mid-air, sing in the Aeolian tone.” Therefore, we can say that Philoxenus was the first author or regulator of the Aeolian mode. As to the Aeolian, the matter is more obscure, except for the fact that Athaenaeus reports that Pythernus of Teus, an Ionian island, composed certain Ionian verses in the particular style of singing specific of that population, which was very close to his own tradition and was of admirable gracefulness. However, one must be aware that it is same to say Iastian Harmony or Mode as Ionian, although the first adjective is more used in the writings of good authors, because the word [iasti] is a Greek adverb that means simply [-<365>-] in the Ionian way, because [ias, iados] means the Ionian style, both in music as in other subjects, and the adjective Iastian derives from that adverb. I am very surprised that Glareano did not notice this. As to the fact that Athenaeus that the form of the word Hypodorian or Subdorius is similar to that one of the one of words such as subdulcis, subvoltus et cetera, and that it means a type of Harmony which has some features and partakes of the Dorian, but that it is nor truly Dorian, he cannot be justified in this except because he was not an expert in practical music, because that prefix [hypo] in that place means that it lays in the lower register below the Dorian. This is so clear that it requires no further proof. I wanted to make this clear because it appears that our Mei was prompted by Athenaeus’ authority to believe that where Aristotle in the musical problems mentions the Hyperphrygian and Hypodorian modes (where he says that they were adopted in the tragedy by the main actors, while the Mixolydian was used in the Choruses of the same tragedies) one should correct the text to read Phrigian instead of Hyperphrygian and Dorian instead if Hypodorian, because Aristotle called them in that way in the Politics, or that we should consider as Hypodorian and Hypophrygian the Modes that have something of the Dorian and of the Phrygian, according to Athaenaeus’ interpretation. Let me say this without rebuking Mei: the matter does not lay in these terms, as I shall explain elsewhere the reason why tragic actors used the Hypodorian and Hypophrygian rather than Dorian and Phrygian. In fact, if Aristotle named those in the Politics and these in the Problems, this does not cause any contradiction because the principal modes (as Dorian and Phrygian are) as they are the source and the origin of their subordinates, they contain them in a certain way, as the genus contains the species. Hence, in the Politics, as [-<366>-] a philosopher he makes a general statement, while in the Problems, as a musician, he deals with specific features. Moreover, in the Politics he talks about the modes which were used in the common melodies, and these are the Dorian and the Phrygian, while in the Problems he talks about the melodies which were used specifically in the tragic Monodies. Moreover, the fact that he ascribes the same properties to those as to these does not make any difference, because just as the Hypodorian and the Dorian and the Hypophrygian and the Phrygian have similar names, thus they are also similar in their nature, and if there is some difficulty, it merely a quantitative difference. Also, if the Hypodorian did not partake of the nature of the Dorian, that name would not suit it, and equally in the case of the Hypoprhygian and of the Phrygian. It seems to me that this is so certain that to doubt it is naivety, in my opinion. Therefore, we can believe with certainty that the three principal Modes were created by nature than by man and that those who are named as their inventors simply ordered them and reduced them to a form that could be used in art, as Thamyris must have done with the Dorian, and imported them into Greece, as did, who imported the Phrygian, and , who imported the Lydian. As to the others, it seems to me that they were added in this way, namely by adding a tone underneath each one of them and progressing through the Conjunction rather than through the Disjunction, since it is possible to see that if one adds ad Tone under the Dorian and changes the [sqb] mi to b fa, and does the same in the others, these tones are transformed into their corresponding plagal. [-<367>-] On certain other Modes mentioned by the ancients, Chapter Apart from the aforesaid Modes, one finds that others are mentioned, which, because they might produce confusion and make one believe, as it happened to many, that this subject of the modes is very confused, full of contradictions, and that everybody adjusted them according to their whim, as Glareano says, it will be good that we proceed reporting and examining diligently the passages of the authors who mention them. Once one is aware of this, one shall see manifestly that, if there is come contradiction, this occurs only in appearance rather than in substance, and that there is no doubt that this contradiction can be resolved for the best. Therefore, Plato in the , where he examines what sorts of music hast to be accepted and what types must be rejected as useless to the Republic, mentions only these six: Dorian, Phrygian, Iastian, relaxed Lydian, Syntonic Lydian or intense and the Mixolydian. Finally, he concludes that those that have too tearful and sad character, such as the Sintonic Lydian or Mixolydian or the ones that are too relaxed or languid, such as the simple Lydian or the relaxed Lydian [aneimene], which are more suited to banquets and celebrations must not be accepted. On the contrary, the Dorian must be retained because it has a honest, modest and serious character, and it is apt to preserve good and laudable habits in the young. Also, the Phrygian must be preserved because it has a masculine, inspiring and war-like character, and, [-<368>-] because it is suited as Proclus says in his Commentary on Plato’s Republic to sacrifices and enthusiasm, namely to fire up the mind with divine fury. What shall we say about those two species of Lydian which he mentions, namely the Relaxed and Intense or Syntonic, which is also called Syntonolydian and [syntonolydisti] with a single word, which was not understood by the translator of Pollux? Here Aristides Quintilianus dispels any doubt teaching us also with which intervals these Harmonies were composed, because [to men oun lydion diastema synetithesan ek dieseos kai tonou kai tonou kai dieseos kai dieseos kai tonou kai dieseos; kai touto men oun teleion systema; to de dorion ek tonou kai dieseos kai dieseos kai [[tonou]] [tonou kai add. supra lin.] ditonou kai dieseos kai dieseos kai ditonou. Oun de touto tono tod diapason hyperekhon; to de phrygion ek tonou kai dieseos kai dieseos kai ditonou kai tonou kai dieseos kai tonou. oun de kai touto teleion diapason. to de Iastion synetithezan ek dieseos kai dieseos kai ditonou kai triemitoniou kai tonou. oun de touto tou diapason elleipon tono; to de mixolydion ek duo [-<369>-] dieseon kata to exes keimenon kai tonou kai tonou kai dieseos kai trion tonon. oun de kai touto teleion systema; to de legomenon syntononlydion oun dieseos kai dieseos kai ditonou kai triemitoniou diesin de noun eti panton akousteon ten enarmonion], which means: “Therefore, they composed the Lydian Interval (namely, the harmony) of a diesis, another diesis, a tone and another diesis, and this was (its) perfect system. They created the Dorian with a tone, a diesis, another Diesis, a ditone and another tone, of a diesis, another diesis and a Ditone, and it exceeded the Diapason by a tone. They created the Phrygian with a tone, a diesis, another diesis, a ditone, a tone, a diesis and a tone, and it corresponded to an entire diapason. They contituted the Iastian with a diesis, another diesis, a Ditone, a Trihemitone and a tone, and this was a tone short of a full Diapason. The Mixolydian was formed of two dieses one after the other, a tone, a tone, a diesis and three consecutive tones, and this was the perfect system. However, the one called Syntonolydian was composed of a diesis, another diesis, a Ditone and a Trihemitone. Diesis must be always understood here as the Enharmonic one.” I wanted to quote this passage in its entirety as it is because [- <370>-] it is worth a treasure, and I can derive a lot of important information from it. The reader must be aware that there is a mistake in Zarlino’s text [Institutioni part 4, chapter 6 in marg.], because the fourth interval of the Dorian must be a Ditone, as it is in the manuscript copies, and not a tone. This is also proven from the fact that Aristides says that this mode exceeded the Diapason by a tone, which otherwise would not turn out to be true. Let us place here the table of all of them: [Doni, Treatise on the Genera and the Modes, second book, 370; text: Lidio. Dorio. Frigio. Iastio. Missolidio. Sintonolidio. Tuono Ditono. Diesi. Trihemituono]. Thus the Lydian was sung only through a minor sixth or Diatessaron and trihemitone, the Dorian though the span of an octave and a tone, the Phrygian through an octave exactly, according to what Aristides says, although the description of the intervals is short of a diesis, which, I believe, was lost because of the copyists, as it is not plausible, moreover, that a diesis may stand alone, except at the extremities of a mode, otherwise it would cause everything to be in disarray and very few consonances would be found even across an entire octave. Therefore, it is certain that after the sixth interval of a Diesis there should be another one. Equally, in the Mixolydian that Diesis in the middle cannot stand alone, but must be accompanied by another one which completes the octave. The Iastian, instead, was sung across the span of a minor seventh, namely a fifth and a minor third, while the Sintonolydian, as the Lydian [-<371>-] across a minor sixth. Aside from the above mentioned elements Alexander mentions the Mixophrygian attributing its invention, as well as of the Mixolydian and of the Phrygian to Marsyas. However, I do not find it mentioned in any other author, so I do not know what to believe, unless we want to say that the Myxophrygian has to be understood as the one that Aristoxenus called the lower Hyperphrygian, namely the Hyperiastian, and that it was called thus because it was close and almost mixed with the Hyperphrygian, as the Mixolydian is with the Lydian. Athenaeus also mentioned the music of Caria ascribing to it [mele kateagota] and [rhythmos goerous], namely, dissolute melodies and airs and querulous movements, hence perhaps it had a particular sort of harmony suitable mostly for funereal and erotic subject, with frequent and interrupted intervals, as I interpret that [mele kateagota]. The Carians were the population in that corner of Asia which is contained between Lydia and Lycia towards Rhodes, part of whose territory was occupied by the Dorians mentioned above, especially the peninsula called Doris. The main city of this population was Halicarnassus, which was famous for Mausolus’ tomb. These people were also more different from the Greeks than the Lydian were and spoke a stranger language, hence Solo calls them [barbarophonous] or speaking the language of a barbarian population. One can believe that the Carians, the Mysians and similar Asiatic populations of those surroundings had particular styles of singing, which have not been regulated under specific Harmonies, hence one cannot discuss them on the basis of solid evidence. However, since we use [-<372>-] this term Harmony almost indifferently to mean tone or mode, one must be aware that we do it following the example of all the best ancient authors like Plato, Aristotle, Aristoxenus, Ptolemy and others of this kind, who use this term as well as the others indifferently, and even more frequently. However, one must be aware that it indicates not only the sequence of the notes and intervals produced with musical reason in general, but the foundation and the matter which creates the Melos will be, more particularly, a specific species of notes and interval ordered to produce the melody according to a particular tone appropriately selected and according to this type of melody which as used in the Melopoeia, and in this meaning it is the same as Tone or Mode. However, if one wants to keep to the appropriate use of the words, the term Harmony shall have even a more particular meaning and it shall indicate a particular group of notes or intervals occurring in this or that tone with the obligation to sing no more and no less than the number indicated, as in the example of the Syntonolydian where one places two dieses, then an uncompounded ditone and an uncompounded Trihemitone. This strict rule not to divide the ditone or the semiditone and not to exceed this interval must be called Harmony rather than Tone or Trope. Thus, we can say in general that any specific disposition of notes will not reach the Diapason or, if it does complete the octave, it will have more than eight and less than nine and it will have to be called Harmony rather than mode, although it follows one of the seven species and that it has its specifically regulated instrument sounding and built like a flute, in order to play on it and [-<373>-] sing certain notes rather than others. Therefore, harmony will be a specific from of Mode. From this we can derive the corollary that, if we place all the Diatonic, chromatic and Enharmonic notes in one of the tones, for istance in the Dorian from E to e in this way: [Doni, Treatise on the Genera and the Modes, second book, 373, 1; text E, F, G, A, [sqb], c , D, Tuono, diesis, diesi, Semituono], which are twelve notes, not counting the conjunct tetrachord so that they may be played all at will a genus after the other or mixed together, it will be possible to called it tone, mode and Dorian Harmony according to the three genera. However, the lower of the two tetrachords is laid out only Diatonically and the one above Chromatically or Enharmonically, thus: [Doni, Treatise on the Genera and the Modes, second book, 373, 2; text: Semituono, tuono, Semiditono, E, F, G, A, [sqb], C e], the name of Harmony will suit it better, because it implies the restriction to play only these or those notes specifically rather than all the ones of the Mode, in such a way that the meaning of Harmony in some sense is wider and in some other sense it is more restricted. Therefore, if one lays out only the Chromatic notes, thus: [Doni, Treatise on the Genera and the Modes, second book, 373, 3; text: E, F, A, [sqb], c, c, e, [signum]] one can call it Dorian Chromatic Harmony or according to the chromatic genus or Chromatic Harmony of the Dorian tone, or on the Dorian tone or mode, rather than Chromatic Dorian Mode or Tone. Similarly, should I force a composer to write some melodies in the Dorian tone without exceeding this major sixth E, F, G, A, [sqb] c, this will be the same as ascribing to it [-<374>-] a particular Harmony or Harmonic species, however we want to call it, just as if who assigned a Melos, with or without words of so many bars (it will not make any difference how many you will choose) but with this restriction that after two of binary or dactylic measure, there should follow one of ternary or iambic measure and thus he should proceed always with two bars, two binary and one ternary, this would amount not only to prescribing him what type of Rhythm he will have to use, but also which aggregation of Rhythms in particular, which are Rhythms composed of a larger number and almost incomprehensible in comparison with the simple ones. Thus, the Harmonies in this sense can be rendered very varied and almost without rhythm, but the modes can only be seven and the Tones equally seven, as to the principal ones, although the ancients employed thirteen, or even fifteen of them. There is also this other difference, namely, that the mode appears to be more properly exactly of the size of a Diapason without any relation to the others, while the use of the word tone implies always a relation to the others. Also, Harmony indicates mainly some variety of intervals, as one shall see more clearly further on. [-<375>-] On the number of the Tones I will prove that this is true not only on the basis of the authority of some ancient writers and of Alypius’ notes. It is clear that one can one can built instruments, flutes for instance, divided not only according to Ptolemy’s seven tones, but according to Aristoxenus’ thirteen and even according to the fifteen of his followers and more, if one wants, because we could separate them one from the other not only according to tones and semitones, but also according to quartertones. Thus, although they shall always be one of the seven modes, taken according to the species of the octave, nevertheless they will always be different tones and they shall also have different harmonies as we vary the distances of the holes and their size according to the three genera and also according to the colours of each one. This shall be clearer when we see that the tones were placed not always with the same intervals one from the other and with the same order, as Aristoxenus illustrates in the secondo book, where he talks about the Tones nor on purpose but in passing, saying these words: [Pempton d'esti ton meron to peri tous tonous eph'hon tithemena ta systemata melodeitai; peri hon oudeis ouden eireken; oute tina tropon lepteon, oute pros ti blepontas t'arithmon auton apodoteon estin. Alla pantelos eoike te ton hemeron agoge ton harmonicon he peri ton tonon apodosis; hoion hotan [-<376>-] Korintihioi men dekaten agosin, Athenaioi de pempten, heteroi de tines ogdoen; houto gar hoi men ton harmonikon legousi barytaton men ton Hypodorion ton tonon hemitonio de oxyteron touton to Mixolydion. Toutou de hemitonio ton Dorion; tou de doriou tono ton Phrygion; hosautos de kai tou Phrygiou ton Lydion hetero tono; Heteroi de pros tois eiremenois ton Hypophrygion aulon prostitheasin eti to bary. Hoi d'au pros ten ton aulon trypesin blepontes treis men tous barytatous trisi diesesin apallelon horizousi ton te Hypophrygion kai ton Hypodorion kai [[tes]] ton Dorio; ton de Phrygion apo tou Diou tono; ton de Lydion apo tou Phrygiou palin treis dieseis aphistasin; hosautos de kai ton Mixolydion tou Lydiou. Ti d'esti pros ho blepontes outo poieistai ten diastasin ton tonon protethymentai oude'eirekasin; hoti d'estin he katapyknosis ekmeles kai panta tropon akhrestos phaneroi ep'ahtous estai tes pragmateias], which mean: “The fifth part (of Harmonics) deals with Tones in which the Systems are laid out and sung. Nobody has written anything about them, on how they are taken and on what basis their number is established. On the contrary, it appears that the tradition of the Harmonics in relation to the Tones corresponds precisely to the succession of the days, as a day which is counted as the tenth by the Corinthians is the fifth according to the Athenians [-<377>-] and the eighth according to others. Similarly, some theorists say that the lowest of all the Tones is the Hypodorian, that the Mixolydian is higher than the Hypodorian by a semitone, that the Dorian is also higher than the Mixolydian by a semitone, while the Phrygian is higher than the Dorian by a tone, and similarly the Lydian is higher than the Phrygian another tone. Moreover, others added the Hypophrygian flute in the lower register. Others, however, considering the holes of the flutes separate the three lowest Tones, namely the Hypodorian, the Hypophrygian and the Dorian one from the other with three dieses, but they separated the Phrygian from the Dorian with a tone and the Lydian from the Phrygian, as well as the Mixolydian from the Lydian, with the other three Dieses. Nevertheless they say nothing about what they considered when they established those distances between the Tones. However, we shall make clear that the thickening ([katapyknosis]) is impossible to sing and totally fruitless when we reach this topic.” It will be appropriate that we examine this passage in sections because it enlightens us about many notable details of the Music of the ancients, after we have provided the illustration of the Tones according to Aristoxenus’ description: [-<378>-] [Doni, Treatise on the Genera and on the Modes, second book, 378, 1; text: Ordine de suoni secondo alcuni musici auanti Aristosseno, Lidio, Frigio, Dorio, Missolidio, Ipodorio, C, c, D, d, E, e, [sqb], A, a], which can be illustrated also in this way: [Doni, Treatise on the Genera and on the Modes, second book, 378, 2; text: D, #, C, c, b, [sqb], G, F, E, D, C, A, g Hypophrygio agigunto da altri]. [-<379>-] Distribution of the tones according to other authors [Doni, Treatise on the genera and on the Modes, second book, 379; text: Missolydio, Lydio, Phrygio, Dorio, Hypophrygio, Hypodorio, 3, diesi, Tono] From this we gather many conclusions, firstly, that there was never any variation within the three principal tones, whether with regard to the sequence of one with the other one, or because one of them was left aside, nor as to their distances because those six dieses which are placed between the Phrygian and the Lydian can be considered a whole tone. However, the same has not happened in the case of the others which have been laid out in different ways, as they are less principal. Secondly, I notice from the first order that they placed those three (Dorian, Myxolydian and Hypodorian) next to each other because of the resemblance that they have in their species and, consequently, in their nature, and that the Myxolydian under the Dorian has the same position as the Hypolydian, to which is very similar, since it is nothing but an inverted Hypolydian. Thirdly, I observe that not all theorists held necessary that the tones with the prefix Hypo- corresponded to their principals being placed at the interval of a fourth lower, and that, equally, not all of them, as one can see, separated the Hypodorian and the Dorian and the Hypophrygian and the Phrygian at the distance of a tone. Nor all of them had to be at the distance of a Diatessaron in the same way, as one can see that they placed the Hypodorian at the distance of a tone from the Dorian, although [-<380>-] Aristoxenus does not say so. I notice also that the practical musicians of that time and the builders of instruments, such as those who made flutes and recorders (of which there was a great number at the time, and they were built exquisitely) used normally the measurement of a Diesis or quartertone to divide the intervals, just as nowadays we are used to garnish a note more or less, but much more imperfectly and without even distinguishing the tones from the semitones. Moreover we gather that each tone had its particular flute, as I always believed and as I shall illustrate further on. Also, we learn that the Hypolydian Mode must have been less highly regarded than the others because it does not appear among the others in any of these two distributions. I observe also that to locate the Hypodorian above and below the Dorian by the distance that we can see, namely, a semitone, is not otherwise uncomfortable. On the contrary, it facilitates very much the mutations from a tone to the other, since the note b flat in the Hypodorian is the first natural note of the Myxolydian, which is, however, very different from that one, as the notes written according to the modern system show, since they are almost all altered with the sign #. Hence, I presume that that position of the Mixolydian was mostly practised in tragedy because, if the Hypodorian and the Hypophrygian we swapped by Tragic actors, who chose a low and low voice to represent the Heroes and changed when they wanted to move on to lamentations and tears, to which the Mixolydian is most suited, as Aristotle teaches us in the Problems, they could do this more easily as it was closer to their own, [-<381>-] had they had to do it a sixth or a seventh higher. In this Distribution one moves with great difficulty from the Hypodorian to the Dorian, because, as one can see from the note, only the fourth interval is altered, which turns from a semitone into a tone with the addition of the # to the F. From Aristoxenus’ words where he states that the thickening ([katapyknosis]) is impossible to sing and useless, I also gather that they believed that the System had to be divided into a large number of small particles, as modern theorists do, for instance, Zarlino and Salinas from a theoretical standpoint, and Don Nicola from a practical one. However, they do this because they do not have knowledge of the true Tones which renders that thickening useless rather than for any other reason. Therefore, it is criticised by Aristoxenus with good reason. [-<382>-] On the musical notes of the ancients, chapter Although I had decided not to discuss the notes of the ancients to avoid being too longwinded, nevertheless, since from the complete Diagram of the conversion of the Modes one can derive very important information to understand them, and because it would be redundant to present them without knowing the notes that compose them, hence I considered it necessary to explain them before I move any further. Therefore, it has to be known that the ancient Greeks did not use the lines and the spaces that we use, but placed their musical notes above the syllables and the words themselves of the verses with great ease, because, where it was needed for a syllable to be lengthened by several subdivisions of the note, as one does in the accenti and passaggi, as they call them, they separated it from the other syllables of words with a space sufficient to contain all the notes and sounds that they wanted to be sung under one and the same vowel. This is what Boethius means when he says: They had to sorts of these notes [[(against the opinion of modern theorist who make no mention at all of these)]], namely, some which were used for the sung melody and indicated the intervals and the notes to be sung or the steps of the System, whether Diatonic, Chromatic and so on, and others that were used to represent the Rhythm or the timing within which each note [-<383>-] had to be uttered. Although modern theorist write and think commonly that the ancients had no other ways to indicate timing than the metric quantity, nevertheless I, who never considered the ancient as so unsophisticated and simple, could not convince myself of this. Therefore, after long research, I found them in an anonymous ancient text belonging to the Vatican Library. However, since they are not of interest for our current purpose, I leave them out for now, planning to publish them within the treatise that I am writing at the moment on the Rhythm and Rhythmopoeia. I have learned from the same author that they had a specific sign to divide the bars, which is something very useful indeed and of great help to those who sing or keep time because they did not place any sign on the downbeat, or thesis, but they added a dot to the note which happened on the rising of the hand or of the foot, which was called arsis. However, they had two sets of notes to indicate the sound, as Aristides Quintilianus and Gaudentius report, because the ones that were used to the sound of the instruments, which we would call basso continuo, were different from the ones used for the singing of the voice, which is what Boethius means when he says: I remain surprised that Zarlino did not understand this matter, since he believed, as he states, that the first indicated the Notes and the other ones their length, long or short, although they could gather their duration, whether long or short, from the syllable placed in the verse, which was long or short. Zarlino, however, must not have remembered that [-<384>-] [krousis] in Greek means the sound or the voice of an instrument, whichever it may be, so that it has the same meaning as percussio in Latin, which is how Boethius translates it. Therefore, the notes to be sung by the human voice were places above the verse, while the ones that were played by the instruments were placed underneath, as the same writers state. Moreover, if someone is surprised by the fact that they did not use the same notes for the voice and for the sound of the instruments, one must know that they did so because it would have produced confusion in certain situation. It has to be known also that they used to build a table or Diagram containing all of the eighteen Tones, dividing them into as many columns as they are and at the distance of a semitone one from the other. All this span was divided into seventy-seven equally distant lines containing seventy-six intervals or Enharmonic Dieses. In fact, since the distance between the lowest note of the Hypodorian, the lowest tone of all, to the highest of the Hyperlydian, the highest tone, covers three octave, and they assigned to each diapente twenty-four dieses, twenty-four dieses with added with the four of the tone reach that number. The tones were laid out in such way so that [-<385>-] the musician may detect the distance from a tone to the other and of each note of one to each note of the other at a glance as well as understanding which notes and sounds are the same in two or more. In short, this table allowed the musician to have in front of his eyes the entire complex of almost all the notes which can be produced humanly. Some of them used the letters of their alphabet to mark them, and, since twenty-four were not enough, apart from the letter themselves as they were, they wrote many altered in a way or another, either back to front, or upside-down or distinguished with some line and similar devices, while they tried to keep their number as small as possible. Therefore, they used the same in the Diatonic and in the Chromatic except for the addition of one or two lines. This had a very positive result, because a note that was Chromatic in a mode was Diatonic in another one. These characters are described in brief by Alypius, an ancient musician, in a brief Introduction of his, in which he names them chapter by chapter according to the three genera and fifteen modes, arriving to the number of forty-five chapters, although he last ones of the Enharmonic genus are missing, both in the manuscripts that I have see as in the one published by Meursio in Holland, although he did not publish the characters of the notes, as he recognised them to be very incorrect. However, having worked on them for a while and having compared them to other Greek writers, and in particular with a very ancient anonymous text contained in the Vatican Library, which deals with the thickening of the notes [peri tes katapyknoseos] [-<386>-], and particularly, by examining side by side the ones of one mode with the ones of another one, I corrected them to such an extent that nowadays one would be able to decipher any ancient melody not only in the Diatonic, but also in the Chromatic, although they are more incorrect than the Diatonic ones in Alypius’ text. However, I have not been able up to now to correct the Enharmonic ones, because Alypius is completely useless in this matter, because I have seen that the manuscripts do not correspond to the printed version entirely in the modes that have come down to us, and that, equally, the same notes are that are placed in the Diatonic and Chromatic are repeated in all of them without adding lines or other circumstantial signs. This is due only to the negligence of the copyists and because it is very easy to make mistake in such precise detail and when there are some repetitions. For this reason the notes appear to be incorrect also in Aristides’ text, although he does not display them separately tone by tone. I shall order them here as I ordered them in the two genera with this addition of a line under the specific Chromatic notes, as the ancients used. However, it would be better to distinguish them with a red colour, as I did in my original table and as some believe that it was the case in antiquity, and this would be the reason why this genus was called Chromatic. Nevertheless, they are really mistaken in this. Aristides himself sates that the Diagram of the Tones was similar to and A, which is exactly how I laid it out, hence we can be sure that this was how the ancient distribution appeared. Moreover, Gaudentius teaches us that the ancient disposed these notes starting from the lowest to the highest without distinction of modes in three general sequences, one by tones, another one by semitones and a third one by dieses, and after the they started again adding only the sign of the acute accent, [- <387>-] which indicated that a particular note belonged to the part above and was higher than the one below which did not have said sign. Aristides himself placed these series in his book as well, but they are all full of mistakes in both the characters and their disposition in the texts which we have seen, which are all modern in writing and were copied from a single original archetype, as far as one can tell, hence they are of little use. [[May the courteous reader enjoy the illustration which I share with him, which is laid out as best as I could, and in which, as in a compendium, one sees the content of the music of the ancients. Diagram and connection of the fifteen Tones according to the two genera Chromatic and Diatonic.]] However, the Gaudentius’ words which I mentioned above are these and they follow the small passage referred to above: [Oukh'enos dei oun semein kath hekaston ton phthongon hekastos dynatai; to men oun hstis parauxanesthai dynatai ton phtongon hekastos hemitoniois ou radion aphorisai; pros gar tas kataskeuas ton organon kai ten dynamin tes anthropeias phones ta toiauta orizetai; to de hopos parauxanomenon en diaphorois semeiois aposemainetai [-<388>-] ek ton diagrammaton en tais mousikais radios an tis katamathoi; theoreteon de ], [-<390>-] which means: “A single sign is not enough for each note or sound, but it is not easy to determine by how many semitones each one can be increased (or raised) because this depends on the (different) way in which instruments are built and on the power (namely, the tension of the human voices). However, how each one is increased (or raised) with different signs, this can be gathered easily from the musical illustrations and Diagrams. However, for now do let us consider only how the series of the notes laid out by semitones. Therefore, let us place a note which is, by its nature, the lowest of all and the first one that can be sung and be distinguished by the ear. The ancient notated it with half a [phi] written sideways [signum]. It is clear that this sound cannot occur on another note than the Proslambanomenos, because, should we place it elsewhere, where shall place the proslambanomeons, which is the lower by its nature that the sound of this halved [phi]? Then, place a note a semitone higher than this one. The ancients marked it with the letter tau [Tau], and it is certain that the tension or sound of it can correspond only to a proslambanomenos, because, if it is associated with the Hypate hypaton, where shall the Proslambanomenon be placed, which must be a tone lower than the Hypate, but here there is only the distance of a semitone. Now, place another note [-<391>-] in the same way, so that it is a semitone higher than the [Tau], which the ancients marked with a double sign [epsilon]. This one can be the Proslambanomenos and the Hypate Hypaton of some System because it is at the distance of a tone from the lowest voice. Thus, raising the following note always a semitone more than the previous one they arrived to the thirtieth box of the semitones, and above these thye marked the other notes raised by a semitone with the same signs used starting from the beginning adding only the mark of the acute accent, starting from the nineteenth box which has the note indicated by the [omikron] and cappa [omikron. Kappa]. They placed two notes in each place, since the ones above indicated the melody of the voice and the ones underneath the sound. Then, they disposed the ones that are called Unisons, of which we can use one or the other without difference, because it will make no difference to use more notes in unison with this or that one. These unisons have also another use, because the Dieses in the Enharmonic and Chromatic genus are expressed with these placed in succession, as we have explained in our introduction. Therefore, we shall place in a small table the notes of the semitones with their sounds in unison, which are placed in the same boxes, as well as the notes one a semitone distant from the other in consecutive succession. The first box, which is assigned to the lowest note of all has the half oblique phi and the half phi upside down [signum] The second box, which is at the distance of a semitone from the one of the first note, contains this sign, namely the turned gamma and the straight one [signum]. The hooks on these, [-<392>-] which indicate the same power [dynamin] and tension, are the turned tau and the straight [Tau] [sign]. Similarly, the third box belongs to the third note, in the same way, namely, it contains a note which is a semitone higher than the previous one, and it contains a double turned sigma and a straight sigma [signum] The fourth box contains the Rho turned upside down and the double Sigma turned upside down [signum]. Its unisones are the pi upside down and the double Sigma turned. Equally, the fifth is a semitone higher than the fourth and contains these notes, namely, the [omikron] with a line beneath it and the [eta] [signum]. The sixth one has the double csi turned upside down [signum] [signum] and has the turned hy and the double p as its unison Proslambanomenos, [Omikron] [Kappa] with a line beneath them and the eta [signum] [Eta], et cetera.” He continues to describe the notes of the Hypolydian and Lydian in this way (which was used mostly by the ancients to provide their examples, as one can see from Boethius) without any other notable observation, but with many errors caused by the copyists. Therefore, this shall suffice. So, although one can see only the beginning of one of the three general series and the particular notes of each tone in the copies of Gaudentius’ text that can be found nowadays, they are even more lacking than the one of Alypius. Nevertheless, we could withstand this loss had Aristides’ text been better preserved in this section, but, because of a fateful accident, this text is more deficient in that part than in the rest. Therefore, it will be always impossible to extract much useful information, unless another very ancient text were to be discovered. I want to highlight also what he says about the diesis, namely that they only had twenty-four, which means that twenty-four were needed for a whole Diapason, hence they were placed in sequence in the first twenty-four spaces of the lowest system, which was the Hypodorian, and then they repeated them in the higher registers. [-<393>-] Observations on the same Diagram First one must note that the ancients ordered these letters in alphabetical order to maintain a good sequence and to aid the memory, but they started from the high register downwards, according to the distance of the semitones, so that, in a System, two notes next to each other and at a distance not wider than a semitone are notated with two letters of the alphabet that are next to each other, while the notes that are at a distance of a tone are not marked with successive letters, but, if one is notated with the first letter, the other one will have the third one. One must note also that they applied the full and straight letters judiciously to the notes in the middle between the high and low register, as it was appropriate, because they were more used [Hence one can see that in the lower modes the letters from the Mese upwards are intact, and conversely in the upper ones in marg.] and that the same letter fashioned in the same way is used sometimes for the notes of the voice and of the instrument, but not it does not indicate the same sound. The notes that are to the right in each column are the notes of the Conjunct Tetrachord, of which the first one (Trite) is b fa, as we said already, which corresponds to the space contained between the mese (a la mi re) and Paramese. The others follow on in corresponding fashion. One must note principally that the notes that have the sign in the same box are really in unison, while the ones that do not have the same sign are not really [-<394>-] in unison, if not when these intervals of Tones, Semitones and dieses are placed equally divided, and, in short, equal both in Theory and in practice. That this occurred only in Theory, as I said above, and these very notes demonstrate it to us because the ancients, who where so diligent and precise in everything and did not add anything that was redundant, would only have placed in a box a type of notes, if they used to sing and play in practice equal intervals, as Aristoxenus describes them and the others, as it is believed commonly nowadays, because it would mean adding a difficulty and signs without meaning. Nor the fact that the signs that are placed in the same box and are called unisons [homotona], as Gaudentius says, for this reason must be considered only in Theory, in which we imagine that all this content of notes and interval is divided into equal parts. To prove that this is true, note that the nete Diezeugmenon and the paranete synemmenon, which we call with the same name of d la sol re, is represented with the same notes throughout, as indeed they are in unison, since there is the same distance from a la mi re [[(mese)]] to d la sol re both through [sqb] square as through b flat, which in the perfect temperament would be a fourth with a comma added, or two larger Tones and a larger tone, except for the fact that one can see openly that the ancient placed two d separated by a comma at least in [-<395>-] practice, as finally modern theorists have realised that it should be done by acquiring that fourth, although Zarlino and Salinas mark it in their demonstrations. Now, on this basis, the same interval of a perfect fourth occurs between a and d through [sqb] square and through b flat, with this difference, that, through [sqb] square the semitone falls in the first place, and through [sqb] flat in the second one. Then, taking the example from the Dorian through [sqb] square o in the disjunct tetrachord, the Mese marked in this way [signum] [signum] is removed from the paramese [My] [Pi] by the distance of a larger Tone (let us remember that this tone is always immutable and sesquioctave) the Paramese from the Trite Dizeugmenon [Lambda] [signum] a larger semitone 16/15. Therefore, consequently, the difference from that one to the Nete Diezeugmenon [Eta] [signum] is only a smaller tone 10/9. Conversely, in the case of the conjunction, or b flat, it is certain that the distance between the Mese and the Trite Synemmenon has to be the same as from the Paramese to the Trite Diezeugmenon, namely, from [sqb] mi to sol fa and the same from b fa to [sqb] mi, which is a larger semtione. Therefore, if there is the same distance from the Trite Synemmenon b fa to the Paranete synemmenon c sol fa ut as from the mese a la mi re to the Paramese [sqb] mi, the Trite Diezeugmenon and the paranete synemmenon, namely, the c sol fa ut through [sqb] and b flat, should be in unison and at the same distance of a minor third from the Mese a la mi re, according to that rule of equivalence (aequalibj aequalem) et cetera. However, the fact that these two notes Trite Diezeugmenon and Paranete Synemmenon do not appear to be marked with the same note as the Paranete Diezeugmenon and the Nete Synemmenon points argues in favour of the fact that they are not in unison. This is true, because the fact that one can see [-<396>-] that the paranete Synemmenon is marked with the [Kappa], which is a higher note and nearer to the [Eta] than the lower and further removed[Lambda] with which the Trite Diezeugmenon is marked demonstrates that the Paranete Synemmeon, which is the c of Synemmenon, is more removed from the Trite b fa than the Paranete Diezeugmenon d la sol re is removed from the Trite Diezeugmenon c sol fa ut through [sqb] square. Hence, one sees that there is a smaller tone from b fa to c sol fa ut through b flat (I use Didymus’ division because this diagram itself shows that it was more popular than Ptolemy’s one) and also from the same c sol fa ut to d la sol re through b flat. However, through [sqb] the larger Tone is placed between a la mi re and [sqb] mi and the smaller one from c sol fa ut to d la sol re, and this is why because the Trite Diezeugmenon and the Paranete Synemmenon do not have the same signs and are not in unisone. This indicates also that Didymus’ division proves more comfortable when one moves from the Disjunction ot the conjunction and that it ensures that the paranete diezeugmenon and the nete synemmenon are in unison, while the trite diezeugmenon and the paranete synemmenon are not in unison, as they are here without producing a different sequence of intervals in these two tetrachords. It is also meaningful that, since these two diatessaron cannot have the same sequence of intervals, the natural order (namely the one that exists in all the tetrachord of the Disjunct System) is ascribed to the conjunct Tetrachord which is whole and is attached to the one of the Mese as the one of the Mese is attached to the one of the Added-on ones rather than to the fourth from the Mese a la mi re to the Paranete Diezeugmenon d la sol re, which is not a natural tetrachord. Hence one can see that Didymus placed the smaller tone in his tetrachords after the smaller semitone, because in practice the same happened sometimes. I believe that this is a very useful observation and that this illustrates the exquisite diligence of the ancients. From it we can gather [-<397>-] this rule, that, when two notes are in the same box they will be regarded as in unison in the participate temperament, but in the perfect temperament, which used to be sung and is still sung partly nowadays, the letter nearer to the next one above indicated the higher sound. However, for this reason we shall illustrate a little further how in some tones the paranete synemmenon has the same notes as the Trite Diezeugmenon. One must also be aware that the tones that have some affinity and share the same name, like the Dorian and the Hypodorian, the most part of the notes are the same not only in the Diatonic, but also in the Chromatic because they proceed almost in the same way, and, as to the species, they have only the difference which lays between those through [sqb] and through b flat among the modern ones. Note that, after the [omega] mega, one starts again from the alpha [alpha]. It is also very worth considering the gradual ascending not only of the mese of a Tone but also gradual one of the next ones which are higher. However, in the Mese (which are considered mostly) one must notice that from the one of the Hypodorian [Omega] to the one of the Hypoiastian, although they are a placed at the distance of a semitone, as the other ones are, there is a letter in between, namely the [psi] trite synemmenon of the Hypodorian. However, the [Khi] mese of the Hypoiastian and the [Phi] mese of the Hypophrygian are adjacent to each other, indicating that in the perfect temperament this middle tone is nearer to the Hypophrygian than to the Hypodorian. Therefore i believe that Aristoxenus called it also lower Hyperphrygian rather than higher Hypodorian. Equally, the Mese of the Hypophrygian does not have a letter adjacent to the one of the Hypoaeolian, but the one of the Hypolydian is indeed adjacent to the one of the Hypolydian, because the Hyperaeolian has more in common with it than with the Hyperphrygian, both in terms of interval and of name. For this reason the one of the Hypolydian is also not adjacent to the one of the Dorian. [- <398>-] Moreover, I do not want to omit to inform the reader than the notes of the Lydian System are very well represented in the Solitario of Pontus du Tiard, although he does not say that they belong to the Lydian Tone, and he does not seem to have known that each Tone had its particular ones and that Alypius described them. On the contrary, he says that he found them in an ancient manuscript, and that they differ in some detail from the ones of Boethius’. Now, note that in the printed text of Boethius’ work they are very incorrect, so they can be of little use to correct Alypius’ text. However, the ones of the Solitario correspond very well to the one that I reported and I have disposed in my diagram, although one can see weel that the Tiard wanted that the notes should be simply written down and not described with their names. In fact, for instance, he calls the paranete Diezeugmenon a turned M, rather than a turned [omega], as it is in fact, with little change in its shape [signum]. The mention of this manuscript makes me hope that perhaps there are other copies of it in others parts of the world, and that one day they will be made public. As to the relationship between the Dorian and the Iastian, although it should be the same as the one that exists between the Hypodorian and the Hypoiastian, nevertheless this sequence is not observed. Moreover, the fact that letter which indicates the Mese of the Iastian is adjacent to the one of the Dorian, rather to the one Phrygian must occur, in my opinion, because one will produce a mutation more frequently from the Dorian to the Iastian than from the Phrygian. Nevertheless, because one cannot have continued in this way, since the letters of the Mese Hypolydian are far removed from the Dorian, because perhaps the appropriate distance that the notes within the same System must have would not have been realised in the other Tones and notes. Other Considerations on this Diagram. One must be also aware of something very notable, namely, that this Diagram indicates to us very precisely the species of each mode. In fact, we shall observe that where the species of each Mode begins, there the whole letters begin, as if to indicate that from there upwards the melody must start, according to the species though, rather than the tone of the voice. Thus, we see that in the Hypodorian system the mese is the first whole note that one finds ascending, which is indicated by the [Omega], where the species begins. Moreover, since the notes of the six other principal modes, parallel or equidistant from this one (the Mese of the Hypodorian) are at the beginning of the species of each, [-<399>-] therefore, they are the first in their orders which are found whole going upwards. For istance, the Lichanos Meson of the Hypophrygian G sol re ut from which its species begins corresponds to the Hypodorian Mese and therefore it is the first whole, and the same occurs to the others that have in that box the [omega] mega as the Hypodorian. It is true, however, that the Hypolydian and the Lydian do not agree in having the [omega] mega, as they have the Beta, but this will not be of use to demonstrate, I believe, that these two modes do not begin their species in the same note in different genera. Hence, they are more out of the ordinary than the others. We can also believe that the Nete Hyperboleon, the last note of the Hypophrygian is [Omega], thus showing that this was the last one towards the lower register, hence it was called [barys], as we said, just as the Hypolydian, the last and highest tone has also the l'[Omega] mega. One can see also that, from the Hypophrygian upwards inclusive, the Mese and the Nete Hyperboleon has the same note, hence one sees that they must ascribe the same letter to the note or letters corresponding at the octave, when the nature of this Diagram allowed it. However, in the two tones under the Hypoprhygian this is not observed, possibly because, since they were added at a later stage, it was not possible to maintain the same strict sequence without disturbing the entire order, or it is possible that they did this to assign the same note [Gamma] [Ny] to the Nete Hyperboleon of the Hypodorian and of the Hypoprhygian, which correspond to each other at the octave, as it occurs also to the other Tones that have the same relation, like the Hypoiastian with the Hyperaeolian, the Hypophrygian with the Hypolydian and so on. [-<400>-] We also added, between a mode and the next one towards the high register, the proportions of the proportion of those intervals that we do not think that belong between the Tones in the perfect temperament, namely, a larger semitone between the Hypodorian and the Hypoiastian [16/15 add. supra lin.], a median tone between the Hypoiastian and the Hypophrygian, as between [sqb] and b 135/12<8> and between the Hypophrygian and the Hypoaeolian, another larger semitone between the Hypoaeolian and the Hypolydian and between the Hypolydian and the Dorian, and a smaller semitone 25/24 between the Dorian and the Iastian and betwen the Iastian and the Phrygian a larger one, and so on. Thus, it appears plausible what I was saying that in practice a smaller interval was paced between the Dorian and the Iastian than between the Hypodorian and the Hypoiastian, and that the repeated occurrence of the median semitone 135/128 between among these intervals derives from the fact that within an octave they are more numerous than the smaller tones. Now, a larger and a median semitone compose the larger tone, and in this way the various dissonances between two sounds are maintained, as well as the interval of a diapason which must occur between the Hypodorian and the Hypophrygian, and the sequence consisting in adding a tone up to the Hypolydian. [-<401>-] On the general Difference among Tones As general differences one has to understand the ones which distinguish a genus of Tones or Modes from the other. Moreover, since this way of speaking will appear new, I state that I describe as genus several modes which derive almost from the same source and beginning and agree with each other is some general distinguishing feature and that differ from the others because of it. However, I noted how the most ancient and principal modes are the Dorian, the Phrygian and the Lydian, and thus they have some difference between them which will not belong to subordinate and special tones which do not derive from one of those tree. I am moved to think so also from the words of Aristides Quintilianus who says that: [Eisi de to genei tonoi treis Dorios, Phrygios. Lydios], which means, but the genera of the Tones are three, namely, Dorian, Phrygian and Lydian. Hence all of them can be reduced under three classes or groups headed each by one of those three. Now, therefore, I have consider that just as those three populations differed very much in every respect, thus they must have differed very much in their style of singing, not only as to height of pitch, in carrying the voice indifferent ways and in employing different melodies and species of octaves, but also in the intervals, because, as I said above, although Zarlino always considers the Syntonic as natural Diatonic, considering that all the nations adopt it in the same way, nevertheless the reality is difference because one will find that many nations differ in this respect. [-<402>-] Hence, although all of them use the Diatonic as it is natural, nevertheless one will be closer to one species and another to another one, so that one shall sing the syntonic, another one the diatonaeus (I do not enquire whether the intervals shall be exact or not) and some other another species. If we observe the natural songs of several nations with diligence, we shall find that this is very true. Moreover, according to the information extracted by the most erudite Father Mersenno from the Relations on the country of Canada, in America, which was visited by the French, it has been observed that those populations use different intervals from ours. I consider very probable that, if someone observes these matters in detail, one shall find that the less civilised and more belligerent nations shall use the smaller diatonic interval larger than the other one, and, for instance, larger than half, as it is the sesquidecimoquinto semitone, called larger and similar intervals to that one, while effeminate and more gentle populations will use the semitone smaller than the median one, such as the 25/24 or the 28/27, and the nations with a character between those two perhaps will use the semitone which is equally divided and median between the two. Also, since we know that the Dorians (to which the Spartans, the Arcades, the Candiots and similar were related) were a belligerent and stern population, and one more devoted to hard work and war than to pleasures, hence we can conjecture that they used the Syntonic (which, although it is described as Ptolemy’s, was not invented by him) rather than [-<403>-] another species of Diatonic. That that species is very similar to their nature is demonstrated by its name, which means intense and vehement, which are the qualities that Athaenaeus attributes to that population. That they had something of the rustic and austere, is confirmed by We can gather that this species is less sophisticated than the others from the fact that it is closer than the others to Ptolemy’s aequabilis which he himself describes as a little unsophisticated, although he invented it. It seems also appropriate to think that this species, although it is the sternest, it is also the most attractive, because it has the most harmonious intervals, and that it was chosen by the Greeks, who had good taste in all things, rather than by the Asiatic populations. In fact, if Pythagoras, who lived among the Dorian nation established the musical system that is heard played and sung tin the Diatonic Diatonaeus, this should not be a nuisance to anyone, since, although he was a great man, he could not know everything, as nothing was begun and completed at the same time, as, had he foreseen everything, neither the followers of Aristoxenus or those of Ptolemy would have noted those known mistakes in the Pythagoras’ Harmonic dispositions. In fact, if he constituted the fourth of two larger tones and a smaller one, this happened because he heard them sung as equal in reality, and, since only the sesquiottavo was known, he presumed as certain that they were all sesquiottavi, although they were participated instead. Therefore, on this basis, [- <404>-] there was no other interval left to him to complete the Diatessaron that the Limma. Thus he was not aware of the Syntonic nor of the consonant Ditone or semiditone. The fact that the Lydians used the minor Semitone also in the diatonic natural is suggested to me by the fact that that nation was very dissolute, lascivious and very effeminate, as many ancient historians report, and by the fact that that interval expresses great delicacy and lasciviousness, as all the smaller interval do, proportionally speaking, compared to the larger ones. Thus, we hear that the minor thirds and sixths are more languid and soft that the major ones. On the other hand, as to the Phrygians, who were more fervent than the Lydians, but not as harsh and serious as the Dorians, I believe that they used commonly the middle interval and specie, namely the Diatonic Diatonaeus or a melody similar to that one. However, as to the Ionians and the Aeolians, at least after the moved to Asia, I believe that they adapted for the most part to the customs and style of singing of that climate and of those populations with which they mixed, and although in the past they were not different in this matter from the Dorians, later on, because of their familiarity and frequentation with the Phrygian, they lost part of their own style and they adopted a style that was closer to the Phrygian (at least the Aeolians who lived closer to that population) than to the Lydian style. Therefore, as the grey is made up of black and white as a third colour, thus they created a third [-<405>-] style by adopting little by little the use of the middle-size semitones, as the Phrygians did. Nor this conjecture of mind is based on thin air, but it is based on the authority of important writers who confirm me in this belief. I believe that for no other reason Ptolemy in the last chapter of the first book states that the numbers that demonstrated the interval assigned by him to the Diatonic Diatonea species in the Hypophrygian Tone corresponded to the melody or harmony Iastiaeolian, which was interpreted, as one can gather from several passages of Ptolemy, by the Citharedes as meaning certain mixtures of the Iastian mode with the Aeolian, which they used mostly as a form of mutation, as in moving from the Dorian or another principal mode to that one, and therefore they called them [metabolika ethe], which means melody of the mutation. He states further on that the Lydian Harmonies and their combination of sounds of those citharedes corresponded to numbers or divisions of the diatonic Toniea species located by him in the Dorian tone, which species specie as from a interval 28/27, which is very small. As to the fact that in effect even in his time the Citharedes used to sing the Diatonic Diatonaea species, he shows it in the first chapter of the second book were he says expressly that the Citharedes tuned their instrument in such a way that they had two sesquiottavi tones within the fourth, and the remainder was in proportion 256/243, which is the limma. This occurred in the Harmonies or Systems which they called Iastioaeolian. In the last chapter of the first book he states that the mixture of the syntonic diatonic suites the modes of the mutations called Lydian and Iastian by the citharedes, except that they tuned their instrument in such a way that they had two exact tones and what was left was similar to the half which they called semitone, but which was really the interval of the limma. Therefore it is not possible to doubt that [- -] that system (which is the Diatonic diatonaeus) was the one of the Iastian modes, while the Diatonic Toniaeus (which was mixed together by placing a fourth of one sort and a fourth of the other within the octave) was the one of the Lydian. We can also believe, and perhaps it is even more probable, that, of the principal modes, which are Dorian, Phrygian, Lydian, Mixolydian, Iastian and Aeolian, the Phrygian will correspond in harmony with the Dorian, namely in rendering the semitone larger, since the character of the Dorians is severe and vehement and the one of the Phrygians possessed and fervent. The Lydian and the Mixolydian used the smaller semitone, as I said; the Iastian and the Aeolian the one of middle size, since it was very appropriate that the Ionians and the Aeolians, as Greek populations, approached the Dorian strict character and, as Asian populations, the Lydian softness. Therefore, it appears that there cannot be even the slightest doubt in the case of the Phrygian. However, I believe more plausible this second opinion, because I see that in the diagram the Phrygian tones, namely the Phrygian, Hypophrygian and Hyperprhygian have the Paranete Synemmenon and the Trite Diezeugmenon different, which shows that they are not in unison in the perfect temperament. Also, as to the Phrygian modes, albeit they used the middle –size semitones in they original form and in the way in which those populations sang them naturally, nevertheless it is not improbable that Greek musicians used to adapt them to the style of the Dorians with the larger Semitone so that they would have two of the three combinations of the six main ones and for greater ease in the mutations they had Dorian and Phrygian (which are at the distance of a tone) divided by the Iastian which has a different tuning from those two. I believe this to have happened after the Iastian and Aeolian were accepted and inserted among the first three. As to those that placed the Dorian, Aeolian and Iastian as the three principal Harmonies and Modes, I believe that they assigned the middlesized Semitone to the Aeolian and the smaller to the Iastian. Now, the following illustration explains how the Paranete and the Trite of the disjunct of the system are in unison in the Diatonea species and not in the others derives from the insertion of the compound tetrachord into the System. We have limited ourselves to adducing the examples in the three main species, taking the Syntonic of Didymus or Ptolemy the one that has the Semitone larger than one half, the Diatonaea species as the one that has it measuring one half and equally divided, and the Toniea as the one that has it smaller. Hence one can gather that the Dorian mode is appropriate and is normally to the Syntonic, the Phrygian to the Toniaeus, the Lydian and mixolydian to the Lydian and the Iastian and Aeolian to the Diatonaeus, placing the subordinate ones in the same class as their principal ones. [--] [Doni, Treatise on the Genera and the Modes, second book, 407; text: Diatonico Sintono, Tonieo, Ditonieo, Congiuntione, Disgiuntione, a, b, [sqb], c, d, e, 9/8, 81/80, 125/124, 16/15, 8/7, 28/27, 10/9, 9/8, 256/243, tuono disgiuntiuo, Dorio, Lidio, frigio, Missolidio, Iastio, Aeolio, limma] Now, for the same reason the soft Diatonic will be more suited to the nature of the Lydian and Mixolydian mode, than to the nature of the others, and, among the chromatic species, the one of Didymus which starts from the larger Semitone will be suited to the Dorian and Phrygian, while the one of Archytas’ which has the proportion 28/27 in the first place and the soft chromatic of Ptolemy will be better suited to the Lydian and Myxolydian mode, and the one which proceeds through the limma and the other semitone 139/128, which is not very different will be suited to the other two, namely, Iastian and Aeolian. However, in order to explain it better not only in the Diatonic, but also in the Chromatic according to Ptolemy’s distribution, one must place two d d separated by the interval of the Comma in the perfect System, and in Didymus’ one [-<408>-] two c c, as I shall place in the following illustration. [Doni, Treatise on the Genera and the Modes, second book, 407, ] How one can find the species of the Tones not mentioned by Ptolemy. It is not very easy to discover nowadays the specific species of each one of the modes which are added in Aristoxenus distribution to the seven of Ptolemy, namely, to those mentioned by Ptolemy. Nevertheless, since musical matters are so well ordered and circularly connected together, that, like someone who finds the end of a bundle of wool can disentangle it all, thus, once someone has found a rule, all the others of that same theory can be found if one proceeds with judgment and with much attention and maturity. For this reason, I believe that one can discover the form and specific species of the Iastian and Aeolian mode with the help of that passage of Aristides Quintilianus and of some other statement which we have of good writers, and I believe that from them we can also deduce the form of their plagal or subordinate ones. We can rest assured, therefore, that the Aeolian shall have the species of the Hypodorian because Laso of Hermione, the first author who wrote about music, who was Aeolian, in a certain Hymn of his of which Athaenaeus reports some verses, calls that song of his [- <409>-] [aiolida harmonian], or Aeolian Harmony and [hypodoria mele] or Hypodorian songs. This is also confirmed by Heraclides Ponticus, a very learned music writer quoted by Athenaeus in the same passage where he says that the Hypodorian mode or Harmony is also called Aeolian. Therefore, we can conclude that their Trope or Harmony, as we want to call it, is the same but not the tone, because in the order given by Aristoxenus he placed both in a different position. As to the Iastian, it seems possible to understand that his form is very different from the ancient one described by Aristides, because it is certain that in the fresher times, when the modes were better ordered and each was assigned its own whole Diapason, the earlier order was not changed but only the missing intervals were added, as the other ones show, in which case we know manifestly that this occurred, namely, the Dorian, Phrygian and Mixolydian. Therefore, since initially the Iastian had these intervals, namely, Diesis, Diesis, Ditone, Trihemitone and Tone, which is equivalent to say Semitone, two Tones, Semitone, Tone and another Tone in the Diatonic, one cannot doubt that a tone in the higher register was added to it to complete the octave, otherwise its nature would have been changed. In this way the Iastian will have the same species of the Mixolydian, which suited it even better than it suited the other ones because is soft and feminine. This seems to me to be even more certain because in this way the Dorian will have the same relation to the Iastian, which is above it, as the Phrygian has to the Aeolian, which is also above it, because, just as the Phrygian through b flat takes the species of the Hypodorian that is the one of the Aeolian, thus the Dorian through b flat takes the species of the Mixolydian which is the same of the Iastian, [- <410>-] and this turned out to be very useful in the mutations, as I shall show in practice. It has to be noted also that Aristides Quintilianus has described the modes used in the most ancient times with their sequence of high and low because the lowest is the Lydian, followed by the Dorian, the Phrygian, the Iastian, the Mixolydian and finally the Syntonolydian, hence one can see that that word [syntonos] indicates the very high position of that mode and nothing else, because the high notes are more tense or intense, as they want to call them. This word is used by Plato and by others with this meaning, hence, to distinguish it from the other Lydian which was located under the Dorian, which was relaxed, this one was called Syntonic or Syntonolydian or [syntonolydisti], to use a single word. Therefore, one understands that it is the same one that was called later Lydian absolutely, although it is also under the Mixolydian, which does not matter, while the one called by the ancients Lydian or relaxed and languid Lydian, after the seven species were ordered was called Hypolydian for the reason we know. As to the fact that the low Lydian was also called relaxed Lydian, or [aneimenos], which means precisely not tense, as the string of a bow which is not very tense, we see that Plutarch teaches us this openly where he says: [Alla men kai ten epaneimenen lydisti, heper enantia te Mixolydisti paraplesia ouse te Iadi hypo Damonos eurhsthai phasi tou Athenaiou], which means: “Moreover, they say that the relaxed Lydian Harmony, which is the opposite of the Mixolydian, which is much very similar to the Iastian [-<411>-] was discovered by Damon of Athens.” However, one must be aware that where one used to read [eiper] instead of [heper], and [paraplesian ousan] without any reasonable sense, I have correct the text as it is, becaus that [eiper] in that position had no function, and if one read [paraplesian] in the accusative, it meant that the Iastian Harmony was similar to the relaxed Lydian, which is completely the opposite, as one can see from Aristides’ description, because the Lydian starts from a single diesis followed by two separate tones, while the Iastian starts from two adjacent diesis followed by an uncompounded ditone, and the in the remainder the Lydian is fragmented and the Iastian proceeds with large intervals, while, according to my correction, everything proceeds very well because in truth the relaxed Lydian or Hypolydian is contrary to the Myxolydian because it has exactly the same species in reverse order, [Doni, Treatise on the Genera and the Modes, second book, 411; text: F, G, A, [sqb], C, D, E, f, T, S, a, [[lydi]] Hypolydio, Missolidio] and the Mixolydain is very similar to the Iastian, as one can see in Aristides’ description where they do not have any other difference except the may uncompounded intervals of the Mixolydian appear as compounded in the Iastian, which also has a tone less. However, we must observe that the Harmonies described by Aristides are Enharmonic rather than Diatonic, because they pre-date Aristoxenus, in which time only the Enharmonic was sung and appreciated by the Greeks. It is true that it is not a pure Enharmonic because those conditions, namely, that it must have only one Tone at the distance of an octave do not apply to it. Nevertheless, they are Enharmonic modes and we must call them as such because they were described in this way by our ancestors who were arbiters of their languages, as we are of ours. Hence one deduces how the Enharmonic was sung, namely, that [-<412>-] it was not always necessary to make those tow Ditones uncompounded, and that they had often more than seven intervals for every octave. Once can see also that they maintained the species of the Dorian in the pure Enharmonic to preserve to it its majesty and gravity, but that they varied it and enlarged it considerably by adding to it a tone in the lower register outside the octave, and that they placed only ne Ditone in the Phrygian to add more movement and to lessen its austere character they put a single uncompounded Ditone. Equally, in the Mixolydian, which was dedicated to womanly laments and tears, they divided it as much as they could without changing its species, using tones instead of ditones. We are also able to know how the more recent Modes of the perfect System were created from these Modes. In fact, starting with the Dorian, it was not altered in any way except that lower tone was removed from its lower register for the reason mentioned by Ptolemy that the Diapason is the perfect System, although it was allowed to use nine notes and also many more. Since the Lydian, which was then called Hypolydian, lacked two tones, these were added in different positions, one in the fourth place and the other in the eighth one so that it would proceed through one diesis, three tones, two diesis, two tones and one diesis. Nothing was changed in the Phrygian, if one understands, as I said above, that the diesis towards the high register was not alone but accompanied by another one. In the Iastian they only divided the first semitone of the Trihemitone compounded, so that one tone and one tone were left, and they added another one to those two tones. In the Myxolydian they did make no change because it completes the octave, if we place those dieses together [-<413>-] towards the high register. The Syntonolydian, which was then called Lydian was enlarged by dividing the first semitone of that uncompounded Trihemitone, by adding two other tones towards the high register and by transposing the first diesis which was in the low register in the last place towards the high one. In this way they were al rendered perfect and they all completed the Diapason. However, since placing two ditones one compounded and the other one uncompounded was liable to produce a great variety of harmony and to produce a larger number of different tones, I hold certain that it was set out in this way in the majority of the modes. As to the Dorian itself, I believe that they decided to preserve it in its majesty of its two uncompounded ditone, and thus some variety of harmony was created not only in the eleven tones but also in the eighteen, but we shall discuss in the next chapter how this was done, as far as we can tell. Why the most ancient musicians used few notes in their Systems. However, in the meantime, I would not want that anybody should believe that the ancients, who used the modes described by Aristides were devoid of judgment in using harmonies that were so poor. In fact, there is no doubt at all that they did it not because they lacked notes or strings on their instruments, because instruments called organa panharmonia and polychorda (or instruments on which any note could be played or of many strings) were know even at the time Plato and before, but because they noted that the fewer the notes of the harmony or the mode, the more the mode is different from the others and the better it preserves its character. This is not surprising, because the three species of the Diatessaron are more different one from the other than the four of the Diapente and these are more different than the seven of the Diapason. Therefore we hear a great variety in the melodies of the psalms [-<414>-] although they differ only according to their Systems rather than according to their tones. Hence Plutarch states: [kai hoi palaioi de pantes ouk apeiros ekhontes pason ton harmonion eniais ekhresanto; ou gar he agnoia tes toiautes stenokhorias kai oligokhordias autois aitia gegenetai; ou de di'agnoias hoi peri Olympon kai Terpandron kai hoi akolouthesantes te touton proairesei perieilon ten polykhordian te kai poikilian martyrei goun ta Olympou te kai Terpandrou poiemata kai ton toutois homoiotropon panton trikhardia gar onta kai apla, diaferei ton poikilon kai polykhordon hos medena [[.]] dynasthai mimesasthai ton Olympou tropon; hysterizein de toutous en to polykhordo te kai polytropo katageinomenous. et cetera], which means: “Moreover, all the ancients, although they were expert in every type of harmony, they availed themselves only of some, but their ignorance was not the reason for such restrictions and lack of notes, nor Olympus, Terpander and the others who followed that style removed the large number of notes and the ensuing variety. In truth, Olympus’, Terpander’s works and those of the followers of their style support this, because, although they are simple and only composed of three notes, they are much superior to those that are greatly varied and composed of many notes, so that nobody can imitate Olympus’ style and those who adopt the modern style of many notes and Modes are left behind. “ [-<415>-] Then Plutarch (or rather Aristoxenus through him) says that they did not use the tetrachord of the Hypate from [sqb] to E in the Dorian mode not because of their ignorance, since they used it in the other Tones, but on purpose and by choice, to preserve better its character and its majesty: [Delon de kai peri ton hypaton (ouero kai peri ton hyperypaton) hoti ou di'agnoian apeikhonto en tois Doriois tou tetrakhordou toutou; autika epi ton loipon tono ekhronto delonoti eidotes; dia de ten tou hthous phylaken apheroun epi tou Doriou tous timontes to kalon aoutou.], which means: “It is clear, on the subject of the Hypate or of the Hyperhypate that the did not abstain from this tetrachord in the Dorian modes because of their ignorance, while they used it on purpose in the other tones, but they removed it from the Dorian because of respect towards its majesty.” From this witness report one can gather that not a single disposition of the Tones was in use in the most ancient times, namely, before Timotheus, which is the one reported by Aristides, but others as well according to the times and the musicians who lived then. In fact, albeit we see that the Dorian has more notes than the other Tones in this one, nevertheless at other times it had fewer. Therefore one can believe that. even when it had nine notes, the others would have had eleven or more. We can also deduce that also at the time of Aristoxenus as well as in those of Plutarch there was no shortage of people who criticised the ancients unjustly for being ignorant because they did not use devices which were introduced later, in the way that Glareano and others criticises as ignorant the Ecclesiastical musical writers and Franchino because they were content with [- <416>-] the eight tones and because he wanted to avoid malpractice and unnecessary corruption, because, if anything, they deserve to be criticised now because they did not reduce their number to seven or four as those used before Guidone. [-<417>-] Explanation of that Problem of Aristotle’s where he discusses the three tones Mixolydian, Hypodorian and Hypophrygian. Aristotle’s Problem of Lesson nineteen, where he deals with musical matters is not obscure in itself, but because of the fact that certain words that it contains, which must have been known to everyone at the time, are not known nowadays. Therefore, it has not been explained by anyone so-far, to my knowledge. Hence, I wanted to try to see if I could interpret it. This is what it says: [-<419>-] The entire difficulty resides in what it means to have or not to have the antistrophon. Therefore, in order to understand this correctly, let us remember what Ptolemy writes on the ancient Modes, namely that they were of different sizes because some filled the Diapason exactly, while others exceeded it and others did not complete it, as we have seen also from Aristides’ description. To say that a mode does not have the antistrophon is the same as to say that a mode has not got a note which corresponds to one of its notes at the octave. We can interpret this in two way, namely, either that a mode does not have the antistrophon when it does not span the Diapason, as a mode that has seven notes, or when it does not reach the disdiapason. Hence, in this case a mode will be understood to have the antistrophon when the mode itself which reaches completion in the octave will have another octave corresponding either above or below it, and, consequently, each note of an octave will have its correspondent which they called [antiphonon] equally at the distance of an octave, but in the first interpretation this term antistriphon will refer only to the single term, namely it will refer to the first note and not to the entire system, hence, according to the first meaning it will be absolutely impossible to sing in consonance in any way, and according to the second meaning it is impossible to sing in the way that the chorus sang, namely that all the voices sang the same melody but the highest sang an octave higher and the lowest an octave and the variety of the composition was entrusted to the instruments, although some consonance might occur. Therefore, I consider certain that Aristotle means that the Hypodorian and the Hypophrygian were not good for the music of the Choir because the octave above corresponding was located beneath them, as in the case of the Mixolydian. In which of the two meanings we interpret it, it is not important, because, as long as those two [- <420>-] modes had the Diapason complete, it did not matter that they did not reach the Disdiapason. Therefore, while the Basses (which were the main part in those two tones) sang the System specific of those two modes of eight, nine, or eleven notes, the Soprani could sing the octave of each of them. Nevertheless, they did not think that the System was enlarged, on the contrary, the one of the Basses and the one of the Soprani was used all the same according to the practice of the ancients, hence one can believe that at the two modes which were used in Tragedy (namely, for the actors on the stage, since the Chorus was made of musicians and dancers, rather than of actors) did not exceed a seventh, and musicians had planned this to keep those modes mostly in the lower register and confined to their own character without allowing them to deviate too much into the realm of the theirs. Hence one can believe that the Hypodorian was created by adding a Diatessaron under the Dorian and removing a fifth above it, and equally the Hypophrygian from the Phyrgian, in this way: [Doni, Treatise on the Genera and on the Modes, second book, 420; text: Dorio, Phrygio, a, d, c, [sqb], g, G, F, E, D, c, A, Diatessaron, Diapente Hypodorio, Hypophrygio], [-<421>-] and that at the time in practical music and the wind instruments (flutes and recorders) said modes did not exceed the interval of the seventh. Investigation into the form and harmony of the remaining of the thirteen and fifteen Tones. From what was said one can conclude with certainty that the Iastian Tone had the same species as the Mixolydian and the Aeolian the same as the Hypodorian. However, it will not be difficult to establish what particular difference they had in their harmony if one accepts the difference that the two large intervals produce in the Chromatic and Enarmonic, when one is placed uncompounded necessarily, the other one compounded and uncompounded from the Dorian onwards because it seems that this can be derived from the Harmony of the Phrygian and from considering the Tone of the Disjunction. Therefore, we see that in this series [Doni, Treatise of the Genera and of the Modes, second book, 423; text: D, Tuono, E, diesi, F ditono, G, a, [[Ditono, [sqb], tuono]], c] of the Enharmonic Phrygian, which contains the other two genera virtually, the intervals are adjusted with such artfulness that the do not mar the natural order of the Diatonic, nad that the tone [-<422>-] of the Disjunction occurs in the same place as in the two genera, Diatonic and Chromatic, and it is, so to speak, the mark and the distinguishing sign of the modes, as one gathers from Aristides, Cleonides and the other Greeks. Therefore, it they wanted to keep this tone in its proper place, which is the third one from the high register downwards, they take the dense as a single interval, and if they wanted to have it, or better, if we want for the Phrygian to preserve its character and to resemble as much as possible its Diatonic original, it could not have been placed in any other way, but it was necessary to leave the first tone as it is and to divide that following semitone and the others to create the dense. Also because the large interval must follow the Dense, for this reason the uncompounded Ditone was placed after it, after the Ditone there follows the tone of the Disjunction and then two dieses corresponding to the two beneath. Finally, there was only room for a single tone, because we placed its correspondent in the low register, as in the Diatonic. Now, since all the ancient tones are not limited to a single octave, if one continues this species, one encounters the tone corresponding to the first one, and, because in the Enharmonic genus it will be possible to take these two tones by leap with an uncompounded Ditone, hence it will be left to the individual judgment either to sing them separately to adjust them to the species or compounded to maintain the property of the genus. This does not happen in the case of other ditones, since, because it was in the middle, it was not placed hard but compounded. Also, since the Tone of the Disjunct ones in all the genera can be divided by interposing the conjunct Tetrachord, when one wants to make this its first semitone, [-<423>-] it comes to be divided in this genus into two dieses, after which, skipping the other semitone and the dense that follows, in the disjunct tetrachord one comes to proceed to the tone and the to the other, or, to the ditone uncompounded in a single leap, since it is not less subjective that in proceeding through the Disjunct ones. This is what transposing a fourth higher the tone of the Tone of the Disjunction means, which comes to correspond to the one which occurs in the first place below D E instead of A [sqb]. However it suits the Dorian Tone to have one and the other Ditone uncompounded, because it has the Tone of the disjunction in the middle. As to the other tones, since they do not have at one extremity a tone separated from the others by a semitone in the Diatonic as in the case of the Phrygian, this necessity of maintaining in the two genera the same tone divided in the same place does not occur, and for this reason we shall proceed to establish their harmony following another path. Therefore, the uncompounded Ditone in the lower register befits the Lydian perfected as said above, which was also placed in the Syntonolydian, while we shall place under the Hypolydian the compounded or divisible Ditone, so that it may be distinguished from the Lydian and may be as close as possible to its former form, while we shall place the Uncompounded one or indivisible above it. However, in the HypoPhrygian, so that it may be somewhat different from the Phrygian and it may contain the tone of the division in the second position, as the Greeks prescribe, we shall place the uncompounded ditone int he first place and the compounded and Uncompounded above it. Thus it shall have something of the severe and it will be suiteable for the Tragedy. The two that are left are the Mixolydian and the Hypodorian, similar in part as to their species and in part opposite to each other. It appears to be suitable to order them in such a way that the uncompounded Ditone towards the low register be ascribed to the Hypodorian, so that [-<424>-] this may retain greater gravity, and in the high register to the Mixolydian, so that it may be more broken in the lower register and suited to tears and feminine laments. Thus, I will have ordered appropriately all the seven modes of Ptolemy in the enharmonic genus. Moving on to the other ones, I say that the Iastian must have necessarily the uncompounded ditone in the lower register, firstly because the most ancient has it in this way, according to Aristides, secondly, so that it may differ somewhat from the Mixolydian, and thirdly so that it may be more majestic, since it had already been used in the tragedies as report. Equally, we shall order the Aeolian, which has the species of the Hypodorian, in such a way as to have the compounded Ditone in the lower register, in an opposite way to that one, and the Uncompounded one in the higher register. From these two we shall derive then the form of their plagal modes, Hypoiastian and Hypoaeolian. We shall assign to the Hypoiastian a tone separated in the lower register and then the Tone of the disjunction so that it may resemble the Hypophrygian in having the Tone of the disjunction in the second place, and the Phrygian in having that single tone in the lower register. Thus, the uncompounded Ditone will be pari ad alto. Conversely, we shall ascribe to the Hypoaeolian the compounded ditone in the low register and then uncompounded in the high one, so that it may be similar to the Hypolydian, except that it will have both dieses in the high register, while that one will only have one. As to the two notes corresponding above, it will be similar to the Iastian, but we shall make it start from the Uncompounded Ditone in the opposite part, while it follows in the Iastian after two dieses. We shall distinguish the Hypophrygian from the Phrygian by allotting to it not one but two tones [- <425>-] in the lower register, namely the compounded and uncompounded Ditone, and it will be similar to the Hyperiastian in the position of the Tone of the disjunction, which will occur in both under the Dense in the acute register. As to the other two added by the followers of Aristoxenus, one should not consider them much, because they appear to have the same species as the others (moreover, Athaenaus seems to confirm this as well) and if they had it, it is not easy to ascertain it. Nevertheless, if we want to assign it some form, it appears that the same one of the Aeolian may be ascribed to the Hypearaeolian with the difference that the Uncompounded Ditone shall be placed in the lower register unlike in the Aeolian. The Hyperlydian can be left to have the same form as the Lydian, partly because it is hard to find it a form of its own, and partly to follow Athaenaeus, who writes at book that he cannot see that the Hypolydian had its own rules of Harmony. Thus, it will differ only because of the tension. The same order of intervals has to be assigned proportionally to the same Modes in the Chromatic, as there is no other difference, except that one detracts a semitone from the Ditone that separates the remaining trihemitone from the semitone that was divided in the Enhamonic genus. Finally, I believe that this is the true distribution of all the species in all the fifteen modes according to the three genera of music after having ruminated on it for a long time and since I realise in the end that they cannot be organised in a different way so that all the conditions that must be preserved are preserved. [-<429>-] Explanation of the Tables placed above [-<430>-] Nor anyone should be riled that the species of the Enharmonic Hypophrygian is almost the same as the one of the Diatonic Hypolydian. [-<431>-] Also, I consider very probable that in the ordinary Iastian (I mean the more recent, as they are all the thirteen and fifteen modes) the tone adjacent to the second dense was divided into two semitones with a Chromatic note in the middle, namely the , so that if one wanted it could be used, and that this is the one that made it deserve the description of [glaphyros] according to Lucian. In fact, albeit it cannot be called any more simple Enharmonic, not even the others of the thirteen from the Dorian on can be called so with reason, because each of the ditones is divided. However, we must remember that one thing is to deal with the Tones according to the rigorous rules of the genera, while to deal with them according to their use is quite another. One must believe that Lucian had practical use in mind, since in that other meaning no particular mode is more varied than any other, since they contain the same number of notes and intervals, and such that this would be the Iastian System with the addition of the note F: [Doni, Treatise of the Genera and of the Modes, second book, 431; text: diesis, [sqb], c, Ditono, E, F, G, A, semitono minore. tono]. [-<432>-] That the Dorian Mode or Tone is the species of E la mi in the Choral tone, and what is the Choral tone. From what was said so-far, one has been able to understand easily that the Dorian Mode is the one that spans from E la mi to e la mi, namely from the Hypate Hypaton to the Nete Diezeugmenon, which is clearly stated by the ancients, namely, Ptolemy, Aristides, Cleonides, Bacchius, Boethius and all the others who discuss the Modes. Hence, it is very surprising indeed to see that modern writers understood the matter the wrong way round, attaching to it the species of D la sol re, which is the one of the Phrygian, hence their Dorian is the Phrygiana and the Phrygian the Dorian, which is the difference between water and fire, so different are those modes and opposed to each other. Therefore, we must not be surprised if the properties that the good writers assign to them do not match those assigned by the theorists of our age. Modern writers were not to hide this matter, hence Glareano, against the universally accepted opinion, [book 2, chapter 11 in marg.] regarded the Phrygian, or, better, the Dorian, as suited to sad and funereal matters. At chapter 23 of the second book Glareano interprets the epithet of religious assigned by Apuleius to the Phrygian as meaning a certain tearful quality which is more suited to the Dorian, albeit it has more of the sad and severe than of the tearful or weepy. Moreover, he should not have interpreted that word religious [-<433>-] as tearful and almost regretful and suited to lament one’s sins, according to Christian practice, but as very cheerful and possessed, as they judged suitable to the sacrifices and ceremonies in honour of Bacchus according to their mad belief. However, to move on to the property of the tone, one must note that the ancients adapted each of the seven Tones to the tension of the human voice to which ascribed fifteen notes and two entire octaves. In fact, although some people do not sing as many others exceed that number, nevertheless, on average, this number covers the natural System of each person. Consequently, the middle tone, which is the Dorian, is the only one sung without any straining of the voice, and, therefore, it is considered to be the most attractive and tranquil, and that it represents the demeanour of a serious and grounded man who does not change his emotional state and facial expression because of any event, nor he is softened by excessive cheerfulness or is overcome by fear or inflamed by ire and so on. Therefore, the ancients noted judiciously that the consequence of ire is to raise the voice and that an angry man always talks with a tone of voice which is higher than his natural one, and, conversely, who languishes in pleasures and enjoyment uses a lower and more relaxed sound, and this demeanour can be seen in those who are drunk and full of wine and sleep. Hence, they assigned to these the Hypolydian tone, which is the most relaxed and low, while, conversely, they ascribed the Phrygian to those who are burning with ire and rage, since it uses a higher and more intense tone of voice. Thus, they assigned the others [-<434>-] proportionally according their different or the same emotions, more or less strong. This is the reason why music produces different emotions according to the fact that the singer adopts a lower or higher tone, rather than because the high or low sound by itself produces different effect and that, consequently, modern compositions which use contrary motions (which were used also by the ancients) do not move almost any feeling. On the contrary, the high or low pitch per se has no effect at all, but it has to be viewed in relation to the singer, since it is natural to identify ourselves with the emotions of who speaks and sings. Therefore, that precept s i uis me flere dolendum est (which means: “ if you want me to shed tears, you must show pain”) comes from here, et cetera. If we hear someone using a singing tone that is not natural, we detect immediately with our imagination (apart from the expression and the effect of the words) a great feeling of discomfort in that person, and we are moved because of natural sympathy and we transform ourselves into the same emotional state. The Dorian was more highly regarded by the ancients with reason and it received the highest praise from those who lauded no other music that the sort that was consistent and serious, as opposed to the one that was introduced in the theatres to move the souls from their original state. However, nowadays –and this is why Mei says that this is the only one that we have left of so many ancient Modes – modern musicians do not heed this precaution, hence they sing mostly only in the Dorian Tone, not by choice, or because they want to keep themselves within a serious and dignified deportment (may God desire that the exact opposite was not the result) but because they are not able to do anything else and because they do not possess the art of the Erhopeia and Pachopeia [-<435>-] in music. Hence, they barely provide any other rule outside their usual habits (which is something separate from the Melopoeia) that to stay mainly in the low register when they want to express sadness, and in the high register when the subject is cheerful. Similarly, in the matter of Rhythm, they do not give other detailed advice except in relation to fast or slow speed, prescribing only to use the latter in cheerful music and the former in sad ones. Therefore, this Tone normally used for singing is called Choral, because it is convenient to the choirs of singers in the compositions for several parts and also in the Ecclesiastical ones for one voice alone, and because the voice of the singer can easily adapted to the sond of the organ, which regulates this Choral tone, which also regulates the harpsichords, Spinets and similar keyboard Instruments used commonly nowadays to accompany the voice. Also, although they do not have nowadays a note of absolute pitch that (as the and the Ecliptic in measures the eclipse in the height of the celestial bodies) may serve as norm and boundary to define the notes, nevertheless one could do this with ease taking the note which is exactly in the middle of the Instrument, as long as it is tuned properly, and establishing it as the middle one of the Dorian (namely, the a la mi re) which could be highlighted in every composition so that one may ascertain at sight in which tone one is going to sing. This note should correspond to the middle one of an average Tenor in one of these two ways, either considering all the notes that he can pitch absolutely, and these shall be more or less fifteen, and if they are fifteen the octave will be the middle one and the one that indicates the Choral tone, or one must consider [-<436>-] only those that are easy to sing and are constituted well (which must be noted in this tone particularly) which are normally nine, the number assigned by the most ancient musicians to the Dorian harmony. In that case the fifth shall be the middle note or Dorian Mese which shall correspond to the octave among the fifteen, because the middle note is at an equal distance from the ones at each extremity. Now, since some nations have a higher tone and others lower, and, apart from this, singers are more lazy in one place than in another, hence it follows the choral tone is not the same everywhere. It is true that, since there is no great difference among the main and most noble nations of Europe, we can say that the choral Tone is like the Mark, to which merchants in common markets (for instance at the Fair of Piacenza) reduce and compare all the other types of currency. In a similar way, the Choral tone, although it is not exactly the same everywhere, it is the one that shows the variety of the tension of the voice used in the compositions among musicians who use the same notes and the same instruments and way of using them. The northen nations usually have the deepest voices, especially those that have a similar climate to the one that one sees among the Walloons and the inhabitants of Lorraine, who have the lowest voices. This derives from the temperature of the country (this is the main reason in my opinion) from the food and the drink that are more popular in a place than in another or because of the inclination of the Air of the sky, as Vitruvius appears to believe, providing this as the reason. [-<438>-] It is enough to say that Northern nations have lower and manlier voices while the Southern ones have higher and more feminine ones. However, as to the particular Choral tone of this or that country, it is not easy to ascribe all the differences, and if one could, it would be useless. I have noted simply that in Rome one sings a good semitone lower than in the rest of Italy and in Germany a tone and a half higher, and, consequently, more than a tone higher than in Rome. Hence, if one takes the tone common in Italy as Dorian, the one used in Rome will correspond to the Hypolydian and the German to the Phrygian. It is not necessary that this Dorian Italian tone should correspond entirely to the modern or ancient Greeks so that it may be called Dorian. On the contrary, it will be more reasonable to call Dorian the one that in every province is natural and not strained, although one must take into account the natural degree of high and low pitch typical of the whole nation rather considering a single town, and measuring together what is done and what could be done. For instance, if the singers of Rome depart from the tone of the others not because a lower voice or because they are laze, but in order to achieve a particularly attractive effect, their tone will be called Hypolydian rather than Dorian, while the Dorian will be the one that is common to all Italians, although it will not suit the Lombards because they have a lower voice than the inhabitants of the Reign of Naples, or the other way round. Anyway, one must not consider the matter in such small detail, since the singers of various cities belong to different countries and nations for the most part. [-<439>-] On the quality specific of the species of Diatessaron and Diapente. After we have established what is the Choral tone and after we have seen that the ancient modes differed not only because of the tension of the voice, but also because of the variety of the species, it is appropriate now to consider what properties has a species more than another one, and, because the order of the Diatonic differs from the one of the other two genera, we shall investigate that one first. To start we shall consider the different species of the Diatessaron and of the Diapente, which produce the different types of Diapason. It is easy to observe that the fourth that has the semitone in first place has a kind of attractiveness and grace more than the others have, as Glareano noted. This can be experienced by singing Mi fa sol la. When one descends singing la sol fa mi, one experience a certain cheerful seriousness, which pleases more than the other species, since it seems more than natural to start from a small interval ascending and then coming to a larger one than the other way round. Orators show this, who raise their voice little by little at the beginning of their speeches and do not start screaming at once, as this would appear barbaric and mad. Now, small intervals are commensurable with the soft voice and the large one with the loud one, since the height and the loudness are both produced with greater effort of the vocal organs, while the deep voice and the soft tone in speaking and singing strains the arteries less. However, in descending, it seems to me that the species la sol fa mi is more serious and melancholic, because, starting from the place where it arrived with the tone, it hurtles towards the low register, while the other one, fa mi re ut, starting with the semitone shows the intention of wanting to linger in the high register and for this reason (and perhaps because of other reasons of which we [- <440>-] are not aware) it appears more lively and cheerful. Conversely, the one that has the semitone in the middle, since it is mid-way between those two, we could say that it partakes of one and of the other, and it is less lively and cheerful than the third one, and less calm and majestic than the first one. However, since in everything, and especially in music, the extremes are very powerful, it follows that has the semitone almost hidden in the middle and less highlighted, is more vehement and energetic than the others. This occurs also because it has not that variety that the others have in ascending and descending, because in the first and in the third one the liveliness of the ascent or descent is compensated by the sadness contained in the contrary motion, while the liveliness of the second species is equally apparent both in ascending and in descending, which is so true that one can hear this not only proceeding by step, as one says, through these intervals, but also taking them by leap or in relation to the intervals that are left out or because of some other reason. Hence we hear that this fourth ut fa is more cheerful than mi la, and that fa ut is softer than la mi. For the same reason, the first species of diapente is similar to the first of diatessaron, the second to the second, and the third to the third. The fourth species has the same qualities of the third one but they are stronger, as, for instance, singing fa sol, re mi, fa is so lively that it is somewhat crude, because of those three adjacent tones, and even moving downwards it is more languid than the third species fa mi re ut. I do not agree with Gallilei in believing that, absolutely speaking, the fifth is sad in ascending and cheerful in descending and the other way [-<441>-] round, since I cannot see the difference, except in relation to the middle intervals actually or virtually sung. This intervals can be seen in the minor thirds better perhaps than in any other, because the first species, namely, the one that has the semitone at the bottom, it is cheerful and lively in ascending (re, fa) and malinchonic in descending (fa, re), while the opposite occurs in the second. Moreover, there other two genera differ in some way from the Diatonic, because the third species of the Diatessaron appears to be the most lively and harsh of all, which is placed between the oxypycne notes and is also the Phrygian fourth. The middle one is the first of the Barypycne, which is Dorian, while the sweetest and softest of all is the second of the Mesopycne, which is Lydian. The reason for this is that it has the semitone in the two extremes, just as the reason that the first one is sweeter than the third one is the fact that it has the two semitones towards the lower register, hence the reason is the same that exists between the first and the third diatonic species. The same has to be understood, equally, as to the species of the Diapente also in these two genera, and from the examples shown below and singing these Chromatic fourths one will be able to consider if what I said is true. The same reasoning stands also in relation to the Enharmonic ones. [Doni, Treatise of the Genera and of the Modes, second book, 441; text: mi, fa, la, prima specie nelle corde Barypycne, seconda Mesopycne, terza Oxypycne] As to the intervals of the Tritone and of the Pseudodiapente or false fifth one can learn easily that the first one, ascending either by leap or step, is extremely harsh, hence modern composers avoid it usually with the high b fa, while it is equally languid in descending and in both ways it is hard to pitch. However, the false fifth is soft and tearful ascending and descending by step mi fa re mi fa fa la sol fa mi, and by step it is not different from the Tritone but in the relation of two semitone which make that leap a little more languid and feminine to the imagination of the listener. Since the Diapason is composed of these intervals as its integral parts, it follows from here that its species are the same as the ones which make it up. Hence the first species, which is the one of the Myxolidian, is sad because it begins from the semitone, and because it [-<442>-] sings two adjacent minor thirds, not only is it sad, but soft and languid, and because it ends with a tritone it is very harsh. For this reason, it expresses tears and feminine laments admirably. The fifth species of the Dorian, which is similar to that one and is placed, similarly, among stable and Barypycne notes, is certainly sad, because it has that semitone in the first place, but it is not tearful. On the contrary, it is rather severe and majestic because it begins with a small interval and the, as three tones follow, it seems as if it gains strength. Also, since the tritone is left in the middle, it does not turn out to be harsh, but generous and rather severe. The seventh species of the Hypodorian, Re mi fa re mi fa sol la, partakes of the nature of the Dorian and a little of the one of the Mixolydian because of the two minor thirds in the lower register, but also of the Phrygian, because it continues in the same way. Therefore, this more is very emotional and tearful, but not languid, sad but not austere. The third species of the Phrygian, Re mi fa sol la re mi fa sol, is very close to the Hypodorian, but it is more intense and cheerful because it has the tritone in the middle, unlike the Hypodorian. Its nature can be ascertained through its diatessaron and its diapente, which is the second one considered a little earlier. The sixth species of the Hypophrygian, re mi fa re mi fa sol, because it contains the third species of diatessaron and of diapente, partakes more of the Lydian than of the Phrygian. Since it is no longer a note of the Phrygian, it is lively, but less emotional. The second species of the Lydian, ut re mi fa sol re mi fa, has the above mentioned properties of the third species of fourth and fourth species of fifth, since it is more cheerful and lively than the others. However, because it has the semitone at its high extremity, it is sweeter and beautiful than the Hypophrygian, but not so complete and bold. Finally, the fifth species of the Hypolydian is almost the same because it was the same species of fourth and fifth, but placed in the opposite way. Also, because it has the Tritone, it is harsher from the bottom upwards, and [-<443>-] it is more languid and enervated from the top downwards. Maillard (part 2, chapter 12 in marg.] says that it is difficult to pitch, which is true because of that tritone. It is not severe and grave, unless one intends harsh as severe. [[ma]] non che sia seuero e graue se però non intende cruda per seuera. That the nature and effectiveness of the Modes derives from their own species joined to the Tone that they require. After we have seen what the properties of each species of octave which form the Modes are, there is no doubt at all that when each is sung in its own particular tone, which suits it and is different from the others, it shall be much more vigorous and effective in producing the effects that pertain to each of them. Therefore the modes that are lively and energetic, if they are sung in a tone which is higher and more intense than the natural one, will be much more lively and energetic without comparison, while the languid and relaxed ones, if they are sung in a languid tone and one that is lower than the natural, will become more languid and more relaxed. Conversely, if they are sung in their natural and choral tone they will loose a good part of their nature, while, if they are sung in a tone which is higher and more intense than the natural, they will change completely and will acquire an opposite character. Hence, just as a medicine that has ingredients of a hot nature and is administered to warm up some part of the body is taken cold naturally or it does not produce its effect very effectively, [-<444>-] while one that is taken to cool the body, will do this more effectively if it is cooled artificially that if it were taken hot, the same occurs in music. In fact, in antiquity the modes were sung in tones that were appropriate to them, hence they produced the effects that we read about, while nowadays they are sung all in the same tone, hence they are less effective or work in a way that is the opposite of what they should achieve, and they have almost no effect. We shall demonstrate with examples that this is true. If a melody of the fifth mode is sung with one or more voices, as it is customary, which corresponds to the ancient Dorian as to its species and produces its cadences on e, if there are no instruments, each part shall sing in its natural tone, observing the Dorian Tone, which will produce good effect. However, if the voices will be tuned to a instrument with fix tuning, as a harpsichord – but it will be almost the same in the case with alterable intervals, such as viole da braccio, because the tone is not transposed in its right place, as it should be – id the instrument has the choral tone on D, as it is customary, the voices will sing a tone higher than the natural, so the Dorian mode will be sung in the Phrygian. However, if after this piece, the same singers sing a composition in the species C c, which is the Lydian, without instruments, they will sing in the usual choral tone, but, if they adapt to the tuning of the organ or of the harpsichord, they will sing it two tones under the Dorian and one under the Phrygian, which is exactly the opposite of what one should do. Hence, they will sing a very lively and cheerful species and mode in a relaxed and languid one, and a sad [-<445>-] and gentle in a tension of voice which is energetic and high. Then we are surprised that modern music is not effective at all! However, if, in order to remedy this situation, we wanted to use the species of [sqb] mi on the instrument by adding the b flat in E la mi so that it may have the species of the Dorian, another drawback would follow, because the Dorian melody would be sung a tone and a half under the choral tone and it would be too languid and relaxed. This disorder would occur more significantly in the extreme Tones, because, within the notes [sqb] mi [sqb] mi, it would result languid and soft, while it should be sung in an energetic and driven manner in order to express the acute pain and desperation of who weeps and cries. Therefore, instead of expressing these feelings it would express only a certain languid and lazy sadness. However, everything works out for the best in the ancient tones, because the Dorian, which was born to express constancy and a quiet and calm disposition, as the one of a Stoic philosopher, is placed in the natural tone in which one speaks and converses normally, edging sooner towards the lower register than the higher, as Kings and Judges do they pass a sentence or give an order. A tone of voice higher than the said interval suits the Phrygian because this mode suits who raises one’s voice above its usual tone because of anger or another strong feeling or possessed by a divine and prophetic fury. Therefore, that tone would suit an actor who took the part of the Lord Jesus in some Sacred Drama in the act of banishing the sellers from the temple. However, who is happy and jubilant in an extraordinary way as children do often raises ones voice much higher, hence the Lydian harmony, which is a Ditone higher than the Choral tone, would suit this person. Conversely, those who [-<446>-] erupt with cries and laments because of overbearing pain and desperation, as women do when something said and out of the ordinary happens, they raise their voice even more, hence a tone a fourth higher than the Choral tone suits them, which is the Mixolydian. Moving on to the low ones, those who languish because of tenderness of spirit, excessive pleasure, sleepiness, laziness and drunkenness, are used to lower their voice more than usual, hence the Hypolydian suits them, which is a semitone lower than the Dorian, or Choral tone. The Hypophrygian, which is a tone and a half under the Dorian suits someone who threatens or acts in a scary way because it mixes the low and deep sound with a pompous and threatening species. For this reason, together with the Hypophrygian is assigned often to Heroic characters on stage, since they were deemed larger than men, hence their stature was increased as well as their demeanour. Thus, we can believe that they chose large men with baritone voices to represent them in the best way. Therefore, I believe that this tone, the Hypodorian and the extremely high Mixolydian were not sung by characters with ordinary voices but the first two only by Baritones or deep Basses, and the Mixolydian by contraltos and falsettists in its middle range and as a rule by women and children with very high voices. The reason of this is that nobody will be able to sing well both the extreme tones which are at the distance of a seventh. In fact, if one has a voice that suits the low register, that voice will not suit the high register, and conversely, if one has a high voice it will not be suited to sing low tones. However, every ordinary voice will be able to sing up to two tones above the Dorian. Also, because there is also difference among the tenors and among the other voices, since one will have a higher tenor voice than another one, who has the higher voice [-<447>-] will be able to arrive to the Lydian with some effort, and it will be barely able to exceed the Hypolydian beneath it, while who has a lower tenor will be able to arrive to the Hypophrygian with the appropriate effort, but he will not be able to exceed the Phrygian in the high register, since everyone has eight reasonable notes, and we are referring to tones what will not accept more than eight or nine notes. Moreover, what has been said about the middle part must be applied also to the other ones. Conversely the Hypodorian Tone or Mode is more suited than the Hypophrygian to the Heroes’ laments, since the Hypoprhygian, according to what Aristotle reports, has an active character, hence he says that the Disarmamento, namely that part of the Drama in which Hercules was represented as depriving Geryon of the arms with the Enharmonic, while the Hypodorian has a somewhat passive and pathetic character, hence it is more appropriate to laments (the serious ones though, which befit heroes) than the Hypophrygian, which has the same relation to the Phrygian as the Hypodorian with the Dorian. [-<448>-] On the most evident property of each Mode Therefore, we shall review briefly the nature and properties of each mode and to which matters they are suited according to the authority of good authors and experience itself. Then, we shall report the exact words of the same authors for explain better their work and to reconcile them when there appears to be some contradiction. Therefore, the Dorian is in its true character or property – this is the meaning of that term [ethos] – in serious music, where it is serious and modest, and also suave and mature. Moreover, since it is in the middle, it is adaptable to lively and cheerful emotions as well as sad and relaxed. The Phrygian is energetic and inflamed and therefore, as reports, was represented by the colour red. It was effective in firing up the souls with divine fury and anger and, since it is also of a pliable nature, it can be adapted to sad subjects. Therefore we read . Monteverdi composed the laments of Ariadne with great artistry and proportion in this mode, albeit altered with frequent mutations. [-<449>-] [ small , it will make it softer and plangent than the other two, hence more suitable to tears and lugubrious subject, hence it is not surprising that we read that this mode is in marg.] The Lydian is more cheerful and festive than the others. In short it is naturally suited to dances, which are very often in this mode [[and especially the French corrente]]. It is really lively and cheerful and somewhat child-like and light, hence not very suited to serious and sad matters. In fact, if we read that This was because of the Tone rather than because of the harmony, which had to be also different from the ordinary Diatonic as well. Moreover, since it has the chromatic fourth and enharmonic of this Mode, the large interval between the two The Mixolydian is totally plangent and querulous, and the chief emotions that it provokes are pain and compassion. In short it is suited naturally to feminine laments and cries, and it is harsh as well as languid. The Hypolydian appears to have pleasure as its object. It seems to express a languid and relaxed attitude and one that is provoked by pleasures or drunkenness. Also, since it is the opposite of the Mixolydian and the extremes in music meet each other, it will also be apt to express sad feelings, laments and pain not without reason because in this world excessive pleasure often transforms itself into excessive pain. However, in general it is useful in everything which suits its principal tone. And this equally . Outside of its tone, as it is commonly used nowadays, it turns out almost as cheerful as the Lydian, with which it symo. It is less lively than the Phrygian because it does not have a tritone. Similarly, the Hypophrygian has almost the same nature as the Phrygian, but, while that one appears to have been born specifically to express the sort of divine fury that the Greeks called Enthusiasm, thus this represents instead disdain and anger, it is suits threats perfectly and it is more sad and serious than the Phrygian, thus it appears more manly. However, sung [[in]] As to the Hypodorian, although it suits almost any subject as to its species, nevertheless in a specific sense it is more sad and languid than the Dorian, but with a cheerful majesty and a certain pleasing maturity. Sung by an appropriate voice, it suits perfectly [-<450>-] tragic subjects, because it is somewhat magnificent but also emotional, since it is more emotional than any others and, transposed to the Phrygian, it would produce almost the same effect, although it would not be as lively because it does not have the Tritone, hence, it is also softer than the Dorian. However, when used in the lower range of a singer who does not a very deep voice, it will express the fear and the agony of someone who trembles and who is scared, hence the trembling fear can be ascribed to it among the emotions. However, in order to reduce these differences to their most principal points, one must know that the Greek authors list three different varieties of Melody and Melopoeia. They call one of them Hesychastika [Hesykhastika] from the term [hesykhia], which means quiet. This is the one that does not move the soul at all, but calms it and disposes it in a constant and tranquil state. Its aim is the calming of the soul. They called the Second Diastaltic [diastaltike] (although one reads it described mostly as Diastematic [diastematika] because it adopts many leaps and large intervals which are called Diastemata in Greek) from the verb [diastellein], which means to lengthen. Hence the lifting and dilataion of the arteries that is the vital virtue of the heart is called Diastole. Those feelings that appear to enlarge our hearts, such as joy, delight, courage et cetera, belong to this species. The third species is the one that they call systaltic [systaltika] from [systellein], which means to constrict and restrict. Hence systole means the contraction of the heart and the lowering of the arteries. To this sort belong the feelings that appear to constrict our heart and sap every strength, such as fear and sadness. We can also add the Enthustiastic as a fourth species to these three. In fact, although it may be reduced to the Diastaltic, nevertheless it appears to have a different character and that it pertains more specifically to the attitude of who is irascible, while the attitude of who has strong desires belongs to the Diastaltic and to the Systaltic, since philosopher class under that category [-<451>-] the feeling of pain and sadness, as well as the one of pleasure and happiness. Now, each of the four principal modes belongs to each of these. Each of them corresponds to them perfectly and it is specifically effective in producing the required effects. In fact, Hesychastic music suits the Dorian, Enthusiastic music suits the Phrygian, Diastaltic music the Lydian and Systaltic music the Mixolydian, while the other three are linked to one of the main ones, amely the Hypolydian to the Lydian, the Hypophrygian to the Phrygian, and the Hypodorian now to the Dorian and now to the Mixolydian. However, since one may doubt that the Phrygian is really more lively and daring than the Lydian, because, although its species is more lively than the Lydian, since the Lydian is a tone higher than that one, it will require a much greater vocal tension than that one, and will have to appear much more lively and energetic, to this I reply that, since the Lydian is much too high than choral tone, it cannot be sung easily by someone with an ordinary voice, as the Phrygian can with a little effort, hence, since it is sung by someone with a voice higher than the ordinary and approaches a woman’s voice, not only it will not impress in the listeners the quality of that vehement strength, but rather the feminine property of the voice, which is naturally high in pitch. [-<453>-] That many properties that are ascribed by modern musicians to our Modes are sophistic and imaginary. Apart from the fact that, as I said above and as Gallilei often repeats, our modes have very little and almost no variety between them and little effectiveness in arising emotions, nevertheless many modern theorists attribute to them very singular qualities that cannot be attached to any sort of music, if one judges it correctly, if it is considered without the words, for instance, when we called the sixth Mode, which has the species of the Mixolydian [sqb] [sqb] mode of adulation, deceit and derogatory judgment, which are all categories that denote an attitude so specific that I cannot imagine which combinations of sounds and intervals they may express, if they are not described by the meaning of the words that are sung with or without gestures and scenic movements that illustrate such leanings. I leave everyone to consider if the expression of peace and tranquillity suits this mode considered in its tone. As to the species G g, whether divided harmonically or arithmetically, I do not believe that it can be called lascivious if it is constituted in its own tone. Also, I believe that it is naive to say that a mode is placed under the other according to contemplation, and similar statements that have to much of the abstract and have nothing to do with Tones and semitones, as well as [-<454>-] to say that a type of verse suits one and another type another one, since it is hard enough to pin on them the most general differences. Now, in order to try to reach some definition as to the effectiveness of the modes in moving the emotions through the rules of philosophy, one must know that, just as there are two sorts of material quality, the first one consisting of heat, coldness, humidity and dryness, and the second ones, such as density and rarity, hardness and softness et cetera, which derive from the first ones, thus it follows that the passions are of two sorts, which have their root in the particular complexion of men, namely, from the varied mixing of the four humours, since some are rightly first in order, such as cheerfulness, melancholy, ire and fear, others are second, such as love, envy, shame and so one, because the latter derive from the former, since someone who is naturally timid and of delicate feelings and of good and upright morals will be naturally private and reserved, someone who is timid and naturally dishonest and of dry temperament shall be envious, and thus in the other passions, which do not derive directly from the composition of the four humours, but from the reaction between them and other circumstances of particular passions and demeanours. Hence, it is not reasonable to believe that music alone and naked, namely, without the accompaniment of the text, may have any effectiveness in raising such feelings. However, it will be effective in raising the ones of the first type, because even nowadays we feel that some melody cheers us up and another one saddens us. It is also possible to believe that Alexander, whose character was red-blooded, keen on war and perhaps heated by the consumption of wine, when he heard a melody composed of energetic movements and daring and possessed harmony was moved abruptly to take up arms in his young and martial fury, especially if [-<455>-] at the time something that moved his ire or disdain occurred to his mind. However, that a melody or musical composition without words may represent adulation or move compassion and envy is something that one must not believe in any way. This suffices as far for what concerns the discussion on arising emotions through music. What the authors say on the number and disposition of the Modes. There are some modern writers who have paid much attention to the variety that one finds in the authors who count a larger or smaller number of Modes, and, without taking the precaution of informing the less knowledgeable that those that deal with them ex professo, as we say, do not disagree with each other, while one must not take into account the others who name some or all of them in passing, have almost taken aim to the ancient writers to discredit them in the eyes of those who are not experts, so that they may be regarded as useless and confused and to prove that they cannot be considered otherwise nowadays and that they cannot be used in practice. Therefore, I judge appropriate to demonstrate that the ancients do not contradict each other, and, although there appear to be some disagreement, nevertheless they concord perfectly, when one distinguishes them according to the time when they lived, the school to which they belonged and similar factors. Zarlino [Institutioni, chapter 6 in marg.] noted this difference as well where he places Euclid, or Cleonides, as he may be, Ptolemy, Gaudentius, Aristides, Boethius, Cassiodorus [-<456>-] and Martianus among those who deal with the subject ex professo, while he names Plato, Plutarch, Lucianus, Pollux and Apuleius among the others. I add to these Aristotle, Athaenaeus, Proclus, Iamblicus and other Platonists who wrote commentaries to the works of Plato. Therefore, starting from Plato, I say that, although he names only those six mentioned by Aristides, and not in order, but as he finds appropriate when he passes judgment upon them, this does not suit us because only those were either known or employed in this time, some were called with different names, as we have seen and others were added later. However, the fact that Julius Pollux places the Dorian before any other in two passages, as Zarlino points out, means nothing, because he names only the main ones and he starts from the most dignified. Similarly, the reason why Plutarch mentions the Dorian is because the thread of the discourse leads him towards that direction, rather than because he considered it as the first one in sequence towards the low and high register, since it is only the first one in the sequence of the three main ones. Equally, Cassiodorus in a Letter mentions it before the Phrygian and before the other principal ones, and then in his pamphlet on music he names all the same using the same sequence as the other ones, starting from the Hypodorian and ending with the Hypolydian. Nor does it matter that Lucian mentioned the Phrygian first and Apuleius the Aeolian, because both of them mentions them in passing and as they occurred to their imagination. Martianus Capella begins with the Lydian, starting from the highest of the principals, as Alypius does as well, who does not provide a table in sequence but, starting first from the Diatonic, composes a chapter on the signs that are specific of the notes of the Lydian, the another one on the Hypolydian, a third one [-<457>-] on the Hyperlydian, and then does the same with the Iastian, which is the second of the principal ones going downwards, as the Greeks progressed. Therefore, it is not surprising if Cleonides and Gaudentius start from the Mixolydian, because, discussing only the seven accepted by Ptolemy, they had to start from the highest according to the practice of the Greeks. Apart from these Porphyrion, Horace’s commentator, names the seven modes of Ptolemy, starting himself from the Dorian as the main one, while Censorinus, who wrote the pamphlet ‘On the birthday’, in the passage where he deals with music, mentions the three modes of Aristoxenus. [--] On the nature and property of the Modes according to the ancients. Apart from what we said above, Plato reports in the third book of the Republic that the Mixolydian and Syntonolydian harmonies are plangent and funereal, while the Lydian and the Iastian are relaxed, soft and suited to the banquets. [Mixolydisti kai syntonolydisti threnodeis harmoniai; iasti kai lydisti haitines khalyrai kalountai malakai kai sympoticai]. Aristotle in the third book of his Politics, in the last chapter, distinguishes melodies and harmonies into Moral, Active and Enthusiastic, which we could call divine or inspiring fire in the soul, saying that some were fired up at the sound of the sacred chants which were used in the feasts and ceremonies in honour of Bacchus. He calls similar melodies also [kathartika mele] purifying, because they purified the soul from the affects which disrupted it, prompting it instead to the contemplation of matters concerning the divine. He also says that they produced a joy and a jubilation which was not noxious [Kharan ablaben] in the hearts of men, and that morally sound melodies, such as the Dorian is [tois ethikois ton melon khresteon; toiaute de he doristi], must be employed to educate they young [pros paideian]. He interprets as Moral melody the one that has as it aim not to provoke certain emotions, such as joy or sadness, but to accustom the listener to grave and laudable habits by inducing similar thoughts, and that the Phrygian among the harmonies [-<459>-] has the same power that the recorder or the flute has among the instruments, namely, it has a very daring and war-like character, as it is described by according to Scaligero in his Poetics. This type of flutes produces a sounds which is very close to the trumpet, which is also very Phrygian in character. Therefore, Athaenaeus writes that the Horn (some sort of trumpet-flute instrument) was apt to the Phrygian melodies, as an instrument that resembles the shape and the sound of the trumpet. However, what do we believe that the Musician Agias meant when he states, according to Athaenaeus, that the storax that burnt in the orchestra of the Theatre of Athens during the festival in honour of Bacchus produced a Phrygian smell to the nostrils of the audience? Personally, I would interpret this as meaning that he wanted to express with this metaphor the height and the strength of the smell in comparison to the Phrygian melody, which resembled the Phrygian harmony more than the others, or that he meant the sweetness of the smell which that harmony appeared to him to possess, or that that particular smell was somewhat sacred and represented the festival and the temples, as the Phrygian represents it among the other harmonies. Hence, Theophrastus writes in his book on Enthusiasm, quoted by Athaenaeus, that those who suffered from sciatica appeared to regain their health if someone played near them the Phrygian harmony on the flute. It is certain that in the Dithyrambus, which was a type of composition of a gonfio and allegoric style sung by a choir with the sound of flutes and danced with movements and gesture full of fury and lightness in honour of Bacchus, the Phrygian mode was used for the most part, hence Philoxenus, [-<460>-] who was keen on novelty and on what was unusual, as reports, despite having tried to compose it in the Dorian mode, he was not able to do so, but was forced by its nature to write it in the Phrygian mode. It is also famous the story adduced about Pythagoras (although others ascribe it to Socrates, albeit mistakenly) who, having met one night a young licentious and dissolute an who, excited by the sound of a flute which sounded in the Phrygian mode and inflamed by passion and jelousy, was about to set fire to the front door of a courtesan, ordered to the flutist to change the mode and to play the spondaeus, namely the Enharmonic melody of Olympus in the Dorian tone which was used in the sacrifices, and thus he appeased him completely and rendered him calm. As to the Lydian, Aristotle in the above mentioned passage maintains that it is very suited to children because it has , namely gracefulness and a good demeanour, apart from the fact, I would add, that it is pitched in the high register. [-<461>-] As to the Hypodorian they say [[Ptolemy, book three, chapter seven, confirmed by Quintilian]] that the Pythagorean philosophers (one can note from this that they devoted themselves also to the practice of playing and singing) had the tradition to use the Hypodorian between the day, when they were tired because of their work, and the evening when they went to rest, because that mode invited tranquillity and relaxation. This is not surprising because, being sung in a languid manner by a deep bass, has the power to soften and to induce sleep, since this cannot be achieved with fast and alert movements and Rhythms. Conversely, when they awoke at night and wanted to encourage themselves to their daily work and to their studies, they used to clear what was left of the night obnubilated by the darkness and by sleep. Athaenaeus was right in considering as the Aeolian as to the species, because it was the same, but Zarlino was wrong in believing that it provoked a certain pomposity, haughtiness and high-handedness in the soul of the listener because it is rather soft in nature, and these qualities are opposed to each other, as everyone can realise. As to what some say about the Hypophrygian, namely that he has a character that is opposed to the Phrygian and that Timotheus calmed down and brought to his senses Alexander enthused and prompted by the Phrygian mode to take the arms, and that the Candiotti sounded the retreat with this mode, while they inspired the soldiers to the battle with the Phrygian, I cannot understand how this may stand because the Hypophrygian has no quality that is contrary to the Phrygian, but, on the contrary, it is similar to it. The fact that it has the tone perhaps will render it less possessed, but not completely placid and tranquil. However, considering what Cassiodorus writes on the quality of the modes, in certain aspects he appears to contrast what is curious and strange to what is probable, making Theodoricus King of the Goths write [-<462>-] (more as a licence that with appropriateness) a long digression regarding musical matters in that Asian style of his to the king of the French who had asked him for a Citharede. So, he states: “The Dorian is produces modesty and adduces chastity, the Phrygian invites fights and inflames the mind with madness, the Aeolian soothes the moods of the soul and provides rest for those who are not at peace, the Iastian sharpens the mind of the less intelligent and, as a provider of what is good, supplies the desire of celestial goodness to those who carry the weight of earthly desires, the Lydian was invented to protect against excessive worries and mental boredom, invigorates with its relaxation and fortifies with its attractiveness.” Here one can see that he says that the Dorian mode has the power to preserve chastity because of the story or myth according to which Agamemnon left Clytemnestra to go to the Trojan war under the charge of , a musician, so that he may entertain her with his serious and morally sound singing, and some use this example to demonstrate how upright and virtuous ancient musicians were. If this is true, it should not be ascribed to the specific strength of the Dorian melody but to the prudence and knowledge of the musician and to the laudable teachings contained in the texts that he sang. Similarly, one can gather that Cassiodorus was prompted by what we said about the Pythagoreans to write that the Aeolian, which corresponds to the Hypodorian, calms the mind and induces sleep. However, as to the fact that the Iastian sharpens the mind and elevates the intellect, I cannot find where he extracted this information. In fact one should trust Plato and the others who write that [-<463>-] that mode was tender and appropriate to the banquets, rather than Cassiodorus. However, do let us see what Lucian writes about it in his Dialogue Harmonides, to which he gave the title of the name of a follower of the flutist Timotheus.Therefore, he says that Timoteus reminded this pupil of his that, when he played in this or that mode, he should observe the specific nature of each in assigning its melody, its gracefulness and its timing. He says: [kai tes harmonias hekastes diaphylattein to idion. Tes phrygiou to entheon tes Lydiou to bakkhicon tes Doriou to semnon tes ionikes to glaphyron.], which means: “One must observe the property of each harmony, namely, the possessed nature of the Phrygian, the Bacchic quality of the Lydian, the serious character of the Dorian and the beautiful one of the Ionian.” Apulesius in the first book of the Florida says: Tibicen quidam fuit Antigenidas, omnis voculae melleus modulator et idem omnimodis peritus modificator. seu tu velles Aeolion simplex sive Asium ( read Iastium) uarium seu Lydium querulum seu Phrygium religiosum seu Dorium bellicosum, which means: “Antigenidas was a very sweet flute player, he was able to modulate every smallest interval and the most accomplished performer in any mode, whether you wanted the simple Aeolian, the variegated Iastian (or Asian) the plangent Lydian, the religious Phrygian or the belligerent Dorian.” Here one must make a few observations. Firstly, although Lucian ascribes to the Lydian something of the Bacchic character, it seems more suited to the Phrygian and it appears to have the same meaning as [entheon] or possessed by a God. Nevertheless, it is possible that he interpreted the term Bacchic as cheerful or full or spirit, since the high tone and the tritone that it has in the middle renders it such, as opposed to the two lower ones, the Hypodorian and the Hypoprhygian that do not have it, while the word [entheon] of the Phrygian can be translated also as divine or religious, which is how Apuleius calls it, and does not suit the Lydian because it was not used in the sacred ceremonies. Nor this prevents it [-<464>-] from being also querulous, because its acuteness renders it suitable to laments, particularly those of Lovers, which are not true laments and are not as deep as those that lament deaths and extreme miseries and that were sung with the Mixolydian. Moreover, the word querulous can indicate also high and rapid passaggi on the flute, although they are cheerful in character. For this reason Horace calls the flute querula. That [glaphyron] referred to the Iastian means varied or beautiful, namely, varied with many intervals and ornamented rather than joyful and sweet as Glareano interprets it. Hence, one must me referred to the more recent Iastian or Ionian because the ancient one, which was also used in the tragedies, does not appear such, but, on the contrary, it rather poor and lacking of intervals. As to he fact that he calls the Aeolian simple, I do not believe that it can derive from anything else than from its having to use few notes within the octave and many large and uncompounded intervals which render the harmony large, pompous and haughty, which are qualities that suits it, just as they suit the Hypodorian, rather than tenderness, as we said above. Another possible reason is because it used the diatonaea species in the Diatonic, which does not allow the consonances called imperfect. Hence it must have had little variety in performance. However, as to the epithet of belligerent that Apuleius ascribes to the Dorian, albeit Zarlino accepts it explaining it with the change the modes encountered in some periods because of the alteration of the systems of the nations that used them, nevertheless, although this explanation can be accepted very well in relation to the Iastian, because we do not read the Dorians changed in this way, I would not consider it inappropriate to believe that this does not contradict the other qualities ascribed to it by others, since Apuleius might have understood as belligerent what others called constant and masculine, which is really the basis of courage and expertise in war. [-<466>-] On the notes that the ancients used instead of Ut, Re, Mi, fa, sol, la I could never convince myself that the ancient Greeks, who are renown for their exquisite taste and extraordinary musical expertise, did not have, as we do, certain notes or syllable which they used to pitch the intervals and to practise singing before singing the complete melodies which included the words of their poems. Hence, I observed that the word [teretizein] means in their language the sort of singing that does not include meaningful words, and that, consequently, such singing was called [teretismata] among other meanings of the word, I imagined that they would have used the syllables te, re, re, so much so that I understand that even nowadays on Scyros the same tradition is still alive. Moreover, even the Greeks of our day call [tereuzimous] the melodies of a Flute or of another similar instrument, using a corrupted form of the term. However, in the end I rediscovered the true syllables that they used and I concluded that those syllables te, re, re had been created to imitate the sound of the flute and of similar wind instruments, which, according to the way the tongue hits the palate or the teeth correspond now to the syllable Thus it appears that the ancient used the term [teretizein], namely, ‘teretise’ to mean to sing a melody loosely without meaningful words in the way that wind instruments do and how is is common nowadays with these syllable fa, la, ler, ra, which [-<467>-] derived, as it seems, from the six syllables of Guidone. Also, so that nobody may think that I have invented them myself, I will indicate the book from which I took them, namely the volume marked with the number in the Vatican Library, which contains, among other things some anonymous fragments of authors extracted, as one can see, from ancient and legitimate authors. This volume contains many notable things. Now, just as in our scale, each note has its letter and syllable, thus in the perfect System of the ancients they had just these syllables [to], [ta], [te], [te], which were totally sufficient as they were for all the variety of sounds that one wanted to apply them to. In fact, they followed the very beautiful sequence of the tetrachord, and some touched the stable notes and others the mobile ones. Thus, in whichever mode or tone the Proslambanomenos were called and pronounced [to], the Hypate [ta], the Parhypate [te], the Lichanos (which were called [Diatonoi] in the Diatonic) [to], the Mese [te], the Paramese [ta], the trite [te], the Paranete [to], and the Nete [ta]. These are the exact words of that author, except that the Paranete are lacking in the text, but the text can be integrated easily, because they correspond to the Lichanos, so they must have the same syllable [to]. Now, so that one may see how these syllables were useful and invented incomparably with greater reason than our own, I shall deal with their pronunciation and then of the practice of adapting them to the clefs and of pitching them. As to their pronunciation, care had to be takes so that they would be easy and suitable to be pronounced by everyone, even those who had some speech impediment. Therefore, [-<468>-] they avoided the letter rho, which is harsh and cannot be pronounced by everyone, they sigma, which si equally harsh, the mute consonants which, are drier and less sweet, the aspirate, and, in short, all the ones that had some difficulty, they chose the tau, which was the easiest to pronounce and was common to all the nations. Moreover, in order to avoid any redundant one and the difficulty of following a syllable with another one, they confined themselves to a single vowel. Of the seven they chose the four that sounded better, avoiding the i and the u (which were pronounced like the u of the French and of the Piedmontese half-way between the common u and the i) because of their small sound and the o for its rustic character. Thus, they chose the alpha [alpha] because it has the clearest sound of all, the [omega], which was pronounced as a large o, as in these words Botto or colpo, the [epsilon], which was pronounced as a long e, as in the word cappello and pileus, and the [eta], which was pronunced as a close e, as in capello, capillus. This is of no small importance because certain vowels are so alien from music that the Masters prescribe not to sing passaggi on them because they produce a poor resuult. These are the u and the i. Moreover, Vicentino observed that certain friars [-<469>-] However, as to their application, they entailed none of the difficulties that we experience nowadays in our notes, which, for this reason, make our poor young people waste a lot of time because of the mutations of fourth and of fifth that everyone finds hard to understand, and that require long practice them to apply them effortlessly, once they have been understood. This difficulty has caused some people that I know to be of good sense and intellect to abandon the practice of singing which they had embarked on with great passion. Therefore, some have added the seventh syllable to the six fo Guidone, namely, Si or Bi, to remedy this draw-back, as the very learned Ericio Puteano did showing its application in an elegant pamphlet of his entitled . Others, however, such as Keplero changed them, employing Bo, ce, di instead of these seven. Apart from the fact that these have a barbaric sound which is ill-suited to the Latin language and to its daughters, the French, Italian and Spanish languages, and htat they often use the letter i which is unpleasant, they do not avoid all the difficulties and drawbacks either, for instance, in passing from the [sqb[] to the b flat, since in that case two syllables are needed in the key of the B and in its neighbour, in making a mutation from the natural notes to the accidental ones, namely from a tone to the other one, where one does not sing a different syllable, as one should, and without mentioning that the chromatic notes are marked on the same Diatonic one, which produces great confusion. All these kinds of disorder were avoided in the ancient tablature and syllables because there was no need for any mutation [-<470>-] either upwards or downwards, except in passing through the conjunct notes, which was done with great clarity and order, because, whereas in the disjunct, namely through [sqb] square, we say re mi and through the conjunct ones or through b flat we say la fa, they used to say [te] [to] through the disjunct and [te] [te] through the conjunct ones, changing only a syllable and indicating also the conjunction of the tetrachord as well as the proximity of the note with a vowel of similar sound. Hence, according to their method, they did not encounter the difficulty of the mutation of fourth and fifth and of ascending or descending. Also, in the passage from the conjunction to the disjunction, the same series of syllables represented immediately to the imagination the interposition of another tetrachord amid the tone of the disjunction and the transposition of said tone a tetrachord higher, as one can see here: [Doni, Treatise of the Genera and of the Modes, second book, 470; text: A, B, C, D, E, F, G, a, [sqb], b, c, d, e, f, g, a a, re, mi, fa, sol, la, [to], [ta], [te], [te], Tetracordo Hypaton, Meson. Diezeugmenon, Hyperboleon] [-<471>-] Moreover, they expressed the transposition of that tone outside of its specific position by the fact that two [ta] followed one after the other. The species of the consonances are also distinguished with these syllables because the first species of fourth is called [ta] [ta], the second [te] [te], the third [to] [to], the first of the fifth says [ta] [te], the second [te] [to], the third [to] [ta] and the fourth [te] [ta]. It is considerable in this sequence the different syllable that the three clefs Proslambanomenos, Mese and Nete Hyperboleon have, which, because they are located at the distance of one octave, it seems that they should have the same syllables as the others. Nevertheless, the ancients named them differently, so that, since they were stable notes, there could follow no confusion, as in the case of the mobile ones. As to the fact that the gave the Mese the privilege of its own syllable which was not common to any other, I believe that this is due to the fact that it is regarded with particular consideration in the connection of the modes and it is used more than the others. Hence it was appropriate that it should have its own syllable, so that one may not employ another one instead of it when passing from a mode to the other, and so that the note of median tension, around which the melodies coalesce, might fall always onto it. It is also necessary to differentiate it from the Nete as, since the Paramese must have the same syllable [ta] in the disjunction, one would have encountered two [ta] one after the other. Therefore, to avoid this, we make the mutation in the second tetrachrod by saying sol, re, changing that one to G and this one to a rather than mi. Then there follows the mi of [sqb] hard. For the same reason it was necessary to ascribe a different syllable to the Proslambanomenos so that one may not start a tetrachord in the same way as the Mese does, progressing through the disjunction. Thus, it could not have the [ta] of its corresponding Nete Hyperboleon, since the Hypate next to it had it. However, they did not ascribe to it the syllable [te] because only the mese shall have it as its distinctive sign, or in order for it to have the same syllable as the other fourths, since it sounds a fourth with the D Lichanos Hypaton. Hence one can gather that the entire disjunct System uttered with our own syllables according to the ancient practice would say Re, Mi fa, Re, Mi, fa, Re, La, Mi, fa, Re, Mi, fa, Re Mi and the conjunct System or through be flat would correspond to the sequence of syllables Re, Mi fa, Re, Mi fa, Re, la, fa, Re, Mi, Mi, fa, Re, Mi. In this way one would do without the two syllables Ut and Sol, and those who do not like to utter two Mi one after the other could pronounce the mese a la through [sqb] hard, as it is here, and Mi through b flat, and the Nete Synemmenon La instead of it. Thus, a single note Mese would have a different syllable in the sequence through [sqb] hard and b flat, because the Nete Synemmenon, to which we shall assing the la albeit it is different in name from the Paranete Diezeugmenon, does not differ in sound. One could remedy to this inconvenience by assigning to the Paramese only the note la, reserving the mi for the Mese, the ancients had to distinguish better the mese. In short, who wanted to correct the scale, in my opinion, would have to leave out two syllables as redundant instead of having to add a seventh syllable, as some did, as frustra fit per plura et cetera, and because this tetrachord, among the others, is so beautiful that without it one could not restore music to its ancient splendour. As to the six syllables of Guidone of Arezzo, it is certain that he discovered them almost by chance while singing that Hymn to Saint John the Baptist Ut queant laxis, taking them all from the first strophe, which was later done so much better. He reports that he found them with the exact distances as they occur nowadays in the System and as they say that they are sung in the Gregorian chant. Hence one should not believe that he selected only these because of the perfection of the numbers six as Signor Puteano conjectures (who was devoid of any speculative preparation) or because he had prescience of the twelve Modes, as Maillard states in order to certify them with Guidone’s authority, although each sillable is like the foundation of two. [-<472>-] On the Difference between the ancient Modes and ours. Firstly, one must note that the species that Glareano and some others before him to the seven principal ancient modes are mainly the ones that are opposed to the true ones, as one can see from the illustration placed here, in which the parallel modes have the same species. As one can see, only the Hypodorian has its very authentic one, while modern writers asscribe the one of the Mixolydian to the Hypophrygian, and, conversely, the one of the Hypophrygian to the Mixolydian, and the same occurs in the case of the others. [Doni, Treatise of the Genera and of the Modes, second book, 472; text: Modi degli antichi, de Moderni, Mixolydio, Lydio, Phrygio, Dorio, Hypolydio, Hypophrygio, Hypodorio] [-<473>-] However, as to the difference between the ancient Modes and ours, one must note first of all that they had their firm and stable tension of foice from which they did not depart ordinarily, since each had wind instruments suited to it, while ours are sung ordinarily all in the same tone of voice, and, although they are varied, this happens accidentally and without any order or rule, in such a way that those that should occur in the low register turn out in the high and the other way round. Secondly, the ancients had a system of fifteen notes, so that each could sing the entire span of one’s voice without changing mode, while, since ours contain only eight notes, this cannot be done. In fact, if one exceeds the limits of the octave, one exceeds the limits of the mode as well. Thirdly, they all had (I mean the seven main ones) a specific species of diapason, hence their melodies could be varied in as many ways, while five of our twelve modes do not differ as to their species but are completely identical. The fact that they have the fifth above or below is only a nominal difference rather than an actual one because, when one sings in the two extremities of the octave, one takes the fifth and the fourth above and below when there is, while, in compositions for several voices not even this difference is observed, because it is preferred to place the fifth in the lower register rather than the fourth, albeit the species requires the fourth. It follows from this that a composition for several voices is always considered to follow a variety of modes, although in practice it belongs only to one. [-<474>-] Fourthly, the ancient modes differed because of the variety of the cadences, leaps and stepwise movements which were within the limits of thier fifths, fourths, sixths and so on, and one can believe that they employed the longest notes on the main notes. Our composers, on the contrary, observe these rules hardly at all and the modes are distinguished barely at all by anything else except the final note of an individual part. Fifthly, the ancients sung and played their Modes often pure and simple, while we never do that in figured music, because all the compositions that have accidental signs apart from the [sqb] and the b flat in their key signature exceed the boundaries of the mode. Sixthly, the ancient did not consider the act of moving from the [sqb] square to the b flat a change of mode, or the other way round, while we do, but it is not true. Seventhly, the ancients could sing some verse or some small section of a composition in a mode, make a cadence and then move on to another mode for many bars and make its own particular cadence which were different from the ones of the first mode and then change to other modes when they wanted, and this produced great variety and delicacy in their music, while we do not know any mutations other than to grasp confusely and without a rule a note of one mode and another one of another one without being able to continue in the mode into which we move or making its cadences. On the contrary, all the mutations that one does consist simply in taking some note of the higher or lower mode, which is at the distance of a semitone from the principal which is our original theme. In this we are not able to proceed orderly, or, on the contrary, we believe that we are mixing the Diatonic and the Chromatic in doing that, which is not true. Eightly, one can believe that in the ancient modes the intervals of fourth, fifth and sixth were not employed ordinarily except among their specific notes according to the species of each of them, and, equally, that the passaggi were not made except within intervals contained by two principal notes of the mode. [-<475>-] As to these accidental differences, I shall discuss one that I extract by conjecture, while I shall discuss the other ones in the discussion of the practice. Therefore, I believe that this consists in the strength and in the density of the voice and in its opposite, which is the week, even and languid voice. Therefore, there can be four varieties of it, one which is strong throughout, a second one which is weak and relaxed throughout, a third one which is relaxed to start with and strong at the end and a fourth one strong at the beginning and relaxed at the end. The first one suits the Phrygian, the second one the Hypolydian, the third one the Dorian and the fourth the Lydian. Aristotle seems to hint to this in his work [peri akouston] where he says that, when the trumpet was played in the entertainments and in the banquets, this was done with relaxed and sweet sound, while in war and in battles the trumpet was played with a strong and forced tone. Eighthly, the ancient modes, at least the more general ones had a different colour, which means that they had a great variety in the same intervals of a single genus, namely, in making the semitones larger or smaller, while this is not practised in ours. This cannot be done in singing, if not by mistake or because of the difference among the instruments. Ninthly, various Rhythms, different ways of proceeding and making cadences, different ornaments, accenti and similar features occurred, which, although they were not essential to the modes and could be left out, nevertheless, since each mode had its use and was applied to a particular sort of music, normally these differences were observed. Tenthly, the ancient modes had more variety in the Chromatic and in the Enharmonic than in the Diatonic, but, following the ideas of some modern writers who had the intention of restoring these genera, one cannot see in them any difference from one mode to another one. Eleventhly, the ancient modes had specific signs and a separate system or scale so that they could be employed and swapped with ease and coherence. This is hard in our modes, because they have all the same System and the same notes. Twelfthly, the ancient Modes, since they are only seven, contain many beautiful correspondences and secrets, not only because of the property of the number seven, but because of many other things that have seven notable differences. [It is probable that those seven ancient Modes were sung often pure and simple, while those that have the species of F fa ut and of [sqb] mi among our own are not usually sung as they are, because the Tritone that occurs in the extreme part of a melody is always sweetened as a rule by changing the mi to fa. in marg.] However, our modes, whether they are eight or twelve, have very few secret qualities and they can be associated with few physical differences. The mutations of the ancient modes illustrate even better their sympathies and antipathies between them, as one can see from the illustrations of the chapter. [-<476>-] That the properties of the Modes are recognised also nowadays in the song of individual nations. Although, as I mentioned above, a great mixture of languages, traditions and, consequently, of singing styles has occurred because of the mixing of different populations and of the domination of a nation on others, nevertheless we can also recognise a great difference between a nation and the other, because of certain stylistic features and melodies that have great similarity with the principal modes practised by the ancients. In fact, to mention some of the main ones, we see that the natural melodies of the inhabitants of Tuscany and Rome preserve a very grave and majestic character of the galliard which is specific of the Italians and a particular type which is the Romanesca, which I consider to have been invented a few centuries ago, as it is the calata, an ancient Florentine dance still in use, and the ballo del Granduca, although it was invented by Signor Emilio del Cavaliere, a Roman gentlemen. Therefore, perhaps the Dorian is the most suited to these, while the Iastian appears to suit very much the peasants who work the land, whose melodies and villanelle, as the ones popular in Naples show, have a more tender and dissolute character both in the Rhythm and in the Melos. As to the Rhythm, Don Nicola reports that the Neapolitan villotte require speed at the beginning, which matches the Ionian verse which starts with two short syllables and are followed by two long ones. As to the Melos, they are used to tune the semitones that occur between the notes altered by accidents smaller on the harpsichord, because they sing them in that way as well. The Aeolian Harmony [-<477>-] possesses gravity together with a certain pomposity and could be associated to the older Spanish population of the north of the country (as the most southern ones, which are really inhabitants of the mountains and of the countryside, as they say, have absorbed a lot from the singing style of the Mores, and have a more effeminate style as their gavottes and sarabands show). These northern Spanish populations invented the Pavaniglia, a very slow and majestic melody, which Harmony would also suit the Portuguese, as I mentioned above, because of the language. In fact, if someone associates the Dorian Mode to the Spanish nation and the Aeolian to us, because of the severity shown by the Dorian and because the ancient Italian blood was more mixed with the Aeolian nation than with the other Greek ones, as Dionysius of Halicarnassus illustrates (something which Glareano could not understand) in my opinion one shall be right to do so, since I regard this as very appropriate, even more so because, as I learned from some Greek people, they regarded our way of singing pompous and haughty, regarding the Turkish one, which is more melancholic and relaxed, as sweeter. However, I would believe that they were very opposed in taste to their ancients in this respect. The Phrygian mode is so well suited to the German nation that no other would suit it better. Therefore, it is not surprising if they love wine so much, while the Phrygians worshipped Bacchus above all the false gods of antiquity. Hence, both nations are fervent and impetuous, but the Frisian nation (one of the most ancient and intact of the German nations) than the Phrygian. [-<478>-] It persuades me with this not only the fact that their Choral tone is a tone higher than ours, which appears to be the Dorian, but also the character and melody of their compositions, as one can gather from some Almands (this is the name of certain German compositions of cheerful character which are very popular in France) printed by Claudio Jacollot of Lyon, which are mostly in the species of D la sol re. However, the Lydian is more suited nowadays to the French than to any other nation, because of its lively and cheerful character and for its natural inclination to the dances, for which it is more suited than any other. Hence, almost all the dances, and especially the French ones, are written in the species of C sol fa ut, which is characteristic of the Lydian. Finally, the Myxolydian mode is eminently suitable to the Sicilians, whose compositions are normally plangent and very similar one to he other. [-<479>-] What species or Mode is more frequently used nowadays and in which Instruments. If we consider the tunings of the most noble and popular Instruments used nowadays, we shall know manifestly that any other Mode, except the Dorian is sung in the Choral tone and that the Phrygian or the Lydian (which are the most popular ones, and especially the first one which is considered almost universally as the most beautiful of all) are used instead of the Dorian, because the note D la sol re is normally exactly in the middle of the keyboard of the organ and of the harpsichord. Therefore, if these instruments are tuned correctly as it is right, said note will correspond to the middle note of a tenor. The tuning of the viols as well convinces me of this, because it is applied to the top string and to the sixth one of the soprano and of the bass. Equally, in the lute the disdiapason [the six main strings in marg.] occurs between g solre ut and gg sol re ut, which are the ones of the Hypophrygian, subordinate to the Phrygian. On the other hand, it would appear that the Lydian species applies commonly to the Choral tone because the clef of C sol fa ut which represents the Tenor when it is placed in the middle line, as it is often, appears to show that the middle note of an ordinary tenor should have corresponded to that position. However, in the System of twenty notes from [Gamma] ut to e e la mi, one could take D la sol re as its middle note instead of C sol fa ut, if it is reduced to twenty-one notes as . Thus, since it is placed appropriately inte middle between the highest and lowest notes of the human voice, it will correspond to D la sol re placed above C sol fa ut, which is indicated in the melodies. We can also believe that the Phrygian is the most [- <480>-] perfect of all because of its property of maintaining the same species, namely the same disposition of tones and semitone both upwards and downwards, as one can see here: [Doni, Treatise of the Genera and of the Modes, second book, 480; text: D, E, F, G, A, [sqb], c, d, Tono, Semitono] [-<481>-] On the excellence of the Modes compared one to the other. If we consider the Modes located in their own place and tone as they were in antiquity, there can be no doubt that the Dorian is the most noble and excellent of all because it is located in the most natural tension of the human voice and because it appears to be neither languid nor forced. However, if we consider them separately from the Tone and only in their species, it will not be so easy to determine this, because, on one side the Dorian shall be superior with its severity and sweet melancholy and on the authority of so many great men who thought it so great, on the other side the Phrygian will be superior because it is placed between the Dorian and the Lydian and because it is more suited to express the contrary feelings of joy and sadness than the other two, going on the authority of Boethius who calls it Prince of all the others. This effect is more natural and more commonly regarded as pleasant by almost everyone that it is not easy to decide this matter. All the more that, if in any field human taste is more varied, this happens especially in music, hence everyone shall judge this question according to one’s own inclination and complexion. As for myself, should I have to cast my vote, I would side with modern composers and would judge in favour of the Phrygian because of that property if it to partake of the extremes, although it is very considerable the property of the Dorian to have the Tone of the Disjunction right in the middle between the two tetrachords, which is something that proves very useful, apart from the fact that, when applies the numbers in this species, the proportions are easier to find. Therefore the three principal and most ancient tones which derive from the variety of the Diatessaron are certainly the most beautiful and perfect, firstly, because they do not lack the Tritone, such as the Hypodorian and the Hypophrygian do, which for this reason [-<482>-] are languid, and because they do not have it in their extremities, such as the Mixolydian and the Hypolydian have, hence they prove harsh, but because they have it in the middle, which renders them lively without harshness and sweet without being languid. In second place I place the Hypodorian and the Hypophrygian because it is better not to have the tritone at all than to have it in the extremities, and because they have the diapente and the diatessaron under and above, which does not occur in the other ones because the Hypolydian has the diapente in the lower position and the diapente above, but not the other way round. Therefore, I believe that these two are the worse of all, although each is considered beautiful on its own merit. Moreover, the modes that have a tritone in one extremity consequently have the Pseudodiapente in the other one, hence, in one respect they prove too harsh and in another they appear too soft, so they are not as well harmonised as the others. However, the Hypodorian and the Hypophrygian, although they have not got the Tritone in the middle, neverhteless they have the Pseudodiapente or two minor thirds adjacent to each other, which render them more melancholic and tender. [-<483>-] On the notes that distinguish the Modes. The notes that distinguish or characterise the modes can be described as the extreme notes of the Diapason of each of them and the syllable that sung above them. In the Hypodorian they are Re La, in the Hypophrygian Ut sol, in the Hypolydian Fa fa, in the Dorian Mi la, in the Phrygian Re sol, in the Lydian Ut fa and in the Mixolydian Mi mi. Therefore, we can consider that the modes that have some notes in common have one of those two notes in common, such as the Re in the Hypodorian and Phrygian, the Sol in the Hypophrygian and Phrygian, and the La in the Hypodorian and Dorian. The Hypodorian is a mixture of the Dorian and of the Phrygian because it has the Dorian Diatessaron and the Phrygian Diapente. The Hypophrygian is a mixture of the Phrygian and of the Lydian because it has the Phrygian Diatessaron and the Lydian Diapente. The Hypolydian is mixed with the Lydian because it has the Lydian Diatessaron but its own Diapente. The Myxolydian is related to the Dorian because the Diatessaron and the Diapente are the same but with the order inverted. The Hypodorian with b flat or with the conjunct tetrachord turns into the species of the Dorian, the Hypophrygian turns into the Phrygian, the Hypolydian into the Lydian, the Dorian into the Mixolydian, the Phrygian into the Hypodorian, the Lydian into the Hypophrygian and the Mixolydian into the Hypolydian. In this way they can be turned always circularly one into the other. However, if we consider the form that a tone takes by turning it upside down, we shall see that the Hypodorian becomes Hypophrygian, the Hypophrygian Hypodorian, the Hypolydian Mixolydian and the other way [-<484>-] round, the Dorian becomes Lydian and the other way round, while the Phrygian stays the same, as I mentioned above. This corresponds admirably to the property and the emotional character of each, since fear is ascribed to the Hypodorian, which is the opposite of courage, which is ascribed to the Hypophrygian; pleasure is ascribed to the Hypolydian, which is the opposite of pain, typical of the Myxolydian; gravity and sadness are ascribed to the Dorian, while their opposite, lightness and joy, are assigned to the Lydian. Finally, the enthusiasm or divine fury proper of the Phrygian has no opposite. Therefore, the following illustrations will be useful to remember which mode has the diapente and the diatessaron in common with which one and with which one it is similar or to which one it is opposed or is derived from changing to the conjunction. [-<485>-] That the seven Modes match the seven principal climates and that on their sympathy with the four complexions. Ptolemy, who not only was a very subtle Mathematician, but also a very profound philosopher, as one can see from his works, not only compares the diversity of the modes with some general differences of habits, as one can see from the sixth chapter of the third book, but he also compared the Modes themselves with the course of the planets according to whether they deviated more or less from the centre which is the line of the equinox to which he ascribed the Dorian and the approach more closely one of the tropics in which he placed the extremes of the two modes Myxolydian and Hypodorian. This proceeds ingeniously and pleases the mind, but, since human music (since we cannot discuss here the music of the Universe, which is metaphoric and imaginary) must be considered principally in relation to human nature and to the diversity which is found in the traditions and feelings, namely, in the individual and in entire nations. Perhaps we shall be able to compare together with greater success one of the seven modes with one of the seven main climates of the earth, to which not only the different distances from the Pole and from the equinox are determining factors, but also the variety of natural characters of the populations which inhabit them, with this greater level of coherence than in Ptolemy comparison, because, since the two tropics are similar between each other in his comparison, it does not appear successful to ascribe the Mixolydian to one of them [- <486>-] and the Hypodorian to the other one, which are one very high and the other very low in pitch. Therefore, it will be more plausible to ascribe the first climate to the Mixolydian and the seventh to the Hypodorian, imagining then that they are repeated in as many climates towards the Antarctic, since that other hemisphere is similar to our own as to the lay-out of the sky and of the circles. Therefore, the first climate is the one of Meroe according to the ancient and modern Cosmographers. It derives its name from a famous town and a city of the Nile in Ethiopia through which has its circular parallel removed from the Equinoctial degrees, which is the amount of hours more than the equinoctial, which is the longest day of hours. The Myxolydian tone, which is the highest of all, suits this climate perfectly since the celestial Axis produces the most acute angle with the horizon and the observation of the Pole is minimal. Moreover, the population who live in the parts of the world characterised by this climate, such as the Ethiops the Arabs an the Indians, have very high voices and of feminine nature. The second climate is the one of Siene, called nowadays Asna, a town situated in Egypt, but at the border with Ethiopia, under the tropic of the Cancer, hence the sun in the day of the solstice produces no shade in the middle of a stile because the sun is at the Zenith, hence Lucan says “and Siene that projects no shades in any place”. Consequently here the longest day exceeds twelve hours of . The Egyptians, a joyful people and fond of singing and dancing and much love-making are associated with this, hence the Lydian tone suits them very well. The third climate crosses Alexandria by the sea, an Egyptian city where the longest day spans more than twelve hours and crosses the Numidia and Mauretania, which are the main provinces of Africa, [-<487>-] whose populations, according to Cicero, Leone Africano and other authors, are litigious, irascible, belligerent and very superstitious, hence the Phrygian tone suits them very well. The fourth one crosses Rhodes, as the day of hours and suits the Dorian admirably, not only because Rhodes itself was a Dorian province, but the Peloponnese, Crete and the most part of the Dorian populations belong to this climate as well as Spain, which is home to populations of Dorian traditions or serious and severe. The fifth one, which crosses Rome and the strait of the Hellespont, has the longest day of hours and corresponds admirably to the Hypolydian tone, not only because, as we said already, this is the same tone used nowadays in Rome, but also because it crosses Asia minor and the boundaries of Lydia itself and large part of the Tuscany, inhabited already, according to the opinion of several writers and, according to Athaenaeus’ account, by many nations very fond of pleasures that they even whipped their servants to the accompaniment of the sound of the flute. The sixth climate is the one of the Pontus, which crosses Lombardy, Lyon in France, Thrace and Constantinople, whose nations has something of the savage, belligerent and threatening, hence the Hypophrygian tone suits them perfectly. Finally, the seventh and last climate is the one that crosses the estuary of the river Boristene, which is called Edel and divides the Podolia from the Tartaria minor. Its longest day is and is inhabited by nation which are partly pompous and haughty, such as the Germans of the north and the Sarmatians, and in part melancholic and saturnine, such as the Tartars, the Muscovites and the original Turks, hence this climate corresponds perfectly to the [-<488>-] Hypodorian tone in itself and because it is similar in its species to the Aeolian. However, as to the four different complexions which constitute the greatest differences that can be compared to the four main modes, the Dorian suits the melancholic complexion, the Phrygian the choleric, the Lydian the sanguine and the Mixolydian the phlegmatic. [-<489>] On the correspondence between the seven Tones with the seven Planets. It was the opinion of Pythagoras and of his followers that the celestial bodies, in their movement around the earth, produce, in doing so slowly, a marvellous and incomparable music which, although we cannot hear it, they maintained that this derived from the continuous habit of hearing it, and that this is why we cannot hear it. This opinion has been related by many ancient writers and very elegantly by Scipio Africanus quoted by Cicero in the sixth book of the Republic, where he tells the Dream that came to him in Africa, and this was the subject of a learned commentary by Macrobius. There was disagreement about ascribing the low and high sound to the species above or below, because some thought that the high sound was produced by the highest spheres because of their greater speed, since they presume, with most of the ancient philosophers, that the high sound is produced by high speed and low sound by low speed. Others, on the contrary, did not consider speed but only the size of celestial bodies, hence they maintained that sky the moon produced the highest sound and the sky of Saturn the lowest. This seems to be what Plato alluded to in his Republic, when he assigned its siren to each celestial Sphere, while some others ascribed to each of them one of the eight Muses, while they considered the music that is born of the other eight as the ninth, as Macrobius explains. However, leaving aside these considerations which have too much of the poetic, it has to be known that opinions on the [-<490>-] distance between each sky and the earth and on the depth and sequence of the planets were, and still are, varied. As to the order of the skies, it appears that the opinion of Pythagoras and of the Chaldeans who invented astronomy was universally accepted. They place the sun at the centre and the other planets, as it done commonly. However, they compared the seven modes with the seven planets with great reason because they had observed that the property of the former correspond perfectly to the latter. Pliny explains the matter with these words, which I shall quote as they are because they contain some difficulties. Therefore, this is what he states at chapter twenty-two of the second book: “But Pythagoras sometimes defines with musical proportion the distance from the earth to the Moon. From the Moon to Mercury there is half the distance and from Mercury to Venus there is the same distance and from which to the Sun there is one and a half that distance. From the sun to Mars there is a Tone, which is the same distance from the earth to the moon, from Mars to Jupiter there is half the distance and from Jupiter to Saturn is also half and it is one and a half from Saturn to the sky of the Stars. Thus six tones are completed, which they called the Harmony of the Diapason, namely the complete system of sounds.” This passage suffers from this difficulty that if one adds up the intervals mentioned by Pliny, the result is seven tones, rather than six, namely a ninth rather than an octave. Giorgio Valla believed to be able to solve the conundrum by referring that one and a half not to the tone, but the Semitone, interpreting it as three of the four parts of the Semitone. However, apart from the fact that in this way they would add up to five tones and a half, rather than six, I do not like this entire explanation because the tuning of this System would be neither Diatonic or Chromatic or Enharmonic, but completely irrational. [-<491-] however, if we want to apply well the Seven Tones to the Planets, let us remember that their order was not completely stable and certain according to the ancients. In fact, it seems that the Lydian was placed above the Phrygian and the Phrygian itself above the Dorian and the ones that have the prefix Hypo- had the same distance under their principal ones. The rest, it seems, could be laid out in various ways, as long as there was some reason do so. Therefore, if one assigns the lowest sounds to the highest and largest spheres, as it is reasonable, and starting from Saturn, it seems necessary that one should ascribe the Hypodorian to it, which oversees fear, laziness and the melancholy which is typical of older people and that suits the Hypodorian Harmony. Then, we shall apply to Jupiter the Dorian instead of the Hypophrygian, which symbolises the virtue of that planet, which prompts one to great and majestic works. We shall attribute the Hypophrygian to Mars, as it is somewhat threatening, courageous and active, hence it suits the enterprises of war, while we shall attribute the Phrygian to the Sun because of its warmth and strength, and because it was commonly regarded as Bacchus himself, to which he Phrygian and the sun were dedicated. We shall assign the Hypolydian to Venus, since this mode, as we said, expresses pleasure and joy, while the Lydian will be paired with Medcuty because it is high and cheerful, and it is represented as subtle and young in age. Finally, we shall ascribe the Mixolydian to the Moon, because it is a humid planed which rules the night and this tone inspires tears, expresses the pain that occurs at the corner of every door, so speak, during the life of a man, [-<492>-] since children burst into tears as soon as they are born and they feed on tears, so to speak, for a long time. This planet governs our birth, according to the opinion of all the astrologers. Therefore, just as the ages of man have a particular planet that governs them, thus they have one of the Seven Tones that suits them more than the other. Therefore, the Myxolydian suits infancy because of the above mentioned reason and because of the hight pitch of the voice up to the age of seven years. The Lydian suits the childhood up to the age of fourteen because it is a cheerful age and suited to acquire the principles of all the arts and the sciences, and, in short, it is ruled by Mercury. The Hypolydian suits adolescence because one is more sensitive to sexual urges and devoted to the pleasures, up to the age of twenty-five years. The Phrygian suits youth because physical strength is at is peak. That age is suited to military training and to withstand the strains of war. The Hypophrygian suits the mature age because that age is not only suited to carry on the activities of war and to obey orders, but also to command armies, and it spans up to forty-five years of age. The first part of old Age, or greyish age, suits the Dorian and extends up to the age of sixty-three, because gravity and coherence of demeanour is most suited to that age, and it is apt to judge, to govern and to refrain the boundless youth. Finally, the Hypodorian suits old age upt to seventy years, because that age is subject to the proprieties and passions mentioned above. Also, since after the seventh tone one goes back to the first one, as it occurs in the days of the week, which are also subject to the planets, thus one continues circularly to the eighth tone, of one wants to add it, which shall be the same as the Hypodorian or Myxolydian and will express perfectly the decrepit state [-<493>-] of those last years when old people almost repeat the journey of their life. We describe this process as becoming a child again, or repuerascere in Latin. This confirms the ancient proverb Bis pueri senes, which means, “old people go back to being children”. Moreover, since who has reached this term can be said to have completed his Diapason, after which one enters into an order completely new, nobody can tread beyond this point. [-<494>-] On the correspondence between the Tones and the main colours. So that we may not overlook anything that may shed light on this subject of the tones, we shall draw up a comparison between them and the colours, which, after the sounds, are the qualities more able to express the changing habit and property that the Greeks call [ethos]. Therefore, I state that, just as the low tones, according to Aristotle and on the basis of experience, contain the high ones, thus the colour black contains the white. Therefore, it is appropriate to assign the colour black to the lowest lour and the white to the highest one. However, since the main tones are seven and the elementary colours, namely, the ones that make up the others and are not made up by any others themselves, are six in my opinion, and they are the white, the black, the yellow, the red, the green and the blue, it follows that from the mixture of the first two, which are the extreme ones, another one is created, which belongs to the secondary colours, namely those which are made up by two elementary ones. The first one of these is the Grey, to which we shall assign the Mixolydian, because it is the colour of sadness, bereavement, penance and pain. We shall assign the white to the Lydian, because it is described as a clear and cheerful tone, the red to the Phrygian, following in this the authority of the ancients, who described it as we said above. This colour is more intense than the other and expresses ire and warmth. We assign the yellow to the Dorian because it resembles the sun, which is in the middle among all the planets and because that colour has a certain hidden sadness, and the green to the Hypolydian because it is the most pleasing of all, hence tired eyes are refreshed by it, [-<495>-] the blue to the Hypophrygian because of the correspondence between this colour and the red and because it has a certain profound cheerfulness engrained in its character and mixed with great gravity and decency, and the black to the Hypodorian because of its profundity and melancholy, hence deeps sounds, as well as dark colours, represent darkness. However, if we want to leave black and white aside as elements of colours rather than colours in their own right, we will be able to assign to the modes the main mixed and secondary colours in this way: the gray to the Mixolydian, the green to the Lydian, the red to the Phrygian (as no change is required here) the orange to the Dorian because it is deeper than the yellow but represents the sun as well, the aquamarine, called the Venetian colour by the ancients, to the Hypolydian, so that it may resemble the Lydian, as this mode resembles the colour green, since it is a mixture of green and blue, and finally the purple to the Hypodorian, because it relates somewhat to the orange and because it is a grave and majestic colour and typical of the purple dye, which in the most ancient times was reserved for great personalities. Alternatively, we shall be able to assign the grey to the Mixolydian, the yellow to the Lydian, the red to the Phrygian, the blue to the Dorian, the green to the Hypolydian, the aquamarine to the Hypophrygian and the black to the Hypodorian. In fact, should we want to accept even the tertiary colours, we shall be able to assign one of them to each of the thirteen modes of Aristoxenus or to the fifteen of Ptolemy. Therefore, we were saying that the secondary colours are the ones that derive from the mixture of two primary or elementary colours in equal measure, while the tertiary are the ones that are made up of two of those mentioned above, or by the equal [-<496>-] mixture of three of them. In fact, the secondary ones are the aquamarine, which is composed of green and blue, the orange, which is made up of red and yellow, [[the Incarnate of Red and white, the pink colour of red and green, the hay-ish colour of white and yellow, the turquoise of white and blue]], the green-yellow of the colours contained in the name, the purple of red and blue, the ground colour of black and yellow and the grey of white and black. However, the tertiary ones are the turquoise, which is mostly blue with a little white, the incarnate that is mostly red with a little white, pink which is mostly red and a little green and the hay-ish that is mostly yellow with a little white. We shall say that we should give the primary colours or the secondary to the principal tones and the tertiary to the others, preserving the property of each, so that the subordinate tones have a colour corresponding to the one of the principal ones and the high tones have lighter colours and the lower ones darker ones. Therefore, if we want to assign its colour to each of the fifteen, we will do it in this way: we shall assign the turquoise to the Hypolydian, the incarnate to the Hyperaeolian, pink to the Hyperphrygian, the hay-ish to the Hyperiasitan, the grey to the Mixolydian, the blue to the Lydian, the orange to the Aeolian, the red to the Phrygian, the green-yellow to the iastian, the yellow to the Dorian the green to the Hypolydian, the aquamarine to the Hypoaeolian, the purple to the Hypoprhygian, the colour of the ground to Hypoiastian and the black to the Hypodorian. Moreover, if we do not want to leave out the green-ish or the light green, so that all the conceivable colours may be used, as the others that can be called quaternary are almost infinite, and that each of the six principal and median Modes and median should have its correspondent both above and below, we shall add above all of them the Hypermixolydian ascribing to it the light green, and thus we shall have sixteen tones and as many colours, all noble and different one from the other.