Author: Riccati, Giordano
Title: The laws of counterpoint deduced from phenomena and confirmed on the basis of reason by  Count Giordano Riccati, Second Book
Original title: Le leggi del Contrappunto dedotte dai fenomeni, e confermate col razioncinio dal Conte Giordano Riccati, Libro Secondo
Source: Udine, Biblioteca Comunale, MS 1026/II, 250-494

[-<250>-] The laws of counterpoint deduced from phenomena and confirmed on the basis of reason by Count Giordano Riccati [[Nobleman from Treviso.]] Second Book [-251-] First Chapter. On the passages from a natural accompaniment to another one, and principally on those that move from one of the accompaniments based on the first, fourth and fifth note of the mode with the major third or with the minor third. One deals also with the true origin of the artificial notes and accompaniments. [signum] 1. In my previous research I defined all the natural accompaniments that can belong to a given tone, either with the major third or with the minor third. I also succeeded in establish that, when one writes in a given tone, one encounters five subordinate tones, two that are similar to the principal one and three of a different nature to which one is permitted to move with an orderly modulation. Therefore, since every tone with the major third derives a similar series of accompaniments as also a very tone with the minor third, it is clear that, if one considers a given tone together with its subordinate ones, and if one bases on it a musical composition, I shall have access the sum of all the natural accompaniments belonging to the said tones, and I shall be able to employ them while observing the appropriate rules. I investigate these rules now, and I establish which passages from one accompaniment to another one are allowed and which ones are forbidden, which ones are more elegant and which one are less elegant. At the same time I shall take the opportunity to illustrate to the Reader the true origin of the artificial notes and accompaniments that can occur in the mode with the major third or in the one with the minor third, and also to discuss some principal passage in which the artificial accompaniments occur. The aforesaid passage are the only ones that help us to illustrate the origin and the most familiar use of the artificial notes and of their accompaniments. I promise myself to deal separately and distinctly (chapter 4, 5, 6, 7) of the passages that contain the artificial accompaniments. [signum] 2. When one examines that musical passages, it is necessary to consider carefully the musical bar, whose rules (Book 1, chapter 8) have been already explained by me. What is suitable on a weak beat shall not be so on a strong one, [-252-] or vice versa, while some movements that are forbidden entirely on the strong or weak beat of a bar, shall be tolerated on the subdivisions of a weak beat. The observations that I shall express along the way shall illustrate what I was able to mention now only in passing and in general. [signum] 3. However, so that I may proceed gradually ad methodically, it is best that I consider a fundamental accompaniment of the third ad of the fifth as one together with its derivative accompaniments, in such a way that in these investigations I shall not mean to say that I move from the accompaniment C 5 3 to the other one F 5 3 when I move from the fundamental note C to the fundamental note F, but also when I move from the fundamental accompaniment C 5 3 to a derivative one of F 5 3, or from a derivative accompaniment of C 5 3 to the fundamental one F 5 3, or, finally, from a derivative one to another derivative. Therefore, whenever I state that a certain passage is forbidden absolutely, such prohibition shall fall not only on to the passage from a fundamental accompaniment to another fundamental accompaniment, but also from a fundamental accompaniment to a derivative one and vice versa, or from a derivative to a derivative. In fact, it it occurs that, while the movement from a fundamental chord to another fundamental chord is forbidden, while then it is permitted to move from a fundamental to a derivative passage or from a derivative to fundamental, or from a derivative to another derivative, in that circumstance I shall not say that said passage is forbidden absolutely, but I shall express clearly that it is not allowed from a fundamental note to another fundamental note. For instance, while one writes in the tones C with the major third or A with the minor third, one is not allowed to move from B 5 3 to F 5 3, but one is allowed to move from B 5 3 to A 6 3, where the second of these accompaniments derives from F 5 3. Therefore, where I deal with the B 5 3 F 5 3, I shall not forbid it absolutely, but such instruction not tu used it shall be accompanied by the specification that said passage is forbidden when one moves from a fundamental note to another fundamental note. There will come a time when, after a passage has been declared as permitted, I shall consider separately all the ways in which one can move from an accompaniment to another one. I shall separate good and bad passages and I shall teach (Book 3, chapter 5.) how to combine them in four, eight, three and two parts. [signum] 4. Since the natural [-253-] or perfect accompaniments, or those that are sounded as perfect, belonging to a particular tone are thirteen, and six are the ones of the subordinate tones, it is necessary to consider them separately in order to avoid confusion. I start, therefore, from those that have the closest relationship with the tone to which they belong. These are the three, with the major third or with the minor third, that are based on the first, fourth and fifth note that constitute the system of the melody on which it depends, as I explained in the relevant place, where I explained that the origin of the natural scale of a given tone with the major third or with the minor third that takes the first note as its foundation. The aforesaid three notes and, consequently, the perfect accompaniments based on them are connected to each other so strictly, that, as I described (Book 1, chapter 2, [signum] 26.) one can move from one to the other note, and, consequently, from one to the other accompaniment in any combination. I shall continue to use the tone C as example and model of all the tones with the major third, and of the tone A as example and model of all the tones with the minor third. Moreover, what I am going to say about the three accompaniments C 5 3, F 5 3 and G 5 3, which produce the tone of C with the major third, or about the three tones A 5 3, D 5 3, E 5 3, which produce the tone A with the minor third, shall have to be understood also in relation to the respective accompaniments that belong to all of the other tones, either with the major third or with the minor third. It will be appropriate to pay particular attention to the tones G and F with the major third and to those with the minor third E and D, since they are subordinate to the tones C with the major third and A with the minor third. [signum] 5. If one wants to move from the accompaniment based on the first note to another one different from it, the best movement that I could realise consists in passing to the accompaniment that is based on the fifth note, which corresponds to the first one in the ratio 3:2. The movement from the accompaniment of the first note to the one of the fourth note is very exquisite, but to a lesser degree. It is expressed by the ratio 3:4. The reason of this is very simple and easy to understand. In fact, leaving aside the two aequisonances, namely, the unison and the octave, through which one cannot change chord when they are employed melodically, the most perfect consonances are first of all the fifth 2:3 and, secondly, the fourth 3:4. In fact, if the composition [-254-] arrives on the accompaniment of the fifth note and one does not want to exceed the boundaries of the tone, one is presented with two passages, either towards the first note or towards the fourth one, the first of which must be preferred to the second. Finally, the two movements that I can make from the chord of the fourth note are either to the first not or to the fifth, bearing in mind that the latter is less perfect than the former. I place here the illustration of the sixth passages mentioned in the two tones C with the major third and A with the minor third. [Riccati, The laws of counterpoint, 254, 1; text: 5 3] [signum] 6. Our passages can be compared to each other in another and not less important way. The movements from the fifth to the first note, those from fourth to the first note and those from the fourth to the fifth note shall prove more elegant than their opposite ones because the first ones have the advantage of moving from a less perfect note to a more perfect one. The order I which I lay out the six passages herewith shall help to illustrate the comparison just now described. [Riccati, The laws of counterpoint, 254, 2; text: 5 3] As the combinations of the sixth terms in pairs rise to the umber of fifteen, the comparisons that can be established between the pairs of the sixth passages that we are describing are exactly as many. So-far I have considered six of said comparisons, but I shall not stop to consider separately and in detail the other nine that remain. In order to asses the relative pleasantness of two passages, one has to consider the higher or lower degree of perfection [-255-] of the notes that constitute the passages themselves and to the advantageous movement from a less perfect note to a more perfect one or disadvantageous from a more perfect one to a less perfect one. Compared two passages, if both the aforesaid conditions will prove favourable in a particular passage, or, if a condition is favourable and the other one unfavourable, there is no doubt that said passage has to be preferred. [signum] 7. The ambiguity may arise when the two conditions are the two conditions shall be one favourable and the other one unfavourable. This occurs in three instances, namely, when one compares the movement from the first to the fifth note with the one from the fourth to the first one, when one compares the one from the first to the fifth one with the one from the fourth to the fifth, and then one compares the passage from the first to the fourth one to the one from the fourth to the fifth one. I write here the three pairs of passages in the usual tones of C with the major third and A with the minor third. [Riccati, The laws of counterpoint, 255; text: 5 3] The preceding passages enjoy the advantage of consisting of a more perfect quality of the combination of their notes, but they move from a more perfect note to one that is less perfect. The consequent passages, on the contrary are less perfect than the preceding ones as to the quality of the combinations of their notes, but the are more perfect than the preceding one as to their circumstance, since their movement proceeds from a less perfect to a more perfect note. Experience teaches us that the two passages from the first note to the fifth note and from the fourth to the first are almost as perfect, but ([signum] 5.) the movement from the fourth note to the fifth is better than the other one from the fourth to the fifth. Therefore, also the passage from the first to the fifth note is better than the other one from the fourth to the fifth, which is confirmed also by experience. It is is left for us to consider the last pair of passages, namely, the one from the first to the fourth note and the one from the fourth to the fifth note. The passage from the fourth to the first [-256-] note is more perfect than the one from the fourth to the fifth note ([signum] 5.). However, the mentioned passage from the fourth to the first note is also more perfect than its opposite one from the first to the fourth note ([signum] 6.). Therefore, our two passages from the first to the fourth note and from the fourth to the fifth note are balanced almost equally as to their perfection. When we deal with the cadences, we shall see, however, that the second one must be considered a cadence, rather than the first one, where as cadences we describe those movements that are capable to conclude a musical composition or a particular passage of it while pleasing the ear. [signum] 8. I wrote all the passages that one can see expressed with musical notes in the last three paragraphs because said part, which is the foundation of harmony, likes very much to move from a fundamental accompaniment to another one. The other passages, namely, from fundamental passage to a derivative one or, vice versa, from a derivative to another derivative are typical of the upper parts. One must understand that this occurs in the majority of cases, because variety requires that such passages sometimes are also intermingled with the bass, while the upper parts include, in selected places and circumstances, the passages from a fundamental chord to another one. However, we are more pleased to hear in the bass the derivative chords A 6 3 and F 6 3 than the fundamental ones F 5 3 and D 5 3 than this one, that, moving from the fifth the the fourth note in the tones with the major third (from G 5 3 to F 5 3 in the tone C with the major third) and also in the tones with the minor third, when the artificial accompaniment of the major third and of the fifth (from E C # to D 5 3 in the tone with the minor third) is ascribed to the fifth note, as it happens for the most part. Consequently, we encounter the passages G 5 3 A 6 3 and E 5 3 F 6 3, and the other ones G 5 3 F 5 3 and E 5 3 # D 5 3 less frequently. The reason depends on the fact that, while I hear the consequent accompaniment F 5 3 or D 5 3, I preserve alive the memory of the sounds that constitute the preceding chord G 5 3 or E 5 #. Now, among those sounds, B, major third of G forms a major fourth with the base F of the following accompaniment F 5 3, and thus, similarly, G #, major third of E, and D, base of the following [-257-] accompaniment D 5 3 forms the interval of the augmented fourth. I shall show in the part where I deal with the consonances that the augmented fourth and the augmented eleventh are very harsh, and, because of this harshness, it is added to the consonant accompaniments very rarely. It is very true, however, that in our case we only have a mere trace of it, but even this mere trace is sufficient to make it such that the very sensitive ear requires that one should eliminate the base F or D of the following chord in the basso continuo, with which the main comparisons are established, and that one should use the derivative accompaniment A 6 3 and F 6 3 instead of the fundamental one. [signum] 9. Should anyone reply to me that even the fundamental passage from the fourth to the fifth note is subject to such an exception, as for instance F 5 3 G 5 3, which is the opposite of the one just now considered G 5 3 F 5 3, where the passage F 5 3 G 5 3 is used otherwise extremely frequently from a base to another base, it seems to me that I would dissolve this objection with only a few words. One cannot deny that, when one listens to the second chord G 5 3, one does not preserve the memory of the previous chord based on F, which corresponds at the major fourth to B with the major third of the chord G. Now, the major fourth our case is of a very different nature from the one that we have considered in the passage G 5 3 F 5 3 from the fifth to the fourth note. There, it was a fundamental dissonance added to the consonant accompaniment F 5 3, which, whenever it is added, requires to be treated with the utmost rigour and to be employed very sparingly. Here, our tritone is only a consequence that the enduring trace of the sound F, which, were it added to the accompaniment G 5 3, as it often added, it would introduce a minor seventh, which is the mildest of all the dissonances. Therefore, the fact that the trace of the major fourth F B in relation to the passage F 5 3 G 5 3 may adduce a not even minimal beginning of unpleasantness to the ear is as false as it is the fact that, added to the following accompaniment G 5 3the minor seventh F, the following passage F 5 3 F 6 4 is used very frequently. In it said seventh is placed in the bass with an excellent effect, although it makes us hear an actual tritone F B related to the sound F that is employed as the bass. The reader shall be able to understand more clearly the aforesaid [- 268-] doctrine after reading my theory of the dissonance. [signum] 10. Of the six passages that I considered so-far, one can count four to which the name of cadence is ascribed. The cadence is the last movement that one realises when one concludes the composition or a section of it, which movement must leave the ear satisfied, and it is equivalent to the conclusion of a period. Just as I have to ensure that the period ends with a conclusion that is as sonorous as possible, similarly, when I conclude the sense of the composition, so to speak, it shall be necessary that I chose the sort of passages that are the most perfect and, consequently, the most pleasant of all. In a speech one does not find only the final full-stop, but one finds frequently some intervening ones. Thus, similarly, a musical composition is not satisfied with a single final and conclusive cadence, but it desires that one should insert in it a number of them in such a way that they do not prove too frequent, and thus they become boring, or too infrequent, causing the attention of the listener, who can never hear the expected conclusion, to tire excessively. [signum] 11. Since both the tones, which are a model for the all the others that are similar to them, namely, C with the major third and A with the minor third, accept the same scale, it is easy to understand that, if one writes in the tone A with the minor third and one employs it in the same way as its previously described origin offers it to us (book 1, chapter 3, [signum] 2.) the ear shall form the idea of the tone C with the major third that accepts the same scale, and it shall realise very soon that said scale has a base C that is more perfect than A. Therefore, the ear shall consider itself satisfied if the composition shall not start on the tone C with the major third, which anyone can easily confirm with the aid of experience. Therefore, one may infer from this that the mode with the minor third employed with artifice has the role to add greater beauty to the corresponding one with the major third that accept the same scale, since it lends to the latter its accompaniments to be inserted in the composition. In this way, the title of subordinate and secondary suits the mode with the minor third very well. Therefore, if one wants to employ it as a principal mode, one must resort to artifice, and, since the ear [-259-] awaits the cadence in the mode with the major third that accepts the same scale with such great anticipation, one must deceive it by making it hear a similar conclusion of the composition in the notes of the mode with the minor third, so that it may be satisfied and happy. This similarity between the cadences of the two modes with the major third and with the minor third is not limited only to the fundamental movements of the bass but involves also other ones that pertain to the upper parts, which are noted more readily by the ear. I noted (Book 1, chapter 2, [signum] 6, 7.) that if the ass moves from the base of a perfect accompaniment to another one with a fundamental passage, the derivative passages that please more are the ones that move by step. Now, among the stepwise motions, tone and major semitone, the second tickles our ear more than the first one. The major semitone is half-way between the minor semitone and the tone, since it contains roughly three of the five parts contained by the tone, while the minor semitone contains two of them. For this reason the major semitone does not have the mawkishness of the minor semitone or the seriousness of the tone, but it shares the diatonic majesty with the chromatic delicacy, since, as a matter of fact, it performs the function of a common element between the two mentioned genera. Therefore, here is a general rule to modify all the cadences of the mode with the minor third and to enable them to satisfy the ear. Assigned the same fundamental passages of the melody to the cadences of both modes, let us consider the most natural movements that the upper parts may realise, and, observed the position where a part moves by a major semitone, we shall introduce the major semitone by means of the artificial notes in the place of the corresponding cadence of the mode with the minor third, observing nevertheless the condition that these artificial semitones must not destroy any natural semitone. This shall suffice so that the ear may remain satisfied fully with such cadences. [signum] 12. Established the aforesaid extremely important law, I begin to discuss the cadences, as to their order and their perfection. If a composition or a section of a composition recognises as sound as its foundation, for instance C, it is certain the the most pleasant movement that I shall be able to create to end on C will consist in choosing [-260-] the note that is different from C that corresponds to C in the most perfect ration. This note is G, which forms a fifth with C. Therefore, the most elegant conclusion shall move from the fifth note to the base of the tone. In order that our cadence may satisfy the ear when it is employed in the tones with the minor third, it is necessary, raised the seventh note with a sharp, to assign to the fifth note the perfect accompaniment of the major third and fifth. Thus one shall ensure that the mode with the minor third becomes artificially equivalent to the one with the major third in the passage of the semitone moving from the seventh note towards the octave. I invite the reader to consider the examples of the perfect cadence in the two tones of C with the major third and A with the minor third. I took care to indicate the simplest movements of the upper parts with a series fo lines that connect a note to the other. I have distinguished with a curved line the movement of the semitone that is found naturally in the perfect cadence of the mode with the major third and that is introduced artificially in the perfect cadence of the mode with the minor third. Such curve embraces the notes that indicate the seventh and and the octave. [Riccati, The laws of counterpoint, 260; text: Cadenza perfetta del Tuono C per Terza maggiore. A minore, Semituono, 5 3, 5 3 #] [signum] 13. added the minor seventh to the consonant perfect accompaniment of the fifth note, said dissonance is resolved by descending from the third note of the tone. The aforesaid seventh would be F in relation to the tone C with the major third, and it would descend with the passage of a semitone F E on to E, major third of C. If we turn to consider to the tone A with the minor third, the seventh that we are discussing is D, which resolves onto C, minor third of A, once it has moved by a major second. To ensure that the seventh added to accompaniment of the fifth note resolves by the movement of a semitone with the perfect cadence of the mode with the minor third as well, it is necessary to raise with a sharp the third note of the minor mode. [-261-] Once said increase is accomplished, the natural semitone by which one rises from the second to the third note is removed, and one infringes the law established at [signum] 11, which teaches us that the artificial semitone must not destroy the natural ones. Moving from the general to the particular, the second and third natural notes B and C of the tone A with the minor third are at the distance of a semitone. If one rises the note C with a sharp, the natural semitone B C is destroyed because of the acquisition of the artificial one D C #, through which the note D, minor seventh of D resolves on C # major third of A. The major semitone B C acts as a marker for the ear so that it may distinguish the perfect cadence of the tone A with the minor from the one of the tone A with the major third, and who has good taste must interfere with that semitone. When we encounter the irregular passage B C # in the perfect cadence of the tone A with the minor third, we try to sweeten it immediately when we practise it by ascending from B to D and then by descending on to C # so that the ear may be somewhat compensated of the loss of the natural semitone by the acquisition of the artificial semitone D C #, however insufficient to replace that loss. In the most recent past few centuries, since when music was cultivated and composer began to write for several voices, it was considered an indispensable rule to assign the first note the accompaniment of the major third and of the fifth in the perfect final cadences of the mode with the minor third. In our age, who employed said cadences in concerti, motets, operas and in any other composition written in the style that we call theatrical, would be derided by everyone. The most expert masters of the chapel have abandoned them even in their sacred composition, so that it will not be long before they shall fall out of use completely. This is so very true, that the judgement of the ear, when it listens, is a very powerful tool in eradicating the most ancient preconceptions. [signum] 14. The other three cadences that I can discuss satisfy the ear very well, although one cannot deny that they leave the sense somewhat suspended. The first one that occurs to me is the ecclesiastical one, so called because it is employed in sacred compositions. The fourth not is the one that, after the fifth one, has the best relationship with the first one. Now, [-262-] the ecclesiastical cadence, which consists in moving from the fourth note to the first one, employs said fourth note. In order that the ecclesiastical cadence of the minor mode may conform to the one of the mode with the major third, it is appropriate to raise with a sharp the third note of said mode with the minor third in the movement of a semitone from the fourth to the third note. Such sharpening does not compromise any natural semitone through which any upper part may move when said cadence is realised. I write herewith the examples of the ecclesiastical cadence in the two usual tones C with the major third and A with the minor third. [Riccati, The laws of counterpoint, 262; text: Cadenza ecclesiastica del Tuono C per Terza maggiore. A, minore. 5 3, 5 3 #, Semituono] I confirm that the ecclesiastical cadence is very effective in the tones with the major third. Nevertheless, it is not very suitable to the tones with the minor third, in which it is not practised except in the act of concluding a composition and in the role of a final cadence. The ear does not like that one alters the most important accompaniment of the first note to produce an imperfect cadence, but it tolerates only that the third note is sharpened when it realises that said sharpening is practised only to avoid that the sense of the composition remains suspended completely when one wants to end with an ecclesiastical cadence. When the third is sharpened in this way, which can occur only in the last accompaniment, it is not counted in the number of the artificial notes of the mode with the minor third. [signum] 15. The fifth note is so connected so closely with its principal that a cadence can end on said note with good reason. Also, since there are another two notes of the system of the melody besides the fifth, we deduce from this two other cadences that derive from [-263-] the first to the fifth or from the fourth to the fifth, which are given the artificial accompaniment of the major third and of the fifth in the tones with the minor third, as in the perfect cadence, in order to satisfy the law explained above ([signum] 11.). The sense of suspension felt by the ear when it hears the cadence from the fourth to the fifth note, especially in the mode with the major third, is more pronounced that in the other two imperfect cadences. Our cadence satisfies the ear more in the minor tones that in the major tones. One of the reasons because the sense is left suspended in a certain way by the artificial major third that one ascribes to the fifth note, and it derives from it such an impression that can imitate the question mark admirably. [signum] 16. In order to research the origin of the mentioned suspension felt by the ear, I observe firstly that one can deduce from what was explained in the sixth and seventh paragraph that, out the four movements that are used as a cadence, the one that moves from the fourth to the fifth note is less elegant than the other ones. Secondly, I note that all the cadences, except the one of which we talk presently, have the property of being the best passage that one can realise, in relation to the tone on which the compositions are based and with regard to the note on which the first accompaniment of said cadences is founded. The best movement that I can realise fro the fifth note is towards the first one, and this passage is called perfect cadence. The best movement that begins from the first note has to be the one to the fifth, which is nothing but a cadence from the first to the fifth note. If I find myself on the fourth note, the best passage of all is the one that moves towards to the first, which is called ecclesiastical cadence. Therefore, if the best passage that starts from the fourth note is the one that heads to the first, such property does not belong to the passage from the fourth to the fifth note. Consequently, the cadence that moves from the fourth to the fifth note is the only one lacking a prerogative that is common to the other cadences. Once one has heard the chord based on the fourth note, if one wants to cadence, the ear expects that this should be done through the best movement, namely, the one from the fourth to the first note. [-264-] Therefore, if one substitutes the best passage with the one from the fourth to the fifth note, which is not as excellent, once the expectation of the ear has been thwarted, it is clear that it will not be possible for the sense to enjoy complete satisfaction. This premise would apply both to the tones with the major third and with the minor third, if the cadences of the latter consisted only of natural chords. However, since one finds always an artificial chord in the cadences of the modes with the minor third, there follows, consequently, that we like to hear a cadence consisting of a passage that is not the best, which cadence nevertheless employs an artificial accompaniment introduced into counterpoint by the perfect cadence and specifically necessary to the mode with the minor third so that it may be employed as principal, rather than another one cadence consisting of an excellent passage but such that it introduces irregularly into the accompaniment of the first note an alteration that is not necessary to the aforesaid mode in order that it may be employed as a principal cadence. [signum] 17. On certain occasions, the fourth note is raised by a sharp because of the cadence that we are discussing. The noted sharpening of the fourth note renders the passage from it to the fifth no longer indifferent, but causes it to become necessary to some extent. The raised fourth note answers the first at the major fifth, an interval that does not please the ear very much when it is employed melodically. Moreover, there are two other errors in the passage from the enlarged with a sharp to the first, which I shall discuss at chapter 2, [signum] 6., where I shall discuss the passage B 5 3 F 5 3, which is similar to the one mentioned and which, as we shall see, is completely forbidden from a base to another base. The passage from the fourth note to the first one with this device proves not only less pleasant than the one fro the fourth to the fifth, but faulty. This is enough to ensure that the ear yearns for the latter passage and that, once it has managed to hear it, it remains satisfied. [Riccati, Le regole del Contrappunto, 265; text: Cadenza, che passa dalla prima alla quinta corda nel Tuono C per Terza maggiore, alla quale comunemente si dà il nome di Controcadenza. A, minore, Semituono, 5 3, 5 3#, quarta, quinta, aumentata d'un Diesis, 5 3 [sqb]] [signum] 18. As to the accompaniment F# A C with the minor third and minor third which eblongs to the artificial note F # of the tone C with the major third, I direct the reader to what I said on the similar accompaniment B D F (Book 1, chapter 4, [signum] 9, 10, 11, 12.) which can be ascribed to B, seventh note of the tone C with the major third and second note of the tone A with the minor third. Nevertheless, [-266-] I shall reflect at some length on the accompaniment D # F A of the diminished third and minor fifth, which is introduced by the cadence from the fourth artificial note to the fifth one in the tone A with the minor third. The ear listens with pleasure to our accompaniment, not only because the diminished third and the minor fifth represent the minor third and the fifth, being a semitone lower than they are, but also because said dissonances by representation fall back appropriately onto very simple proportions. I demonstrated (Book 1, chapter 4, [signum] 11.) that the minor fifth embraces the proportion 1: 10/7 or 7: 10. Therefore, assigned to the number 7 the sound D #, one shall express the sound A with the number 10. However, F A is a major third, whose ratio is 4:5 or 8:10. So, marked the sounds D # and A with the numbers 7 and 10, the number 8 shall be assigned to 8, while the entire accompaniment D # F A of the diminished third and minor fifth shall be expressed by the series 7, 8, 10, whose first two numbers present us with the ratio 7:8 or 1: 8/7 adopted by the diminished third. The augmented sixth, which added to the diminished third forms the octave, accepts the ratio 4:7 or 1: 7/4, while the two accompaniments, derivative of the fundamental which we are discussing, namely, F A d # of the major third and augmented sixth, and A d # f of the major fourth and the minor sixth are expressed, the former through the series 4, 5, 7, and the latter through the series 5, 7, 8. The series 4, 5, 7 is the most simple of the three placed above, and, consequently, the accompaniment F A d # of the major third and augmented sixth proves more elegant than the other two. Such an accompaniment is known currently even to the most trivial composers and it is found applied with great frequency and gracefulness. I place herewith the fundamental accompaniment D # F A of the diminished third and of the minor fifth with its derivative and I do not omit to add, between one letter and another one, the ratios in which they correspond to each other. I conclude this paragraph with an example transcribed from Signor Giuseppe Tartini's Opus one, where all three of the accompaniments that have been discussed in this paragraph itself are contained in relation to the tone of D with the minor third. [-267-] [Riccati, The laws of counterpoint, 267, 1; text: Accompagnamento di Terza [diminuita add. supra lin.] e Quinta [[entrambe diminuite]] proprio della quarta corda artificiale D # del Tuono A per Terza minore. F, A, d#, f, 8/7, 10/7, 5/4, 7/5, derivato, maggiore, Sesta superflua. 7/4, Quarta [[superflua]] [maggiore add. supra lin.], minore. 7 5 3 #, 5 3, 6 # 3, 5 3 #, 6 3, 7 5 3 b, 7 [sqb] 5 3 #, 6 b 4 #, 5 6 3] [signum] 19. The Reader shall remember (Book 1, chapter 3, [signum] 15.) that I clarified the reason why the sixth artificial note, which rises a minor semitone above the natural one, becomes necessary in the mode with the minor third. Since the artificial seventh note is introduced into said mode by three cadences, namely, by the perfect one and by the other two that move from the first to the fifth note and from the four to the fifth, it is necessary, similarly, to admit the sixth artificial note in order to avoid the passage of the augmented second from F, sixth natural note, to the artificial seventh or vice versa, as its intonation proves quite unnatural. Therefore, if one wants that, in the cadences from the fourth to the fifth note, one part moves from [-268-] the sixth note to the seventh, it is necessary to employ the sixth artificial note through which one can rise to the seventh artificial note with the movement of a major second, which is easy to sing and tune. [Riccati, The laws of counterpoint, 268; text: 5 3 #] The change of the sixth natural note into the artificial one, namely, from F to F # in the tone of A with the minor third renders our cadences totally similar to the corresponding ones of the mode with the major third. The tone C with the major third has the two following passages, namely, F 5 3 G 5 3, F # 5 3 G 5 3, as its cadences that move from the fourth note – natural, or augmented with a sharp – to the fifth one. I invite the reader to compare them with the ones that we are discussing, namely, D 3 # E 3 #, D # 3 # e 5 3 #, and it shall be clear that no difference at all can be found between them. One can observe that the sixth artificial note F # removes the natural semitone F E through which an upper part likes to move from the sixth note to the fifth one. The sixth natural note and the semitone from the sixth to the fifth note are the distinguishing features between the cadences of the mode with the minor third from the fourth not to the fifth and the corresponding similar ones that belong to the mode with the major third. Therefore, we must not be surprised if the passages D 5 3 # E 5 3 #, D # 5 3 # E 5 3 #, which break the law established above ([signum] 11.) are not very apt at completing the sense of the composition. Composers employ them when they do not mind or they are pleased that the sense should be left suspended. The second artificial passage D # 5 3 # # 5 3 is more satisfactory than the first one D 5 3 # E 5 3 #, because the artificial semitone D # E ensures that the lack of the natural semitone F E is less prominent. [signum] 20. I shall recapitulate and conclude now what has been said so-far on the cadences, and the artificial notes and accompaniments. Cadences end on the first or on the fifth note. One moves on to these notes from the two remaining notes of the system of melody that remain if one removes the first or the fifth. If I move from [-269-] the fifth or from the fourth note to the first note, I encounter two cadences, namely, the perfect and the ecclesiastical. I encounter the other two imperfect cadences when I move from the first or fourth note to the fifth one. The artificial seventh note and the accompaniment of the major third and fifth that belongs to the fifth note of the aforesaid artificial mode have wormed their way into the mode with the minor third through the three cadences from the fifth note to the first one, from the first note to the fifth one and from the fourth note the fifth one. We shall see at the appropriate place (chapter 2, [signum] 12, [signum] 19.) that the seventh artificial note is employed also in two other accompaniments. Once the seventh artificial note has been introduced, the sixth note also artificial becomes necessary in those occasion where it is necessary to write the passage of the augmented second, which occurs from the sixth artificial note to the seventh artificial note and vice versa. Nevertheless, we have observed that the sixth artificial note can occur in the accompaniment of the major third and fifth that sometimes is ascribed to the fourth note of the mode with the minor third. The sixth and seventh note deserve the first place among the artificial ones because one cannot employ without them the mode with the minor third as a principal mode. The other artificial notes are employed more as a means of greater perfection and in order to achieve it, rather than because of strict necessity. The cadence from the fourth to the fifth note has opened the way to the artificial fourth note in both modes. Both in the mode with the major third and in the mode with the minor third the accompaniment of the minor third and minor fifth belongs to said fourth artificial note in relation to which the sixth artificial note is employed as well. When the sixth artificial note is not employed the accompaniment of the diminished third and of the minor fifth, which I discussed diffusely at paragraph 18., it belongs to the fifth artificial note of the mode with the minor third. [signum] 21. Once the different species of cadences that belong to the same tone are laid ut one after the other in such a way that the last place is reserved mostly to the perfect cadence, some excellent conclusions of compositions are produced, which are employed by good masters of counterpoint in their final cadences. I invite the reader to consider their examples. [-270-] [Riccati, The laws of counterpoint, 270; text: 6 3, 6 4, 4 5 3, 5 3, 5 3 #, 4 5 3 #, 5#, Cadenza ecclesiastica, Controcadenza, perfetta, dalla quarta alla quinta] The move from a fundamental accompaniment to another fundamental accompaniment as in the following examples belongs to the fundamental bass and base of the harmony. It is the task of the upper parts to move from a derivative accompaniment to a fundamental one, from a fundamental to a derivative one or from a derivative to another derivative one. Moreover, variety requires that such accompaniments should interact with the bass. Since it is a clear and undeniable true that a cadence, as we shall call it for now, that ends on a derivative accompaniment cannot satisfy the ear, it follows that, if the movements from a fundamental accompaniment to a derivative one and from a derivative to a derivative one are placed in the bass, they are not accepted by the ear as cadences. This produces very beautiful effect, namely, to avoid too frequent conclusions, so that the composition can be called periodic, so to speak. [signum] 22. I conclude the discussion on the cadences by informing the reader tha, since a cadence consists of two accompaniments, a preceding one and a consequent one, the first one must always fall on a weak beat and the second one on a strong beat. I invite the Reader to consider the examples placed above where one shall see that the cadences are contained in an orderly sequence, and that the preceding accompaniments correspond to the even beats, namely, the second and the fourth, while the consequent ones correspond to the odd beats, namely, first and third. Now, one knows that in the bars of four beats the even beats are the strong ones and the odd ones are the weak ones. The reason for the rule that I provided derives from the fact that the sound that occurs on a weak beat, as I explained when I discussed the bar (Book 1, chapter 8, [signum] 5.), must fall onto the sound that we hear on the adjacent strong beat, which is self-supporting. [-271-] The aforesaid fall express perfectly the last passage that he occurs in a composition, which moves forward until it reaches the sound that is self-supporting, where it stops. If one operated in the opposite manner by placing the first accompaniment on a strong beat and the second one on a weak one, would produce some good passages, but, strictly speaking, they would not deserve the name of conclusions. I said strictly speaking because many authors have availed themselves of this licence. In Corelli's Opus one and Opus two one finds often a cadence on the third beat of a ternary bar or on the second beat of a binary bar. In the subsequent collections, where he shows himself to be ever more perfect, he abandoned such irregular practice. In fact, I have not been able to find a cadence ending on the third beat of a ternary bar except in his sixth collection. This cadence, however, does not produce an unpleasant effect, since the famous composer placed half way through the first part of a minuet, after which it continues the composition without interruption. In this way, the note that concludes the cadence does not remain suspended, but leans onto the beginning of the following bar. Second Chapter. On the remaining passages from a natural accompaniment to another one both belonging to the same tone. Continuation of the discussion on the true origin of the notes and of the artificial accompaniments. [signum] 1. I have shown (Book1, chapter 4, [signum] 2, [signum] 19.) how elegan the passage from one to the other of the seven modes that accept the same scale, tow regular ones with the major and minor third, and the five remaining, mixed, irregular and derivative. It is easy to understand that the passages of the three accompaniments C 5 3, F 5 3 and G 5 3 that produce the tone C with the major third to the other three A 5 3, D 5 3 and E 5 3 that generate the tone A with the minor third are nine in all, as one can move from each one of the first chords to all three of the second ones. For the same reason the passages from the three accompaniments A 5 3, D 5 3 and E 5 3 to the three C 5 3, F 5 3 and G 5 3 shall reach the number of nine as well. In the chords mentioned now we encounter sixth passages, three with the major third [-272-] and three with the minor third, leading to the accompaniment B D F with the minor third and minor fifth, which is based on the note B, which is the seventh in relation to the tone C with the major third and ninth in relation to the tone A with the minor third, and it was introduced in music by the mixed, irregular and derivative tones E, F and G. The same number of passages move from the chord B 5 3 to the sixth chords C 5 3, F 5 3, G 5 3, A 5 3, D 5 3, and E 5 3, which produce the tone C with the major third and A with the minor third. The aforesaid passages that arrive in total at the number of thirty constitute the subject of this chapter, where I shall accomplish my aim to show the Reader the true sources of the artificial accompaniments and of the artificial notes. [signum] 2. Following the method employed elsewhere (Book 1, chapter 4, [signum] 3.) I shall divide our thirty passages into three categories. Six move from a fundamental note to another fundamental note through truly perfect consonances or others that are taken as such. Ten move by step, five upwards and five downwards. Finally, fourteen move from a base to another base through an imperfect consonance, seven descending by a third and seven ascending by a third. The passages of the first two categories do not wander from one tone to another one, because the bases of the two accompaniments always belong to the system of melody of a given mode of which each of the mentioned passages consists. This does not occur in the passages of the third species which truly move from a mode to another one that accept the same scale. I invite the reader to peruse the aforesaid thirty passages divided into the three separate categories. [Riccati, The laws of counterpoint, 272; text: Passaggi di Quarta, e di Quinta all'insù, e all'ingiù. Seconda, Terza, 5 3] [-273-] [signum] 3. I begin from the first category, and I observe that the three passages D 5 3 G 5 3, B 5 3 E 5 3 and F 5 3 A 5 3 descend by a fifth or ascend by a fourth, which amounts to the same. Each of them can assume the double role of perfect cadence from the fifth note to the first one or of a movement from the first to the fourth note in relation to two different tones. For instance, I move according to the circumstances from the fifth to the first note of the tone G or from the first to the fourth note of the tone D by means of the passage D G. The three passages G 5 3 D 5 3, E 5 3 B 5 3 and B 5 3 F 5 3, which are the opposite of the ones written above rise by a fifth or descend by a fourth in an equivalent manner. These passages are suited to performing a double role. The movement G 5 3 D 5 3, as belonging to the tone G, is the inversion of a cadence, which moves from the first to the fifth one; as belonging to the tone D, it is a cadence that moves from the fourth note to the first one. Also, since returning from the fifth note to the first one is a more perfect movement than moving from the first note to the fifth one, and, conversely, the movement from the first to the fifth note satisfies the ear less than returning from the fourth note to the first one. It follows that, if one compares one of our passages with its inversion, unless there are particular circumstances coming into play, it is found to be sometimes more elegant and sometimes less elegant according to whether said passages are employed in one context rather than in another one. [signum] 4. The passage B 5 3 E 5 3 pleases the ear because, as the piquant chord B 5 3 of the minor third and minor fifth is heard first, soon we yearn to move promptly to a genuinely consonant accompaniment. This is achieved with a perfect movement B E of a fifth [-274-] downwards or of a fourth upwards, and the ear cant help being satisfied with it. The perfection of the passage B 5 3 E 5 3 leads us to discover the imperfection of the opposite passage E 5 3 B 5 3. One moves from the genuinely consonant accompaniment E 5 3 to the chord B 5 3, which is truly dissonant, through an exquisite leap of the fifth upwards or of a fourth downwards. B 5 3 is truly dissonant, although it is employed as a consonant chord where one hears the sound F, which forms the minor fifth with B, in a deliberate and unprepared fashion. I have already explained (Book 1, chapter 7, [signum] 14.) how a dissonance should be prepared in music. All of the noted circumstances highlight for us all too clearly the irregularity of the derivative tones E and B which share our passage in ascribing to the note E, which is the fifth of the tone E and the first one of the tone B, the accompaniment of the minor third and of the minor fifth. Such a perfect leap as E B of the fifth upwards or of the fourth downwards produces a feeling of great expectation in our ear, which remains dissatisfied when, instead of a genuinely consonant accompaniment, is made to listen to the chord B 5 3 of the minor third and of the minor fifth, which is only consonant by representation. Therefore, if one avoids the fundamental movement of the melody E B, and one proceeds instead from E 5 3 to D 6 3, an accompaniment derived from B 5 3, the passage that we are discussing will be more pleasant to the ear, which can be confirmed admirably through experience. Although the use of the passage E 5 3 B 5 3 occurs rarely, in order to save the Reader the effort of finding an example of it, I myself present the Reader with a couple of them. I took the first one from a Sonata for organ by Signor Antonio Lotti written in the tone A with the minor third, where the composer employs the device of avoiding the fundamental passage of the melody E B while the basso continuo moves from the chord B 6 4 derived from C 5 3 to the fundamental one B 5 3. [-275-] [Riccati, The laws of counterpoint, 275, 1; text: Basso continuo, fondamentale, 5 3, 5 4, 7 b 5, 5 4 b, 3, 5 3 [sqb], 5 3 #, 3 #,7 5 # 3 #, 5 4 3 b, 7 5 3 #] In the second example, copied from a Miserere for two voices by Padre Maestro Francescantonio Vallotti, the basso continuo moves with a fundamental passage from E 5 3 to B 5 3. Moreover, it is worthy of consideration the device of adding the the dissonances of the minor fourth and minor sixth prepared in advance to the accompaniment B 5 3 that occurs at the beginning of the bar, which dissonances then resolve on the minor third and minor third. If the minor fifth is introduced in this way on a less prominent part of the bar, it worms its way into the ear with greater sweetness. [Riccati, The laws of counterpoint, 275, 2; text: et malum coram te feci ut iustificeris, Basso continuo, fondamentale, 5 # 3 #, 3 #, 7, 6 4 5 [sqb] 3 [sqb], 11 9, 10 8] [-276-] [signum] 5. The passage F 5 3 B 5 3, that moves from the first note to the fourth one in relation to the tone F and from the fourth note to the first one in relation to the tone B, contains within itself a sweet and sour character that does not prove unpleasant and that is often found in musical compositions. The leap F B of the major firth upwards or of the minor fifth downwards justifies the use of the accompaniment B D F of the minor third and minor fifth, and in this way the accompaniment B accounts to de ear of the harsh leap of the melody F B. We hear the minor fifth that occurs in the accompaniment B D F as prepared, while the trace that remains of the sounds A and C that belong to the preceding accompaniment F A C and are not shared by the following accompaniment B D F forms the dissonances of the seventh and of the ninth, both minor, on the base B, which are very common in counterpoint. [signum] 6. The passage B 5 3 F 5 3, the opposite of the one just considered, was considered faulty when one moved from a base to a base. If we ask the ear, it disapproves of it undoubtedly, and I believe that this derives from the fact that it contains [three defects add. supra lin.], which, added together, render it unpleasant. The first defect, which I observed also in the passage F 5 3 B 5 3, consists in the rather inelegant melodic movement of the bass. In the passage F 5 3 B 5 3 the bass leaps a minor fifth downwards or an augmented fourth upwards. In the passage B 5 3 F 5 3 the aforesaid part moves by the opposite leap, namely by a minor fifth upwards or by a major fourth downwards. To uncover the second defect, note that the note F, which corresponds to the base of the first accompaniment B D F at the minor fifth, later becomes a fundamental note or the octave of the following accompaniment F A C. I explained earlier (Book 1, chapter 7, [signum] 14.) how such inverted preparation enhances the harshness of the dissonances. It is true that the minor fifth B F is employed as a consonance and it must not be subject to the laws of the dissonances; nevertheless, one cannot deny that the common use of the passage B 5 3 F 5 3 does not render it harsh beyond its ordinary character. The third defect depends on the fact that, when I hear the accompaniment F 5 3, I still preserve the memory of the sound B, base of the preceding accompaniment, which sound forms with F the major fourth or the major eleventh, which is a very severe dissonance hardly ever used. See what I wrote on a similar defect at chapter 1, [signum] 8., where I talked of the passage from the fifth note to the fourth one of a tone. Therefore, it is the sum of the three noted defects [-277-] that banishes the fundamental passage B 5 3 F 5 3 from music. If one considers that the little liked leap of the melody B F performed by the bass allows the ear to understand more clearly that the sound F, which corresponds to B at the minor fifth, becomes the base of the following accompaniment F A C, and that the sound B, whose traces lingers on, forms the major fourth or eleventh with the base F, one should deduce that, if one avoids the mentioned melodic leap B F, so that one may remove one of the three defect described and two are lessened, the reason to exclude those passages derived from the fundamental one B 5 3 F 5 3, ceases to exist, at least absolutely and in general. I invite the Reader to observe the example where the composer, Padre Maestro Vallotti, moves from B 5 3 to A 6 3, which is a chord derived from a F 5 3. [Riccati, The laws of counterpoint, 277; text: Basso continuo, 5 3, 6 3, 7 5 3, 6 5 3, et cetera] [signum] 7. The two tones C with the major third and A with the minor third appropriate in particular the cadences of the derivative diatonic tones (D, E, F, G, A) that conclude in the first, or octave, and fifth of said regular tones C and E, and, in order to render them sometimes more conclusive, they assimilate them in part or completely to the corresponding ones of the mode with the major third in the movements of the semitone. Such alterations are all the more pleasing to the ear the fewer the artificial notes that the counterpoint needs in realising them, apart from the artificial notes of the seventh and of the fourth already introduced. As the cadences of the modes with the major third and with the minor third conclude the sense of the composition on the first and fifth note, one cal see clearly the reason why the aforesaid cadences of the derivative modes are chosen among all the others. The cadences D 5 3 G 5 3 and B 5 3 E 5 3 begin on the second note and end on the fifth one, the first one belongs to the tone C with the major third, while the latter belongs to the tone A with he minor third. If one substitutes the fourth artificial note F # to the natural one F in the preceding accompaniment of the first cadence, it becomes entirely similar to a perfect cadence of the mode with the major third. The second cadence B 5 3 E 5 3 shall resemble the one of the mode with the [- 278-] major third in the passages of the semitone, if one borrows the artificial notes of the fourth and of the seventh from the tone A with the minor thirds and one employs D # instead of D in the preceding accompaniment, and G # instead of G in the following one. However, since the cadences that we are discussing can never bring to a complete conclusion, the alterations D # and G # shall not always go together, but they shall be used individually as well. Finally, one shall employ the sixth artificial note F # in the preceding accompaniment when one requires a part to ascend from said note to the artificial seventh G #. I shall write herewith firstly the perfect cadence of the mode with the major third, and then all of the alterations of the cadences D 5 3 G 5 3 and B 5 3 E 5 3, so that one may observe how the former concord with the latter in the movements of the semitone. [Riccati, The laws of counterpoint, 278, 1; text: Cadenza perfetta del Modo per Terza maggiore. artificiale del Tuono derivato G appropriata al Tuono C, relativamente a cui si trasferisce dalla seconda alla quinta corda, 7 5 2, 5 3, 7 5 3 #, Semituono] [Riccati, The laws of counterpoint, 278, 2; text: cadenze artificiali del Tuono derivato E appropriate al Tuono A per Terza minore, relativamente al quale si rasferiscono dalla seconda corda alla quinta. 7 5 [sqb] 3 #, 5 3 #, 7 5 3, 7 5 # 3, 7 5 # 3 #, Semituono] [signum] 8. The only chord of unknown character that we encounter for the first time, among the chords that constitute the cadences shown above, is the chord B D # F, of the major third and minor fifth, based on the second note B of the tone A with the minor third. If we compare our accompaniment with the one of the diminished third and minor fifth that I considered above (chapter 1, [segnum] 18.), for instance, D # F A, I note their property of dividing the minor fifth one in the opposite way to the other. In the accompaniment D # F A the minor fifth is divided into two thirds, a diminished one that belonging to the bass and the major one that refers to the middle part. The complete opposite occurs in the accompaniment B D # F, where the major third is assigned to the bass, while the diminished one corresponds to the middle part. Were there someone who says that the accompaniment B D # F of the major third and minor fifth cannot be used, such opinion should be based either on the unreasonable origin of said accompaniment or on the lack of elegance of the proportions that constitute it. It derives, as we have seen, from a sort of cadence that moves from the second note B to the fifth E of the tone with the minor thirds. The cadences A 5 [sqb] 3 # E 5 3 # and D 5 3 # G 5 3, both of which move from the second to the fifth note of the respective tones A with the minor third and C with the major third, correspond to it, as well as preceding accompaniments B 5 # 3 # and D 5 3 #, all of which derive from substituting the fourth artificial note to the natural one. Now, since the artificial accompaniment D 5 3 # is practise every day, and since its origin is agreed to be reasonable, an equal consequence in favour o the accompaniment B 5 [sqb] 3 # must be drawn without fail. I move on to the proportions that constitute the chord B 5 [sqb] 3 # of the major third and minor fifth. I have just pointed out that the chords D # F A, B D # F consist of the same proportions laid out in a different way. The practice of the first accompaniment is not in doubt, hence, the use of the second accompaniment must not be called into question either. The previous discussion was necessary because the accompaniment of the major third and minor fifth is ignored completely by music theorists and almost completely by practical musicians. If the discovery of the chord of the diminished third and minor fifth, which was unknown to the ancients, is owed to modern musicians, why should one be surprised that the chord of the major third and minor third was late in being recognised and used? I write herewith the accompaniment B D # F and its derivative, noting [-280-] the mutual relationships between a sound and another one by following the usual method. There follows an example of the passage B 5 [sqb] 3 # E 5 3 # which I found after a long and diligent search in the fifth volume of the Psalms by Signor Benedetto Marcello, page 115. Lastly, I conclude with an example of the passage B 5 [sqb] 3 # E 5 3 provided to me by Padre Maestro Vallotti, who added the minor seventh a to the accompaniment B D # F (in this way: B D # F A) and placed in the bass the derivative accompaniment A B D # F, of the major second and minor sixth. We shall see the the appropriate time that the figure of the second, fourth and sixth indicates the inversion of the seventh, which means that the seventh is transferred to the lowest part that serves as the bass. Taste for now the excellent effect produced by the accompaniment B D # F, especially in the last example. This accompaniment is of severe and piquant nature and needs to be employed with caution and sparingly. [Riccati, The laws of counterpoint, 280; text: Accompagnamento di Terza maggiore, e Quinta minore [[diminuita]], che può competere alla seconda corda B del Tuono A per Terza minore. B, D #, F, [sqb], d #, 5/4, 10/7, 8/7, 7/5, derivato di diminuita e Sesta minore, 8/5, Quarta [maggiore add. supra lin.], [[ambedue]] superflua, 7/4, Basso continuo, fondamentale, 5, 7 5, 6 5, 7 5 [sqb] 3 #, 5 3 #] [-281-][Riccati, The laws of counterpoint, 281; text: Basso continuo, fondamentale, 6 3, 6 [sqb] 4 # 2, 6 4 # 2, 7 5 3 [sqb], 5 3 #, 5 3, 6 4, 7 5 [sqb] 3 #, 5 b 3, 7 5 3 [sqb], 8 5 3 #, 7, 5 3 #] [signum] 9. As the perfect cadences of the modes with the major third and of those with the minor third consists of two accompaniments that are genuinely consonant, the ear shall enjoy the fact that this property is shared with the passage B 5 3 # E 5 3, which represents a perfect cadence where the accompaniment B D F of the minor third and minor fifth occurs naturally. Said accompaniment can be made genuinely consonant in two ways, either by raising the note F through a sharp or by reducing the note B through a flat. As we observed ([signum] 7.), the sixth artificial note is employed when one has to move from it to the seventh note that is also artificial. Meanwhile, the transformation of the accompaniment B D F into a perfect consonant accompaniment of the major third and fifth shall prove more pleasant once the second artificial note B b is substituted to the natural one B, because in this way one does not alter the natural semitone F E, through which a part moves from the sixth to the fifth. If one employs the note B b in the preceding accompaniment B D F instead of B, and the note G # in the following accompaniment E G B instead of G, the two corresponding passages B b 5 3 E 5 3 # and D 5 # G 5 3, that move from the second to the fifth of the tones A with the minor third and C with the major third shall be completely similar harmonically one to the other. As much as the harmony of the passage B b 5 3 E 5 3 # is improved, by the same measure the fundamental melody is made worse, since it does not move any longer through a truly perfect consonance, such as B E was, but through a minor fifth downwards and through a major fifth upwards. Such inconvenient shall be compensated if one avoids the fundamental movement B b E and if one does not use our passage from a base to another one. The disadvantage of the [-282-] fundamental melody is compensated by a very graceful derivative melody. A part moves from the second or ninth artificial note B b to the artificial seventh G # through the passage of the diminished third B b G #, which, from the eighth note A, the added seventh to the accompaniment B b 5 3, divides into two major semitones B b A and A G #. A melody similar to this one is found between the sixth note F and the artificial fourth D #, which form with each other the diminished third, also divided by the note E into two major semitones, F E and E D #. The noted uniformity opens the way to that graceful imitations with which musical compositions are embellished. [signum] 10. When one realises the passage B b 5 3 E 5 3 #, the most usual way is to move from the derivative accompaniment D 6 b 3 to the fundamental E 5 3 #. I invite the reader to observe our derivative passage D 6 b 3 E 5 3 # with the simplest motions in the upper parts, followed by an example taken from a work by Arcangelo Corelli. [Riccati, The laws of counterpoint, 282; text: 6b 3 3 #, Semituono, Basso continuo, fondamentale, 4, 3 #, 7, 6, 7 5 3 #, 6 3, 6 b3, 7 3 #, 5 3, 6 4, 5 3 #, 5 4, 7 5 3, et cetera] I placed the fundamental bass under the basso continuo, as I do normally, not because it has to be played or sung, but in order that it may teach us two which fundamental chords to which the derivative ones contained in the basso continuo are reduced. In the fundamental bass placed above, the first half of the first bar would be very faulty, since first we find the leap of a tritone B b E and then, with the mere interspersion of a single passage, a leap of the minor fifth F B, [-283-] which is made harsher than its natural character by the memory still fresh of the sound B b. However, let us return to the passage that we are discussing. I showed at the appropriate place (Book 1, chapter 2, [signum] 17.) that, of the two accompaniments that derive from the fundamental one of the third and fifth, namely the one of the third and sixth and the other one of the fourth and sixth, we give preference to the first one, which, in fact, is employed more frequently than the second in musical compositions. Now, when in moving from a fundamental chord to another fundamental chord we encounter a melody that is not very pleasing, in that case the best passages that can be placed in the basso continuo are these two, namely, the one that proceeds from the derivative accompaniment of the third and sixth to the fundamental or the one that proceeds from the fundamental accompaniment to the derivative of the third and sixth, as long as we encounter in these some elegant melodic movements. In relation to the passage B b 5 3 E 5 3 #, the two mentioned passages would be D 6 b 3 E 5 3 #, which is contained in the aforesaid example, and B b 5 3 G # 6 3. The former is found to be employed much more than the latter because the stepwise passage D E from the fourth note to the fifth one is very appropriate to the bass and it is abundantly favoured by the majestic character of the diatonic genus, which is very typical of said part, while the movement B b G # of the diminished third suites the upper parts better, since it belongs to the chromatic genus, from which it derives a graceful, languid and passionate character. In the example that I add herewith Signor Tartini employs our passage from F 6 4 b ad E 5 3 # in a beautiful fashion. I took said example from the fifth Sonata of his Opus one, and I transposed it from the tone E to the tone A with the minor third. [Riccati, The laws of counterpoint, 283; text: Basso continuo, fondamentale 5, 6 5, 9, 8, 4, 3, 7, 6 b, 6 4 b, 5 [sqb] 3 #, 6 4, 5 4 3 #, 6, 3 #, 5 3, 7 5 3#, 7, 5 3 #] [-284-] When the minor seventh D is added to the second accompaniment E 5 3 # of the passage B b 5 3 E 5 3 #, the bass loves to rest several times on the sound D, which is given firstly the accompaniment D 6 b 3, derived from B b 5 3, and then the accompaniment D 4 # 2, derived from E 5 3 #. This derivative passage is encountered so frequently that I deem it redundant to present any example of it. [signum] 11. After I discussed the six passages of the first class sufficiently, I move on to deal with the tenth contained in the second class. Five of these, namely, C 5 3 D 5 3, E 5 3 F 5 3, G 5 3, A 5 3, A 5 3 B 5 3 and B 5 3 C 5 3, rise by a second and are only species of cadences that move from the fourth to the fifth note in the derivative tones G, B, D, E, F. An equal number of passages, namely, D 5 3 C 5 3, F 5 3 E 5 3, A 5 3 G 5 3, B 5 3 A 5 3 and C 5 3 B 5 3, which are the opposite of the ones above, descend by a second and move from the fifth note to the sixth in the aforesaid tones. As the passage from the fourth to the fifth note proves more pleasant to the ear than the one from the fifth note to the fourth, one should deduce that the last five passages are less perfect than the first five. All of the five passages that ascend by a second are often employed in the tones C with the major third and A with the minor third. One should note in the passage E 5 3 F 5 3 the feature described (chapter 1, [signum] 8.) in the passage G 5 3 F 5 3, namely, that the memory of the sound B contained in the preceding accompaniment makes us hear, albeit very faintly, a major fourth or an eleventh added to the consonant accompaniment F 5 3. We observed in the quoted place that the passage G 5 3 F 5 3 is not practised very often from a base to another base, which does not occur in the passage E 5 3 F 5 3. Such difference derives undoubtedly from the fundamental melodic movements E 7 and G 7, the first of which of the second upwards is more perfect than the other of the second downwards. [signum] 12. The two cadences B 5 3 C 5 3 and G 5 3 A 5 3 belonging to the derivative tones F and D start from the seventh note and end on the octave of the respective tones C with the major third and A with the minor third. Therefore, they belong to the number of cadences adopted by the aforesaid regular tones. Composers employ widely the passage B 5 3 C 5 3, which has the property of being able to imitate without any artifice and with precision [-285-] that cadence of the mode with the major third that moves from the fourth note raised with a sharp to the fifth. In the tone c with the major third said cadence is F # 5 3 G 5 3. The fundamental passages of the semitone B C, F # G, the preceding accompaniments B 5 3 and F # 5 3 of the minor third and of the minor fifth and the consequent accompaniments C 5 3 and G 5 3 of the major third and fifth resemble each other perfectly. The cadence G 5 3, A 5 3 accepted by the tone A with the minor third in which it moves from the seventh to the eighth note shall prove similar to the cadence of the mode with the major third from the fourth artificial note to the fifth one in those movements of the semitone that not affect adversely the natural semitone B C through which one of the upper parts moves, if the seventh artificial note G # is substituted to the natural seventh note G. One should apply to the artificial passage G # 5 3 A 5 3 what I said of the natural passage B 5 3 C 5 3 (Book 1, chapter 4, [signum] 13.). If the composition finds itself on the accompaniment G # 5 3 based on the fourth artificial note G # of the derivative tone D and it does not want to abandoned said tone, the passage G # 5 3 A 5 3 becomes somewhat necessary and also very pleasant, because, for the reason adduced on the movement B 5 3 F 5 3 ([signum] 6.), the fundamental passage G # 5 3 D 5 3 from the fourth artificial note to the first one of the derivative tone D is forbidden completely, and certain derivative passages, for instance G # 5 3 F # 6 5, where the artificial note F # is employed to avoid the augmented second G # F, must be used sparingly. Meanwhile, one must not overlook the important reflection that the species of cadences that moves from the seventh note to the octave has opened the way in the tone A with the minor third to the accompaniment G # B D of the minor third and minor fifth, which is based on the seventh artificial note G # of said tone. [-286-] [Riccati, The laws of counterpoint, 286; text: Cadenza artificiale dalla quarta alla quinta corda del Tuono C per Terza maggiore. naturale, derivato F appropriata al, relativamente a cui si muove dalla settima all'ottava. D, minore, Semituono, 5 3] [signum] 13. However the double role that each of our passages can assume, according to whether it is employed in the tone C with the major third or in the tone A with the minor third. If one considers the latter tone, the passage G 5 3 A 5 3 moves from the seventh note to the octave and it admits the alteration that I mentioned just now. Such alteration does not occur in said passage when it is employed in the tone C with the major third, in which it moves from the fifth note to the sixth. Also, as to the movement of the ascending second considered in the previous chapter, namely, F 5 3 G 5 3 and D 5 3 E 5 3, if they are employed the former in the tone C with the major third, and the latter in the tone A with the minor third, they are cadences that move from the fourth to the fifth note in the said [-287-] primary tones, and in these cadences one finds that some artificial sounds have been introduced according to the laws established in the quoted chapter. However, if one established a sort of permutation and if one employed the passage F 5 3 G 5 3 in the tone A with the major third, in which one moves from the second to the third note, in that case the tone C is subordinate to the tone A, the Tone A to the tone C and the passages F 5 3 G 5 3 and D 5 3 E 5 3 have to obey the laws of the tone in which they are used rather than those of the tone from which they come. The tone C with the major third employs the passage D 5 3 E 5 3 without any alteration, while the passage F 5 3 G 5 3 in the tone A with the minor third occurs to us frequently in these ways A 6 3 G # 5 3 and F # 5 3 G # 5 3. In the previous paragraph I uncovered the way through which the artificial accompaniment G # 5 3 was admitted to the tone A with the minor third. The sixth artificial note F # is employed when one wants that a part should ascend from said note to the artificial seventh G #. What I noted in the matter of the ascending passages of the second that we are discussing must be applied entirely to the all passages consisting og the seven natural accompaniments of the third and fifth that belong to the modes that share the same scale. In the case of the tones A, B, C, D, E, F and G that accept the same scale, two of which are regular and five are derivative, which I always take as a model for the ones that are similar to them, the mentioned accompaniments consisting of letters not altered by the sharp or by the flat sign are entirely complete. Now, these passages that provide the subject matter to the previous chapter and to the current one accept no alteration or they accept several of them according to whether they are employed in the tone of C with the major third or in the tone of A with the minor third. I considered it appropriate not to omit the following considerations, which shall clarify further for the Reader the nature of the artificial sounds, which prove pleasant to the ear only when they are employed with good reason and according to the reason why they have been introduced into music. [signum] 14. Returning to the passage of the second upwards, the most frequently employed are the ones that in both of the modes with the major third and with the minor third move from the first to the second note and from the fifth note to the sixth. As the first and the fifth note require, by virtue of the origin [-288-] of the mode the perfect consonant accompaniment, which, therefore, is applied to them most often, we also encounter frequently the opportunity to move with a movement of the second upwards to the accompaniment of the third and fifth based on the second note and on the sixth one. The first examples, taken from Corelli's works, contain the movements from the first to the second note and from the fifth to the sixth in the two tones C with the major third and A writhe the minor third. I took the third and fourth examples from the first Sonata of Signor Tartini's Opus one and I transposed them from the tone A with the major tone to the similar tone C. The Reader can observe that all the passages that rise by a second, except for the one that moves from the second to the third note, are employed in the most beautiful manner. [Riccati, The laws of counterpoint, 288; text: Basso continuo. Fondamentale, 6, 7, 5, 6 5, 7 5, 6 3, 9, 7 3 #, 3 #, 4 3, 9 8, 3 #, 6 4, 5 3, 4 2, 7 5 3] [-289-] [signum] 15. In order that anyone of the five passages of the second downwards may be employed with some frequency, especially from a base to another one, it is necessary that many important circumstances should prove favourable to it. Such are the passages D 5 3 C 5 3 and A 5 3 G 5 3, especially when they are employed in the tone C with the major third, in which they move from the second note to the first one and from the sixth to the fifth one. Said passage consist of two accompaniments that are truly consonant. The memory of sounds that occur in the preceding accompaniments, namely, D 5 3 and A 5 3, produces with the consequent accompaniments C 5 3, G 5 3 rather mild dissonances and of the sort that is very common in counterpoint. Through this passage the accompaniment is improved, since the preceding one is with the minor third and the following one with the major third, while one passes from an accompaniment borrowed from tones that share the same scale to another one which is strictly specific of the tone of C with the major third. The later feature does not occur when our passage are employed in the tone of A with the minor third, in which they move, on the contrary, from an accompaniment that is strictly specific of said tone to another one borrowed from the tones that share the same scale. Therefore, the passages D 5 3 C 5 3 and A 5 3 G 5 3 are employed more often in the tone C with the major third than in the tone A with the minor third. After examining some sacred psalms by Padre Francescantonio Calegari, I find that the passage from the second note to the first one in the mode with the major third, with which passages he prepares the dissonance of the ninth, added to the accompaniment of the first note, is employed frequently. The renown author adopts the mentioned passages in the following ways: D 5 3 E 6 3 (the accompaniment [-290-] E 7 6 3 is derived from the fundamental one C 9 5 3) F 6 3 C 9 5 3 and F 6 3 E 7 6 3. The other passages of the second downwards can be practised with some elegance in a similar way, unless there is a particular reason that prevents it. Soon I shall provide an example of the fundamental passage D 5 3 C 5 3. The introduction of the passage A 5 3 G 5 3 from a base to another one is rendered much easier by its property that allows the bass to descend from A to G while an upper part can ascend with stepwise contrary motion from E, fifth of A, to F, minor seventh of G, a dissonance that, employed immediately and without preparation, pleases the ear. Such a prerogative is not shared by the passage D 5 3 C 5 3, because an upper part should rise from A, fifth of D, to B, major seventh of C. Moreover, such dissonance is practised without preparation by good composers only when a part descends onto it from the octave, as such clash would prove unbearable because of the memory of the sound F, minor third of D, that forms a major fourth with B. Sometimes composers employ the passage D 5 3 C 5 3 to modulate from the tone D with the minor third to the tone C with the major third, by adopting the device of considering the accompaniment D 5 3 firstly as belonging to the tone D with the minor third, and then to the tone C with with the major third. I took the example that I present from the fifth psalm by Signor Benedetto Marcello. One often moves beautifully from the Tone A with the minor third to the tone C with the major third through the passage A 5 3 G 5 3 by employing the accompaniment A 5 3 firstly as belonging to the Tone A with the minor third and then as belonging to the tone of C with the major third. See the example that I transcribed from a Miserere for two voices by Padre Maestro Vallotti, where an upper part rises from E, fifth of A, to F, minor seventh of G, while the bass descends from A to G with a fundamental movement. [Riccati, The laws of counterpoint, 290; text: Basso continuo, fondamentale, et cetera] [-291-] [Riccati, The laws of counterpoint, 291; text: Auditui meo dabis gaudium, Basso continuo, fondamentale, 6 4, 5 3, 6 3, 5 3 #, 7 5] [signum] 16. We observed that the passages D 5 3 C 5 3 and A 5 3 G 5 3 in the mode C with the major third move from the second to the first note and from the sixth to the fifth. The corresponding passages, which move in the tone A with the minor third from the second note to the first one and from the sixth to the fifth one, are the following: B 5 3 A 5 3, F 5 3 E 5 3, but one shall struggle to find the first passage employed from a base to another base. The ear likes to hear that from F, which produces a minor fifth with the base B of the previous accompaniment, one should descend to E, fifth of A and base of the following accompaniment, which performs the function of a sort of resolution for said diminished fifth. The other movements by leap, namely, F A and F C, which can move from the sound F to the sounds A and C that occur in the accompaniment A 5 3, prove rather unpleasant, since the sound F, which is truly dissonant, is involved in them, although it is employed as a consonant sound, as well as a passage of the second downwards that is not considered as one of the most elegant ones. Added the minor seventh G to the accompaniment A 5 3, the passage F G, with which one rises by step from F, minor fifth of B, to G, minor seventh of A, shall not please either. We shall point out (Book 3, chapter 2. [signum] 9) that the privileged minor seventh is only the one that is added to the chord of the major third and fifth based on the the fifth note of either of the modes, namely, with the major third or with the minor third. Now, if the fundamental passage B 5 3 A 5 3 is employed, and, if the better liked movement F E is chosen for the part that touches the sound F, [-292-] one falls into the mistake of producing two consecutive fifths, namely, B F and A E, which, although they are one minor and the other one perfect, do not produce a good effect. If one avoids such an error, one finds that in the other one the part that sings the note F moves inelegantly, if one wants it to move from F to D before the passage to the following accompaniment A 5 3 follows. One shall be able to remedy the aforesaid errors entirely, if one substitutes to the fundamental passage B 5 3 A 5 3 a derivative one, for instance D 6 3 E 6 4, which one sees employed beautifully in the passage copied from Padre Maestro Vallotti's Miserere for two voices placed at the end of the previous paragraph. All the prerogatives that I mentioned with reference to the passage A 5 3 G 5 3 from the sixth note to the fifth one of the tone C with the major third are shared by the passage F 5 3 E 5 3 from the sixth note to the fifth one of the tone A with the minor third, except one. In fact, in the former tone one can move to the advantage of the accompaniment A 5 3 of the minor third and fifth, while in the latter the entire opposite occurs, since the third of the preceding accompaniment F 5 3 is major, while the third of the following accompaniment E 5 3 is minor. If one substitutes the artificial note G # to the natural third note G, said accompaniment shall become similar to the previous one F 5 3, and, since the ear pays more attention to the artificial accompaniment E 5 3 # than to the natural one F 5 3, so it shall not call itself displeased to hear sometimes the fundamental passage F 5 3 E 5 3 #. The example that I present to the Reader is contained in the fourth Psalm by Signor Benedetto Marcello. [Riccati, The laws of counterpoint, 292; text: ma da molti dir sento, Baso continuo. Fondamentale, 3 #] [-293-] [signum] 17. The passages C 5 3 B 5 3 and A 5 3 G# 5 3 from the eighth note to the seventh of the tones, respectively, C with the major third and A with the minor third, because, when the ear hears them, it wants them to be followed by the sort of cadences, like B 5 3 C 5 3 and G # 5 3 A 5 3, that ascend from the seventh note to the eighth by contrary motion. The accompaniments B 5 3, G # 5 3 shall often benefit from the addition of the seventh, to which one part ascends by step from the fifth of the preceding accompaniment C 5 3, A 5 3. The other parts can also be moved with grace. The fundamental passages are used, namely, C 5 3 B 5 3, A 5 3 G # 5 3, but one encounters the derivative passages more frequently, namely, C 5 3 D 6 3, A 5 3 B 6 # 3, E 6 3 D 6 3 and C 6 3 B 6 # 3. The derivative accompaniments D 6 3, B 6 # 3 are more pleasing than the fundamental ones B 5 3, G # 5 3, because in the latter a true consonance and one by representation correspond to the bass, while in the former two true consonances correspond to the bass. Before I move one, I want to inform the Reader that several masters of counterpoint employ many passages of the second upwards and downwards when they let us hear a series of accompaniment of the third and sixth that move by step. Corelli employs such passages too much. See a passage taken from the eighth Concerto of his Opus six. [Riccati, The laws of counterpoint, 293; text: Basso continuo. Fondamentale, 6, 5] Such a large number of consecutive fourths in which the violins correspond to each other are certainly not to be praised. These fourths played without the bass would be intolerable. As for me, I would not allow them in the upper [-294-] parts, except up to the number of two, which in certain circumstances are unavoidable, and, since there are only two of them, they would be hardly noticed by the ear. The following very beautiful passage by Signor Tartini teaches us how to lay out several consecutive sixths by alternating the accompaniments of the fourth and sixth, second fourth and sixth and third and sixth. I took it from the first Sonata of his Opus one, and I transposed it from the tone A to the tone C, both with the major third. [Riccati, The laws of counterpoint, 286; text: Basso continuo. Fondamentale, 6 4, 6 4 2, 6 3, 6 5 3, 7 b, 7, 7 3 #] [signum] 18. It remains for us to discuss the fourteen passages of the third class, seven of whom, C 5 3 A 5 3, D 5 3 B 5 3, E 5 3 C 5 3, F 5 3 D 5 3, G 5 3 E 5 3, A 5 3 F 5 3 and B 5 3 G 5 3 descend by a third, while the same number, namely, A 5 3 C 5 3, B 5 3 D 5 3, C 5 3 E 5 3, D 5 3 F 5 3, E 5 3 G 5 3, F 5 3 A 5 3 and G 5 3 B 5 3, which are the opposite of the ones previously mentioned, ascend by a third. I have explained (Book 1, chapter 4, [signum] 4, e 5.) of our passages, which roam from a mode to another. This means that the accompaniments in which they consists have two sounds in common and that one moves by step from the sound that is not in common to the other one. The most familiar ways in which the movements of the thirds downwards are employed are from a base to a base or by assigning to a given note first the accompaniment of the third and fifth, and then the accompaniment of the third and sixth, to which sixth one often descends from the seventh added to the preceding accompaniment. All seven of the passages of the third downwards are encountered very frequently in musical compositions. They are used in preparing the seventh added to the consequent accompaniment, but I shall discuss this at the appropriate point. However, I consider it appropriate to dwell on some of our passages that are useful to prepare and to sweeten certain consonances by representation, such as the minor fifth B F and also some other ones introduced by the artificial notes into the tones C with the major third and A with the minor third. Consider the following five passages, where I took care to highlight, apart from the artificial movements [-295-] the sounds that, since they are truly consonant in the beginning, then occur in intervals that are consonant by mere representation, which for this reason are presented to the ear only after being prepared. [Riccati, The laws of counterpoint, 295] The minor fifth of the consequent chord is prepared in all five of our passages with the minor or major third of the preceding accompaniment. The diminished third from D # F belonging to the consequent accompaniments of the second and third passage is prepared by the sound F, which is in one case the minor third and in the other the fundamental note of the preceding accompaniment. I note that in the fourth passage the sound F # can perform the role of fourth artificial note of the tone C with the major third or of sixth artificial note of the mode with the minor third, according to the circumstances [signum] 19. The passage E 5 3 C 5 3, when in it the seventh natural note G of the tone A with the minor third is substituted with the artificial note G #, proves appropriate to prepare a consonance by representation, namely, the augmented fifth C G #. However, since the accompaniment C E G # of the major third and augmented fifth, which can belong artificially to the third note of the mode with the minor third, proves almost completely new to the Reader, since I have not mentioned earlier except in passing (Book 1, chapter 7, [signum] 4.) and since it derives mainly from the passage E 5 3 # C 5 # 3, it was truly necessary to deal separately of the passage E 5 3 # C 5 # 3 and of the accompaniment C 5 # 3. It is known how often the artificial accompaniment E 5 3 # is assigned to the fifth note E of the tone A with the minor third. Now, if the natural accompaniment C 5 3 follows the mentioned artificial one, one moves from the tone A with the minor third to the tone C with the major third. The passage E 5 3 # C 5 [sqb] 3 is very familiar in counterpoint. Here is an example transcribed from the psalm Bonitatem fecisti for eight parts a cappella by Padre Calegari. [-296-] [Riccati, The laws of counterpoint, 296, 1; text: Basso continuo. fondamentale, 8 7 3 #, 10 9, 8, 6 3, 6 4, 8 7 5 3 #, 6 # 4 2, 7 4 2, 8 5 3, 7 # 5 2, 6 3, 5 b 2, 9 8 5 3, 4 5 3 #, 3 #, 5 [sqb] 3] However, if one wants to continue in the tone A with the minor third, one holds the sound G # also in the accompaniment C 5 3 #, so that one encounters the artificial passage E 5 3 # C 5 # 3 from the third note of the tone A with the minor third corresponding to the natural one G 5 3 E 5 3 from the fifth to the third note of the tone C with the major third. Consider the two following passages that I place herewith, one in the tone C with the major third and the other one win the tone A with the minor third. [Riccati, The laws of counterpoint, 296, 2; text: Basso continuo. fondamentale, 5 3, 6, 7 5 3, 54, 3, 5 3 #, 7 5 3 #, 5 4, 3 #, 5 3 #, 5 [sqb] 3] [signum] 20. I said that the accompaniment C 5 # 3 of the major third and augmented fifth derives mainly from the passage E 5 3 # C 5 # 3. In fact, since the augmented fifth is a very harsh interval, and since our ear likes it that we let it hear it prepared, it owes its principal introduction into music to the passages that establish the mentioned preparation. Such preparation is achieved in two ways, when the note G # forms the thir d of the preceding accompaniment E 5 3 #, so that we encounter the passage E 5 3 # C 5 # 3, or when G is given as base to the chord G # 5 3, so that the passage G # 5 3 C 5 # 3, which derives from adapting the passage G 5 3 C 5 3 to the tone A with the minor third, and by substituting in it the seventh artificial note G # to the natural note G. It is easy to understand that, of the two aforesaid ways of preparing the augmented fifth, the first one must be preferred to the second one by a long way. In the former one, our interval is prepared with a [-297-] perfect consonant accompaniment of the major third and fifth, and one moves from one chord E 5 3 # to the other one C 5 # 3 with a very pleasant melodic passage of the descending major third. In the latter, the preceding accompaniment G # 5 3 of the minor third and minor fifth is sweeter than the following one C 5 # 3, but it cannot be called a perfect consonant accompaniment if not by representation. Moreover, the fundamental movement of the melody G # C of the diminished fourth upwards or of the augmented fifth downwards is so resentful in character that deserves to be excluded completely from the art of counterpoint. Were the Reader to consult the compositions of good composers, he shall find that the chord E 5 3 # precedes the augmented fifth C 5 # 3 in most cases and that the derivative accompaniment E 6 3 # of the major third and minor third is placed in the basso continuo instead of the fundamental accompaniment C 5 # 3. The two consonances that correspond to the bass E of the derivative accompaniment E G # C, please the ear sufficiently and distract it enough so that it is not very aware of the diminished fourth G # C in the fundamental accompaniment C E G #, where the fifth C G # corresponds to the bass, which, although it is performed as a consonance, as it represent the fifth C G, nevertheless it is a true dissonance in itself. A similar defect is also found in the derivative accompaniment G # C E. In the tone C with the major third the natural passage B 5 3 E 5 3 corresponds to the passage G # 5 3 C 5 # 3 which is artificial and belongs to the tone A with the minor third, since both passages move from the seventh note to the third one of their respective tones. The following corresponding passages, the first of whom belongs to the tone C with the major third and the second one to the tone A with the minor third, deserve to be studied closely. [Riccati, The laws of counterpoint, 297; text: Basso continuo, fondamentale, 5 3, 6 3, 7 5 3, 5 6 3, 6 3 #, 7 5 3 #,7, 7 5 # 3, 7 3 #] [signum] 21. Someone may ask me the reason [-298-] why the ear is less averse to accept as a consonance by representation the minor fifth and the major fourth than the augmented fifth and the diminished fourth. I reply in the first instance that the minor fourth and the major fifth are more pleasing than all of the other consonances by representation, because they occur in the diatonic system between the notes B F, F A, and, even when they are employed artificially in music, they never lose their natural and diatonic character. This is the reason why the minor fifth and the major fourth are more pleasing than the diminished third and than the augmented sixth, although the ratios adopted by the former two 7:10, 5:7 are less simple than the ratios 7:8, 4:7 adopted by the latter two. Secondly, I add that, while an odd number larger than 7 is not involved in the ratios of the other consonances by representation, the augmented fifth and the diminished fifth have the drawback of admitting in their ratios, that are notably more complex, the odd number 9. The major fourth D G # is represented by the ration 5:7 or 10: 14. If one adds the tone C D, represented by the ration 9:10, the result shall be the augmented fifth C G #, represented by the ration 9:14 or 1: 14/9. The same proportion comes also from adding to the fourth C F, represented by the proportion 3:4 or 9:12, the augmented second, which corresponds to F G # 6:7 or 12:14. Consequently, the diminished fourth G # c, which constitutes the octave with the augmented fifth C G #, shall be expressed by the ratio 7:9, or 1:9/7. Thirdly, the artificial minor fifth and the diminished third together with the intervals with which they complete the octave, namely, the major fourth and the augmented sixth have wormed their way into counterpoint through certain cadences, to which, if they are not necessary, at least they are greatly beneficial. The augmented fifth and the diminished fourth lack such privilege. Therefore, one should draw the conclusion from this premise that the accompaniment C E G # and its derivative must be employed sparingly, carefully and in passing. I took care to write them herewith, notating the mutual approximate or exact ratio between one sound and another one according to our usual method. [-299-] [Riccati, The laws of counterpoint, 299; text: Accompagnamento di Terza maggiore e Quinta superflua, che può competere allat erza corda C del Tuono A per Terza minore. C, E, G #, c, e, 5 4, 14/9, 9/7, derivato di Sesta minore. 8/5, Quarta diminuita] [signum] 22. As I proceed to discuss the seven passages of the ascending third, namely, A 5 3 C 5 3, B 5 3 D 5 3, c 5 3 E 5 3, D 5 3 F 5 3, E 5 3 G 5 3, F 5 3 A 5 3 and G 5 3 B 5 3, I note that, if we follow the judgement of the ear, it is more pleasant to move from a fundamental accompaniment to another one with a leap of the third downwards, as for instance from C 5 3 ad A 5 3, than through a similar leap upwards, as from A 5 3 a C 5 3. In order to explain such a phenomenon, I invite the Reader to observe that, when I move from C 5 3 to A 5 3, the sound A is not contained in the accompaniment C 5 3, and, consequently, said sound, which is the base of the second chord A 5 3, appears new to the ear, so that I can assign to it the accompaniment that I prefer. This does not occur when, conversely, the melody moves from A 5 3 to C 5 3. The sound C forms the third of the chord A 5 3, and from this it follows that, when I hear the chord C 5 3, the derivative chord C 6 3 corresponds to the note C, and this accompaniment C 6 3 is the only one that belongs to the note C without moving from a mode to another one. Therefore, when the bass moves from A to C, the ear expects that one should assign to the note C the derivative accompaniment of the third and sixth without changing the fundamental accompaniment. Therefore, if I assign the fundamental accompaniment of the third and fifth instead of the derivative of the third and sixth, the expectation of the ear remains thwarted. [-300-] This must be understood not as aiming to exclude from the practice of counterpoint the passage from a perfect accompaniment to another one through the leap of a third upwards, which is a good passage and it is found applied with some frequency especially in the compositions for unaccompanied voices. The only consequence that the Reader has to deduce from my considerations is that the passage mentioned as last is less exquisite than the opposite one that moves from one fundamental accompaniment to another one through the leap of a third downwards, and, therefore, it needs to be employed more sparingly. The following example of the fundamental passages F 5 3 A 5 3 and A 5 3 C 5 3 comes from a setting of the psalm Legem pone for eight unaccompanied by Padre Calegari. [Riccati, The laws of counterpoint, 300; text: Basso continuo. Fondamentale, 64, 5 3, et cetera] [signum] 23. I have never seen the passage B 5 3 D 5 3 used from a base to another base. Apart from the fundamental movement of the third upwards, which is not one of the most pleasing, one notes the fault consisting in the fact that the sound F, which forms a minor fifth with B then becomes a minor third in the accompaniment D F A. Instead, one finds that the corresponding fundamental passages G 7 5 3 B 7 5 3 and E 7 5 3 # G 3 7 5 3 from the fifth to the seventh note of the tones C with the major third and A with the minor third, with the addition of the seventh to both the preceding and to the consequent accompaniment, are employed with a beautiful effect. The following accompaniments B D F and G # B D of the minor third and minor fifth are contained entirely in the previous ones G B D E and E G # B D of the major third, fifth and minor seventh, which renders our passages more elegant. The seventh added to the following accompaniments B 7 5 3 and G # 7 5 3 serves as foundation to the ear, so that it may realise that the fundamental accompaniment was changed. Without the addition of said seventh, one would judge that the accompaniment B 5 3 and G # 5 3 derive from the fundamental ones G 5 3 and E 5 3 #. one must observe that the minor seventh of the preceding chords becomes minor fifth in the [-301-] following ones, which is equivalent to saying that it is not a true consonance, but merely a consonance by representation. Were the said seventh turned into a perfect fifth, as in the natural passage E 7 5 3 G 5 3, this would prove wrong with the addition of said dissonance, and worthy of being banished from counterpoint. Here is an example of the passage E 7 5 3 # G # 7 5 3 transcribed from the tenth Sonata of Signor Tartini's Opus one, which I transposed a third lower, in order to show the Readers the passage that I am discussing in the tone A with the minor third, as a model of all the other tones of a similar genus. [Riccati, The laws of counterpoint, 301, 1; text: Basso continuo. Fondamentale, 6 3, 5 3, 7 5 3, 6 5, 5 4, 3, 6 4 2, 7 5 3 #, 7 [sqb] 5 3, 7, b 7, 7 [sqb]] [signum] 24. The most familiar passages derived from the fundamental ones of the ascending third are three. The first one moves with a downward leap of the fourth from a fundamental chord to a derivative of the third and sixth. The following passage, taken from the second Sonata of Signor Tartini's Opus one, and transposed from the tone F to the tone C, both with the major third, contains the two passages C 5 3 G 6 3 and A 5 3 E 6, which are derived from the fundamental ones C 5 3 E 5 3 and A 5 3 C 5 3. [Riccati, The laws of counterpoint, 301, 2; 6 3, 5 3, 3 6 4, 7, et cetera] The passage B 5 3 F 6 3 derived from the fundamental one B 5 3 D 5 3 must not be allowed in music because of the leap B F of the [-302-] major fourth downwards, because the memory that remains of the sound B forms the major fourth with the bass of the second chord F 6 3, and because, finally, the bass F of the second truly consonant chord F 6 3 makes the ear understand too clearly that the sound F, which corresponded to the base B of the preceding accompaniment B 5 3 at the interval of a minor fifth, has become a true consonance. The second passage that I decided to discuss, derived from the fundamental passage of the third upwards, is created by assigning the same note first to the derivative accompaniment of the third and sixth and then to the perfect one of the third and fifth. An offertory by Adriano Willaert provides me with the example, which I write herewith, of the passage F 6 3 F 5 3, derived from the fundamental one D 5 3 F 5 3. [Riccati, The laws of counterpoint, 302, 1; text: 6 3, 5 3, 7 5 3, 6, 7, et cetera] Modern composers employ the derivative passages that we are discussing with greater artistry. They add the seventh to the following accompaniment and they make two upper parts that are at the distance of a third touch first the sixth and the octave of the preceding accompaniment and the the fourth and then the fourth and the seventh of the following accompaniment. The passages from the second to the fourth note practised in the described way in both the modes with the major third and with the minor third produce an excellent effect. [Riccati, The laws of counterpoint, 302, 2; text: Passaggi dalla seconda alla quarta corda. Nel Tuono C per Terza maggiore. 8 6, 7 5, 5 3, Basso continuo.fondamentale, A, minore, 5 3 #, 8 6 b] [-303-] In the passage F 8 6 F # 7 5, the fourth artificial note F # becomes useful also because the seventh added to the second accompaniment becomes minor and, therefore, it can be used more assuredly without preparation. Among the passages of the tone A with the minor third, the second shall please more the first one because the sound F, minor fifth of the preceding accompaniment, remains consonant by representation even in the following accompaniment, as it forms with the base of the latter, namely, with the fourth artificial note D #, a diminished third. Since the last passage D 6 3 D # 7 5 proves to be harsh, since it contains two artificial notes, namely the second one B b and the fourth one D # that are so distant one from the other that they render the fundamental passage B b 5 3 D # 7 5 3 completely absurd, we shall see (chapter 4 [signum] 7, 8, 9.) that the augmented third, such as B b D #, cannot be employed harmonically or melodically. I derived the following example of the passages F 8 6 3 F # 7 5 3 and D 8 6 3 D # 7 5 3, derived from the fundamental ones D 5 3 F # 7 5 3, B 5 3 D # 7 5 3, which I put forward for the attention of the Readers, from the Miserere of the often lauded Padre Maestro Vallotti. [Riccati, The laws of counterpoint, 303; text: misericordiam tuam, Basso continuo. Fondamentale, 9 7, 8 6, 7 5, 5 3, 5 3 #, 6 4, 9 7 5 3, 10 8 5,7 5 3, 7, 6 4 5 3 #, 5 3 #] [-304-] I shall say a few things on the third category of passages derived from the fundamental ones of the ascending third. They move with the passage of a descending second from a perfect accompaniment of the third and fifth to a derivative accompaniment of the fourth and sixth. This sort of passages are found to be employed often from the second to the fourth artificial note of the mode with the major third and from the fifth to the seventh note of both the mores with the major third and with the minor third. For instance, the passage B 5 3 A 6 [sqb] 4 # derived from the fundamental one B 5 3 D # 5 3 [sqb] from the second to the fourth artificial note of the tone A with the minor third is perceived as harsh and one shall struggle to find it in musical compositions. Nevertheless, employed at the appropriate time and in the appropriate place it can produce an excellent effect. [Riccati, The laws of counterpoint, 304; text: Passaggi dalla seconda alla quarta corda nei Tuoni C per Terza maggiore, A per Terza minore. Basso continuo. Fondamentale, 5 3, 6 4 # 3, 6 3, 6 [sqb] 4 #, 6 3, 5 3, 7 5 3, 7 5 3 [sqb], 5 3 #, quinta, settima, 6 4 3, 6 4 # 3, 7 5 3] I transposed from the tone D to the tone C both with the major third the following example of the passage D 5 3 C 6 4 # 3 derived from the fundamental one D 5 3 F # 7 5 3. It is found in the fourth Sonata from the Opus one by Signor Giuseppe Tartini. [-305-] [Riccati, The laws of counterpoint, 305, 1; text: Basso continuo. fondamentale, 6 3, 5 3, 6 4 #, 6 4, 5 3, 7 5 3, 6 4 5 3] [signum] 25. From what was explained in the previous chapter and in the present one, one can draw the conclusion that, among the passages of the fifth, of the fourth, of the second and of the third both upwards and downwards, those of the second downwards and those of the third upwards deserve the last place. I stated (Book 1, chapter 4, [signum] 25.) that the music masters of the sixteenth century employed certain passages that are not of the most perfect ones in their compositions too frequently. I had in mind then the passages of the second downwards and of the third upwards, which, to tell the truth, are too abundant in the counterpoints of the aforesaid century. Five passages of the third upwards and one of the second downwards are contained in only four bars of an offertory by Adriano Willaert, as I pointed out a little earlier. Here they are. [Riccati, The laws of counterpoint, 305; text: Basso continuo. Fondamentale, 6 5, 4 3, 4 5 3] The very acute judgement of the ear has taught modern masters to employ such passages sparingly. I also said in the quoted passages that the composers of the sixteenth century made little use of the artificial notes. Now that we are fully informed on the notes and on the artificial accompaniments, we only have to consult the best works of the masters of that age to realise the truth of my statement. [-306-] Third chapter On the passages from a natural accompaniment to another one that belong to two tones, one principal and the other one subordinate, or vice versa. [signum] 1. In the first and second chapter I taught the reader only how to move from one to the other one of the seven natural accompaniments that suite the same tone, three of them rigorously, because they produce it, and the remaining four with a less strict connection because they are borrowed from tones that accept the same scale. I considered earlier on (Book 1, chapter 5, [signum] 12.) that two tones, one with the major third and the other one with the minor third that employ the same scale, have all of the seven natural accompaniments in common, so that, compared these tones with four that are subordinate to both, one notice that four accompaniments are in common, and that, thanks to the shared accompaniments, which can be considered firstly as belonging to one tone and then to another one, we are presented with the simplest method to move from the principal tone to any subordinate one and to return then from any subordinate tone to the principal one. Now, I proceed and I direct my considerations to the passages that move from an accompaniment to another one, which accompaniments belong naturally to tow tones, one principal and the one subordinate, or vice versa, in such a way that no accompaniment is in shared between the two tones. The passage B b 5 3 G 5 3 [sqb], for instance, through which one wants to modulate from the tone D with the minor third to the tone C with the major third, is of this sort. The preceding accompaniment B b 5 3 belongs to the tone D with the minor third rather than to the tone C with the major third, while the consequent accompaniment G 5 3 [sqb], which belongs to the tone C with the major third, does not belong naturally to the tone D with the minor third. Here is a short table of the natural accompaniments that the tones C with the major third and A with the minor third, both of which can perform the role of principal tones, do not share with the subordinate tones and that, vice versa, the subordinate tones do not share with the two principal ones, namely, C with the major third and A with the minor third. [-307-] [Riccati, The laws of counterpoint, 307; text: Accompagnamenti dei Tuoni F per Terza maggiore, D per Terza minore non comuni ai Tuoni C, A. B b 5 3, G 5 3 b, E 5 3 b, B 5 3, G 5 3, E 5 3, G, E, F 5 3, D 5 3, B 5 3, F # 5 3, D 5 3 #, B 5 # 3] the passages from the accompaniments B 5 3, G 5 3 and E 5 3, which belong to the tones C with the major third and A with the minor third, to the accompaniments B b 5 3, G 5 3 b and E 5 b 3, which belong to the tones F with the major third and D with the minor third, are nine, since it is possible to move from each of the first three to each of the second three. The same same number of passages return from the accompaniments B b 5 3, G 5 3 b and E 5 b 3 to the accompaniments B 5 3, G 5 3, E 5 3. Similarly, nine passages move from the accompaniments F 5 3, D 5 3 and B 5 3 belonging to the tones C with the major third and A with the minor third, to the accompaniments F # 5 3, D 5 3 # and B 5 # 3 belonging to the tones G with the major third and E with the minor third, and the same number of passages allows the return from the latter to the former. Therefore, the passages that we are discussing reach the number of thirty-six. In the most varied way among those that are legitimate, they move away from the two tones, one with the major third and the other one with the minor third that accept the same scale, one of which acts as principal, towards the four subordinate ones, or, vice versa, they return from the four subordinate ones to the two mentioned in the first place. [signum] 2. As our passages always contain a modulation from a tone to another tone that is the less simple of those that are permitted, unless they are endowed with an exquisite melody and harmony, although the ear, absolutely speaking, does not feel positive disgust for them, it requires at least [-308-] that they should be employed sparsely and with great caution. Moreover, our ear is so delicate that, even if melodic movement from one base to the other one of the two accompaniments were extremely elegant, it is enough that the harmony is not so perfect, or, vice versa, if the harmony is endowed with the necessary perfection, it is enough that the melody is not considered of the most pleasant, in order for the ear to judge that a given passage should be employed very sparingly in musical compositions. We need to consider another circumstance in the passage that we are discussing. It is very useful that the preceding accompaniment are based on the first or on the fifth note of the principal tone and of the subordinate ones, in which the cadences reach conclusion, or that they should be truly consonant, so that in them the sense of the composition may be sufficiently complete, if not totally complete, before changing tone. In fact, if the first accompaniment shall be of the minor third and of the minor fifth, namely, consonant by mere representation, and the second truly consonant accompaniment shall not differ from the first one except by a minor semitone, the perfection of the consequent chord shall highlight the imperfection of the preceding one too much, showing to which bad situation a tone abandons itself in order to modulate to another one. Therefore, such passage shall have to be placed among those that need to be employed sparingly and with great care. All that I simply announced in this paragraph need to be dealt with in detail with the appropriate consideration. [signum] 3. If we start to consider our passages as to what pertains to the melody, eight of them consist of the sort of accompaniments that, albeit different, have the same base. Such a melody is most perfect, given that that the bases are in the proportion of equality, which is the most simple of all. In two passages one moves from a chord to the other one though the leap of a fifth upwards or of a fourth downwards, and one does the exact opposite in another two. I explained elsewhere how pleasant are this melodic passages. Eight passages move from an accompaniment to another one with a movement of the third downwards. The bases of four passages differ by a minor semitone, which in two passages rises and in two descends towards the lower register. I have already invited the Reader to observe (Book, 1, chapter 3, [signum] 3.) that the minor semitone [- 309-] is such a small interval that when two notes are tuned to it, when one strikes one of them the other one oscillates as if it were tuned to a perfect unison. Therefore, two bases whose difference consists of a minor semitone, are considered in some way as in unison. Similarly, this must be said of the two chords that constitute our passages, which share all their other sounds except for the bases. This near identity of the two chords that constitute the passages that we are discussing renders them pleasing to the ear, unless there is any other reason to the contrary, although the bases that correspond to each other at the distance of a minor semitone produce a melody that cannot be classed among the most exquisite. Up to this point the ear considers itself satisfied, but the same does not occur when one wants to employ less perfect melodic passages, such as the leaps of the third upwards, contained in eight passages, the leaps of the minor fifth downwards or of the augmented fourth upwards, contained in two passages, and, finally, the leaps of the minor fifth upwards or of the major fourth downwards which are the opposite of the ones mentioned just now an which occur in two passages. The Reader shall remember that I demonstrated (chapter 2. [signum] 22.) that the passages of the third upwards are of less perfect and that they are inferior to the ones of the third downwards. I have discussed several times (Book 1, chapter 4, [signum] 13, Book 2, chapter 2, [signum] 5, [signum] 6.) the harsh sensation produced in our mind by the leaps of the minor fifth downwards or of the major fourth upwards, of the minor fifth upwards or of the major fourth upwards, and of the minor fifth downwards or of the major fourth downwards. I lay out the thirty-six passages in the same sequence in which I ordered them in the current paragraph. In respect of their melody and of their harmony, they are of eighteen different species, each of which contains two passages that are perfectly similar. A few brief notes shall explain the reason why I consider certain passages defective. For now, I invite the reader to consider the notes that concern the melody, while the remaining notes shall be illustrated in the two following paragraphs. [-310-] [Riccati, The laws of counterpoint, 310; text: Passaggi formati da due accompagnamenti, le cui basi sono unisone. 5 3, 5 3 b, 5 3 #, 5 3 [sqb], 5 b 3, 5 # 3, 5 [sqb] 3, Specie 1. Difettosi per l'inversa preparazione della Quinta [[si]] minore. di Quinta all'insù, e all'ingiù. motivo d'armonia siccome composti di due accordi di Terza e Quarta [[diminuita]], Semituono minore, [diminuita ante corr.], pel salto] [-311-] [signum] 4. As we consider our passages in relation to the melody, I shall speak briefly about their harmony, in relation to which the sixteen paragraphs consisting of two accompaniments that are truly perfectly consonant are better than the others. These are followed by a similar number of passages consisting of an accompaniment wither with the major third or with the minor third, and of another one of the minor third and minor fifth. The last placed is reserved to the four passages consisting of two accompaniments of the minor third and minor fifth. Here the harmony is so deprived of perfection that, since we are dealing with passages that move from a tone to another one in the way that is the most complex among the ways permitted, the ear loves that the four passages, in which are involved only six chords that, albeit sounded as perfectly consonant, they are not such, should be employed extremely rarely. I said ([signum] 2) that it is extremely beneficial that the preceding accompaniments of the passages that we are discussing should be based on the first or fifth note of the principal and subordinate tones on which notes the cadences come to a close, so that they may precede said passages and allow us to hear the sense of the composition as complete before one moves from a tone to another one. If one examines several musical compositions, one shall find that a cadence precedes the change of the tone in most cases, although it is executed in the most simple forms. Therefore, one should deduce that it shall be extremely appropriate to precede our passages that contain the modulations from a tone to another one that are not counted among the most simple. The accompaniment founded on the first or fifth note of the principal tone C with the major third or A with the minor third and of the subordinate ones that occur in our passages are F 5 3, D 5 3 #, D 5 3, B # 5 3, B 5 3 #. Eighteen passages begin from these, among which one encounters the very pleasant melodies of the unison, of the descending third more frequently than all the others in musical compositions. [signum] 5. From what was said one can see clearly why certain passages that are similar one to the other, as, for instance, the two of the seventh species B b 53 G 5 3 [sqb] and F 5 3 D 5 3 #, and the two of the eighth species, G 5 3 b E 5 [sqb] 3 and D 5 3 B 5 # 3, are not employed as frequently. The preceding accompaniments B b 5 3, G 5 3 b of the first and of the third passage [- 312-] do not belong either to the first or to the fifth note of any tone, either principal or subordinate. The same cannot be said of the preceding accompaniments F 5 3, D 5 3 of the second and of the fourth passages, because the first one belongs to the first note of the subordinate tone F with the major third and the latter to the first note of the subordinate tone D with the minor third. For the aforesaid reason, therefore, whenever the principal tone is the one of C with the major third or the one of A with the minor third, the passages F 5 3 D 5 3 # and D 5 3 B 5 # 3 are found to be employed more often than the similar passages B b 53 G 5 3 [sqb] and G 5 3 b E 5 [sqb] 3. The latter are employed very often in the following fashion. After the perfect cadence C 5 3 F 5 3 in the tone F with the major third and A 5 3 # D 5 3 in the tone D with the minor third, one considers then the accompaniment F 5 3 as belonging to the tone C with the major third and the accompaniment D 5 3 as belonging to the tone of A with the minor third. Moving from F 5 3 to D 5 3 # and from D 5 3 to B 5 # 3 #, one executes the cadence D 5 3 # G 5 3 in the tone G with the major third and the cadence B 5 # 3 # E 5 3 in the tone of E with the minor third, thanks to which the artificial seventh note D # is introduced into the accompaniment B 5 # 3 #. Here are the two series of corresponding passages and chords, written herewith. [Riccati, The laws of counterpoint, 312; text: C 5 3, F 5 3, D 5 3 #, G 5 3, A 5 3 #, D 5 3, B 5 # 3 #, E 5 3] Through the first one one modulates from the tone F to the tone G by means of the tone C, all three of which with the major third. Through the second one one modulates from the tone D to the tone E by means of the tone A, all three of who are with the minor third. I inform the reader that the two cadences C 5 3 F 5 3 and D 5 3 # G 5 3, as well as the other two A 3 # D 5 3 and B 5 # 3 # E 5 3 attract the attention of the ear to such an extent and the ear compares the chords that constitute it with such distinction, that in the case of B 5 # 3 # it proves extremely secondary. Those who want to investigate the relative perfection of the passages F 5 3 D 3 # ad D 5 3 B 5 # 3 # should read again what I said on the two pairs of accompaniments C 5 3 A 5 3 #, D 5 3 B 5 # 3 # (Book 1, chapter 5, [signum] 19.). [signum] 6. When I stated that it is laudable that a cadence should precede the change of tone, I was referring to the cadences of the regular modes with the major third and with the minor third, in which the artificial notes necessary to render them conclusive have been introduced according [-313-] to what was explained in the previous two chapter. If such cadences are lacking, the ear shall appreciate that one should precede the change of the tone either with the cadences of the regular modes without the aid of said artificial notes or with the cadences of the modes derived by the regular ones with the major third and with the minor third. See how Padre Maestro Vallotti moves from the principal tone C with the major third to the subordinate tone E with the minor third. [Riccati, The laws of counterpoint, 313; text: Basso continuo. fondamentale,Tuono principale C per Terza maggiore, E, minore, 6, 6 3, 6 4 5 3, 3 #, 6, 10 9, et cetera] The passages C 5 3 G 5 3, G 5 3 D 5 3, D 5 3 A 5 3 and A 5 3 E 5 3, are all inverted cadences, the first one of the principal tone C with the major third, and the other ones of the derivative tones G, D and A. The change of tone indicated by the inverted cadence E 5 3 B 5 # 3 # belonging to the subordinate tone E with the minor third follows the inverted cadence A 5 3 E # 3 5 proposed by the tone A with the minor third that in this case must be employed as derivative of the tone C with the major third. Of the cadences of the derivative tones, the ones that please the the most are the ones that conclude with a truly consonant accompaniment. Therefore, all other circumstances being the same, the passages reaching the number of twelve that begin with a chord of the minor third and minor fifth must be considered less perfect than the others because the modulation from a tone to another tone contained in them can only follow a cadence of the derivative mode that concludes with a consonant accompaniment by mere representation. I have praised, but I did not prescribed that a cadence should precede our passages. When I produce the examples of the ten species of passages that I indicated as faulty, one shall see some of them that are not preceded by a cadence. [signum] 7. It remains for me to discuss the two species of passages through which the preceding accompaniment of the minor third and minor fifth turns into the truly consonant consonant accompaniment by altering a singe note by a minor semitone. The two mentioned species are the fourth and the [[tenth]] twelfth, under which one reads in the table placed after the third paragraph: defective passages because of the inverted preparation of the minor fifth. As to the passages of the twelfth species, it is evident that they contain an inverted preparation of the minor fifth, given that, for instance, in the passage B 5 3 B b 5 3 the sound F, minor fifth of the preceding accompaniment becomes a perfect fifth in the following one. In order to uncover the inverted preparation of the [[diminished]] fifth in the passages of the fourth species, one needs a little consideration. If we take by the hand the passage E 5 b 3 E 5 3 [sqb], one of the two that belong to said species, one should note that, as the sound B b minor fifth of the first accompaniment is a semitone higher, it turns into a the perfect fourth of the second accompaniment. However, the two sounds B b and B are in some way the same sound. Therefore, a sound that in some way remains the same and was first consonant by representation becomes then a truly consonant sound. As this occurs in relation to the same base E, which is common to both the chords, the perfection of the consequent accompaniment highlights too much the imperfection of the preceding one. Were the fundamental note of the two accompaniments not the same one, the mutation of the base and the enlargement of the dissonant sound B b would affect the ear so profoundly that it would not aware at all of the inverted preparation when it hears the consonant sound B. For instance, the passage E 5 b 3 G 5 3 [sqb] is very defective because of the leap of the third upwards, but not because the B b, minor fifth of E, transforms into B, major third of G. Avoided the fundamental passage, the most elegant way to employ the passages of the fourth and twelfth species consists in moving from a chord to another one both of the third and sixth, namely, from G 6 3 b to G 6 5 [sqb] and from B 6 3 to D 6 b 3. In both of the preceding accompaniments [-315-] G 6 3 b and D 6 3, only true consonances of the minor third and major sixth correspond to the basso continuo G or D. Therefore, the inverted preparation of the major fourth B b E of F B is hardly noticed, because this consonance belongs to the middle sound of the preceding chords G 6 3 b and D 6 3. It is beneficial to employ the consequent derivative accompaniments G 6 3 and D 6 b 3 instead of the more elegant fundamental ones E 5 3 and B b 5 3 because the reduced perfection of the consequent accompaniments G 6 3 and D 6 b 3 shields the imperfection, also reduced, of the preceding accompaniments G 6 3 b and D 6 3. [signum] 8. since one shall be able to consult very many musical compositions without coming across any passage of the ten species that I distinguished as imperfect, I believe it appropriate to place herewith some examples, mostly provided by the works of Padre maestro Vallotti, which shall show the Reader the manner and circumspection with which such passages must be employed in a sombre fashion. [Riccati, The laws of counterpoint, 315; text: Basso continuo. fondamentale, 5, 6, 5 3 b, 6 3 [sqb], 6 5, 3 b, 5 b 3, 5 [sqb] 3, Passaggio della quarta specie. 3 [sqb], 6 #, quinta, 6 4, 7 5, 7 5b, 7 3 #, 7 [sqb] 5, 7 5 3, 7 5 b 3, 7 5 3 #, 7 [sqb] 5 3, sesta, 7 3, 6 b 3, 6 5 b 3, 4b 3, 9 5 3, 8, 5 3, 7 b, 4 b 5, 3, duodecima, 7 5 2, 6 4 3 b, 7 b 5 3, decimaterza, 5 3 [sqb] 4 2, 7 b 5, 6 b 4, 5 3 #, 6 3 b, 3 #, decimaquarta, 5 b 3, 3 [sqb], decimaquinta, 6 b, 7 5 3 b, decimasesta, 5 [sqb] 3, decimasettima] [-317-] One may deem it strange that, as I have banished from counterpoint the passage B 5 3 F 5 3 (chapter 2, [signum] 6.) and anyone similar to it, such as E 5 b 3 B b 5 3 when one moves from a base to another base, one finds used in the basso continuo of the second example the passage E 5 b 3 B 5 3 of the fifth species from a fundamental note to another fundamental note. It is sufficient that one should recall the reason why I excluded the passage E 5 b 3 B b 5 3 between to bases, and, after considering that they do not occur in the passage E 5 b 3 B 5 3, one shall be persuaded soon that our passage from one fundamental note to another one has been employed correctly. I rejected the passage B 5 3 F 5 3, or E 5 b 3 B b 5 3, because of the combination of three faults, namely, because from E to B b there is the unpleasant melodic passage of the minor fifth upwards or of the major fourth downwards; because the sound B b that constituted the minor fifth [-318-] with E in the first accompaniment E 5 b 3 becomes later the base or the octave in the second accompaniment B b 5 3, which highlights the harshness of the mentioned minor fifth further; and, finally, because the enduring impression on the ear of the sound E base of the preceding accompaniment E 5 b 3 forms with B b, base of the following accompaniment B b 5 3, the augmented fourth, or eleventh, which is a harsh and seldom used dissonance. Now, none of the noted drawbacks can be seen in the passage E 5 b 3 B 5 3. From E to B one moves with the very pleasant leap, I shall say, of the perfect fifth upwards or the perfect fourth downwards. The sound B b, which forms a minor fifth with E does not belong to the chord B 5 3, strictly speaking, but it turns into B, which is a minor semitone higher than B b. It is true that the semitones B b and B are in some way at the unison, but one cannot deny, nevertheless, that the minor semitone by which B exceeds B b, does not distinguish notably the second sound from the first one and that it does not dissolve for the most part the memory of the sound B b, and, consequently, of the minor fifth, especially because it consists of the passage E 5 b 3 B 5 3 consisting of two accompaniments founded on two different bases. Finally, the trace of the sound E that remains in the ear forms an eleventh with the fundamental note B of the following accompaniment, which is a much sweeter dissonance than the major eleventh, and one that is employed very often in counterpoint. [signum] 9. As to the caution employed by that famous Author in the examples written above, the following observations come forwards. The passages that we are discussing, begining in five of the mentioned examples with a truly consonant accompaniment, are all preceded by a cadence that belongs to the regular tones with the major third or of the minor third or of they derivative ones. The five examples are the fifth, the sixth, the seventh, the ninth and the tenth. Of the passages that begin from an accompaniment of the minor third and minor fifth in the five remaining examples, one counts two in the third and eighth example, which are preceded by a species of cadence that belongs to a derivative tone. The other three passages contained in the first, second and fourth example are not preceded [-319-] by any sort of cadence. Therefore, there are only three cases in ten examples, where there is no cadence that precedes the passages that we are discussing. Moreover, note that the cadences are lacking in those circumstances in which they cannot satisfy the ear if not in the most imperfect way, as they conclude with a chord of the minor third and minor fifth that is consequent in respect of said cadences and preceding in respect of one of our passages that follow the cadence immediately. [signum] 10. As to the beats of the bar or to the subdivision of said beats, a given passage can be ordered in three different ways: either the first chord is introduced on a weak beat and the second one on the strong beat immediately following, or both the chords are introduced on a strong beat, or, finally, the first chord is introduced on a strong beat, or, finally, the first chord is introduced on a strong beat and the second one on the adjacent weak beat. In the first instance, the ear compares the chords between the distinctly, in the second one it devotes them a medium level of attention, and in the third one the comparison occurs in passing and in a very secondary way. In order to understand the reason for this, one should have a sequence of various beats in alternating between a weak and a strong beat. It does not matter if they are beats of the bar or if they are subdivisions of said beats, as they also represent strong and week beats. As the first weak beat falls onto the following strong beat and the second weak beat onto the following strong one, it is evident that such fall invites the attention to focus strongly onto the pairs of chords one of whom leans against the other. Consequently, the comparison between the first strong beat and the second adjacent weak beat shall prove less principal, since such beats to not interfere with each other, so to speak, but, as former supports the first weak beat, the weak beat, conversely, falls onto the second strong beat. The attention that the ear devotes to comparing the two chords that are introduced on a strong beat and each occupies, for instance, a ternary bar or half of a bar with four beats. In fact, if there is a sequence of strong beats, the reason why the second strong beat should be compared more distinctly with [-320-] the first one than with the third one shall never be assigned. Premised such undeniable truths, one understands clearly that, when one needs to employ any of those passages in which it is necessary to apply precautions, one shall never place the first accompaniment on a weak beat and the second one on a strong beat, in order to avoid that the ear discovers clearly the scant elegance of the aforesaid passages by comparing those chords to attentively. It shall be best to act entirely in the opposite way by assigning to the first chord the strong beat and the weak beat to the second, as one can see executed in the six examples placed above. It shall be also legitimate to introduce both the chords on a strong beat, as in the fourth, sixth, ninth and tenth example, because such hypothesis has the advantage that the passage of limited use is not the most noticeable of the two, the preceding one and the consequent, that must be in the number of those that are employed assuredly. [signum] 11. I observe that another device is employed in the fifth, sixth, seventh and tenth example, namely, that, after a musical idea is heard in a particular tone, the same idea is heard in a subordinate tone, and the composition is laid out in such a way that the preceding idea concludes with the first of the accompaniments that constitute one of our passages, while the following musical idea begins with the second accompaniment. As said chords belong to different musical ideas, one understands clearly that the ear is bound to compare them with each other very little. However, it would be too long an enterprise and, I am about to say, an impossible one to complete successfully, to describe all of the devices that can render the passages that we are discussing agreeable. It is well known that a good modulation does not depend on the mere passage from an accompaniment to another one, but on many preceding ones and many consequent ones. Now, if the passages that we have considered and that we still have to consider, which consist of only two accompaniments, reach such a large number, it is enough to consult the rules of combination to ascertain which exorbitant number the combinations of eight or ten accompaniments would reach. One must set a limit to the rules themselves, since, [-321-] when they are too many, they are more create more uncertainty than they provide help. It is necessary to leave something to the hard work of the composer, nor a good master of counterpoint must be ashamed to consult the judgement of the ear at times, when a passage is uncertain but free from a positive error. [signum] 12. I shall conclude the discussion of our ten passages of different species by informing the Reader that almost all of them (this is something that in he case of some of them occurs often) can be employed as if they consisted of two accompaniments, one natural and the other artificial, both belonging either to the same tone or to two tones of different nature that accept the same scale. In that case, either because said passages do not contain a modulation from a tone to another one, or, at the most, because one moves from a tone to another one both of whom share the same scale, for this reason there need to employ them with such great circumspection is removed. As to the passage from the second to the fourth artificial note of the mode with the major third, which is similar to the two of the fifteenth species, I have talked about it already (chapter 2, [signum] 24.). that is the series of the preceding and consequent accompaniments that is used as a rule by the ear to judge if one of our passages is employed either as consisting of two natural chords belonging to two tones that do not share the same scale, or as consisting of two chord, one natural and the other artificial, or vice versa, that belong to the same tone or to two tones that accept the same scale. Int he passage that I write herewith, the preceding and consequent chords demonstrate that the accompaniments than constitute the passage B b 5 3 E 5 [sqb] 3 belong, the first naturally and the second artificially, to the tone D with the minor third. Let one introduce in the accompaniment E 5 [sqb] 3 the sixth artificial note B in order that a high part moves from B to C #, seventh artificial note what occurs in the following accompaniment A 5 3 #. Our passage B b5 3 E 5 [sqb] 3 is similar to the two of the seventeenth species. [Riccati, The laws of counterpoint, 321; text: Basso continuo. fondamentale, 7 5 3 #, 5 3, 6 3 [sqb], 3 #, 4, 5 [sqb] 3, 5 3 #] [-322-] However, since we have mentioned the passages of the seventeenth species, I invite the Reader to remember that I mentioned (chapter2, [signum] 9, [signum] 10.)the passage B b 5 3 E 5 3 # from the second artificial note to the fifth natural note of the tone A with the minor third, which resemble the two accompaniments of the seventeenth species, as long as the consequent accompaniment contains the seventh artificial note of the respective tone with the minor third. The opposite passage E 5 3 # B b 5 3 can belong entirely to the tone A with the minor third, as it is similar to the ones of the eighteenth species, if one substitutes in the preceding accompaniment the seventh artificial note to the natural of the tone with the minor third on whose fifth said accompaniment is based. The first one was provided to me by the Sonata IX of the Signor Tartini's Opus one. I have transposed it a third down in order to match the passage B b 5 3 E 5 3 #. The second and third example are by Padre Maestro Francescantonio Vallotti. [Riccati, The laws of counterpoint, 322; text: Esempio del passaggio B b 5 3 E 5 3 #, con cui si fa transito dal Tuono D al Tuono A amendue per Terza minore. Basso continuo. fondamentale, 6, 6 3, 5 3 [sqb], 5 3 #, 7 5 3, 7 5 3 #, 6 [sqb] 4 # 2, 6 4 # 2, 3 #, 3 [sqb], 7, 7 3 #, 7 5 [sqb] 3 #, F, maggiore. 6 b 3,6 4, et cetera, E 5 3 # B b 5 3, artificialmente, piano, forte, 5, 6b, 5 [sqb] 3 #] [signum] 13. In order to avoid omitting anything that may concern the passages consisting of two of the thirteen accompaniments of the third and fifth, which consists only of sounds belonging to the natural scales of the tones C with the major third and A with the minor third and of their subordinate tones, I state that there are a further eighteen passages besides the ones that I have mentioned in this chapter and in the two preceding ones. Nine of these derive from the passage from each of the chords B b 5 3, G 5 3 b, E 5 b 3 to each of the chords D 5 3 #, B 5 # 3, F # 5 3,while we encounter an equal number of them if we move backwards from any of the last three accompaniments to anyone of the first three. I informed the reader ([signum] 1.) that the chords B b 53, G 5 3 b, E 5 b 3 belong to the tones F with the major third and D with the minor third in this way, as neither of them is shared naturally by the tones C with the major third and A with the minor third. Similarly, none of the three chords D 5 3 #, B 5 # 3 and F# 5 3 of the the tones G with the major third and E with the minor third that belongs naturally to the tones C with the major third and A with the minor third. The reason why our passages shall be prove to be consisting of two natural accompaniment which belongs to tones that are not subordinate to each other. Taken as principal tones the two of F with the major third and D with the minor third, the tones of G with the major third and E with the minor third are not counted among those subordinate to them. If one ascribes the character of principal tones to G with the major third and E with the minor third, these two do not accept as subordinate the two tones F [-324-] with the major third and D with the minor third. Were the composition based on one of the four tones F and G with the major third and D and E with the minor third, as I observed elsewhere (Book 1, chapter 6, [signum] 5.) moving directly from the tones F with the major third and D with the minor third to the two tones G with the major third and E with the minor third, or vice versa, would prove intolerable and the movements from one to the other of the extreme tones through the intermediate tones C with the major third and A with the minor third would not be without drawbacks. If the composition is based either on the tone C with the major third or on the tone A with the minor third, the passage from the tones F with the minor third and D with the minor third to the two tones G with the major third and E with the minor third, or vice versa, by means of the mentioned tones C and A, proves excellent. In fact, when I move from the tone F to the tone C, both with the major third, I do nothing but passing from a subordinate tone to the principal one, and, when I move from C to G, I move again from the principal to another subordinate. However, in the same instance, namely, when the tone C with the major third or the tone A with the minor third is principal, the direct passage from the tone F with the major third and D with the minor third to the tones G with the major third and E with the minor third, or vice versa, proves extremely unsatisfactory. The reason is that an immediate passage form a tone to another one implies a subordination between said two tones, which, as it does not occur between the two pairs of tones F with the major third, D with the minor third and G with the major third and E with the minor third, it follows as a consequence that an immediate passage from the first two to the other two, or from the second pair to the first one, is forbidden. Since said modulation is always contained within the eighteen passages that I am discussing, it is clear that they deserve to be banished from musical composition. [signum] 14. One should not object to me that, since the following passage, illustrated in the present chapter ([signum] 5.), is found often in the works of good composers, [Riccati, The laws of counterpoint, 324; text: 7 b 5 3, 5 3, 7 5 3 #] the minor seventh added to the perfect accompaniment C 5 3, which consists of the sound B b belonging to [-325-] the scale of the tone F with the major third indicates that the movement C 7 b 5 3 a F 5 3 is a perfect cadence of the tone F. In fact, the passage from D 7 5 3 # to G 5 3 is also a cadence of the tone G with the major third, therefore, when I move from F 5 3 to D 5 3 #, I move directly from the tone F to the tone G, both with the major third, which are not subordinate to each other. The solution to the aforesaid matter is contained in the quoted fifth paragraph, and it becomes clear to us when one considers that the accompaniment F 5 3 is shared by the two tones F and C both with the major third. One cannot deny that the passage C 7 5 3 F 5 3 is a perfect cadence in the tone F with the major third and that the accompaniment F 5 3 in relation to said passage belongs to the said tone. Then, while I move from F 5 3 to D 7 5 3 #, I do not consider the tone F 5 3 as belonging to the tone F with the major third any longer, but as part of the similar tone C. Here we see, therefore, that in the quoted example one moves from the tone F to the tone G both of them with the major third not directly, but by means of the tone C. Hence the passage is correct because the chord F 5 3 can be considered firstly as belonging to the tone F with the major third and then as belonging to the tone C with the major third. The eighteen passages that I rejected cannot be defended in a similar way e they consist of two accompaniments, none of which is shared by the intermediate tones C with the major third and A with the minor third. In ordering in a sequence our eighteen passages my sole aim is that the twelve that contain the accompaniments D 5 3 # F # 5 3 together with the three accompaniments G 5 3 b, B b 5 3 and E 5 b 3 should come before all the others, and this because of what I am about to say. [Riccati, The laws of counterpoint, 325; text: Passaggi viziosi, e da escludersi dal Contrappunto; perchè modulano da un Tuono all'altro, fra i quali non passa una vicendevole subordinazione. 7 3 #, 5 3 b, 5 3 #, 5 [sqb] 3, 5 3, 5 b 3, 5 # 3] [-326-][signum] 15. In order that the Reader may not be mistaken, I inform him that all the eighteen passages placed above are defective if one presumes that the composition is based on the tone C with the major third or on the tone A with the minor third and that the chords that constitute said passages consists entirely of notes belonging to the natural scale of the tone to which they belong. However, if this condition is changed and one supposes that the composition is based on a tone different from the ones mentioned, those twelve passages placed before the others and containing the accompaniments D 3 #, F # 5 3, G 5 3 b, B b 5 3 and E 5 b 3, can be all good and some of them endowed with some great excellence. I invite the Reader to agree that I should demonstrate that the twelve mentioned tones can belong to the tone G with the minor third. The chord G 5 3 b B b 5 3 belong naturally to said tone. Then, the accompaniment E 5 b 3, D 5 3 # and F 3 5 3 belong to it artificially, since they contain the artificial notes E, the sixth, and F #, the seventh. Therefore, since the tone G with the minor third is subordinate to these five tones, namely, F, B b and E b with the major third and D an C with the minor third, and it recognises the five mentioned tones as subordinate, on whichever of the described six tones the composition is based, the passages consisting of the chords D 5 3 #, F # 5 3; G 5 3 b, B b 5 3 and E 5 b 3 belonging to the tone G with the minor third naturally or artificially are good. Now one can see clearly why the same passages that in relation to certain tones are defective, in relation to other tones must be admitted. Since the composition is written either in the tone C with the major third or in the tone A with the minor third, the eighteen passages written above that are presumed consisting of two natural accompaniments must be rejected because they contain a forbidden modulation from one tone to another one that are not subordinate to one another. In fact, if the principal tone of the composition is one of the three with the major third (F, A b, E b) or of the three with the minor third (D, C, G), the first twelve passages elected from the group of eighteen shall have the prerogative of being all more or less good. In fact, if they are considered as belonging to the tone G with the minor third, this tone is either principal or subordinate to the principal one. I invite the Reader to consider the series of twelve passages similar to the aforesaid consisting of chords belonging to the [-327-] tone A with the minor third, and to apply what I said to the tone of G with the minor third what I said that I am about to say of the tone A, which is the model and basis of all the tones with the minor third. [Riccati, The laws of counterpoint, 327; text: Dodici passaggi formati da accordi proprj del Tuono A modello di tutti i Tuoni per Terza minore, e simili agli altrettanti, che precedono gli altri nella sovrapposta serie. 5 3 #, 5 3, 5 [sqb] 3, 3 #] [signum] 16. Several of our passages can appear frequently in a form that is different from the one that we have considered and, instead of belonging entirely to the tone G with the minor third, they can be employed to move from said tone to a subordinate one or vice versa. One shall modulate mostly from the tone G with the minor third to the tone B b and vice versa, which share the same natural scale, with the major third through the passages D 5 3 # B b 5 [sqb] 3 and B b 5 3 D 5 3 #. I mentioned earlier (chapter 2, [signum] 19.) the passage D 5 3 # C 5 [sqb] 3 similar to the first of the two quoted above D 5 3 # B b 5 [sqb] 3, and I said that it moves from the tone A with the minor third to the tone C with the major third, both of whom accept the same scale. In fact, the example by Padre Calegari with which I provided you contains this kind of modulation. One shall move almost always from the tone B b with the major third to the tone G with the minor third also through the passage B b D # 5 3. The accompaniment E 5 b 3, occurs in four passages, suits the tones F with the major third and D with the minor third naturally, and, when it is employed in this role, said passages modulate from one of the mentioned tones to the tone G with the minor third or, conversely, from the this last tone to one of the first ones. However, this is not the place to articulate minutely all the roles that our twelve passages can assume. Therefore, I conclude that they shall almost never be excluded totally from [-328-] counterpoint, when they are employed as consisting of two chords belonging to the same tone or to two tones that are subordinate one to the other. [signum] 17. Before I enter the detailed discussion of the artificial passages, I believe it to be useful to recapitulate briefly all the natural passages that I explained so-far. In the two preceding chapters and in the present, I have exhausted the list of the passages consisting of two of the thirteen chords that consist only by notes belonging to the natural scales of the tones C with the major third, A with the minor thirds and of their subordinates. If we resort to the rules of the combinations, those rules teach us that thirteen terms can be combined in 156 ways. Now, the passages considered up to now reach precisely the number of 156, and I am about to demonstrate this both to clarify further what was said and in order that the reader may remember it more clearly. [signum] 18. I stated (chapter 1, [signum] 5.) that the passages that can move from one to the other of the three accompaniments C 5 3, G 5 3 a F 5 3, on which depends the origin of the tone C with the major third, are six. In fact three terms can combine in pairs in six ways and no more. For the same reason, the passages through which one can move from one to the other of the three chords G 5 3, D 5 3 # and C 5 3 that generate the subordinate tone G with the major third shall amount to six, and the possible reciprocal passages from one to the other of the three chords F 5 3, C 5 3, b b 5 3 that generate the subordinate tone F with the major third shall also amount to six. However, because the principal tone C has the two accompaniments C 5 3 and G 5 3 in common with the similar subordinate tone G, and the two accompaniments C 5 3 and F 5 3 in common with the other subordinate tone F, since two terms can be combined together two by two in only two ways, it follows that the two tones C and G with the major third shall share the two passages C 5 3 G 5 3 and G 5 3 C 5 3, and that the two passages C 5 3 F 5 3 and F 5 3 C 5 3 shall belong to the two tones with the major third C, principal, and F, subordinate. Therefore, if all three the tones with the major third, C, principal and G and F, subordinates, are counted, the different passages that I am describing reach the number of 14. Apply a similar [-328-] concept to the three tones with the major third, A, principal, and E and D, subordinate, and one shall discover furthermore that the passages that can move from one to the other of the three accompaniments that generate the tone A or the tone E or the tone D are fourteen. [signum] 19. In the chapter 2, [signum]1. I pointed out to the Reader tat one can move in nine different ways from the three chords C 5 3, G 5 3 and F 5 3, that produce the tone C with the major third to the three chords A 5 3, G 5 3 and F 5 3, that produce the tone A with the minor third, which agrees with said tone C in accepting the same scale. Similarly, the passages that can move from the three chords G 5 3, D 5 3 #, C 5 3, that produce the tone C with the major third, to the three E 5 3, B 5 # 3 and A 5 3, that produce the tone E with the minor third, which tones share the same scale, are nine. Nine are also the passages from the three accompaniments F 5 3, C 5 3 and B b 5 3 to the three accompaniments D 5 3, A 5 3 and G 5 3 b, of which the former generate the tone F with the major third and the latter the tone D with the minor third, which adopt the same scale. Therefore, the mentioned passages would amount to a total of 27. However, since the accompaniments C 5 3 and G 5 3 are common to the two tones with the major third C, principal, and G, subordinate, and also the two chords A 5 3 and E 5 3, since they belong equally to the two tones with the minor third A, principal, and E subordinate, and since it is possible to proceed in four different ways from two terms to another two, there follows the consequence that the four passages C 5 3 A 5 3, C 5 3 E 5 3 and G 5 3 A 5 3 and G 5 3 and E 5 3 belong both to the nine from the three accompaniments C 5 3 and G 5 3, F 5 3 that generate the tone C with the major third to the three A 5 3, E 5 3 and D 5 3 that generate the tone with the minor third and to the nine from the three accompaniments G 5 3, D 5 3 # and C 5 3 that generate the tone of G with the major third to the three E 5 3, B 5 # 3 and A 5 3, that generate the tone E with the minor third. For a similar reason the accompaniments C 5 3 and F 5 3 are involved in the production of the tones C and F with the major third, and the other two A 5 3 and D 5 3 in the production of the tones A and D with the minor third, while the four passages C 5 3 A 5 3, C 5 3 D 5 3 F 5 3 A 5 3 and F 5 3 D 5 3 are counted both in the number from the three accompaniments C 5 3, G 5 3 and F 5 3 belonging to the tone C with the major third to the three A 5 3, E 5 3 and D 5 3 belonging to the tone A [-130-] with the minor third, and also in the number of the passages, also nine, that move from the three chords F 5 3, C 5 3 and B b 5 3 belonging to the tone F with the major third to the three passages D 5 3, 5 3 and G 5 3 belonging to the tone D with the minor third. From what was said one should draw the conclusion that the different passages that we encounter are twenty-seven rather than nineteen, if one wants to proceed from the three respective chords that generate the tones with the major third C, principal, and G and F, subordinate, to the other three chords that produce the scales of the tones with the minor third A, principal, and E and D, subordinate, where the the first one is coincides with the scale of the tone C with the major third, the second one with the scale of the tone G with the major third and the third one with the scale of the tone F with the major third. In the same passage quoted above (chapter 2, [signum] 1.) I also discussed the passages that are the opposite of the ones above, which move from the three accompaniments that generate a tone with the minor third to the three that generate a tone with the major third, which tones share the same scale. Therefore, if one counts the three tones with the minor third, namely, A, principal, and E and D, subordinate, and the three three tones with the major third, C, principal, and G and F, subordinate, it is clear that the passages that differ one from the other that we are discussing are nineteen, which is as many as their reciprocal ones. [signum] 20. From the quoted paragraph of the second chapter we have learned that passages that constitute constitute two tones that share the same scale from the same number of accompaniments, namely three with the major third and three with the minor third, and that they move towards an accompaniment of the minor third and minor fifth that belongs to a note that is the seventh of the tone with the major third and the second of the tone with the minor third. Consequently, the passages that are opposite of passages mentioned, which move from said accompaniment of the minor third and minor fifth to six accompaniments, three with the major third and three with the minor third, are also six. If we consider the three pairs of tones, one with the major third and the other one with the minor third, C and A principal, and G, E and F D subordinate, each of them occupies twelve passages, of which we are dealing now. In the quoted chapter I mentioned only the twelve that belong to the tones C and A, the former of whom [-331-] is the model and rule of all the tones with the major third, and the latter of all the ones with the minor third. Now, since none of our passages belongs to a given couple of tones shared by another pair of tones, because the accompaniment of the minor third and minor fifth that belongs to all the passages of a given pair of tones is not shared by any other pair, the passages that we are discussing shall reach the number of 36. [signum] 20. Similarly, thirty-six is the number of passages that move from the principal tone to the subordinate ones or, conversely, from the subordinate ones to the principal tones in a way that is the most complex of the ones allowed, as one can gather from the first paragraph of the present chapter. Finally, the faulty passages that modulate from a tone to another tone that is not subordinate, of which I spoke last ([signum] 13, [signum] 14.) are eighteen. I invite to observe these passages briefly recapitulated and orderly disposed in the following table. Their number, as I said, ([signum] 17.) reach the number of 156. Passages from one to the other of the thirteen natural accompaniments that belong to the tones C, G and F with the major third, and A, E and D with the minor third. The passages from a chord to another one that generate one of the tones C, G or F with the major third are 14 in number. The passage from a chord to another one that generate one of the tones A, E or D with the minor third are 14 in number. The passages from a chord that concurs to the creation of a tone with the major third to one that concur to the creation of the tone with minor third on the same scale are nineteen in number. The passages opposed to the previous ones from a chord that belongs to a tone with the minor third to one that belongs to the tone with the minor third based on the same scale are nineteen in number. The passages from the six accompaniments that generate two tones, one with the major third and the other one with the minor third that share the scale and an accompaniment of the minor third and minor fifth corresponding to the seventh note of the tone with the major third and to the second of the tone with the major third, and, conversely, from the last accompaniment to the six mentioned earlier are thirty-six in number. The passages that modulate in the less simple way among those that are legitimate from the principal tone to the subordinate ones and vice versa are thirty-six in number. The faulty passages that modulate from one tone to the other one that not contain subordinate passages are eighty in number. The total sum of these passages is one hundred and fifty-six. Fourth Chapter. The artificial chords are described and some rules that serve as a guide for the good practice of the passages containing said artificial chords are established. [signum] 1. After I dealt amply within three chapters of the passages consisting of two of the thirteen accompaniments that belong naturally to the tones C with the major third, A with the minor third and to their subordinate, it is necessary to move on and to approach the detailed and precise discussion of the passages where the artificial accompaniments of the aforesaid tones occur. Moreover, since I described to the Reader the true origin of all the artificial accompaniments in the first and in the second chapter, I consider it necessary to refresh its memory by listing them briefly. The seventh artificial note, for instance G # in the tone of A with the minor third, was introduced in music because of the cadences and to imitate artificially in the mode with the minor third the natural semitone through which one ascends to the seventh note to the eighth, or through which one descends from the eighth note to the seventh in the major mode. Said artificial note G # occurs in three different accompaniments, namely, E 5 3 #, G # 5 3 and C 5 # 3. The perfect cadence, the inverted cadence and the cadence from the fourth to the fifth note, as well as the sort of cadence from the second to the fifth note that the tone A with the minor third [-333-] borrows from the derivative tone E, have opened the way in counterpoint to the accompaniment E 5 3 #, which is the main one of the artificial ones. The chord G # 5 3 originates from the cadence that moves from the seventh note to the eighth, which cadence is derived by the tone A with the minor third from the derivative tone D, in which it moves from the fourth note to the fifth one. Although the accompaniment C 5 # 3 of the major third and augmented fifth does not occur in any cadence that belongs strictly to the tone A with the minor third or that is borrowed by said tone from one of its derivative, I deduced its principal introduction in musical compositions from the two passages E 5 3 # C 5 # 3, G 3 5 3 C 5 # that mitigate most the harshness of the augmented fifth C G #, allowing one to hear it as prepared. [signum] 2. Admitted the seventh artificial note G #, the sixth artificial note F # is equally necessary in those occasions where it is necessary to avoid the interval of the augmented second F G # or G # F, which is the interval between the natural sixth note F and the artificial seventh note G #. the accompaniments where the sixth artificial note F # occurs unaccompanied by any other artificial note are the following three: D 5 3 #, B 5 # 3 and F # 5 3. I am used to saying that the six accompaniments mentioned so-fare belong to the firs genus, because the artificial notes seventh and sixth that belong to them are expressly necessary to the mode with the minor third when one wants to employ it as a principal or as subordinate to a principal one, rather than derivative tone of the corresponding mode with the major third that accepts the same scale. The other artificial accompaniments that it is enough that I should mention, are the ones that I call of the second genus, because the fourth and second artificial notes that penetrate into them prove more useful than necessary, in such a way that the composition maintains its meaning, so to speak, even without their help, although it shall be less attractive at certain points. [signum] 3. Both the modes, those with the minor third and those with the major third, have their fourth artificial note that rises a semitone above the natural one. [-334-] D # and F # are the respective fourth artificial notes of the tones A with the minor third and C with the major third that I consider always as model and rule for all the tones similar to them. The fourth artificial note was accepted in music mainly in order to render the cadence from the fourth to the fifth note more conclusive. Therefore, the artificial accompaniments D # 5 3 [sqb] and D # 5 3 # have wormed their way into the tone A with the minor third, while the artificial accompaniment F # 5 3 has been introduced into the tone C with the major third. The act of assimilating the cadence from the second to the fifth note in the movements of the semitone with the perfect cadence of the mode with the major third has also opened the way in counterpoint to the artificial fourth. By means of this, the tone A with the minor third has been enriched with the accompaniments B 5 [sqb] 3 # and B 5 # 3 #, and the tone C with the major third by the accompaniment D 5 3 #. [signum] 4. The second artificial note, which belongs only to the mode with the minor third, falls, unlike all of the other artificial notes, from the second natural note by a minor semitone. In the tone of A with the minor third the second artificial note is B b. Thank to this note, the cadence B b 53 E 5 [sqb] 3 # from the second to the fifth note becomes similar harmonically to the perfect cadence of the mode with the major third without altering the natural semitone F E through which an upper part moves from F, fifth of the preceding accompaniment B b 5 3 to E, basis or octave of the following accompaniment E 5 3 #. The second artificial note is only employed in the accompaniment B b 5 3. Here it is appropriate to establish a law, namely that the artificial notes of the second genus, as they are not exactly necessary to the modes with the major third and to those with the minor third, as employed only in those accompaniments into which they were introduced thanks to the cadences. For instance, in the accompaniment B 5 3, considered as belonging to the tone C with the major third, I shall never substitute the artificial note F # to the natural note F, because there is no cadence in said tone that requires said alteration. I present the Reader with all the artificial notes and accompaniments [-335-] that belong to each of the sixth tones A, E, and D with the minor third and C, G, and F with the major third. The first three tones contain artificial accompaniments of two sorts, namely, those that do not contain other artificial notes excepts the two of the first genus, which are the seventh and the sixth, and those that contain the artificial notes of the second genus, namely, the fourth and the second. Each of the three tones with the major third, C, G and D admits a single artificial note of the second genus, namely, fourth, which enters into two different accompaniments belonging to the second genus of the artificial ones. [Riccati, The laws of counterpoint, 335; text: Corde artificiali del Tuono A per Terza minore. Del primo genere. secondo, settima G #, sesta F #, quarta D #, seconda B b, Accordi, e fondamentali, E 5 3, G # 5 3, C 5 # 3, D 5 3 #, B 5 # 3, F # 5 3, proprj, D # 5 3 [sqb], D # 5 3 #, B 5 s[qb] 3 #, B 5 # 3 # [[B 5 # 3 #]] B b 5 3, Corda, maggiore, quarta F #, F # 5 3, D 5 3 #, E, D #, C #, A #, F. B 5 # 3 #, G 5 # 3, A 5 3 #, F # 5 # 3, C # 5 3, A # 5 3 [sqb], A # 5 3 #, F # 5[sqb] s #, F # 5 # 3 #, F [sqb] 5 3, quarta C #, C # 5 3, D, C #, B, G #, E b, A 5 3 #, C # 5 3, F 5 # 3, G 5 [sqb] 3, E 5 [sqb] 3 #, E b 5 3, quarta B. B 5 3, G5 3 [sqb]] [-336-] [signum] 5. The artificial notes of the second genus, which belong to the second genus and to the subordinate tones, need to be employed sparingly and in passing, when the idea of tones that are not subordinate to the principal one is introduced through them. This occurs when a note and, much more considerably, an entire artificial accompaniment of the second genus in a particular tone belong nevertheless, as artificial of the first genus or as natural, to another tone similar and subordinate to the given tone that the is not considered among the ones that are subordinate to the tone that plays the role of the principal one. If we move from the general rule to particular instances, and if we take the tone E with the minor third as subordinate to the tones C with the major third and A with the minor third, the artificial chords of the second genus, namely, A # 5 3 [sqb], A # 5 3 #, F # 5 [sqb] 3 # and F # 5 # 3 #, must be used with caution because they contain the fourth artificial note A #, which is also the artificial seventh of the similar tone B, which is nevertheless subordinate to the tone E with the minor third, either of whom are considered as principal tone. I invite the Reader to take particular care in applying the accompaniments A 3 3 # and F # 5 # 3 #, that are entirely in common between the tones with the minor third E and B, since they belong to both of them as artificial accompaniments, of the second genus as to the tone E and of the first genus as to the tone B. The two chords C # 5 3 and A 5 3 # appear to be subject to a similar [-337-] exception, as they belong, as artificial accompaniments of the second genus, to the tone G with the major third, and as natural accompaniments to the tone D with the major third, which is in truth subordinate to the tone G, but not to the two principal tones C with the major third and A with the minor third. For a similar reason I invite the Reader to take particular care in employing the chord E b 4 5 b, which is an artificial accompaniment of the second genus in the tone of D with the minor third, and natural in the similar tone G. In fact, although it is counted among the subordinate ones to the said tone D, it is not such in the tones of C with the major third and A with the minor third, one of which has to be the principal one. [signum] 6. Here are a considerable number of artificial accompaniments of one and of the other genus that belong to the tones of C with the major third, A with the minor third and to their subordinate ones that, coupled with each other and with the chords that belong to the mentioned tones, produce a great number of passages. Nor we are allowed to conclude that the number of those chords is considerably smaller because the same chord appears to us several times in different guises and as belonging to different tones. For instance, the chord A 5 3 # is artificial and belongs to the first genus of the tone E and of the tone D, both of them with the minor third, and is also counted among the artificial accompaniments of the second genus of the tone G with the major third. The preceding and consequent chords serve as a fix rule to the ear to distinguish accurately in which role a particular accompaniment is employed and certain passages that are permitted, as, for instance, when the chord A 5 3 # is employed as artificial of the first genus of the tone D with the minor third. However, they prove intolerable in different circumstances and when they precede such chords that show the accompaniment S 5 3 # as artificial of the first genus of the tone E with the minor third. The reason shall be that it is necessary to consider one of our chords under all the roles that it is capable to perform in the tones C with the major third, A with the minor third and in their subordinate ones. [signum] 5. However, before I explain to the Reader the method according to which I intend to deal with the artificial passages, which method must avoid confusion and also excessive [-338-] prolixity, I consider it appropriate to prove that it is not possible to accept in music any new species of artificial accompaniment that are different from the ones that are contained in the series of artificial chords placed above. I keep my considerations to the tones C with the major third and A with the minor third, as I usually do, which I take as model an rule of all the tones that are similar to them. Of the artificial chords belonging to those tones, four, E 5 3 #, D 5 3 #, B 5 # 3 # and B b [[5 3]], are of the major third and fifth, one, C 5 # 3, is of the major third and augmented fifth, three, C# 5 3, F # 5 3 and D # 5 3 #, are of the minor third and minor fifth, one, D # 5 3 [sqb] is of the diminished third and minor fifth, and, finally, one, B 5 [sqb] 3 # is of the major third and minor fifth. Therefore, I say that one is allowed to introduce into counterpoint only these six species of fundamental accompaniments, two of which are truly consonant, and four that are employed only as representing consonant accompaniments. It is known that the two consonant perfect accompaniments are formed by the fifth divided into the the two thirds, either the major one belonging to the bass and the minor one to the inner part, or, conversely, the minor one to the base and the major one to the inner part. Now, a given interval cannot be employed as fifth if it differs from it by more than a minor semitone. Were the difference to be greater than a minor semitone, that interval would not be at the unison in some way with the fifth, nor could it represent it. Therefore, it follows that only the augmented fifth or the minor fifth must be employed to represent the fifth. The first of them is a sharp higher than the perfect fifth and the second is lower than the fifth by the same distance. The same should apply to the intervals that one wants to employ as representing the major third or the minor third. If I enlarge the minor by a sharp, it becomes major; if I reduce it by a flat, it becomes diminished. If the major third is lowered by a minor semitone, it turns into minor; if it is enlarged by a sharp it becomes augmented. However, the augmented third is excluded from counterpoint, because it is necessary to introduce in a musical composition, [-339-] irregularly and without a reason (in the modes with the major third or in those with the minor third) some new artificial note of the second genus that, compared with another natural or artificial note forms the augmented third; or it is necessary to join in the same accompaniment the two artificial notes of the mode with the minor third, the second and the fourth, that are the only ones of all the notes that belong to the same mode to correspond to each other at the interval of the augmented third. [signum] 8. Starting from the first instance, I observe that all the artificial notes of the second genus pertaining to the tone with the major third belong, either naturally or as artificial notes of the first genus, to a similar and subordinate tone from which the given tone borrows them, so to speak. The fourth artificial note F # of the tone C with the major third belongs naturally to the similar or subordinate tone G. The two artificial notes D # and B b, fourth and second of the tone A with the minor belong, the first one, as artificial of the first genus, to the similar and subordinate tone E, the latter one as natural to the similar and subordinate tone D. Any new artificial note capable to produce an augmented third lacks the aforesaid property; therefore, it would be admitted in in counterpoint irregularly and without reason. I show the Reader an example that is also one of the less incorrect. If one wants to employ the augmented third F A # in the tone A with the minor third, it shall be easy to note that the new artificial sound A # belongs as artificial sound of the first genus to the similar but not subordinate tone B with the minor third. I am presented with a tone that is not similar not subordinate to C. If I consider A # as natural of the tone B with the major third, I am presented with a similar tone, but one that is placed at a great distance. Moreover, one shall understand more clearly that one must not accept in general any artificial note, and, [-340-] in particular the ones that form an augmented third together with other notes that belong to a particular tone either with the major third or with the minor third, if one considers that all the artificial notes of the second genus, which would contain certainly the new note, have been introduced into music by means of a particular cadence that belongs to the modes with the major third or with the minor third. However, all these cadences, that belong closely to the modes themselves or that have been borrowed from the derivative modes, have been considered in detail by me, and I introduced into them all the artificial notes suited to render them more conclusive and more pleasant. Therefore, any new artificial note would not be useful in any cadence that belongs to the two mentioned modes and its acceptance into counterpoint, as it would be without reason, would be experienced by the ear as extremely unpleasant. [signum] 9. I move on to consider the second instance, which is much less irregular than the first one, and I investigate whether one may join the third and fourth artificial notes of the mode with the minor third, which produce an augmented third. In the tone A with the minor third these notes are B b and D #. We observed ([signum] 4.) that the second artificial note cannot be used except in the fundamental accompaniment of the second note. The fourth artificial note D # occurs sometimes in the accompaniment of the second note, and, consequently, the only accompaniment where one might think of coupling the notes B b and D # would be the following one, B b 5 [sqb] 3 # of the augmented third and fifth that is founded on the second artificial note B b of the tone A with the minor third. Now, I demonstrate that such an accompaniment must not be allowed. Firstly, the artificial notes B b and D # belong, the former one to the tone D with the minor third as a natural note, the latter one to the tone E also with the minor third as an artificial note of the first genus. It is true that both the mentioned tones are subordinate to the principal tone A with the minor third; however, it is also true that neither the tone D is counted among the subordinate tones of the tone E, nor the tone E among the subordinate tones of the tone D. Therefore, although the notes B b and D # belong as artificial notes [-341-] the same tone A with the minor third, nevertheless, when one includes them in the same accompaniment, because they are borrowed from the mentioned tones with the minor third D and E that are not subordinate one to the other, the ear, which compares them to distinctly together, cannot demonstrate the content of such union. Moreover, one can see that the augmented third B b D # cannot be employed to represent the third B D, naturally belonging to the tone A with the minor third, because the former differs from the latter by two minor semitones. I mentioned above that, if two intervals that are separated by a minor semitone are considered in some way to be at a distance equivalent to the unison, the same cannot be said when their difference consists to twice the minor semitone. Finally, and this is the strongest argument, the coupling of the two artificial notes B b, second, and D #, fourth, contradicts the aim for which the artificial second was admitted in the mode with the minor third. In fact, if the artificial second B b was introduced into counterpoint only to render the fundamental accompaniment B b 5 3 of the second note perfectly consonant, is it not a too open contradiction to disrupt again said accompaniment by substituting the fourth natural note D with the artificial one D # that produces an augmented third with the base? To sum up, the two artificial notes B b and D # cannot occur in the same accompaniment because the fourth artificial note D # prevents the effect thanks to which the use of the second artificial note B b is allowed, as said effect consists in the fact that the accompaniment B b 5 3 becomes a perfect consonant accompaniment with the major third thanks to it. The example that I add here shows a way of introducing in musical compositions the augmented third or the diminished sixth – its complementary chord to produce the octave – in a way that is otherwise irregular and to be rejected. In this example the accompaniment D # F B b of the third and sixth, both diminished, is employed. Such accompaniment derives from the fundamental one B b D # F of the augmented third and fifth. [-342-] [Riccati, The laws of counterpoint, 342; text: Basso continuo. fondamentale, 7, 6 b, 6 b 3, 5, 5 3 #, 6 3, 6 4, 9 5 3, 8, 8 5 [sqb] 3 #, 8 5 3 #, 5 3 #] [signum] 10. Therefore, it remains established that we can employ the three thirds, major, minor and diminished, in the divisions of the perfect fifth or in those fifths that represent the perfect one. The perfect fifth admits only two divisions that derive from the varied combination of the two major and minor thirds that produce the consonant perfect accompaniments with the major third and with the minor one. When I divide this fifth, I cannot employ the diminished third, because, if I did so, I would open the way to the augmented third. For a similar reason, the minor third must not be allowed in the division of the augmented fifth, and even less the diminished one, whose complementary interval to form the augmented fifth is an even more absurd interval, namely the doubly augmented third. For this reason, said augmented fifth shall accept only one division and it shall consist of two minor third. Secondly, it can be divided into two major third. The minor fifth is more abundant in divisions, as they reach the number of three. I am permitted to divide it firstly into two minor thirds. Secondly, it can be divided into a diminished third placed in the bass and a major third belonging to the inner part. Finally, we can order it in such a way that the diminished third is assigned to the middle part while the major third is assigned to the bass. [signum] 11. Now it is time that I should explain the method according to which I intend to deal with the artificial passages. I shall start by establishing certain fundamental canons that belong only to the aforementioned passages, so that they may lead us to ascertain correctly which ones must be allowed and which ones must be banished from counterpoint. After concluding the present chapter with this explanation, I shall then lay out in three chapters the discussion on the [-343-] artificial passages. In the fifth chapter shall discuss the passages that belong to the same tone or move from a tone to another one which share the same scale. The sixth chapter shall contain the passages that do not accept the same scale when the move from a tone to another one and that are reciprocally subordinate, because the artificial notes that belong to the second tone rather than to the first one and are contained in the following chords clarify the change of the tone. For instance, the natural passage E 5 3 A 5 3 belongs to the tone A with the minor third. Introduce in the following accompaniment the sound C 3, seventh artificial note of the tone D with the minor third. This note shall show us clearly the modulation from the tone A to the tone D, both with the minor third. Finally, in the seventh chapter I shall order clearly the artificial passages that represent the natural ones, which I mentioned in the third chapter. These move from a tone to another tone, both of whom do not accept the same scale, and both are reciprocally subordinate to one another. In each of the aforesaid chapters I shall divide the passages into [[seven]] several species according to whether they move downwards, upwards, by a fifth, by a second, by a third, or as to whether they consist of two chords whose bases are at the unison or differ by a minor semitone. While I provide a few short notes on each species of passages, I shall divide them into three classes in the fifth chapter. I shall discuss first the ones that can be used assuredly or at least without too much care. Secondly, I shall address my attention to the passages that need to be employed in music very rarely and with great care. Finally, I shall devote the last class to the passages that must be banned absolutely from counterpoint. In the sixth and seventh chapter I shall join [[almost always]] together the first and second class, but I shall distinguish in my notes the more common passages from those that are employed less frequently. [signum] 12. The artificial passages must be employed with greater care than the one required in the natural passages. We have seen in the previous passages that, in order to judge the quality of a natural passage, it is necessary to consider the [-344-] perfection of the harmonic chords and of the movement of the melody, the good or bad relationship that is formed in our memory from remembering the sounds of the preceding accompaniment compared with the ones of the following accompaniment, and the consonances by representation mitigated by the preparation or introduced without preparation or made more severe by an inverted preparation. Aside from these precautions, the artificial passages require that one should satisfy the scope for which the artificial notes have obtained access into musical compositions. This must be done with so much more rigour, the less necessary are the artificial notes, among which one must place the fourth of both modes and the second of the mode with the minor thirds, and the more exposed is the nature of the accompaniments that contain the artificial sounds. [signum] 13. As the artificial seventh note G # has entered the tone of A with the minor third thanks to five cadences, and especially thanks to the perfect cadence E 5 3 # A 5 3, where one of the upper parts proceeds from G # to A, or from the seventh artificial note, which attracts to itself very strongly the attention of the ear, it occurs that, when a chord containing the artificial sound itself is hear, the ear expects the accompaniment A 5 3 or another one in its place, as, for instance, D 5 3, F 5 3, which contains the note A, so that one may ascend from G # to A, as in the perfect cadence. I place this sort of passages that are frequently employed in musical compositions, unless there is a particular reason against them, in the fist class. The second place is allotted to the passages that move from one to the other of the accompaniments E 5 3 #, G # 5 3, C 5 # 3 containing in themselves the seventh artificial note G #. In this passages the hear is deprived the pleasure of hearing the sound G # ascend to A, but this pleasure is delayed rather than denied. In fact, if I do not want to rise from G # to A, as I can abolish the reason to use the note G # in this case, we encounter the passages that I place in the third class, where from each one of the accompaniments E 5 3 #, G E# 5 3, C 5 # 3 one moves [-345-] one moves to the other ones E 5 3, G 5 3, C 5 3 that contain the natural note G. The final place is reserved for the passages from E 5 3, G # 5 3 and C 5 # 3 to the natural chord B 5 # and to the artificial ones that represent it and do not contain the sound A, the sound G # or the the sound G. It is true, however, that one can introduce the note A in the accompaniment B 5 3 and in the artificial ones that are employed instead of it, by adding to those accompaniments the seventh, which, especially when it is minor, enjoys, as we shall see, the very great privilege of being able to be employed freely and without preparation. Thus our passages rise from the lowest to the first degree, but this imperfect way, by which the sound A can occur in the mentioned accompaniments, demonstrates clearly the lack of elegance of the passages that we are discussing. If the Reader can examine the works of the best masters of counterpoint, he shall be able to observe that the more one of the aforesaid passages belongs to a higher class, the more frequently it is employed, as long as one applies the necessary care also in the other circumstances mentioned by me in the preceding paragraph. [signum] 14. Among the accompaniments that contain the artificial notes, the one of the major third and fifth that is based on the fifth note of a tone with the minor third, for instance, E 5 3 # in the tone A with the minor third, is the best of all, and the passages from said accompaniment to another one are not circumscribed by rules at all rigid. The seventh artificial note G #, which forms the major third of our accompaniment E 5 3 #, has been allowed in music not only because of the perfect cadence and of the cadence from the seventh note to the eighth, but also because of the three that move from the first, from the fourth or from the second note to the fifth. Therefore, since the sense of the composition can achieve a conclusion on the mentioned accompaniment, one can see clearly the reason why, after placing a full-stop, so to speak, it is left to my choice to move to new, and sometimes unexpected, matters. Therefore, on the basis of experience, I establish the First Canon. From the artificial accompaniment of the major third and fifth based on the fifth note of a tone with the minor third one can move to an accompaniment that contains the eighth note or the artificial seventh or the natural seventh or even none of the aforesaid, and this occurs gradually with ever decreasing perfection. [signum] 15. The fundamental accompaniment of the minor third and minor fifth that belongs to the seventh artificial note of the mode with the minor third, as, for instance, G # 5 3 in the tone A with the minor third, has a very mild character, because it consists of simple ratios and because a similar chord, B 5 3, occurs in the diatonic system, and all the derivative tones E, F and B employ it. The more or less frequent use of the passages of the first, second and third degree rests on such foundation. In these passages, the accompaniment G # 5 3 is followed by another accompaniment containing the eighth note A or the artificial seventh G # or the natural seventh G. The passages of the fourth degree, in which G # 5 3 precedes an accompaniment that excludes the aforesaid three notes, shall present themselves to our attention very rarely. Second canon. From the accompaniment of the minor third and minor fifth based on the seventh artificial note of a tone with the minor third, the passage to an accompaniment containing the eighth note or the artificial seventh or the natural seventh is allowed, albeit it becomes progressively less elegant. One does not exclude completely the passage to an accompaniment that does not contain any of the said three notes, although it is rare. [signum] 16. When one hears the sever accompaniment of the major third and augmented fifth, for instance, C 5 # 3, which can be ascribed to the third note of the mode with the minor third, we must not be surprised that the ear is satisfied only by the passages of the first degree, that it merely tolerates the ones of the second degree and then rejects completely the other ones of the third and fourth degree. I provided above (chapter 2, [signum] 21.) the reasons why the augmented fifth C G # proves very harsh. As the ear loves that one should ascend from the artificial seventh note [-347-] G # to the eighth note A, such desire becomes more ardent than usual in the case of the very emphatic accompaniment if the major third and augmented C G #. The aforementioned ascending movement frees the ear from hearing the sound G #, which has become unpleasant because it formed an augmented fifth with C, and serves as a resolution of that interval. It follows from this that the delay in ascending to A, which one sees for instance in the passages of the second degree, does not prove very pleasant, while the failure to make that ascent, as in the passages of the third and of the fourth degree, produces very noticeable discomfort. Third canon. Let one move from the accompaniment of the major third and augmented fifth based on the third note of the mode with the minor third to an accompaniment containing the eighth note of the mode itself. This must be accomplished almost always directly and on a very rare occasion indirectly by interspersing a chord containing the seventh artificial note. The passages of the third and of the fourth degree remain forbidden entirely because they are too harsh. [signum] 17. I observed (Book 1, chapter 3 [signum] 15.) that the sixth artificial note of the mode with the minor third, for instance F # in the tone A with the minor third, was introduced in music with the sole scope to avoid the passage of the augmented second F G # or G # F from the six natural chord to the artificial seventh or vice versa. Therefore, the sixth artificial note F # must precede or follow the seventh note, also artificial G #, so that one many hear one or the other of these movements F # G # or G # F #, thanks only to which the sixth artificial note was accepted in counterpoint. It is true that one can move from the note F # to the note G # or vice versa through the seventh natural note G, and that the following progressions, which are pleasing to the ear, are encountered often in the tone A with the minor third, namely, E F F # G G # A, A G # G F # F E. Fourth canon. One is allowed to employ the sixth artificial note of the mode with the minor third only in those passages that do not reject the movement from the artificial sixth note to the artificial seventh note or vice versa. [signum] 18. Although the fourth artificial note is not necessary for the two modes with the major third and minor third, as its function is only to render them more attractive and to make the cadences from the second and fourth note to the fifth are more satisfying, the ear requires necessarily that the aim, for which said fourth note was accepted in musical compositions, should be achieved. The aforesaid aim is achieved mainly by introducing the artificial fourth note into the accompaniment that precedes said two cadences and it is also achieved in a secondary way by employing the accompaniments that contain the fourth artificial note in succession one after the other and by concluding with the accompaniment based on the fifth note. I take as an example the following passage F # 5 3 D 5 3 # G 5 3, which can be employed with praise in the tone C with the major third, where the artificial note moves to the natural note in the first and second accompaniment thanks to the cadence that ends on the fifth note. Add to this that in the adduced example we have the union of the two cadences F # 5 3 G 5 3 and D 5 3 # G 5 3 from the fourth note to the second and then to the fifth, while the ear preserves the memory of the accompaniment F # 5 3 when it hears the chord G 5 3. Any passage containing the fourth note that does not follow the laws that I prescribed deserves to be banished absolutely from counterpoint. Nor anyone should tell me that the passage D 5 3 # E 5 3 appears faultless, for instance. In fact, I shall add, in order to remove any misunderstanding, that this is so when it is employed in the tones G with the major third and E with the minor third, but, if one wants to apply it in the tone C with the major third, it is employed without reason and, consequently, it becomes faulty. In order to understand clearly the truth of this matter, it is necessary to add the premise that certain chords introduce the sound F # undoubtedly as fourth artificial note of the tone C, and, therefore, if one employs the passage D 5 3 # E 5 3, it shall cause the ear to experience a very unpleasant effect. The following series of accompaniments can be used as an example, namely, E 6 3 F 6 5 3 F # 6 5 3 G 6 3. The last passage in this series derives from the fundamental passage D 5 3 # E 5 3. The second accompaniment F 6 5 3 shows clearly that the sound F # contained in the third chord F # 6 5 3 is the fourth artificial note of the tone C with the major third and the unpleasant impression that he passage F # 6 5 3 G 6 3 generates comes from this. Fifth canon One must move directly or by means of some chord that contains the artificial fourth note of one or of the other mode with the major or with the minor third from an accompaniment that contains the same fourth artificial note to the accompaniment based on the fifth note. Any other passages that contains the fourth artificial note but cannot abide by the prescribed law deserves to be forbidden completely. [signum] 19. The freedom we that we have to employ the passages containing the second artificial note of the mode with the minor third is restricted in the same way. This artificial note occurs in a single accompaniment which is based on it. For instance, in the tone A with the minor third, said chord is B b 5 3. I have shown (chapter 1 [signum] 9.) that the second artificial note B b is admitted in the tone A with the minor third only thanks to the cadence B b 5 3 E 3 #, which, at any rate, does not need said note necessarily. Therefore, it is necessary to form said cadence when one wants to employ the second artificial note. However, since the cadence from the second to the fifth note of the mode with the minor third can be assimilated to the perfect cadence of the mode of the third major without compromising any natural semitone in the movements of the semitone to the seventh added to the accompaniment preceding the third of the following and from the third of the preceding accompaniment to the eighth note of the following one, and because said semitone does not occur in our cadence B b 7 5 3 E 5 3 # rising by a major second from D third of the third chord to E eight note of the second one, the third of the consequent accompaniment E 5 3 # must be necessarily major, so that one may at least [-350-] taste the semitone A G # from the seventh A added to the chord B b 5 3 the the major third G # of the following accompaniment. The passage B b 7 5 3 E 5 3 would not please without such a semitone and, as it does not deserve the name of cadence, it would show us clearly the illogical use of the second artificial note B b, which was accepted in music only thanks to the cadence from the second to the fifth note. When we realise the cadence that we are discussing, one of the upper parts descends by a diminished third from B b to G #. The intonation of this chromatic movement can be often made easier by dividing through the sound A into two minor seconds, namely, B b A, A G #. The aforesaid intervening sound opens our ear and allows us to insert a chord containing the sound A and forming a cadence compared with the sound E 5 3 # between the two chords B b 5 3 and E 5 3 #. For instance, the accompaniments D 5 3 and A 5 3 are of this nature as they contain the note A and, joined to E 5 3 # they from the cadences D 5 3 E 5 3 # and A 5 3 E 5 3 #. Consider the following passages D 8 6 b 7 5 E 5 3 # and B b 5 3 A 5 3 # 5 3 #. If one joins together the two cadences both ending with E 5 3 #, the ear cannot help being pleased by them. The last observation allows us to realise in practice how absurd it would be to place between B b 5 3 and E 5 3 # the accompaniment F 5 3, which contains in fact the sound A, but does not create a cadence when it is compared with the accompaniment E 5 3 #. It is without a doubt that the inconclusive passage F 5 3 E 5 3 # disturbs very much the imperfect completion of sense that is provided by the cadence B b 5 3 E 5 #. Sixth canon From the accompaniment based on the second artificial note of the mode with the minor third one should move to the accompaniment of the major third and fifth based on the fifth note either directly or through an accompaniment that contains the eighth note and that constitutes a cadence with the aforesaid perfect accompaniment of the fifth note. All of the other passages that contain said artificial note and do not agree with ours must be rejected. [-351-] [signum] 20. The inverted preparation of the consonances by representation is unpleasant to the ear, especially in the case of the ones belonging to the chromatic genus that have been introduced in music only thanks to the artificial notes. The augmented fifth, the diminished fifth, the diminished third and the augmented sixth belong to this category. In fact, if the inverted preparation of these consonances is too apparent, which occurs when the representing and the represented consonance share the same lower sound, the passage containing such a notable effect needs to be banished from counterpoint. Leaving aside the examples of the passages that are declared as faulty even by the previous canons, I present the Reader with the following two, namely, D # 5 3 [sqb] D # 5 3 # and B 5 [sqb] 3 # B 5 # 3 #, which both contain the passage from the diminished third D # F to the minor third D # F # sharing the same lower sound D #. Seventh canon The passages in which the consonance by representation that only originates from the artificial notes is followed by the represented consonances that shares the same upper or lower sound with the preceding one. [signum] 21. Since the artificial passages must be employed with all the utmost care, it is necessary to avoid the ones that produce in the ear the idea of an unlawful modulation from a tone to another one that are not linked to each other by reciprocal subordination. If we take as principal tone the one of C with the major third or the one of A with the minor third, as I established earlier (chapter 3, [signum] 13.), the passages that move reciprocally from the three accompaniments G 5 3 b, B b 5 3 and E 5 b 3, naturally belonging to the relative tone F major and D minor, to the three accompaniments D 5 3 #, F # 5 3 and B 5 # 3, naturally belonging to the relative tones and E minor, shall have to be banished because they lead us to a tone that is not subordinate to the preceding one. Although our passages do not contain such a fault when the three consequent accompaniments are consider as artificial, the first two of the tone C with the major third and all three of the tone A with the minor third, nevertheless, [-352-] I would avoid to employ even those that do not contravene the canons already established because they can introduce the suspect of a forbidden modulation. One should not make an exception even when the artificial chord of the tone A with the minor third B b 5 3 is joined together with the accompaniments D 5 3 #, F # 5 3 and B 5 # 3, which belong artificially to the same tone. In fact, should anyone think of introducing the artificial fourth D # of the tone A with the minor third into the accompaniments D 5 3 # and B 5 # 3, one would couple in the passages G 5 3 b D # 5 3 #, B b 5 3 D # 5 3 #, E 5 b 3 D # 5 3 #, G 5 3 b B 5 # 3 #, B b 5 3 B 5 # 3 # and # 5 # 3 B 5 # 3 # chords that are so far removed from each other that the most pure art of an extremely skilled master of counterpoint would struggle to hide their discrepancy. Eighth canon If the passages that appear to modulate from a tone to another one without the link of the due reciprocal subordination, they need at least to be used sparingly and all the more carefully the more they consist of accompaniments removed one from the other. Fifth chapter On the artificial passages belonging to the same tone or that move from one tone to another one and share that same scale. [signum] 1. As I have to discuss the artificial passages that belong to the same tone or that move from one tone to another one and share the same scale, I start from the ones descend by a fifth and rise by a fourth. [Riccati, The laws of counterpoint, 352; text: Passaggio artificiale rappresentante il naturale E 5 3 A 5 3, 5 3 #, 5 3, Passaggi rappresentanti, D 5 3, 5 3 [sqb], G 5 3 C 5 3, 5 [sqb] 3, 5 # 3, C 5 3 F 5 3, D 5 3 G 5 3, B 5 3 E 5 3, 5 [sqb] 3 #, 5 # 3 #, F 5 3 B 5 3, 1. 2. 3. 4. 5. 6. 7. 8. 9.10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.] 1. E 5 3 # A 5 3. Perfect cadence in the tone A with the minor third, as long as one places in the bass the fundamental E A and the preceding accompaniment falls on a weak beat and the following one on a strong beat. See that I wrote on the this matter at chapter1, [signum] 12, 13, 21, 22. 2. A 5 3 D 5 3 #, 3. A 5 3 D # 5 3 [sqb], 4. A 5 3 D # 5 3 #. In the second passage, the accompaniment D 5 3 # can be used as an artificial accompaniment of the tone A with the minor third when one part moves from F # to G #, while it can be used as an artificial accompaniment of the tone C with the major third when it is followed by the chord G 5 3. As to the third and fourth passage, the derivative chords F 6 E 3 and F # 6 # 3 shall be used more often than the fundamental ones D # 5 3 [sqb] and D # 5 3 # that are less perfect. In this way the altered movement of the melody A D # shall be avoided. The fourth passage is employed correctly when one part rises from F # to G #. 5. G 5 3 C 5 # 3, 7. G # 5 3 C 5 # 3. I shall discuss the fifth passage, which I overlook here, in the following paragraph. The sixth and seventh passage shall occur to us mostly in this fashion, namely, G 5 3 E 6 3 # [-354-] and G # 5 3 E 6 3 #, and in this way one shall achieve the advantage of avoiding the melodic passage G # C in the seventh passage. The reader should remember what I said on this passage at chapter 2, [signum] 20. and consider the example that I placed there. Observe also the following example of the sixth passage. [Riccati, The laws of counterpoint, 354, 1; text: Basso continuo. fondamentale, 6 3, 6 4 2, 7 5 3, 5 3, 6 3 #, 7 5 3 [sqb], 7, 5 # 3, sesto, nono] 8. C 5 3 7 # 5 3, 9. C 5 # 3 F 5 3, 10. C 5 # 3 F # 5 3. The accompaniment F # 5 3 in the eighth and tenth passage can be artificial both in the tone C with the major third and in the tone A with the minor third. The ninth and tenth passage shall be employed almost always in this fashion E 6 3 # F 5 3 and E 6 3 # F # 5 3. The way in which the ninth passage is realised in the ninth example by moving from E 5 3 E to E 6 4 2 is also elegant. 11. D 5 3 G # 5 3, 12. D 5 3 # G 5 3, 13. D 5 3 # G # 5 3. Moreover, the twelfth passage creates, in the tone C with the major third, the cadence that moves from the second to the fifth note and that draws a more pleasant flavour from the fourth artificial note F #, and it can be used also in the tone A with the minor third according to the fourth canon. I clarify this with the following example. [Riccati, The laws of counterpoint, 354, 2; text: Basso continuo. fondamentale, 5 3 #, 6 3 #, 5 3, 6 3, 6 # 3, 6 4, 5 # 3, nono, duodecimo, primo, secondo, terzo.] The fact that the preceding chord D 5 3 # of the thirteenth passage may belong artificially to the tone C with the major third contradicts the fifth canon. In the example placed above [-355-] it is employed correctly as artificial passage of the tone A with the minor third. 18. B 5 3 E 5 3 #, 20. B 5 # 3 E 5 3 #, 21. B 5 [sqb] 3 # E 5 3 #, 22. B 5 [sqb] 3 # E 5 3 #, 24. B 5 # 3 # E 5 3 #, 26. B b 5 3 E 5 [sqb] 3 #. I have mentioned earlier the passages 18, 20, 21, 22, 24 and 26 (chapter 2 [signum] 7, 8, 9, 10.), and I adduced two examples of the passages 21 and 22 containing the so-far little known accompaniment B 5 [sqb] 3 # of the major third and minor fifth. Here there are as many examples of the passage 26. I add tow examples of passages that are similar to the passage 22, namely, B 5 [sqb] 3 # E 5 3 # taken from the Psalms by Signor Benedetto Marcello. In the first one, transcribed from the fourth volume, page 15, the seventh is added to the accompaniment of the major third and minor third F # 5 [sqb] 3 #, while the passage F # 5 [sqb] 3 # B 5 # 3 # is used in the following form: C 3 6 # 4 # B 5 # 3 #. The second example, contained in the volume seven, page 69, presents us the passage D 5 b 3 # B 6 3 derived from the fundamental one D 5 b 3 # G 5 3 [sqb]. [Riccati, The laws of counterpoint, 355; Basso continuo. fondamentale, text: 5 6 3, 6 4 # 2, 5 [sqb] 6 3, 3 6 # 4, 5 3 #, 6 3, 7 5 3 #, 7 [sqb] 5 3 #, 7 5 [sqb] 3 #, 3 #, pronto o Signor a sottopormi io sono, 6, 3 b, 6 3 4, 7 3 #, 5 3, 5 b 4, 5 3 #, 8 3, 7 #, 5 3 [sqb], 22. 18. ] Deed the dissonance of the fourth to the accompaniment D 5 b 6 3, that famous author presents us with a masterly artifice the chord D 5 b 4 of the fourth and minor fifth on a strong beat, while [- 356-] he reserves for the following weak beat the harsh accompaniment D 5 b 3 # of the major third and minor fifth, so that it may produce a milder impression on the ear. 28. F 53 B 5# 3, 29. F # 5 3 B 5 # 3, 30. F 5 3 B 5 [sqb] 3 #, 32. F 5 3 B 5 # 3 #, 33. FF # 5 3 B 5 # 3 #, 34. F 5 3 B b 5 3. One can see an example of the passage B b 5 3 E 5 [sqb] 3, similar to the number 28. F 53 B 5 # 3, at chapter 3, [signum] 12., while the passage number 30. F 5 3 B 5 [sqb] 3 # is found in the example of Padre Maestro Vallotti at chapter 2, [signum] 8. Here are the examples of the other passage. [Riccati, The laws of counterpoint, 356, 1; text: Basso continuo. fondamentale, 7 5 3, 5 # 3, 6 5 3, 5 # 3 #, 6 3, 7 5 3 #, 5 3 #, 5 3, 6 5 3 #, et cetera, 7, 5 #, 7 3 #, 7 5 # 3 #, 8 6 b 3, 6 [sqb] 4 # 2, 29. 20. 33. 24. 32. 24. 32. 36.] [signum] 2. The present paragraph is devoted to the passages that descend by a fifth or rise by a fourth that are encountered very rarely in musical compositions. Starting from the passage number 5. G # 5 3 C 5 [sqb] 3, I state that, if the fundamental movement G # C is avoided, it can be used in the tone A with the minor third. I employed in this capacity in the examples that follow. [Riccati, The laws of counterpoint, 356, 2; text: Basso continuo. fondamentale, 5 3, 6 4 2, 7 5 3, 7 5 3 #, 6 # 4 3, 8 5 3 #, 6 4 b 3, 7, 7 5 [sqb], 7 3 # 7 5 [sqb] 3 #, 3 #, 7 5 #, 11. 5. 8. 27. 18. 31. 22. 35. 26] [-357-] [Riccati, The laws of counterpoint, 357, 1; text: Basso continuo. fondamentale, 6 # 3, 5 [sqb] 3, 6 3, 7 5 3 #, 6 4, 5 3 #, 5 [sqb], 8 3 #, 3 #, 11. 5, 8, 27, 18. 1.] The fifth passages proves appropriate also to move from the tone A with the minor third to the tone C with the major third. Moreover, since such modulation arrives unexpected to the ear, the masters of counterpoint can employ it elegantly when by some lucky turn of events sadness suddenly turns into joy. As to the expression of the sentiment of the words in music especially in relation to the emotions of the soul, I shall discuss them later (Book 4, chapter 5, 6, 7.). For now, I invite the Reader to observe the following passage. [Riccati, The laws of counterpoint, 357, 2; text: Basso continuo. fondamentale, Al mio Signore mie preci umili dolente alzai ed ei pietoso mi porse orecchio, e m'esaudì clemente. 9, 8 #, 5 [sqb] 3, 6 3, 5, 7, 8 7, 4, 10, 6 4, 5 3, 5.] 19. B 5 # 3 E 5 3, 23. B 5 # 3 # E 5 3. If our passages belong to the tone e with the minor third, they are endowed with extreme [-358-] perfection and they are employed very often. I say that they are used rarely when they are considered as belonging artificially to the tone A with the minor third, since it is very difficult to employ the passage 23 with the due precautions, so that the ear does not believe that the composition has modulated to the tone E with the minor third. I am not sure of how well I managed to do this in the second of the following examples. [Riccati, The laws of counterpoint, 358; text: Basso continuo. fondamentale, 6 3, 5 3, 6 3 #, 6, 7 3 #, 6 3, 5 4, 3 #, 5 #, 7 3 #, 5 4, 19. 9. Adagio, 7 5 3, 3, 5 # 3 #, 7 [sqb] 5 3, 7 5 [sqb] 5 3 #, 7, 5 # 3 #,7 [sqb], 23. 3.] 27. F # 5 3 B 5 [sqb] 3, 31. F # 5 3 B 5 [sqb] 3 #, 35. F # 5 3 B b 5 3. I have placed all these passages in the first example of the present paragraph, while the passage number 27 is also contained in the second example. We have seen (chapter 3, [signum] 4.) that said passage must be employed sparingly when it consists of two natural accompaniments because of its defective harmony, since both the accompaniments F # 5 3, B 5 [sqb] 3 are of the minor third and minor fifth. I also note that the memory of the sound F # contained in the first chord D # 5 3 of the massages 27 and 31 renders the sound F harsher to the ear than in the following chords B 5 [sqb] 3 #and B 5 [sqb] 3 # where it forms a minor fifth. [-359-] The passage number 35, F # 5 3 B b 5 3 is among those that barely deserve to be accepted in music according to the eighth canon, so they must be employed very sparingly because they appear to move from one tone to another one lacking the link of the due reciprocal subordination. As it was established in the fifth canon, the preceding accompaniment F # 5 3 of the passages number 27, 31 and 35 cannot belong artificially to the tone C with the major third. [signum] 3. I shall liquidate with a few words the passages of the fifth downwards and of the fourth upwards that must be excluded from the practice of counterpoint. 14. D # 5 3 [sqb] G 5 [sqb] 3, 15. D # 5 3 [sqb] G # 5 [sqb] 3, 16. D # 5 3 # G 5 [sqb] 3, 17. D # 5 3 # G # 5 [sqb] 3. These passages are banished on the basis of the fifth canon. 25. A b 5 3 E 5 [sqb] 3. Such passage is defective according to the sixth canon if the chord B b 5 3 is considered as artificial of the tone A with the minor third. In fact, if the previous harmonies lead us to believe that the aforesaid accompaniments belong naturally to the tones F with the major third and D with the minor third, the passage B b 5 3 E 5 [sqb] 3 must be accepted in music. I invite the Reader to recall what I wrote on this very passage (chapter 3, [signum]2, 3, 5, 12.) [signum] 4. I lay out in sequence the passages that ascend by a fifth or descending by a fourth that are the inversion of the ones that constituted the subject matter of the previous three paragraphs. [Riccati, The laws of counterpoint, 359; text: Passaggio artificiale rappresentante il naturale A 53 E 5 3, D 5 3 A 5 3, C 5 3 G 5 3, 5 3, 5 3 #, 5 3 [sqb], 5 # 3, 5 [sqb] 3 #, 5 # 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. `6. `7. `8. `9. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.] [-360-] 1. A 5 3 E 5 3. Cadence from the first to the fifth note of the tone A with the minor third when the fundamental passage is employed, the first accompaniment is placed on a weak beat and the second one on a strong one. I discussed such cadence Cadenza earlier on (chapter 1, [signum] 15.). 2. D 5 3 # A 5 3. Passage not often used that can be employed in the followig way. [Riccati, The laws of counterpoint, 358; text: Basso continuo. fondamentale, 5 3 #, 6 3, 6 5 3, 7 5 3, 2.] The fifth canon does not allow us to ascribe the preceding accompaniment D 5 3 # to the tone C with the major fifth as an artificial accompaniment. 5. C 5 3 G # 5 3, 7. C 5 # 3 G # 5 3. the fifth passage is practised elegantly in several ways, for instance: C 5 3 B 6 # 3, E 6 3 D 6 4 #, G 6 3 G # 5 3. In the seventh passage the sound G #, augmented fifth of the preceding accompaniment remains consonant by representation also in the following ones, where it is used [-361-] as the base artificially altered through a minor semitone. I believe it necessary to provide an example of this extremely rare passage. [Riccati, The laws of counterpoint, 361, 1; text: Basso continuo. fondamentale, 5 3 # 6, 6 4, 5, 5 # 3, 7, 7.] 9. F 5 3 C 5 # 3. The best form that can be assigned to this passage is the following one: F 5 3 E 6 3 #. 11. G # 5 3 D 5 3, 12. G # 5 3 D 5 3 #, 14 G 5 3 D # 5 3 [sqb], 15. G # 5 3 D # 5 3 [sqb] 16. G 5 3 D # 5 3 #, 17. G # 5 3 D # 5 3 #. The examples adduced herewith shows one way to realise in practice the passages 11. and 15. [Riccati, The laws of counterpoint, 361, 2; text: Basso continuo. fondamentale, 5 3, 6, 8 6 4 #, 7 5, 5 4, 3 #, ovvero, 6 4 #, 7, 4, 3 #, 7 5 s [sqb], 11. 15.] The three faults noted by me in the passage B 5 3 F 5 3 (chapter 2, [signum] 6) are common [to the passages add. supr alin.] 11, e 13, where, therefore, it is necessary to avoid the movement from one base to another base. The consequent chord D 5 3 # of the passage number 12. can be assigned easily both to the tone C with the major third and to the tone A with the minor third, according to whether it contains the accompaniment G 5 3 or some chord containing the sound G #. We can em ploy the passages number 13 and 17 thus: G # 5 3 F # 6 # 3. The passage number 14 and 16, through which one moves from the tone C or G with the major third to the tone A with the minor third, can prove pleasant in this similar form: G 5 3 F 6 # 3, G 5 3 F # 6 # 3. 18. E 5 3 # B 5 3, 20 E 5 3 # B 5 # 3, 21 E 5 3 B 5 [sqb] 3 #, 22. E 5 3 # B 5 [sqb] 3 #, 24. E 5 3 # B 5 # 3 #. [-362-] The passages number 18, 20, 21, 22 and 24, contain the imperfection mentioned at chapter 4, [signum] 13. Because of this, one cannot rise from G # to A except by adding the seventh to the following accompaniment. Nevertheless, I warn the Reader that the passages number 18, 2 and 22 share the imperfection noted by me (chapter 2, [signum] 4.) in the natural passage E 5 3 B 5 3. This means that in these passages one ascends to truly dissonant accompaniments via the leap of the perfect fifth E B, although for the rest they are employed as consonant. The passages number 12 and 22 shall not prove more dissonant than the passage number 18, because the accompaniment B 5 [sqb] 3 # of the major third and minor fifth is harsher on the ear than the accompaniment B 5 3 of the minor third and minor fifth. One shall remove such a defect if one avoids the fundamental movement of the melody E B and employs some elegant derivative passage instead of it, as in the following examples. [Riccati, The laws of counterpoint, 362, 1; text: Basso continuo. fondamentale, 5 3 #, 5 6 3, 5 6 4, 5 6 3 [sqb], 5 6 # 4, 8 5 3 #, 6 3, 3 6 #, 3 #, 7, 7 5 [sqb] 3 #, 18. 22. 21.] 29. B 5 # 3 F # 5 3. I do not leave this passage without its example. Here, as the preceding chord B 5 # 3 is employed as artificially belonging to the tone A with the minor third, the following chord F # 5 3 shall also belong to the same tone almost always. [Riccati, The laws of counterpoint, 362, 2; text: Basso continuo. fondamentale, 6 3, 6 4, 7 5, 5 3, 6, 9, 8, 5 3 #, 5 #, 7, 5 3, 3 #] [signum] 5. I enter now the passages that ascend by a fifth [-363-] or descending by a fourth, which we encounter very rarely in musical compositions. 10. F # 5 3 C 5 # 3. The present passage would prove unbearable, if the fundamental movement F # C were employed. Since this passage is very sour, I deployed all the possible devices to mitigate its effect in the following example. [Riccati, The laws of counterpoint, 363, 1; text: Basso continuo. fondamentale, 5 3, 6 4, 6 3, 6 3 #, 6, 6 3 #, 5 3 #, 5 #, 3 #, 5 # 3 #, et cetera, 10.] 19. E 5 3 B 5 # 3, 23. E 5 3 B 5 # 3 #, 25. E 5 3 B b 53, 26. E 5 3 # B b 5 3. The passages number 19 and 23 occupy such a separate position in the tone e with the minor third, that the ear finds it hard to convince itself to ascribe them to the tone A with the minor third on some occasions. In the example that I present to the reader, I made it such that the preceding and following chords lead to believe that our passages belong artificially to the mentioned tone A. [Riccati, The laws of counterpoint, 363, 2; text: Basso continuo. fondamentale, 6 4, 5 3 #. 5 3 [sqb], 5 # 3, 6 [sqb] 3, 6 [sqb] 4 #, 6 3, 6 4 # 2, 6 #, 3 #, 5 3 #, 5 3 [sqb], 7 5 [sqb] 3 #, 7 5 3 #, 3 [sqb], 19. 28. 6 # 4 3, 3 #, 3 [sqb], 7 5 # 3 #, 7 5 [sqb] 3 #, 23] [-364-] Since I have already adduced an example of the passage number 26 at chapter 3, [signum] 12., I shall add one of the passage 25 where one shall see that the forbidden movement from one base to another base has been avoided. [Riccati, The laws of counterpoint, 364, 1; text: 6 5, 4, 3, 6, 5, 6 [sqb] 4 # 3, 6 b 5, 6 b 4 # 2, 6 5 [sqb], 6 3 [sqb], 3 #, 7 3 #, 8, 7, 7 5 [sqb] 3 #, 7 5 3 #, 7 3 #, 8 5 [sqb] 3 #, 25.] 27. B 5 3 F # 5 3, 28. B 5 # 3 F [sqb] 5 3. In the passage number 27 containing the imperfection of consisting of two chords of the minor third and minor third that are consonant merely by representation, the second of said chords can belong artificially to the tone C with the major third and to the tone A with the minor third. I put it into practice it in that double role in the following passages. [Riccati, The laws of counterpoint, 364, 2; text: Basso continuo. fondamentale, 5 3, 5 [sqb] 3, 6 # 3, 5 [sqb], 27, 7 5 3, 27.] The passage number 28 would prove extremely unpleasant, were one to move from a fundamental note to another one, since the movement B F is rendered more unattractive by the memory of the sound F # contained in the preceding accompaniment B 5 # 3. In the second example of the present paragraph I have employed the derivative passage B 5 # 3 A 6 [sqb] 3. [signum] 6. I complete my survey of the passages of the fifth upwards or of the fourth downwards by mentioning the one that deserve to be banished completely from contrapuntal practice. [-365-] The numbers 3. D # 5 3 [sqb] A 5 3 and 4. D # 5 3 # A 5 3 are considered faulty on the basis of the fifth canon. The number 6. C 5 # 3 G [sqb] 5 3 infringes the third canon. The number 8. F # 5 3 C 5 3 contravenes the fifth canon, when the preceding chord is considered as artificial of the tone C with the major third. If this premise is altered and if said accompaniment is ascribed to the tone A with the minor third, I have never found a way that is tolerable to the ear to adapt our passage to the fourth canon. I believe this to depend on two arguments, namely, on the fact that the passage number 8. contains in itself the faults observed in the similar passage B 5 3 F 5 3 (chapter 3, [signum] 6.) and also on the fact that none of the accompaniments that constitute it belongs strictly to the said tone A, which borrows them from the tone C with the major third. 30. B 5 [sqb] 3 # F 5 3, 31. B 5 [sqb] 3 # F # 5 3, 12. B 5 # 3 # F [sqb] 5 3, 33. B 5 # 3 # F # 5 3 contravene the fifth canon. 34. B b F 5 3 and 35. B b 5 3 F # 5 3 are declared faulty according to the sixth canon. [signum] 7. The passages of the fifth are followed by the passages of the second. The first are the passages of the second upwards. [Riccati, The laws of counterpoint, 365; text: Passaggi artificiali rappresenatanti il naturale D 5 3 E 5 3. F 5 3 G 5 3. C 5 3 D 5 3. E 5 3 F 5 3. G 5 3. A 5 3. A 5 3 B 5 3. B 5 3 C 5 3. 5 3, 5 3 #, 5 3 [sqb], 5 # 3, 5 # 3 #, 5 [sqb] 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21.22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.] [-366-] 1. D 5 3 E 5 3 #, 2. D 5 3 # E 5 3 #, 3. D # 5 3 [sqb] E 5 3 #, 4. D# 5 3 # E 5 3, 6. D # 5 3 [sqb] E 5 3, 7. D # 5 3 # E 5 3. I have discussed the first four passage earlier (chapter 1, [signum] 17, 3 19.) as well as of many cadences that move from the fourth to the fifth note in the tone with the minor third. The passages 6 and 7 can produce a cadence because of the semitone D # E from the fourth artificial note to the fifth one. The passage number 6. produces otherwise a better effect, because the semitone F E from the sixth to the fifth note is preserved in it. These two passages can be employed in this way by adding the seventh to the preceding accompaniment: A 6 [sqb] 4 # 3 G 6 3, F # 6 # 5 3 G 6 3, G # 6 5 [sqb] 3 A 5 3. The accompaniment G # 6 5 3, which follows passage number 7. , shows that the sixth artificial note F # was added to the accompaniment F # 6 # 5 3 with good reason, so that one may ascend to the seventh artificial note G # through the natural note G. Since it shall occur to us to find the passage C 5. D 5 3 # E 5 3 only rarely in musical compositions, I present the Readers with one example of it so that they may examine it. [Riccati, The laws of counterpoint, 366; text: Basso continuo. fondamentale, 6 3, 9 5 3, 8, 7 5 3 #, 5 3, 3 #, 6 4 # 2, 6 3, 6 5 3, 5 3 #, 8 5 3 #, 7 5 3, 5.] 8. F # 5 3 G 5 3, 9. F 5 3 G # 5 3, 10. F # 5 3 G # 5 3. The passage number 8 is the cadence that in the tone C with the major third moves from the fourth artificial note to the fifth. I discussed it at chapter 1, [signum] 17. It can be employed also in the tone A with the minor third when one moves from F # to G # through the natural note [-367-] G. If the passage number 9. is put into practice in the form A 6 3 G # 7 5 3, one shall avoid the fundamental harsh movement F G #. See the fifth example of the second paragraph. One employs the passage number 10. elegantly in this form F # 7 5 3 G # 5 3, which is how I have employed it in the sixth example of the fifth paragraph and in the last one of the fourth paragraph. 11. C 5 3 D 5 3 #, 14. C 5 # 3 D 5 3, 15. C 5 # 3 D 5 3 #. The second chord of the passage number 11. can belong both to the tone C with the major third and to the tone A with the minor third. This depends on the accompaniments that follow. The same has to be said also of the second chord of the passage 15. I provide two examples of the passages number 14. and 15. [Riccati, The laws of counterpoint, 367; text: Basso continuo. fondamentale, 5 3 #, 6, 6 5 3, 8 6 5, 7 5 3#, 5 3, 6 4, 5 3#, 3 #, 5 #, 7, 7 3 #, 6 4, 5 # 3, 14. 19. 15. 2.] 18. E 5 3 F # 5 3, 19. E 5 3 # F 5 3, 20. E 5 3 # F # 5 3. These passages are employed very often. In the numbers 18. and 20. the second chord F # 5 3 can assume the role of artificial both of the tone C with the major third and A with the minor third. In the latter tone the passage number 18. is often employed thus: A 6 3 G # 7 5 3 G [sqb] 6 3 F # 7 5 3 F [sqb] 6 3 E 7 5 3 #. I have discussed earlier (chapter 2, [signum] 14.) the passage number 19., which moves in the said tone A from the fifth to the sixth note. I invite the Reader to observe it applied in the second bar of the penultimate example. 21. G # 5 3 A 5 3. Cadence from the seventh artificial note to the eighth in the tone A with the minor third discussed at chapter 2, [signum] 12. Numbers 22. A 5 3 B 5 # 3, 23. A 5 3 B 5 [sqb] 3 #, 24. A 5 3 B 5 # 3 # and 25. A 5 3 B b 5 3. have been discussed earlier (chapter 2, [signum] 12.) 22. A 5 3 B 5 # 3, 23. A 5 3 B 5 [sqb] 3 #, 24. A 5 3 B 5 # 3 #, 25.. A 5 3 B b 5 3. We have noted (chapter 2, [signum 14.) that the passage from the first to the second note is encountered many times in both modes. Therefore, the passages number 22, 23, 24, 25, that move from the first to the second note, natural or artificial, in the tone A with the minor third, [-368-] are all good, as long as the artificial sounds are introduced for a good reason and the accompaniment B 5 [sqb] 3 # in the passage number 23 is employed in the form that are less harsh on the ear. 30. b 5 3 c 5# 3. This passage, consisting of two accompaniments, one of the minor third and minor fifth, and the other one of the major third and augmented fifth, appears at first sight intractable, but the following elegant disposition and the movement of the parts shall make us change our mind. [Riccati, The laws of counterpoint, 368, 1: text: Basso continuo. fondamentale, 6 3, 6 5 3, 6 5 3 #, 7 5 3, 6 # 5 3, 8 6 4, 3 5 4#, 3 6 #4, 6 4, 5 3 #, 7, 7 5 #,7 3 [sqb], 6 4 5 3 #, 7 3 #, 3 #, 30. 3. 21.] [signum] 8. The method that we have started requires now that we should deal with the passages of the second upwards that are rarely introduced into counterpoint. 12. C 5 3 D # 5 3 [sqb], 13. C 5 3 D # 5 3 #, 16. C 5 # 3 D # 5 3 [sqb], 17. C 5 # 3 D # 5 3 #. In these passages it is necessary to avoid the fundamental movement C D #. The passages 12 and 13 shall prove useful sometimes to modulate from the tone C with the major third to the tone A with the minor third. I took care to put this into practice in the two examples below. [Riccati, The laws of counterpoint, 368, 2; text: Basso continuo. fondamentale, 7 5 3, 5 3, 6 3, 7 5 3 [sqb], 5 3 #, 3 #, 7, 21. 12. 3. 1. 6 # 3, 6 3, 6 4 2, 6 # 3, 6 5, 7 5 3 #, 5 4, 3 et cetera, 8 5 3 #, 8. 13. 14.] [-369-] I add the examples of the passages number 16 and 17, the first of whom belongs to the most famous Padre Maestro Vallotti. [Riccati, The laws of counterpoint, 369, 1; text: Basso continuo, fondamentale, 6 5 3, 5 4, 3, 7 5 [sqb], 9 [sqb] 5 3 # 8 6, 6 # 5 3, 3 #, et cetera, 8 5 3 #, 6 3, 7 5 3 #, 7 3 #, 10 5 # 3, 5 3 #, 5 # 3, 7, 3. 16, 17. 4.] 26. B 5 # 3 C 5 3, 31. B 5 # 3 C 5 # 3. I also include the examples of these two passages, which we shall have occasion to encounter rarely despite reviewing a very large number of musical compositions. In order to preserve the fourth canon, I made a passage containing the sound G # follow the passage number 26, so that one part can touch the sequence of notes F #, G, G #. [Riccati, The laws of counterpoint, 369, 2; text: Basso continuo. fondamentale, 6 3, 6 3 #, 5 3 #, 6 4 # 2, 6 3, 5 3 #, 5 3, 5 # 3, 8 3 #, 7, 3 #, 26. 6 3, 6 3 #, 6 5 3 #, 5 3, 7 3 #, 5 4, 3 #, 7 5 # 3, 22. 31. 1.] [-370-] [signum] 9. The present paragraph is devoted to explain the reasons why certain passages of the second upwards are forbidden. 27. B 5 [sqb] 3 # c 5 3, 28. B 5 # 3 # C 5 3, 29. B b 5 3 C 5 3, 32. B 5 [sqb] 3 # C 5 # 3, 33. B 5 # 3 # C 5 # 3 34. B b 5 3 C 5 # 3. The passages number 27, 28, 32 and 33 are considered faulty on the basis of the fifth canon, and the passages 29 and 34 on the basis of the sixth canon. Be aware tthat I say that the passage number 29 is defective as I presume that the preceding chords make the ear believe that the accompaniment B b 5 3 is artificial of the tone A with the minor third. In fact, if said chord is employed as belonging to the tone F with the major third, the passage B b 5 3 C 5 3 is endowed with great and it is the cadence that moves from the fourth note to the fifth one in said tone. [signum] 10. When I dealt with the natural passage, I showed (chapter 2, [signum] 11.) that the passages of the second upwards are more perfect than their opposite passages of the second downwards. Moreover, I noted in the same chapter, [signum] 15, that, [if add. supra lin.] anyone of these passages is employed with any frequency, especially from a base to another base, several important circumstances shall favour it. I mentioned these in the chapter quoted above, to which I refer the Reader. The same must be said, and with much greater reason, of the artificial passages of the second downwards. At the moment I order in a series the ones that belong to the same tone or that move from one tone to another one that share the same scale. [Riccati, The laws of counterpoint, 370; text: Passaggi artificiali rappresentanti il naturale E 5 3 D 5 3, 5 3 #, 5 3, 5 3 [sqb], G 5 3 F 5 3. D 5 3 C 5 3. 5 # 3, F 5 3 E 5 3. A5 3 G 5 3. B 5 3 A 5 3. 5 [sqb] 3 #, C 5 3 B 5 3, 5 # 3 #, 1. 2. 3. 4. 5. 6. 7 .8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.] [-371-] 1. E 5 3 # D 5 3, 2. E 5 3 # D 5 3 #, 3. E 5 3 # D 3 5 3 [sqb], 4. E 5 3 # D 3 5 3 #, 6. E 5 3 D # 5 3 [sqb], 7. E 5 3 D # 5 3 #, are passages from the fifth note to the fourth note, either natural or sharpened with a sharp in the tone of A with the minor third, and they are all good. The passages 1. and 2. are employed by composers more willingly from E 5 3 # to F 6 3 and from E 5 3 # to F # 6 3 than from a base to another base. I explained the reason earlier (chapter1, [signum] 8.), and it consists in this. When we move from one base to another one, the memory of he sound # persists, which forms a major fourth with the fourth note D, a dissonance that is considered among the harshest. The passage number 3. is employed frequently from E 5 3 # to F 6 # 3, because the derivative chord D 6 # 3 is more perfect than the fundamental one D # 5 3 [sqb]. The passages number 5., 6. and 7. shall be practised mostly in the following for G 6 3 F # 6 3, G 6 3 F 6 # 3 and G 6 3 F # 6 # 3. I inform the Reader that in the passages number 2 and number 5 the second accompaniment D 5 3 # can [-372-]belong artificially to the tone C with the major third. 8. G 5 3 F # 5 3. This is a very good passage from the fifth to the fourth artificial note of the aforementioned tone C. The second chord F # 5 3 can belong also to the tone A with the minor third. 14. D 5 3 C 5 # 3 and 15. D 5 3 # C 5 # 3. Since these passages are heard rarely, I provide an example of each of them. [Riccati, The laws of counterpoint, 372, 1; text: Basso continuo. fondamentale, 6 3, 6 3 #, 6 4 2, 6 4 # 2, 6 5 3, 5 3 #, 5 # 3, 7, 7 3 #, 3 #, 6 3, 5 3 #, 6 3 #, 5 4, 14. 15.] 19. F 5 3 E 5 3 # and 20. F # 5 3 E 5 3 #. The passage number 19. is employed elegantly in this way, namely, A 6 3 E 5 3 #, and it often proves useful to prepare the ninth added to the accompaniment E 5 3 #. I adduced earlier on (chapter 2, [signum] 16.) an example of the fundamental passage number 19. Cast an eye over the example of the passage number 20. [Riccati, The laws of counterpoint, 372, 2; text: Basso continuo. fondamentale, 7 5 3, 6 5 3, 6 3, 5 3 #, 7 5 3 # 7 3 #, 20.] [-373-] 21. A 5 3 G # 5 3. This is a passage very often used from the eighth note to the seventh artificial note of the tone A with the minor third. I discussed it earlier (chapter 2, [signum] 17.). I refer the Reader to said paragraph. 22. B 5 # 3 A 5 3, 25. B b 5 3 A 5 3. I begin from the example of the passage number 22. [Riccati, The laws of counterpoint, 373, 1; text: Basso continuo. fondamentale, 6 3, 6 3 #, 11 9, 5 6, 5 4, 3 #, 5 3 #, 22.] The passage number 35. B b 5 3 A 5 3 is permitted because, according to what I said (chapter 4., [signum] 19.) in establishing the sixth canon, the chord A 5 3 is one of the ones that can be placed between the two chords B b 5 3 and E 5 3 # that constitute the cadence from the second artificial note to the fifth one in the tone A with the minor third. The example placed below conforms to the mentioned canon, since the passage 35. is made to be followed by the chord E 5 3 #. [Riccati, The laws of counterpoint, 373, 2; text: Basso continuo. fondamentale, 8 6 b, 6 4, 5 3 #, 6 3, 6 # 3, 9 7, 8 6, 7 5, et cetera, 3 #, 10 8, 7 5 3 [sqb], 25.] 26. C 5 3 B 5 # 3, 27. C 5 3 B 5 [sqb] 3 #, 28. C 5 3 B 5 # 3 #, 29. C 5 3 B b 5 3. These passages are suited to move on a very rare occasion from the tone C with the major third to the tone A with the minor third. [-374-] [Riccati, The laws of counterpoint, 374; text: Basso continuo. fondamentale, 6 3, 5, 6 4 2, 6 3 [sqb], 3 #, 6 4 # 2, 6 4, 6 3 #, 3 #, 6 # 4, et cetera, 8 5 3 #, 7, 88, 7 [sqb], 5 # 3, 5 # 3 #, 27., 26., 28., 7 3, 6, 9, 8, 6 b, 9 3 #, 5 4, 8 b, 29.] [signum] 11. Let us approach now the passage of the second downwards, which must employed in musical compositions with great care and sparingly. 9. G # 5 3 F [sqb] 5 3, 10. G # 5 3 F # 5 3. When employing the passage number 9., it is necessary to avoid the fundamental movement of the augmented second G # 5 3 F [sqb] 5 3. [-375-] [Riccati, The laws of counterpoint, 375, 1; text: Basso continuo. fondamentale, 6, 3 #, 6, 6 #, 6 3, 6 [sqb] 4 # 2, 5 3, 7 5 3 [sqb], 6 4, 5 3 #, 3 #, 7 5 [sqb] 3 #, 7 5 3 [sqb], 9.] The passage number 10. is full of imperfections and it does not deserve great consideration. It is of the second downwards and consists of two accompaniments of the minor third and minor fifth. Moreover the sound C that forms the minor fifth in the following chord F # 5 3 is rendered even harsher by the memory of the sound G #, base of the preceding accompaniment G # 5 3. In the following example I employ our passage in the form B 6 # 3 A 6 # 3, and I abstain from allowing the sound G # to be heard when I realise it, so that the sound C may prove less harsh. I strived to adapt the music to the feeling of the sentiment of the words cresce il duolo. [Riccati, The laws of counterpoint, 35, 2; text: cresce il duolo, Basso continuo. fondamentale, 6 #, 5 3 #, 7 5, 5 3, 7 5 3 #, 10.] In the passage that we are describing the accompaniment F # 5 3 can belong artificiallyt to the tone C with the major third. In this instance the passage itself modulates from the tone A with the minor third to the tone C with the major third. One should apply [-376-] to such an unexpected modulation what I said earlier ([signum] 20.) in relation to the passages G # 5 3 C 5 [sqb] 3. [Riccati, The laws of counterpoint, 376, 1; text: Basso continuo. fondamentale, Vanne lungi o rio dolore cara pace vieni a me, 6 3, 3 #, 7, 6, 6 4, 5 3, 3 #, 7 3 #, 7 5 3, 10.] 11. D 5 3 # C 5 3. If the previous accompaniment D 5 3 # is considered as artificial of the tone C with the major third, the prescription of the fifth canon (chapter 4., [signum] 18.) is not fulfilled, and, consequently, the passage is forbidden. The supposition that said chord belongs to the tone A with the minor third does not contravene the fourth canon (chapter 4., [signum] 17.). The following way is the best that I was able to find in order to adapt the passage that we are discussing to the aforesaid tone A. [Riccati, The laws of counterpoint, 376, 2; text: Basso continuo. fondamentale, 6 3, 5 3, 3 #, 5 3 #, 7 5 3, 6 4, 5 3 #, 8 3 #, 7, 11] [-377-] 18. F # 5 3 E 5 3. The fifth canon teaches us that the preceding chord cannot be ascribed to the tone C with the major third. The tone A with the minor third can recognise it artificially as its own without it transgressing the fourth canon, as the example written herewith clarifies. [Riccati, The laws of counterpoint, 377; text: Basso continuo. fondamentale, 5 3, 6, 6 #, 3 #, 6 3 # 2, 8 3 #, 7, 18.] 30. C 5 # 3 B 53, 31. C 5 # 3 B 5 # 3, 32. C 5 # 3 b 5 [sqb] 3 #, 33. C 5 # 3 B 5 # 3 #, 34. C 5 # 3 B b 5 3. Since the sound G #, which forms the augmented fourth with C, must ascend to A, our passages are permitted only when the seventh A is added to the ensuing accompaniments. The harshness of the augmented fifth and its resolution that one fulfils by ascending to the seventh A are prejudicial circumstances to those passages. In the passage number 34. the artificial reduction of the second note renders major the seventh B b A, which is minor in the other passages. When I discuss the dissonance (book 3., chapter 2. [signum] 5.), I shall observe that the ear considers the major seventh considerably harsher than the minor one and that it does not approve that it should be employed unprepared unless descending to said seventh from the octave. Therefore, I make one part ascend from G #, augmented fifth of C, to B b through the sound A, which proves sufficient resolution to said altered fifth, and then, through the same sound A, major seventh of B b, I make it return to G ', major third of the consonant accompaniment E 5 3 #. [-378-] [Riccati, The laws of counterpoint, 378, 1; text: Basso continuo. fondamentale, 7 5 3 #, 5 3, 6 3 #, 6 5 3, 6 4 # 2, 6 5 3 [sqb], 5 3 #, 5 3, 6 5 3 #, 6 3, 6 b 3, 5, 7 3 #, 5 # 3, 7 5 3, 7 5 [sqb] 3 #, 7 5 # 3, 7 5 # 3 #, 8 5 3, 7, 30. 32. 31. 33. 34. et cetera] [signum] 12. The following passage of the second downwards are declared forbidden by the fifth canon established in the preceding chapter 4., [signum] 18. 12. D # 5 3 [sqb] C [sqb] 5 3, 13. D # 5 3 # C [sqb] 5 3, 16. D # 5 3 [sqb] C [sqb] 5 # 3, 17., D # 5 3 #, C [sqb] 5 # 3, 23. B 5 [sqb] 3 # A 5 3, 24. B 5 # 3 # A 5 3. [signum] 13. I invite the Reader to observe the artificial passages of the third downwards orderly laid out belonging to the same tone or moving from one tone to another one that share the same scale. [Riccati, The laws of counterpoint, 378, 2; text: Passaggio Artificiale rappresentante il naturale C 53 A 5 3, 5 # 3, 5 3, Passaggi artificiali rappresentanti, D 5 3 B 53, 5 [sqb] 3 #, 5 # 3 #, 5 3 #, 5 [sqb] 3, 5 # 3, 5 3 [sqb], 5 [sqb] 3 [sqb], E 5 3 C 5 3. F 5 3 D 5 3. G 5 3 E 5 3. A 5 3 F 5 3. B 5 3 G 5 3. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.] [-379-] 1. C 5 # 3 A 5 3. This passage can be practised in several ways, namely, C 5 # 3 C 6, E 6 3 # C 6 3, E 6 3 # 4, G # 6 4 A 5 3. The second and the third are the most elegant because the interval that correspond to the bass are true consonances. I have employed in the form of the fourth one in the first example of the [signum] 5. 2. D 5 3 B 5 # 3, 3. D 5 3 B 5 [sqb] 3 #, 4. D 5 3 B 5 # 3 #, 5. D 5 3 B b 5 3, 7. D 5 3 # B 5 # 3, 9. D 5 3 # B 5 # 3 #, 13 D # 5 3 [sqb] B 5 [sqb] 3 #, 19. D # 5 3 # B 5 # 3 #. We can employ freely each of the passages recorded above, as long as the conditions that are required by the artificial notes are fulfilled. The passage D 5 3 6 3 # derived from the passage number 2. D 5 3 B 5 # 3 shall be found in the fourth examcple of the [signum] 2. The fourth example of the [signum] 5. contains the passage number 3. D 5 3 B 5 [sqb] 3 # in its derivative form D 5 3 D # 6 3 [sqb]. The passage number 4. D 5 3 B 5 # 3 # is introduced by the first example of the [-380-] [signum] 5. in the form F 6 3 D # 6 3 #. Then we have the passage F # 6 3 4 deriving from the number 7. D 5 3 # B 5 # 3 in the last example of the [signum] 4. The passage number 13. D # 5 3 [sqb] B 5 [sqb] 3 # shall prove very laudable in the following form, namely, D # 5 3 [sqb] 6. 21. E 5 3 C 5 # 3, 22. E 5 3 # C 5 [sqb] 3, 23. E 5 3 # C 5 # 3. In the fourth example of the [signum] 2. I invite the Reader to observe the passage E 5 3 6 3 # derived from the fundamental passage number 21. E 5 3 C 5 # 3. I provided an example of the passage number 22. taken from a work by Padre Calegari (chapter 2., [signum] 19.). We encounter the passage number 23. under the form G # 6 3 E 6 3 # in the first example of the [signum] 5. We come across it in its most familiar form, namely, E 5 3 # 6, in several occasions that I deem redundant to recount. 31. G 5 3 E 5 3 #, 32. G # 5 3 E 5 3 [sqb] and 33. G # 5 3 E 5 3 # are all laudable passages that are illustrated in the previous examples. The passage G 5 3 G # 6 3, which derives from passage number, is contained in the second example [signum] 1. The passage G # 5 3 G [sqb] 6 3, which derives from number 32., has been illustrated in the example that we have produced just now. Finally, the passage G # 5 3 6which derives from number 33., is found in the last examples of the [signum] 4. e 5. 34. A 5 3 F # 5 3. The second chord of this passage can belong to the tone C with the major third or to the tone A with the minor third. I have employed our passage in the first example of the [signum] 1. as belonging artificially to the tone C under the form G 6 4 2 F # 5 3. In several places I have employed [-381-] said passages as belonging to the tone A. see the third example of the present paragraph. 35. B 5 3 G # 5 3, 36. B 5 # 3 G # 5 3, 40. B 5 # 3 G 5 3. We shall find the passage D 6 3 6 4 #, derived from the number 35. in the third example of the [signum] 4. I have introduced the passages number 36. and 40. into the following example. [Riccati, The laws of counterpoint, 381, 1; text: Basso continuo. fondamentale, 6 3, 5 3, 5 # 3, 5 3 #, 6 #, 6 4, 6 3 #, 85 3, 7, 8 5 # 3, 7 [sqb], 8 5 3 #, 5 # 3, 2. 40. 31. 36.] 6. D 5 3 # B 5 [sqb] 3, 8. D 5 3 # BB 5 [sqb] 3 #, 10. D 5 3 # B b 5 [sqb] 3, 18. D # 5 3 # B 5 [sqb] 3 #. The sound F, minor fifth in the second chords of the passages number 6., 8. and 18. is rendered more noticeable to the ear because of the memory of the sound F # contained in the preceding chords. Number 10. is counted among the ones that have the appearance of modulating from a tone to another one and are not linked together by reciprocal subordination. Therefore, their use is barely tolerated in counterpoint within the boundaries of the eighth canon. Here are the examples of the passages number 6., 8., 10. and 18. [Riccati, The laws of counterpoint, 381, 2; text: Basso continuo. fondamentale, 5 3, 6, 6 4 2, 7 3, 7 3 #, 6 # 4 3, 8 3 #, 7, 8 3 #, 7, 3 #, 7 [sqb] 5 3, 7 5 [sqb], 7 3 [sqb], 7 5 [sqb] 3 #, 6 #, 6 4 b 3, 5 3 #, et cetera, 33. 22. 28. 6. 8. 30. 18. 28. 10.] [-382-][signum] 15. Of the passages of the third downwards listed by me at [signum] 13., the following are forbidden. 11. D # 5 3 [sqb] B 5 [sqb] 3 [sqb], 12. D # 5 3 [sqb] B 5 # 3 [sqb], 14. 5 3 [sqb] B 5 # 3 #, 15. D # 5 3 [sqb] B b 5 3 [sqb], 16. D # 5 3 # B 5 [sqb] 3 [sqb], 17. D # 5 3 # B 5 # 3 [sqb], 20. D # 5 3 # B b 5 [sqb] 3 [sqb]. The passage number 14. contravenes the seventh canon (chapter 4., [signum] 20.) because the diminished third D # F [sqb] refers to the same sound D # in the preceding chord as the minor third D # F # in the following one. The other passages do not abide by the fifth canon (chapter 4., [signum] 18.) 37. B 5 [sqb] 3 # G # 5 [sqb] 3, 38. B 5 # 3 # G 5 [sqb] 3, 39. B b 5 3 G # 5 3 [sqb], 41. B 5 [sqb] 3 # G 5 3, 42. B 5 # 3 # G 5 [sqb] 3, 43. B b 5 3 G 5 3 [sqb]. The passages number 37., 38., 41. and 42 contravene the fifth canon. In order to avoid misunderstandings, I warn the reader that, were the accompaniment B 5 # 3 # to be employed as belonging to the tone E with the minor third, the passages 38. and 42. would be good. I exclude them in the cases where the chord B 5 # 3 # is considered as an artificial chord of the tone A with the minor third. The passages number 39. and 43., where the preceding accompaniment B b 5 3 is an artificial chord of the tone A, are declared faulty by the sixth canon (chapter 4., [signum] 19.). [signum] 16. I have explained the reason why, the remaining circumstances being the same, a passage of the third downwards is more pleasing than the opposite passage of the third upwards (chapter 2., [signum] 22). For such reason, therefore, the passages of the third upwards that I am about to discuss are less perfect than their opposite passages of the third upwards that provided the subject matter for the last three paragraphs. [-383-] [Riccati, The laws of counterpoint, 383; text: Passaggio artificiale rappresentante il naturale A 5 3 C 5 3. Passaggi artificiali rappresentanti, B 5 3 D 5 3. C 5 3 E 5 3. D 5 3 F 5 3, E 5 3 G 5 3. F 5 3 A 5 3, G 5 3 B 5 3, 5 3, 5 # 3, 5 3 [sqb], 5 # 3 #, 5 3 #, 5 [sqb] 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12., 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40. 41. 42. 43.] 1. A 5 3 C 5 # 3. We can employ this passages in different ways, namely, A 5 3 E 6 3 #, C 6 3 E 6 3 #, E 6 4 3 #, A 5 3 G # 6 3 and C 6 3 5 #, the first three of which, containing less harsh the accompaniment E 6 3 # of the major third and minor sixth deserve to be preferred. [-384-] [Riccati, The laws of counterpoint, 384, 1 text: basso continuo. fondamentale, 6 5 3, 5 3, 8 6 3 #, 7 5 3, 6 #, 8 6 4, 5 3 #, 7 3 #, 5 # 3, 7, 7 5 3 [sqb], et cetera, 1.] 5. B b 5 3 D 5 3, 7. B 5 # 3 D 5 3 #, 11. B 5 3 D # 5 3 [sqb], 13. B 5 [sqb] 3 # D # 5 3 [sqb], 15 B b 5 3 D # 5 3 [sqb], 17. B 5 # 3 D # 5 3 #, 19. B 5 # 3 # D # 5 3 #. These passages procede from the second to the fourth note of the tone A with the minor third. I mentioned the passages 5., 11. and 15 earlier (chapter 2., [signum] 24. <)>. See the examples. [Riccati, The laws of counterpoint, 384, 2; text: Basso continuo. fondamentale, 8 6 b 3, 5 3 #, 7 5 3 [sqb], 8 6 3, 6 3, 6 5 3 [sqb], 7 5, 5 3 #, 7 5 3 #, 6 5 3 #, 5 3 #, 7, 3 #, 7 5 [sqb] 3 #, 5 # 3, 7 5 # 3 #, 5. 15. 11. 13. 7. 17. 19.] 22. C 53 E 5 3 #. I employed such passage moving from E 6 3 toE 5 3 # in the fifth example of [signum] 8., [-385-] and in the fourth example of [signum] 11. 27. D 5 3 F # 5 3, 28. D 5 3 # F # 5 3. The artificial accompaniments of our passages may belong to the tone C with the major third or to the tone A with the minor third. I have discussed the passage 27. as belonging to the tone C, in which it moves from the second to the fourth artificial note, at chapter 2., [signum] 24. 31. E 5 3 # G [sqb] 5 3, 32. E 5 3 G # 5 3, 33. E 5 3 # G # 5 3. The passage number 31. is not very elegant, not only because it moves by a third upwards, but because it belongs to the third category. As the seventh artificial note G # of the tone A with the minor third is contained in the preceding accompaniment, the following one does not contain the eighth note A or the artificial seventh G #, but the natural note G. I described the categories mentioned above at chapter 4., [signum] 13. [Riccati, The laws of counterpoint, 385, 1; text: Basso continuo. fondamentale, 5 3, 5 3 #, 5 4, 3, 6 4 2, 7 5 2, 6 3, 6 5 3, 3 #, 8 4, 4, 3, 7, 31.] I add an example of the passage number 32. [Riccati, The laws of counterpoint, 385, 2; text: Basso continuo. fondamentale, 8 6, 7 5, 6 4, 5 3, 27. 32. et cetera] I have discussed the passage number 33. at chapter 2., [signum] 23., where I illustrated it with an example by the excellent Signor Tartini. 40. G 5 3 B 5 # 3, 41. G 5 3 B 5 [sqb] 3 #, 42. G 5 3 B 5 # 3 #, 43. G 5 3 B b 5 3. The examples shall illustrate the ways in which our passages [-386-] can be employed. [Riccati, The laws of counterpoint, 385; text: Basso continuo. fondamentale, 6 3, 5 3, 6 3 #, 3 #, 6 # 4 3, 5 3, 8 5 3 #, et cetera, 6 5 3, 7 5 3 #, 4, 7 [sqb] 3 #, 7 5 3 [sqb], 6 5 [sqb] 3, 8 6 b 3, 6 4, 40. 42. 41. 43. 15.] [signum] 17. Now I examine the passages of the third upwards that must be accepted in counterpoint with the usual care. 2. B 5 # 3 D 5 3 [sqb], 6. B 5 3 D 5 3 #, 10. B b 5 3 D 5 3 #, 12. B 5 # 3 D # 5 3 [sqb], 14. B 5 # 3 # D # 5 3 [sqb], 16. B 5 3 D # 5 3 #, 20. B b 5 3 D # 5 3 #. We shall be able to render the aforementioned passages less harsh by a rigorous use of the artificial notes that shall allow the ear to understand clearly the aim for which they were introduced into music. The following passages number 2. and 12. are employed in the following forms B 5 # 3 A 6 [sqb] 4 3, B 5 # 3 A 6 [sqb] 4 # 3. The examples of the passages 6. and 16. are laid out in such a way that one hears willingly the artificial note F # after the sixth natural note F contained in the preceding accompaniment, because such artificial note is allowed to rise to the seventh artificial note G # in the following accompaniment. [-387-] [Riccati, The laws of counterpoint, 387, 1; text: Basso continuo. fondamentale, 5 3 #, 3 [sqb], 5 # 3, 6 [sqb] 4 3, 7 5 3 #, 6, 9, 8, 6 [sqb] 4 #, 6 4, 3, et cetera, 7 5 3 [sqb], 9 7 3 #, 6 3 #, 8 6 3, 7 5 3 #, 7 3 #, 2. 12. 6. 16.] The passage number 14. is similar to the passages number 2. and 12., and it can be practised with a similar precaution. [Riccati, The laws of counterpoint, 387, 2; text: Basso continuo. fondamentale, 5 3, 5 2, 6 3, 7 4, 6 #, 6 #, 5 3, 8 6 4, 5 3 #, 8 6 b 3, 7 5 3 #, 4, 3 #, 3 [sqb], 5 # 4, 3 #, 6 4, 5 3 #, 3 #, 7 5 3 #, 14. 10. 20.] in the examples of the passages number 10. and 20. that appear to contain a forbidden modulation I ensured to render the sixth artificial note F # necessary by introducing the seventh note G #, also artificial, before and after it. [-388-] 23. C 5 # 3 # 5 3 #. In a passage of the third upwards the sound G #, augmented fifth of the preceding accompaniment, delays its ascent to A, and, before realising this ascent, it becomes major third of the second accompaniment. The aforementioned imperfections render our passage almost impossible to practice. The only way, perhaps, to practice it deserving some approval is the following one. [Riccati, The laws of counterpoint, 388; text: Basso continuo. fondamentale, 8 5 3 #, 6, 7 5, 5 3, 63, 5 3 #, 6 [sqb] 3, 5 3 #, 5 et cetera, 5 # 3, 7 5 3 #, 5 3, 3 #, 8 3 #, 7, 23. 31. 24.] 24. D 5 3 # F [sqb] 5 3. Observe the esample in which one moves from D 5 3 # to A 6 [sqb] 3. I invite the Reader to remember what I said earlier (chapter 2., [signum] 24.) on the passages derived from the fundamental passages of the third upwards that are used most often. 34. F # 5 3 A 5 3. To assign the preceding chord to the tone C with the major third contravenes the fifth canon (chapter 4., [signum] 18.). On would not believe how hard I worked to accommodate the passage number 34. to the tone A with the minor third without infringing the rules of the of the sixth artificial note and without contrasting the character of the tone that requires one to prefer the sixth and seventh natural notes to the artificial ones when one descends from the eighth to the fifth note. The use of the sixth artificial note is necessary in the example in order to rise afterwards to the seventh note, which is nevertheless artificial. [-389-] [Riccati, The laws of counterpoint, 389, 1; text: Basso continuo. fondamentale, 6 3, 6 5 3, 3 #, 7, 3 [sqb], 34.] 35. G # 5 3 B 5 3, 36. G # 5 3 B 5 # 3, 37. G # 5 3 B 5 [sqb] 3 #, 38. G # 5 3 B 5 # 3 #, 39. G # 5 3 B b 53. The altered movements of the melody G # D and G # F prevent the use of many passages derived from the fundamental ones that we are discussing. Although the passage G # 5 3 F [sqb] 6 4 derived from the passage number 35. is forbidden for the reason provided, the passage G # 5 3 F # 6 4, derived from the fundamental one number 36., shall be permitted. I employ it in this way in the example placed at the beginning, which is followed by a way to realise in practice our passages that suits all five. [Riccati, The laws of counterpoint, 389, 2; text: Basso continuo. fondamentale, 5 3, 6 4, 8 5 3 #, 9 8, et cetera, 6 3, 8 5 3, 6 4 #, 6 5, 3 #, 10 6, 8 5, 6 4 #, 6, 5, 4 #, 6 3 #, 6 b, 5 # 3, 7, 7 5 [sqb] 3 #, 5 # 3 #, 8 5 3, 36. 35. 37. 38. 39.] [-390-][signum] 18. The following passages of the third upwards, belonging to the same tone or moving from one tone to another one that share the same scale, must be rejected. 3. B 5 [sqb] 3 # D 5 3 [sqb], 4. B 5 # 3 # D [sqb] 5 3 [sqb], 8. B 5 [sqb] 3 # D [sqb] 5 3 #, 9. B 5 # 3 # D [sqb] 5 3 #, 18. B 5 [sqb] 3 # D # 5 3 #. The passages number 3., 4., 8., 9. are considered faulty according to the fifth canon (chapter 4., [signum] 18.) . the passage 18. would transcribe the seventh canon (chapter 4., [signum] 20.). 21. C 5 # 3 E 5 3 [sqb]. This passage contravenes the third canon (chapter 4., [signum] 16.). 35. D # 5 3 [sqb] F [sqb] 5 3, 26. D # 5 3 # F [sqb] 5 3, 29. D # 5 3[sqb] F # 5 3, 30. D # 5 3 # F # 5 3. These passages all contravene the fifth canon. [signum] 19. in order to conclude the present chapter, I have still to discuss the passages that belong to the same tone or that move from one tone to another one that share the same scale. These passages consist of a natural chord and of the artificial ones that represent it or of two artificial chords that represent the same natural chord. [Riccati, The laws of counterpoint, 390; text: Passaggi artificiali formati dall'accordo B 5 3, e da quelli, che lo rappresentano. Naturale C 5 3, dall'artificiale C 5 # 3, rappresenta. D 5 3, E 5 3, E 5 3 #, F 5 3, F # 5 3, G 5 3, G # 5 3, 5 3, 5 [sqb] 3 #, 5 # 3, 5 # 3 #, 5 # 3 [sqb], 5 [sqb] 3, 5 [sqb] 3 [sqb], 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12., 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 39. 40.] 1. B 5 3 B 5 [sqb] 3 #. 4. B 5 3 B b 5 3, 9. B 5 # 3 B 5 [sqb] 3, 10. B 5 # 3 B 5 [sqb] 3 #, 11. B 5 # 3 B 5 # 3 # 14. B 5 # 3 # B 5 [sqb] 3 #. The examples that we sall introduce shall illustrate the way in which our passages can be used. [Riccati, The laws of counterpoint, 391; text: Basso continuo. fondamentale, 6 3, 6 5 3, 6 5 3 [sqb], 5 3 #, 6 b 3, 6 [sqb] 4 [sqb], 2, 6 5 3 #, 5 3 #, 3 [sqb], 5 # 3, 5 [sqb] 3, 6 5 3, 4, 5 # 3 #, 8 5 3, 7 5 [sqb] 3 #, 7 5 3, 7 5 # 3, 7 5 # 3 #, 8 5 [sqb] 3 #, 7, 3 #, et cetera, 1. 4. 11. 19. 10. 14.] [-392-] 21. C 5 3 C 5 # 3. The most elegant form that can be assigned to this passage is E 6 3 E 6 3 #. 23. D 5 3 D # 5 3 [sqb], 24. D 5 3 D 5 3 #, 25. D 5 3 D # 5 3 #, 29. D 5 3 # D 5 3 [sqb], 30. D 5 3 # D # 5 3 [sqb], 31. D 5 3 # D # 5 #, 33. D # 5 3 # D # 5 3 [sqb]. We shall find the passage number 23. under the form F 6 3 6 # in the second example of the [signum] 5. I provide here the examples of the other passages. [Riccati, The laws of counterpoint, 392; text: Basso continuo. fondamentale, 6 5 3, 8 7 5 3 #, 7 5 3 #, et cetera, 6 3, 5 3 #, 6 3, 7 3, 6, 7 3 #, 6 # 3, 8 3 #, 6 #, 8 7 5 3, 8 5 3, 7, 8 5 3 #, 5 3 [sqb], 24. 25. 31. 36. 29. 30. 33.] Here and in two other places ([signum] 7., esempio 1.; [signum] 11., esempio 4.) I put into practice the passage number 24. as belonging to the tone A with the minor third. It is used more elegantly in the tone C with the minor third. I invite those who want to experience its excellent effect to refer to chapter 2., [signum] 14., example 2., and to enjoy the very beautiful passage by Signor Giuseppe Tartini. 35. E 5 3 E 5 3 #, 36. E 53 # E 5 3[sqb]. The Reader shall find the passage number 36. employed in many examples, and especially in the last three written here above. I present an example of passage number 35. provided to be by Padre Maestro Vallotti. [-393-] [Riccati, The laws of counterpoint, 393, 1; text: Basso continuo. fondamentale, 5 3, 6 3, 5 3 #, 6, 7 5 3 #, 6 4 2, 6 5 3, 7 3 #, 7, 35.] 37. F 5 3 F # 5 3, 38. F # 5 3 F [sqb] 5 3. the passage number 37. in the tone C with the major third deserves great praise, as it moves in it from the fourth natural note to the artificial one and it proves useful to make the cadence from the fourth to the fifth note more conclusive. We can employ it in several ways, and especially in this one: F 8 5 3 F # 7 5 3 G 5 3.I considered it as belonging to the tone A with the minor third in the fifth example of the [signum] 11. It is necessary to avoid the fundamental movement in the passage number 38., so that the ear may not notice that C, minor fifth of F # becomes perfect fifth in the following accompaniment F 5 3. 39. G 5 3 G # 5 3, 40. G # 5 3 G [sqb] 5 3. Padre Maestro Vallotti moves beautifully from the tone C with the major third to the tone A with the minor third through the passage number 39. in the example that I provided (chapter 2., [signum] 24). For the same reason provided in relation to the passage number 38. we must abstain from employ the passage number 40. from a base to another base. I add the examples of the passages number 38. and 40. that I have mentioned just now. [Riccati, The laws of counterpoint, 393, 2; text: Basso continuo. fondamentale, 6 3, 7 3, 6 #, 6 [sqb] 3, 6, 9 8, 7, 40. 38.] [-394-][signum] 20. Among the passages that we are discussing there resist being introduced into musical composition to a larger or lesser degree. 2. B 5 3 B 5 # 3, 3. B 5 3 B 5 # 3 #, 12. B 5 # 3 B b 5 [sqb] 3, 17. B b 5 3 B [sqb] 5 3, 18. B b 5 3 B [sqb] 5 [sqb] 3 #, 19. B b 5 3 B [sqb] 5 # 3, 20. B b 5 3 B [sqb] 5 # 3 #. The fundamental passages number 2. and 3. must be avoided, because they contain an inverted preparation fot he minor fifth. [Riccati, The laws of counterpoint, 394, 1; text: Basso continuo. fondamentale, 5 3, 6 3, 6 3 #, 3 #, et cetera, 5 # 3, 5 # 3 #, 2. 3.] The previous examples are ordered in such a way that first one must introduce the sixth natural note F in the violin part, because it would be unwarranted, and then one must employ the sixth artificial note F #, as required by the seventh artificial note G #. The passage 12. B5 # 3 B b 5 [sqb] 3 is one of those that engender in the ear a strong suspicion that one is moving from one tone to another which are not linked by the necessary bond of reciprocal subordination. Moreover, I cannot see how it can be employed in full harmony for four parts in such a way that the ear may be satisfied. Hence, I would be inclined to banished absolutely from counterpoint. I let the Reader decide what effect may produce the following example in two parts. [Riccati, The laws of counterpoint, 394, 2; text: Basso continuo. fondamentale, 6 3, 6 4, 6 4 b 3, 3 #, 10 6 4 #, 3 [sqb], 5 # 3, 8 5 3, 7, et cetera] [-395-] I do not remember tow have ever encountered the other passages number 17., 18., 19. and 20. The last two have the fault, which is not present in the first two, that couple together accompaniments that appear to belong to tones that are not reciprocally subordinate. Said four passages can be ordered thus in full harmony. [Riccati, The laws of counterpoint, 391; text: Basso continuo. fondamentale, 8 6 b, 6 [sqb] 5, 5 3 #, 8 6 b 3, 6 [sqb] 5 3 [sqb], 6 [sqb] 5 3 #, 7, 3 #, 7 5 [sqb] 3 #, 7 5 #, 7 5 # 3 #, 17. 18. 19. 20.] [signum] 21. The passages written below must not be allowed, namely, 5. B 5 [sqb] 3 # B 5 3 [sqb], 6. B 5 [sqb] 3 # B 5 # s [sqb], 7. B 5 [sqb] 3 # B 5 # 3 #, 8. B 5 [sqb] 3 # B b 5 3 [sqb], 13. B 5 # 3 # B5 [sqb] 3 [sqb], 15. B 5 # 3 # B 5 # 3 [sqb] and 16. B 5 # 3 # B b 5 [sqb] 3 [sqb]. The passage number 7. is declared unlawful by the seventh canon (chapter 4., [signum] 20.) while all the others are condemned by the fifth canon (chapter 4, [signum] 18.). The passage 22. C 5 # 3 C 5 [sqb] 3 contravenes the third canon (chapter 4., [signum] 16.). 26. D # 5 3 [sqb] S [sqb] 5 3, 27. D # 5 3 [sqb] D [sqb] 5 3 #, 28. D # 5 3 [sqb] D # 5 3 #, 32. D # 5 3 # D [sqb] 5 3 [sqb], 34. D # 5 3 # D [sqb] 5 3 #. The passage number 28. is forbidden because of the fifth canon and the remaining ones because of the fifth canon. Sixth chapter On the artificial passages where the modulation from the principal tone to a subordinate one, which do not accept the same scale, is manifested only by the artificial notes and accompaniments that belong to one tone and not to the other one. [signum] 1. After dealing with the artificial passages that belong to the same tone or that move from one tone to another one sharing the same scale, let us move on to those that modulate from a principal tone to a sub ordinate one, [-396-] or vice versa, that do not accept the same scale. As the good method requires, we shall start from the most simple ones, in which said modulation is manifested only by the artificial notes and accompaniments that belong to one tone and not to the other one. I continue to use the tones C with the major third and A with the minor third as a model for all the other ones similar to them, and I address my considerations to the artificial passages that move from the said tones C and A with the aforementioned restriction to the subordinate ones F with the major third and D with the minor third, G with the major third and E with the minor third and also to the opposite passages that lead back from the four subordinate tones to the previous two, C with the major third and A with the minor third, each of whom can preform the role of principal tone. The following series will illustrate clearly the easy way in which one can individuate all of our passages. [Riccati, The laws of counterpoint, 396, 1; text: Accompagnamenti naturali, che i Tuoni F per Terza maggiore, D per Terza minore hanno comuni coi Tuoni C per Terza maggiore, A per Terza minore. Si aggiungono gli accompagnamenti artificiali rappresentanti essi accordi naturali, A 5 3, A 5 3 #, C 5 3, C # 5 3, D 5 3, F 5 3, F 5 # 3] [Riccati, The laws of counterpoint, 396, 2; text: Accompagnamenti naturali, ed artificiali appartenenti ai Tuoni C per Terza maggiore, A per Terza minore. A 5 3, B 5 3, B 5 # 3, B 5 [sqb] 3 #, B 5 # 3 #, B b 5 3, C 5 3, C 5 # 3, D 5 3, D 5 3 #, D # 5 3 [sqb], D # 5 3 #, E 5 3, E 5 3 #, F 5 3, F # 5 3, G 5 3, G # 5 3] [Riccati, The laws of counterpoint, 396, 3; text: Acompagnamenti naturali, che i Tuoni G per Terza maggiore E per Terza minore hanno comuni coi Tuoni C per Terza maggiore, A per Terza minore. Si aggiungono gli accompagnamenti artificiali rappresentanti essi accordi naturali. A 5 3, A 5 3 #, A # 5 3 [sqb], A # 5 3 #, C 5 3, C # 5 3, E 5 3, G 5 3, G 5 # 3] Take an accompaniment from the second series that does not occur [-397-] in the first one and couple it with an artificial chord of the first series. Alternatively, take an accompaniment from the second series that does not appear in the third series and couple it with a chord of the series. The artificial passages that we are discussing currently derive from these coupling. If the natural notes are substituted to the artificial ones in our passages, they appear to consist of two accompaniments without any alteration of sharp or flats that belong naturally to the tones C with the major third and A with the minor third. Therefore, the modulation from one tone to another tone that do not share the same scale, which is contained in the passages that we are discussing, is indicated by the artificial notes. Taken any other couple of tones, one with the major third and the other one with the minor third that accept the same scale, one can find with a similar method the passages that are similar to those that we have taught the Reader to determine in the particular tones C with the major third and A with the minor third. [signum] 2. I begin with those, of our passages, that descend by a fifth. [Riccati, The laws of counterpoint, 397; text: Passaggi artificiali rappresentanti il naturale E 5 3 A 5 3. A 5 3 D 5 3. G 5 3 C 5 3. C 5 3 F 5 3. D 5 3 G 5 3. F 5 3 B 5 3. 5 3, 5 3 #, 5 3 [sqb], 5 # 3, 5 [sqb] 3, 5 [sqb] 3 #, 5 # 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.] [-398-] 1. E 5 3 A 5 3 #, 2. E 5 3 # A 5 3, 3. # 5 # A # 5 3 [sqb], 4. E 5 3 # A # 5 3 #. The first passage, through which one moves from the natural accompaniment E 5 3 shared by both tones E and A with the minor third and G and C with the major third to the artificial accompaniment A 5 3 #, based on the fifth note A of the tone D with the minor third, occurs very frequently. The second passage shall be pleasing whether one employs the second accompaniment A 5 3 # as artificial of the tone D with the minor third or of the similar tone E, or of the tone G with the major third. Signor Giuseppe Tartini employs it in this latter role in the following example. [Riccati, The laws of counterpoint, 398, 1; text: Basso continuo. fondamentale, 5 3 #, 7 5 3 #, 3 #, 7 [sqb] 5 3 #, 7 5 # 3 #, et cetera, 2.] the passages number 3. and 4., that modulate from the tone A to the tone E both with the minor third can be employed in this way. [Riccati, The laws of counterpoint, 398, 2; text: Basso continuo. fondamentale. 6 # 3, 8 5 3, 8 5 # 3 #, 6 5 [sqb] 3 [sqb], 6 3, 5 [sqb] 3 #, 5 s [sqb] et cetera, 3 #, 5 3 #, 7] [-399-] 5. A 5 3 # D 5 3 #, 6. A 5 3 # D # 5 3 [sqb], 7. A 5 3 # D # 5 3 #. When the preceding chord A 5 3 # is assigned to the tone D with the minor third, our passages are entirely similar to the passages number 2., 3. and 4., and what I said of the latter can be applied to them. In the passage number 5. the preceding accompaniment can belong to the tone E with the minor third, as long as the sixth artificial note C # is preceded by the seventh note D #, which is also artificial. One shall move on to the tone C with the major third or to the tone A with the minor third through said passage, according to whether the following chord D 5 3 # belongs artificially to one or the other of the mentioned modes. By using the preceding accompaniment of the passages 6. and 7., which is also artificial of the tone E with the minor third, we shall move through them to the similar tone A. See the example of the passage number 6. [Riccati, The laws of counterpoint, 399; text: Basso continuo. fondamentale, 5 # 3 #, 6 3, 5 3 #6 # 3, 8 5 3 #, 7 5 3, 6 4, 5 3 #, 5 3 [sqb], 8 3 #, 7, 7 5, 6.] Those who expected to employ the preceding chord A 5 3 # in of the passages number 6. and 7. as artificial of the tone G with the major third would go against the fifth canon (chapter 4, [signum] 18). The same must be said also in relation to the passage number 5. , when one presumes that the chord D 5 3 # is artificial in it and that it represents the natural chord D 5 3. 8. A 5 3 # D 5 3. The first accompaniment of the passage number 8. has been taken from the tone G with the major third or from the tone E with the minor third and it has been coupled with the accompaniment D 5 3 shared by the tones A with the minor third and C with the major third. In the first case, it is forbidden, as it contravenes the fifth canon. In the second instance, our passage deserves to [-400-] be judged more sympathetically, as long as the sixth artificial note C # of the minor tone E follows the seventh note D #, as in the example placed below. [Riccati, The laws of counterpoint, 400, 1; text: Basso continuo. fondamentale, 6 3 #, 6 4, 5 3 [sqb], 7 5 3 #, 6 4, 5 3 #, 5 # 3 #, 8.] 17. G 5 3 C # 5 3, 18. G # 5 3 C # 5 3, 19. G 5 # 3 C 5 # 3. In the passage number 17. the second accompaniment must be considered as belonging to the tone D with the minor third. If one assigns it to the tone G with the major third or to the tone E with the minor third, the result shall be a passage consisting of accompaniments that belong to the same tone and that proves similar to the passage C 5 3 F # 5 3 mentioned in the previous chapter 5., [signum] 1. The first Sonata from the Opus one of the excellent Signor Tartini, provides me a beautiful example of the passage number 17, which modulates from the tone C with the major third to the tone D with the minor third. I transposed from the tone A to the tone C with the major third. [Riccati, The laws of counterpoint, 400, 2; text: Basso continuo. fondamentale. Grave, 7, 6 5, 6 # 5, 6 4, 5 3, 7 b, 5 4, 3, 4, 17. et cetera] [-401-] Signor Tartini employs the passage number 17 in the Allegro of the same Sonata, under the following pleasant guise: G 5 3 G 3 b F 6 3. The first accompaniment of the passage number 18. G # 5 3 C # 5 3 belongs to the tone A with the minor third, while the consequent can belong to the tone D with the minor third, to the tone G with the major third and to the tone E with the minor third. The passage number 18. must not be employed very frequently, because, when one modulates from one tone to another one that do not share the same scale, it consists of two accompaniments of the minor third and minor fifth that are consonant by representation. I present herewith three examples of our passage. The accompaniment C # 5 3 in the first example belongs to the tone D with the minor third, in the second one to the tone G with the major third and in the third one to the tone E with the minor third. This last role is one one to which our passage struggle to adapt more than to the other two. [Riccati, The laws of counterpoint, 401; text: Basso continuo. fondamentale, 7, 6 #, 7 b 5 [sqb] 3, 7 5 3, 7 5, 6 4, 5 3, 5 [sqb], 4, 3 #, 3 [sqb], 5 3 #, 6 4 [sqb], 7 5 [sqb] 3, 5 # 3 #, et cetera, 5 [sqb] 3, 9, 8, 8 3 #, 5 3, 18.] [-402-]Albeit in the passage number 19. G 5 # 3 C 5 # 3 the augmented fifth D # of the preceding accompaniment can rise to the sound E contained in the following accompaniment, as the third canon prescribes (chapter 4., [signum] 16.); nevertheless I believe that such passage must be banished almost completely from music because of the extreme harshness produced by the two chords of the major third and augmented fifth, especially since the augmented fifth is introduced unprepared in the second chord. I am not sure that I have been able to mitigate sufficiently the harshness of the passage that we are discussing. [-403-] [Riccati, The laws of counterpoint, 403, 1; text: Basso continuo. fondamentale, 5 3, 6 #, 5 # 3, 6 3 #, 7 3, 6, 7 3 #, 5 4, 3 #, 7, 7 3 #, 19.] 20. C 5 # 3, F 5 # 3, 21. C # 5 3 F # 5 [sqb] 3, 22. C # 5 3 F [sqb] 5 [sqb] 3. What I said of the similar passage number 19. must be applied to the passage number 20. As to the passages of the current chapter, the second chord F # 5 3 of the passage number 12. must be ascribed to the tone C with the major third or A with the minor third. If the preceding chord C # 5 3 is ascribed to the tone D with the minor third, the passage number 21. assumes two forms that are similar to the ones of the passage number 18. G # 5 3 C # 5 [sqb] 3. when the second chord C # 5 3 is assigned to the tone G with the major third or to the tone E with the minor third. One would contravene the fifth canon (chapter 4., [signum] 18.) were one to employ the first accompaniment of the passage number 21. as artificial of the tone G with the major third. If one employs it as artificial of the tone E with the minor third, the fourth canon requires (chapter 4., [signum] 17.) that the sixth artificial note C # of the aforesaid tone should be preceded by the artificial seventh note D #. [Riccati, The laws of counterpoint, 402, 2; text: Basso continuo. fondamentale, 6 3 #, 7 3, 6 4 # 3, 6 4 3 [sqb], 6 5 3, 5 # 3 #, 7 5 3, 7 5 [sqb] 3, 8 5 3, 7 [sqb], et cetera, 21.] [-404-] As the passages contained in this chapter must move to one tone to another tone that do not share the same scale, they require such a condition, namely, that the first chord of the passage number 22. C # 5 3 F [sqb] 5 3 must be assigned to the tone G with the major third or to the tone E with the minor third. The first instance is condemned by the fifth canon, while, although there is no canon that forbids the second instance, as long as the seventh artificial note D# precedes the sixth artificial note C #, nevertheless the two accompaniment constituting the passage are so opposed to each other that it is very difficult to reconcile them together. I tried do so though any means in the passage presented herewith, but it is the task of the Reader to decide whether I was successful or not. [Riccati, The laws of counterpoint, 404; text: Basso continuo. fondamentale. 6 3 #, 7 3, 6 4 [sqb[ 3, 7 5 3, 5 3, 5 # 3 #, et cetera, 22.] 23. D 5 3 G 5 # 3, 24. D 5 3 # G 5 # 3. The mutation of the toned contained in the passages that I am discussing at present renders very crude the ones containing the accompaniment of the major third and augmented fifth. The ear shall be more agreeable to listening to the first accompaniment than to the second one, because, given the change of the tone, it reaches the ear new, unexpected and, consequently, more bitter. One may deduce also from this consideration that the passages consisting of two accompaniments of the major third and augmented third are almost completely impossible to tolerate. In the example written underneath the passage in two parts number 23. does not produce a bad effect. I employed the device of making the previous chord the end of a cadence and I ensured that the sound D #, which is responsible for the harshness of our passage, should be as [-396-] hidden as possible by introducing it on a weak subdivision of the beat. [Riccati, The laws of counterpoint, 405, 1; text: Basso continuo. fondamentale, 6 3 #, 6 3, 3 [sqb], 6 # 3, 5, 3 #, 5 # 3 #, 3 #, 5 3 [sqb], 5 # 3, 8, 7, et cetera, 23.] When the first chord of the passage number 24. D 5 3 # G 5 # 3 belongs to the tone C with the major third or A with the minor third, the fifth canon banishes it from counterpoint in its first instance. The second supposed instance requires that he sixth artificial note of the minor mode F# is preceded by the artificial seventh note G #, according to what the fourth canon prescribes. Since there is no cadence of the aforementioned tone A ending in the previous accompaniment D 5 3 #, the passage number the passage number 24. is much more imperfect that the passage number 23. [Riccati, The laws of counterpoint, 405, 2; text: Basso continuo. fondamentale, 6 3, 6 3 #, 5 3, 6 4 2, 5, 5 # 3 #, et cetera, 5 3 #, 5 # 3, 8, 7, 24.] 27. F 5 # 3 B 53, 28. F 5 # 3 B 5 # 3, 29. F 5 # 3 B 5 [sqb] 3 #, 20. F 5 # 3 B 5 # 3 #, F 5 # 3 B b 5 3. I present the Reader with the examples [-406-] of the passages number 27. 28. 29. and 30., which must be employed very sparingly and with the greatest care. In the passages 20. and 30. the augmented fifth C # does not ascend to D, as the tone D with the minor third requires, but it changes to D #, fourth artificial note of the tone A with the minor third, which, it seems to me, cannot be condemned absolutely. [Riccati, The laws of counterpoint, 406; text: Basso continuo. fondamentale, 6 3, 5 3 #, 6, 7 5, 7 b 5, 6 b 3 b, 5, 4 # 2, 5 2, 5 4, 3 #, 6 [sqb] 4 # 3, et cetera, 5 3, 6, 6 #, 5 # 3, 6 3 #, 7 3 #, 6 4, 5 # 3 #, 8 3 #, 5 [sqb] 3, 3 b, 5 3 #, 7 5 3, 7 b, 8, 7, 7 5 [sqb] 3 #, 4 , 3, 8 5 3 #, 27. 29. 28. 30.] [-407-] The second accompaniment F 5 # 3 of the passage number 31. F 5 3 # B b 5 3 suits the tone D with the minor third, while the consequent accompaniment B b 5 3 is considered as artificial of the tone A with the minor third. If it is put into practice in this form, it must be followed by the chord E 5 3 #, so that their result is the series of accompaniments F 5 # 3 B b 5 3 E 5 3 #. as the chord B b 5 3 belongs naturally to the chord D with the minor third, the ear shall consider it a change of tone when one moves from B b 5 3 to E 5 3 #, but never then one moves from F 5 # 3 to B b 5 3. I do not deprive the Reader of an example of the passage number 31. [Riccati, The laws of counterpoint, 407; text: Basso continuo. fondamentale, 6 4, 5 3 #, 6, 6 b 3, 6 [sqb] 4 # 2, 6 3, 7 5 3, 3 #, 5 # 3, 7 5 [sqb] 3 #, 7, 31.] The following passages are exuded from counterpoint. 9. A # 5 3 [sqb], 10. A # 5 3 [sqb] D 5 [sqb] 3 #, 11. A # 5 3 [sqb] D # 5 [sqb] 3 [sqb], 12. A # 5 3 [sqb] D # 5 3 #, 13. A # 5 3 # D 5 [sqb] 3 [sqb], 14. A # 5 3 # D 5 [sqb] 3 #, 15. A # 5 3 # D # 5 [sqb] 3 [sqb], 16. A # 5 3 # D # 5 [sqb] 3 #. These passages are declared faulty on the basis of the fifth canon (chapter 4., [signum] 18.), because the aim,, for which the fourth artificial note A with the tone E with the minor third occurs in the preceding accompaniments, is not accomplished. 25. D # 5 3 [sqb] G 5 # 3, 26. D # 5 3 # G 5 # 3. They contravene the fifth canon. Note that in the passage number 26. the sound D # is presumed fourth artificial note of the tone A with the minor third, and, under that supposition, the use of this passage is deemed faulty. [signum] 4. I enter the examination of the passages that ascend by a fifth. [-408-] [Riccati, The laws of counterpoint, 408; text: Passaggi artificiali rappresentanti il naturale A 5 3 E 5 3. D 5 3 A 5 3. C 5 3 G 5 3. F 5 3 C 5 3. G 5 3. D 5 3. B 5 3 F 5 3. 5 3 #, 5 3, 5 [sqb], 5 # 3, 5 [sqb] 3 #, 5 # 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31.] 1. A 5 3 # E 5 3, 2. A 5 3 # E 5 3 #. The first passage modulates from the tone D to the tone A with the minor third, and it contains the imperfection that the melody of C #, major third of the preceding chord A 5 3 # produces the bad relation of the major fourth with the following chord E 5 3. So that the ear may not notice it, add the dissonance of the fourth to said chord and move from A 5 3 # to E 5 4, followed later by E 5 3. [-409-] The middle accompaniment achieves the aim of hiding the bad relationship between the first and the last one. [Riccati, The laws of counterpoint, 409, 1; text: Basso continuo. fondamentale, 5 4, 3 #, 5 2, 6 3, 7 5 3, 6, 7 5 3 #, 3, 1.] Arcangelo Corelli in the last Allegro of the fifth concerto of his Opus six employe shte first passage in the following form. [Riccati, The laws of counterpoint, 409, 2; text: Basso continuo. fondamentale, 6 3, 5 3 #, 6 3 #, 5 # 3 #, 5 3, et cetera, 1.] The second passage A 5 3 # E 5 3 # useful to move from the tone D to the tone A, both of them with the minor third, can be employed in the following way. [Riccati, The laws of counterpoint, 409, 3; text: Basso continuo. fondamentale, 6 3, 7, 3 #, 5 3 #, 6 # 4, 7 5 3, 8 5 3 b, 5 #, 3 #, et cetera, 2.] [-410-] The example by Corelli placed above is written in the key of B minor in the eighth sonata of his Opus two. I transposed to the tone of D with the minor third to illustrate the passage number 2. It is also legitimate to consider in the passage number 2. the preceding accompaniment A 5 3 # as artificial of the tone E with the minor third, as long as the sixth artificial note C # is preceded by the seventh artificial note D#. In this instance our passage moves from the tone e with the minor third to the similar tone A. See the example where I employ the derivative passage C # 5 3 B 6 # 4 instead of the fundamental one A 5 3 # E 5 3 #. [Riccati, The laws of counterpoint, 410; text: Basso continuo. fondamentale, 6 3 #, 6 3, 6 # 4 3, 6 4 # 2 , 6 # 4 3, et cetera, 5 # 3 #, 5 3 #, 7 5 3 #, 5 3, 2.] 5. D 5 3 # A 5 3 #, 8. D 5 3 A 5 3 #, 9. D 5 3 A # 5 3 [sqb], 10. D 5 3 # A # 5 3 [sqb], 14. D 5 3 A # 5 3 #, 14. D 5 3 # A # 5 3 #. The accompaniment D 5 3 # in the passage number 5. belongs artificially to the tone A with the minor third. The following chord A 5 3 # can perform a double rone, namely, as artificial chord of the tone D with the minor third or of the similar tone E. I have introduced in this latter form in the example that I propose here, where I have the artificial notes F # and C # of the minor tones A and E follow the seventh artificial notes G # and D # in order to render their application logical and rational. [-411-] [Riccati, The laws of counterpoint, 411, 1; text: Basso continuo. fondametale, 6 3 # 5, 6, 5, 5 3 #, 5 # 3 #, 8 5 # 3 #, 7, 5 3 #, 5 # 3 # , 5.] Since our passages must contain a modulation from a tone to another tone, the chord A 5 3 # of the passage number 8. D 5 3 A 5 3 # must be ascribed artificially [to the major tone G or add. supra lin.] to the minor tone E. I employ it in this capacity in the following example. [Riccati, The laws of counterpoint, 411, 2; text: Basso continuo. fondamentale, 8 3 #, 7, 6 #, 5 # 3 #, ovvero 5 3 [sqb] 6 # 3, 6 3 #, 5, 6 #, 5 # 3 #, 7, 7 3 #, 3 #, et cetera, 5 3 #, 5 3 [sqb], 8 5 # 3 #, 9. 8. 13.] the second example contains the derivative passages 9 D 5 3 [sqb] A # 5 3 [sqb], [-412-] 13. D 5 3 [sqb] A # 5 3 #. The third and fourth example show clearly how one may employ the passages number 10. D 5 3 # A # 5 3 [sqb] and 14. D 5 3 # A # 5 3 #. I employed the derivative passages F # 6 3 E 6 [sqb] 4 # and D 5 3 # C # 6 # 3 instead of the fundamental ones. [Riccati, The laws of counterpoint, 412; text: Basso continuo. fondamentale, 6 3, 6 [sqb] 4, 6 3 #, 5, et cetera, 6 5 3, 7 5, 6 4, 6 # 3, 7 5 # 3 #, 5 # 3 #, 3 #, 5 3 #, 5 3 [sqb], 8 5 # 3 #, 7 5 3 #, 7 5, 10. 14.] 17. C # 5 3 G 5 3, 18. C # 5 3 G # 5 3. The passage number 17. contains the imperfection that G, minor fifth in the previous accompaniment becomes base of the following one. Therefore, so that it may become possible to employ it, I have left out the sound G in the first example in tow parts, so that the noted effect may not be revealed to the ear. The passage number 18. is untouched by the inverted preparation of the minor fifth, but then it consists of two accompaniments of the minor third and minor fifth. I illustrate in the second example how it may be made less dissonant by substituting to the fundamental chords the derivative ones E 6 # 3 B 6 # 3 containing in the bass two real dissonances. [Riccati, The laws of counterpoint, 413; text: Basso continuo. fondamentale, 3 b, 6 4, 5 3 #, 6 # 3, 6 3, 6 4, 5 3 #, 3 #, 17. 18. et cetera] I have put into practice the passage 18. C # 5 3 g # 5 3, which must contain the modulation, in its simplest form by assigning G # 5 3 to the tone A and E bot of them with the minor third. The first accompaniment can also belong to the tone E with the minor third and one moves from the minor tone E to the equally minor tone A on the basis of said supposition. This modulation proves otherwise very elegant. In fact, since the only function of the artificial note C # is to avoid the augmented sixth between the natural sixth chord C and the artificial seventh note D #, and since no cadence is not required by the following chord, the ear does not expect C # to be followed by a modulation. 21. F # 5 3 C # 5 3, 22. F 5 3 C # 5 3. The passage number 21 must not be allowed because of the fifth canon, if the preceding accompaniment [-414-] is based on the fourth artificial note F # of the tone C with the major third. Although no canon forbids our passage, if one presumes F # to be the sixth artificial note of the tone A with the minor third, nevertheless no small effort is required to render it pleasant. If one has to use with logically the sixth artificial note F #, it is necessary that the seventh artificial note G # should precede it. The chord C # 5 3, which as an artificial chord can belong also to the tones D minor, E minor and G major, follows the similar tone F # 5 3 of the minor third and minor fifth. The first case required that one should move to D 5 3 [sqb], which is very harsh on the ear because the memory still fresh of the sound F #. The second case requires that one should move from C # 5 3 to a chord that contains the seventh artificial note D # of the minor tone E. Finally, the third instance oblige us to realise the cadence C # 5 3 D 5 3 # from the fourth artificial note to the fifth one of the tone G with the major third. The following example illustrates some of the most natural ways of introducing in music the passage F # 5 3 C # 5 3, whose consequent chord is employed artificially precisely in the minor tone E. I invite the reader to observe that, in order to sweeten our passage further, I omit the minor fifth C in the preceding accompaniment F # 5 3, as I ensure that the movements of the parts are elegant. I also note that the preceding chord F # 5 3 can be ascribed to the minor tone E in the example that I put forward. In this suggested instance the passage from one tone to another tone occurs after the cadence D # 5 3 E 5 3 # from the fourth artificial note to the fifth one. [Riccati, The laws of counterpoint, 414; text: Basso continuo. fondamentale, 5 3 # 7 5, 6 #, 5 3, 5 [sqb] 3, 8 5 # 3 #, 7 et cetera, 21.] [-415-]If one has to modulate by means of the passage number 22. F 5 3 C # 5 3, it is necessary to employ the second accompaniment as artificially belonging to the tone E with the minor third or to the tone G with the major third. After a cadence from the fourth to the fifth note of the tone B derived from the tone A, I move to the tone E with the minor third through the accompaniment e 5 # 3 in the example that I present to the judgement of the Reader. [Riccati, The laws of counterpoint, 415; text: Basso continuo. fondametale, 6, 7 5 3 #, 5 3, 3, 6 # 3 [sqb], 6 # 3, 7 5 3 #, 5 3 #, 7, et cetera, 22.] [signum] 5. the passages of the fifth upwards whose examples I presented deserve to be employed more or less sparingly according to what their character requires. I invite the Reader to banish the remaining ones almost completely from musical compositions. 3. A # 5 3 [sqb] E 5 3 # and 4. A # 5 3 # E 5 3 #. They are declared forbidden by the fifth canon. 6. D # 5 3 [sqb] A 5 3 #, 7. D # 5 3 # A 5 3 #, 11. D # 5 3 [sqb] A # 5 3 [sqb], 12. D # 5 3 # A # 5 3 [sqb] 15. D # 5 3 [sqb] A # 5 3 # and 16. D # 5 3 # A # 5 3 #. The same fifth canon excludes the passages written above, whose preceding chord is based on the fifth artificial note D # of the tone A with the minor third. 19. C 5 3 # G [sqb] 5 # 3 is declared faulty by the second canon. 20. F 5 3 # C [sqb] 5 # 3. The aforesaid canon rejects the passage number 20. 23. G 5 # 3 D [sqb] 5 3, 24. G 5 # 3 D [sqb] 5 3 #, 25. G 5 # 3 D # 5 3 [sqb] and 26.G 5 # 3 D # 5 3 #. All of these four passages deserve to be discouraged because they infringe the third canon: the first two because one foes not find E or D # in the second accompaniment; the last two because, albeit the consequent chord that is presumed to belong to the tone A with the minor third contains D # that formed an augmented fifth in the previous one, this delay in ascending to the note E together with a modulation from the tone E to the tone A, both minor, cannot be tolerated. 27. B 5 3 F 5 # 3, 28. B 5 # 3 F [sqb] 5 # 3, 29. B 5 [sqb] 3 # F 5 # 3, 30. B 5 # 3 # F [sqb] 5 # 3, 31. and B b 5 3 F 5 # 3. The passage number 27. B 5 3 F 5 # 3 is similar to the one F # 5 3 C 5 # 3, discussed at chapter 5, [signum] 5., except the latter is considered to belong entirely to the tone A with the minor third, while the former one is presumed to move from the major tone C, or from the minor tone A, tot he minor tone D. Now, although I permitted a very sparing use of the passage F # 5 3 C 5 # 3 in the place quoted above, I would be inclined to ban completely the passage B 5 3 F 5 # 3 in the supposition that it contains a modulation. It is rue, nevertheless, that, since the chord B 5 3 is common to the two tones either naturally or artificially, the ear can very well ascribe the entire passage number 27. B 5 3 F 5 # 3 to the tone D with the minor third. I invite the Reader to examine the following example where [Riccati, The laws of counterpoint, 416, 1; text: basso continuo. fondamentale, 5 3, 5 # 3, 8 3 #, 7, 8 5 3 #, 3 #, 27.] the fundamental bass would prove intolerable in relation to the passage number 27. if one considers the basso continuo, the accompaniment F 6 4 derived from the fundamental B 5 3 is employed on a strong subdivision of the beat, while the accompaniment F 5 # 3 occurs on a weak subdivision of the beat, hence there is little comparison between them and they are [-417-] hear in passing. Moreover the bass is not repeated under the notes B and C #, which helps so that they may refer to the bass itself less distinctly and noticeably. Add to this that the note B can be considered to be on a weak beat, as they say, which means that it does not require a change in the fundamental bass. Therefore, this is how one must employ certain harsher passage, were they even to be considered as passages. The sound F # that occurs in the preceding chord B 5 # 3 of the passage number 28. B 5 # 3 F [sqb] 5 # 3 renders the augmented fifth that refers to the base F of the second chord F 5 # 3, so bitter that I consider our passage utterly useless in music. The passage 29. B 5 3 # F [sqb] 5 # 3, 30. and B 5 # 3 # f [sqb] 5 # 3 are declared illegitimate by the fifth canon, while the passage number 31. B b 5 3 F 5 # 3 infringes the sixth canon in the supposition that the preceding accompaniment is employed as artificial of the tone A with the minor third. Were the aforesaid accompaniment to belong to the major tone F or to the minor tone D, the passage number 31. would be completely similar to the passage F 5 3 C 5 # 3 discussed in the [signum] 4 of the fifth chapter, as it would be counted among the ones that are employed frequently. [signum] 6. Good order requires that one should proceed to the passage that ascend by a second, which modulate from one tone to another one as this is made clear by the artificial notes. [Riccati, The laws of counterpoint, 417; text: Passaggi artificiali rppresentanti il naturale A 5 3 B 5 3, B 5 3 C 5 3. C 5 3 D 5 3. E 5 3 F 5 3. F 5 3 G 5 3. G 5 3 A 5 3. 5 3 #, 5 3, 5 # 3, 5 3 #, 5 # 3 #, 5 3 [sqb], 5 [sqb] 3 #, 5 # 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.11. 12. 13. 14. 15. 16. 17. 1.8 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.] 1. A 5 3 # B 53, 2. A 5 3 # B 5 # 3, 3. A 5 3 # B 5 [sqb] 3 #, 4. A 5 3 # B 5 # 3 # and 5. A 5 3 # B b 5 3. In all of these passages the accompaniment A 5 3 # can belong artificially both to the tone of D minor and to the tone of E minor. The first role is more suitable. In fact, since three cadences conclude with the cord A 5 3 #, one can move on to the following accompaniment more freely. I shall place firs the examples where A 5 3 # belongs to the tone D with the minor third and then the ones where the same chord is assigned to the tone of E minor. [Riccati, The laws of counterpoint, 418; text: Basso continuo. fondamentale. 8 6, 7 5, 5 3 #, 8 6 b, 6 5, 5 4, 3 #, 6 3 #, 7 5 3 [sqb], 6 5 3 [sqb], 6 4, 5 3, 7 5 3 #, 5 # 3 #, 5 [sqb] 3 #, 3 [sqb], 1. 5. 4. 3. 2. o pure, et cetera] If in the passage number 3. A 5 3 # B 5 [sqb] 3 # the preceding accompaniment A 5 3 # is employed as artificial of the minor tone E, the consequent one B 5 [sqb] 3 #, which belongs artificially to the minor tone A proves very harsh. In fact, since F # is a natural note of the aforesaid tone E, the sound F appears new and increases the bitterness of the minor fifth B F and much more the bitterness of the diminished third D # F. In the example containing the passage number 3. I let the sound F be read first as artificial of the minor tone E, so that the ear may become used to it and may hear it with much less revulsion in the chord [-420-] [Riccati, The laws of counterpoint, 420; text: Basso continuo. ffondamentale, 6, 7 3 #, 7, 7 5 [sqb] 3, 7 5 3 #, 7 5 3, 7 5 # 3, 6 5 3 #, 6 4 # 2, 6 3, 5 4, 3 #, o pure, 7 5 # 3 #, 6 5 3 #, 5 3 #, 6 b 3, 6 [sqb] 4 # 2, et cetera, 5 # 3 #, 7 5 # 3 #, 1. 2. 4. 5. 5 #, 4, 6 [sqb] 3, 6 4, 10 [sqb] 6 5, 6 5, 7 5 [sqb] 3 #, 8 5 3 #, 9, 8, 3.] [-421-] 16. B 53 C # 5 3, 17. B 5 # 3 C # 5 3. We are allowed ascribe the consequent accompaniment C # 5 3 to the minor tones D and E or to the major tone G in both passages. Said accompaniment is assigned more advantageously to the minor tone D, and less so to the tones E minor and G major in the passage number 16. The opposite occurs in the passage number 17. The reason for this depends on the preceding chords B 5 3 and B 5 3 #, the first one containing the note F that belongs naturally to the tone D, while the second one contains the note F #, naturally belonging to the tones E minor and G major. I begin from the examples where C # 5 3 is employed as belonging to the tone D with the minor third; I continue with the ones that employ it as belonging to the tones E minor and G major. [Riccati, The laws of counterpoint, 421; text: Basso continuo. fondamentale, 3 #, 6 3, 7 5, 5 3, 9, 6, 5 3 3 #, 5 3 #, 5 # 4, 3, 5, 6, 5 3 [sqb], 3 #, 7 5 3, 6 4, 5 # 4, 3 [sqb], 7 5 3, 6 3 #, 7 5 # 3 #, 6 # 3 #, 5 # 3 #, o pure, 7 5, 9 4, 8 3, et cetera, 8 3 #, 9, 8, 7 3 #, 3 [sqb] 7 5 [sqb] 3 #, 3, 8 5 # 3 #, 6 # 3 #, 5 # 3 #, 8 5 3 #, 16. 17.] [-423-] C # 5 3 D 5 3, 22. C # 5 3 D 5 3 #, 23. C # 5 3 D # 5 3 [sqb], 24. C # 5 3 D # 5 3 #. Since our passages mus modulate from one tone to another one, the chord C # 5 3 in the passage number 12. cannot be ascribed to the minor tone D. In fact, as the chord D 5 3 belongs to the same passage, said passage would not move from one tone to another one. Therefore, it follows that the preceding accompaniment in the mentioned passages can be assigned artificially to the tone E with the minor third. In the remaining passages number 22. 23. and 24. we are allowed to consider the chord C # 5 3 as artificial of the tone D or of the tone E, both of with the minor third. The practical realisation of said accompaniment as artificial of the tone G with the major third would contravene the fifth canon in relation to the passages 21. 23. 24., and it would require, in relation to the passage number 22., the consequent chord D 5 3 # to be used as natural accompaniment of the aforesaid tone G, hence one would not move from one tone to another tone, against what is the premise of the current chapter. In the following examples the chord that constitute our passages shall take all the forms that can suit them according to the rules. [Riccati, The laws of counterpoint, 423; text: Basso continuo. fondamentale, 7, 6 #, 6 5, 7 5 3 #, et cetera, 6 5 [sqb] 3, 6 # 4 3, 7 [sqb], 7 3, 6 # 3, 7 [sqb] 5 3 [sqb], 3 #, 6 3, 7 [sqb] 5 3 #, 7 5 3, 5 4, 3 [sqb], 7 5, 7 5 # 3 #, 6 # 5, 5 # 3 #, o pure, 5 3 #, 6 4 # 2, 6 5 3 #, 6 # 3, 5 [sqb], 7 5 3 #, 6 4, 6 # 3, 6 5, 6 4 3, 9, 8, 7 [sqb] 5 3 #, 7 [sqb], 5 3 [sqb], 7 [sqb], 8 5 3 #, 7 5 3, 7 5 # 3 #, 6 # 5, 5 # 3 #, 6 4, 5 3, 22. 23. 21. 24.] [-425-] 25. E 5 3 F 5 # 3, 26. E 5 3 # F 5 # 3. These two passages can be used sometimes in the following way. The accompaniment of the major third and augmented fifth that occurs in these passages likes to be prepared. This is achieved in two ways, namely, when one or the other of the sounds that constitute the interval of the augmented fifth is contained in the preceding chord. The two preparations A 5 3 # 6, B b 5 3 A 6 3 # are derived from the accompaniment A 5 3 #, derived from the fundamental one F 5 3. The first of them is more perfect than the second one because the sound C #, which produces the harshness of the chord A 6 3 #, is prepared. Even the second one of them, albeit less exquisite, prepares the ear to tolerate the union of the sounds C # and F, by introducing F first as fifth of B b, and by helping this sound become the diminished fourth of C #. In the examples in tow parts of the passages number 25. and 26. I realise the second preparation in some way, by striking first the minor sixth ad then the major third of the chord A 6 3 #. [-426-] Were they heard at the same time, they would prove very harsh, because the diminished fourth would be employed without preparation in that unfavourable circumstance, especially as one is changing tone. I warn the Reader that it is convenient to add the seventh to the chord of the augmented fifth. In the derivative accompaniment of the major third and minor sixth employed mostly instead of the fundamental one, said dissonance divides the diminished fourth between the major third and the minor sixth and tempers its crudeness. I employ the artifice used in the examples noted below in other similar circumstances, as the Reader can observe. [Riccati, The laws of counterpoint, 426, 1; text: Basso continuo. fondamentale, 6 5 3, 5 3, 6 5 3 b, 3 #, 6 5 3 #, 5 # 3, 5 3, 7 5 b 3 #, 5 3 #, 25. 26. et cetera] 27. F 5 3 G 5 # 3, 28. F 5 # 3 G 5 3, 29. F 5 # 3 G # 5 3, 30. F # 5 3 G 5 # 3. Albeit the passages containing the accompaniment of the major third and augmented fifth need to be employed with great care, as I have noted just now and elsewhere, nevertheless, one should not deny the access to musical compositions to the four noted above in some rare circumstance. I invite the Reader to take a look at the examples. [Riccati, The laws of counterpoint, 426; text: Basso continuo. fondamentale, 7 5 3 #, 5 3, 6 3 #, 6 # 3, 5, 3 #, 5 3 #, 6, 6 3, 9, 8, et cetera, 7 5 3, 6 #, 6 3, 5 # 3 #, 5 # 3, 8 5 3, 7, 8 7 5 3 #, 5 3 [sqb], 7 5 3 [sqb], 8 5 # 3 #, 27. 28. 29.] [-427-] 31. G 5 3 A 5 3 #, 32. G # 5 3 A 5 3 #, 33. G # 5 3 A # 5 3 [sqb], 34. G # 5 3 A # 5 3 #. If the passage number 31. has to modulate from one tone to another one that do not share the same scale, it is necessary to ascribe the second accompaniment A 5 3 # to the tone D with the minor third. In the passage number 32. the consequent chord A 5 3 # can belong to the tone D or to the tone E, both minor, or to the tone G with the major third. The passage number 31. principally, but also the passage number 32. are endowed with elegance. The two remaining ones can be allowed in musical compositions sparingly. [Riccati, The laws of counterpoint, 420; text: Basso continuo. ffondamentale, 6, 7 3 #, 7, 7 5 [sqb] 3, 7 5 3 #, 7 5 3, 7 5 # 3, 6 5 3 #, 6 4 # 2, 6 3, 5 4, 3 #, o pure, 7 5 # 3 #, 6 5 3 #, 5 3 #, 6 b 3, 6 [sqb] 4 # 2, et cetera, 5 # 3 #, 7 5 # 3 #, 1. 2. 4. 5. 5 #, 4, 6 [sqb] 3, 6 4, 10 [sqb] 6 5, 6 5, 7 5 [sqb] 3 #, 8 5 3 #, 9, 8, 3.] [-428-] [signum] 7. I lay out herewith the passages that are not allowed in counterpoint. 6. A # 5 3 [sqb[ B 5 3, 7. A # 5 3 [sqb] B 5 # 3, 8. A # 5 3 [sqb] B 5 [sqb] 3 #, 9. A # 5 3 [sqb] B 5 # 3 #, 10. A # 5 3 [sqb] B b 5 3, 11. A # 5 3 # B 5 3, 12. A # 5 3 # B 5 # 3, 13. A # 5 3 # B 5 [sqb] 3 #, 14. A # 5 3 # B 5 # 3 #, 15. A # 5 3 # B b 5 3. All of the passages written above are condemned on the basis of the fifth canon. To avoid any misunderstanding, note that the passages number 7., 9., 12. and 14. are rejected under the supposition that the artificial consequent accompaniments B 5 # 3 and B 5 # 3 # are employed as representing the natural accompaniment B 5 3 belonging to the minor tone A. It is certain, however, that when the ear hears said passages, it will ascribe the consequent chords to the tone E with the minor third and that they will please it. 18. B 5 [sqb] 3 # C # 5 3, 19. B 5 # 3 # C # 5 3 and 20. B b 5 3 C # 5 3. The passages numbered 18. and 19. are declared faulty on the basis of the fifth canon, and the one numbered 20. on the basis of the sixth canon. I repeat here as well the observation that the passages 19. and 20. are excluded in as much as one supposes that the preceding chords are artificial of the tone A with the minor third. If both chords are attributed to the tone E with the minor third in the passage number 19., [-429-] or, while the preceding one is assigned to the minor tone E, the consequent belongs to the major tone G, said passage is similar to E 5 3 # F # 5 3 considered in the [signum] 7. of the fifth chapter. Similarly, if one presupposes that both the chords of the passage number 20. belong to the minor tone D, the passage resembles the earlier one F 5 3 G # 5 3, which I mentioned in the quoted passage and that is seen realised in the fifth example of the [signum] 2. of the aforesaid chapter. [signum] 8. I lay out the sequence of the passages of the second downwards that are the opposite ones of the ones of the second upwards that I described in the two last preceding paragraphs. [Riccati, The laws of counterpoint, 429; text: Passaggi artificiali rappresentanti il naturale B 5 3 A 5 3. C 5 3 B 5 3. D 5 3 C 5 3. F 5 3 # 5 3. G 5 3 F 5 3. A 5 3 G 5 3. 5 3, 5 3 #, 5 # 3, 5 [sqb] 3 #, 5 # 3 #, 5 3 [sqb], 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34.] [-430-] 1. B 5 3 A 5 3 #, 2. B 5 3 # A 5 3 #, 6. B 5 3 A # 5 3 [sqb], 7. B 5 3 # A # 5 3 [sqb], 11. B 5 3 A #5 3 # and 12. B 5 # 3 A # 5 3 #. The accompaniment A 5 3 # in the passages number 1. and 2. can belong artificially to the minor tone D or to the relative ones of E minor and G major. The first supposed instance is better suited to the passage number 1. and the second one to the passage number 2. because the note F is included in the former, which note naturally belongs to the tone of D minor, while the note F # is included in the latter one, which note belongs to the relative tones E minor and G major. I invite the Reader to look at the examples. [Riccati, The laws of counterpoint, 430; text: Basso continuo. fondamentale, 7 5 3, 6 5 3, 6 5, 6 5 3 #, 7, 3 #, 6 3, 7 [sqb], 5 # 4, 3, 6 3, 7 5, 11 9, 10 [sqb] 8, 10 8, 7 [sqb] 5, 11 9 #, et cetera, 7 5 # 3 #, 8 3 #, 7 [sqb], 8, 8 5 3 #, 10 [sqb] 8, 1. 2.] [-431-] The passages number 7. B 5 # 3 A # 5 3 [sqb] and number12. 5 # 3 A # 5 3 # shall bee employed more freely that the other two, number 6. B 5 3 A # 5 3 [sqb] and 11. B 5 3 A # 5 3 #. In fact, since the preceding chord B 5 3 # is common to the tone of A minor as an artificial accompaniment and to the tone of E minor as a natural accompaniment, if the preceding part of the composition makes the ear believe that belongs to the tone A, the following part of the composition makes the ear consider it as belonging to the tone E, so in this latest instance the passages number 7. and 12. do not contain any modulation from one tone to another one. I shall not omit to place herewith the four passages. [Riccati, The laws of counterpoint, 431; text: Basso continuo. fondamentale, 7 3, 6, 6 #, 5 # 3 #, 6 3, 6 4, 6 3 #, 7 5 # 3 #, 5 # 3 #, 5 3 #, 5 3 #, 6 # 3, et cetera, 5 # 4, 3, 6 5, 9 5 [sqb] 3, 8, 9 5 3 [sqb], 8 5 # 3 #, 7, 9 5 3 #, 5 2 #, 6. 11. 12.] [-432-] 16. C # 5 3 B 5 3, 17. C # 5 3 B 5 # 3, 18. C # 5 3 B 5 [sqb] 3 #, 19. C # 5 3 B 5 # 3 # 20. C # 5 3 B b 5 3. If one assigned the preceding chord C # 5 3 of our five passages to the tone G with the major third, one would contravene the fifth canon. Consequently, the only option left is that they should be assigned to the tones D and E. The passages in which the accompaniment C # 5 3 suits the tone D better than the tone E are the passages number 16. and 20. The opposite occurs in the passages number 17. and 19. The passage number 18. proves harsh in both the circumstances mentioned above, so much so that I would not be able to advise the Reader to employ it, especially when the chord C # 5 3 is employed as artificially belonging to the tone E with the minor third. The sound F # that was previously heard renders the sound F even more bitter, since in the chord B 5 [sqb] 3 # it forms with forms and with D # a minor fifth and a diminished third. I provide first the examples in which C # 5 3 belongs to the minor tone D, then I shall place those in which it belongs to the tone of E minor. [Riccati, The laws of counterpoint, 432; text: basso continuo. fondamentale, 7 3, 6 #, 6 3, 5, 6 4 # 2, 6 3, 6, 7 3, 6 b 3, 8 [sqb] 4 # 2, 6 3 #, 6 4 #, 5 [sqb], o pure, 5 3 #, 6 5 3 [sqb], et cetera, 9 5 3, 8, 8 5 3, 7 5 3 #, 8 5 # 3, 7 [sqb], 8 5 # 3 #, 7 5 [sqb] 3 #, 16. 20. 17. 19. 18.] [Riccati, The laws of counterpoint, 433; text: Basso continuo. fondamentale, 6 3, 5 3 #, 6, 5 3, 6 3 [sqb], 6 5 3 [sqb], o pure, 8 6 b 3 [sqb], 7 5 3 [sqb], 3 #, 6 3 #, 6 5 3 #, 6 5, 5 # 3 #, 5 [sqb] 3, 7 5 [sqb] 3 #, 5 # 3, 5 3 #, 8 5 # 3 #, 7, et cetera, 16. 20. 17. 19.] [-434-] 21. D 5 3 C # 5 3 and 22. D 5 3 # C # 5 3. Were the consequent chord considered, in the passage number 21., as artificial of the minor tone D, said passage would not contain a modulation, against the premise of the present chapter. The reason is that the mention chord shall be able to be employed as artificially belonging to the minor tone E or to the major tone G. As to the passage number 22., we shall have the choice to ascribe the consequent accompaniment to the minor tones D or E, or to to the tone G with the major third. [Riccati, The laws of counterpoint, 434; text: Basso continuo. fondamentale, 54, 3 #, 5 3, 6 3 #, 5 # 4 #, 7 3, 6 #, 6 5 [sqb] 3, 9 5 3, 8, 3 [sqb], 6 5 3, 9 5 3, 8, 6 3, 6 # 3, 5, et cetera, 7 4, 7 3, 6 #, 6 #, et cetera, 5 3 #, 7 5, 7 [sqb] 5 3 #, 3 [sqb], 7 5 3, 8 5 3 #, 7, 7 5 4, 8 5 # 3 #, 8 5 3 #, 21. 22.] [-435-] 26. F 5 # 3 # 5 3 #. In order to make this passage legitimate, it is necessary to add to the consequent accompaniment E 5 3 # the seventh D, so that one may rise from C #, augmented fifth of the previous accompaniment, to D, seventh of the consequent one according to the requirements of the third canon. Among the other particular privileges enjoyed by the minor seventh added to the accompaniment with the major third based on the fifth note of said mode, one should count this one as well, namely, that one can rise to it by stepwise motion from the augmented fifth of the previous chord, as it occurs in the passage number 26. F 5 # 3 E 7 5 3 #, of which I present an example. [-436-] [Riccati, The laws of counterpoint, 436; text: Basso continuo. fondamentale, 5 3, 6 5 3, 5 3, 5 3 #, 6 4, 6, 6 5 3, 7, 7 5, 5 3, 3 #, 8 5 4, 7 3 #, 5 3 #, 5 # 3, 7 5 3 #, 26.] 28. G 5 3 F 5 # 3, 29. G # 5 3 F 5 # 3 and 30. G 5 # 3 F # 5 3. The passages number 28. and 29. are naturally very harsh, because the augmented fifth is introduced unprepared in the consequent accompaniment. As for the rest, the passage number 28. easier to handle than the passage number 29. because in the former the preceding chord is truly consonant, while in the latter it is merely consonant by representation. In the passage number 30. the augmented fifth D # of the preceding chord can be prepared, but one has to add the seventh to the consequent chord in order to make it rise to E. The fact that it is a minor seven and that it is coupled with an accompaniment of the minor third and minor third renders legitimate the aforesaid ascending movement, in my opinion. The consequent chord F # 5 3 can belong artificially to the major tone C or to the minor tone A.I do not consider it as natural of the minor tone E or of the major tone G, because in that case the passage number 30. would not lead us from one tone to another tone that do not share the same scale. Certain passages that do not produce a bad effect in two parts are too harsh when they are laid out in full harmony. This is the reason why I have written the examples in two parts, and especially the first and the second one, which contain the chord A 6 3 #, of the major third and minor sixth, derived from the fundamental chord F 5 # 3 of the major third and augmented fifth, without preparation. I invite the Reader to observe that an imperfect preparation is employed in the top part, where the sounds F and C #, which respond to each other at the interval of a diminished fourth, are introduced one after the other. On this matter, I invite the Reader to recall [-437-] what I wrote in the preceding [signum] 7. [Riccati, The laws of counterpoint, 437; text: Basso continuo. fondamentale, 6 3 #, 5 3, 6 5, 3 #, 6 3, 5 3 b, 5 4, 7 3, 6 #, 6 5 3 b, 5 4, 7 5 3 #, 7, 6, 5 # 3 #, 5, 6 5 3, 7, 5 # 3 #, 6 5, 5 3 [sqb], 6 4, 5 3 #, 5 # 3, 7 5 b 3, 9 5 3, 8, , et cetera, 5 # 3 #, 8 5 3 #, 7 [sqb], 7 5 3 #, 5 3 [sqb], 28. 29. 30.] 31. A 5 3 # G 5 3, 32. A 5 3 # G # 5 3. In both of the passages written above the preceding chord can be mployed as artificial of the tone D with the minor third. This instance has the advantage that, as the chord A 5 3 # concludes three cadences of the aforementioned tone D, the following modulation proves then more elegant. The passage number 31. is good when one avoids the fundamental passage, and it is employed to modulate from the minor tone [-438-] D to the major tone C. I realise in practice the derivative movement A 5 3 # B 6 3 in the example placed here below. As to the passage number 32., one is allowed also to ascribe the preceding accompaniment to the tone of E minor. In such case one moves from the tone E to the tone A both with the minor third. [Riccati, The laws of counterpoint, 438; text: Basso continuo. fondamentale, 5 3 #, 6 53, 6 3, 5 4, 3, 6 # 3, 3 #, 6 3 #, 6 # 3 [sqb[ 7 5, 6 4, 5 3 #, et cetera, 5 3, 5 3 [sqb], 5 # 3 #, 5 [sqb] 3, 7 5, 31. 32.] [signum] 9. One should banish from musical compositions the passages written herewith among those of the second downwards contained in the present chapter. 3. B 5 [sqb] 3 #, 4. B 5 # 3 # A 5 3 #, 5. B b 5 3 A 5 3 #, 8. B 5 [sqb] 3 # A # 5 3 [sqb], 9. B 5 # 3 # A # 5 3 [sqb], 10. B b 5 3 A # 5 3 [sqb], 13. B 5 [sqb] 3 # A # 5 3 #, 14. B 5 # 3 # A # 5 3 # and 15. B b 5 3 A # 5 3 #. The fifth canon declares faulty the passages number 3. 4. 8. 9. 13. and 14.; the sixth canon forbids the passages number 4. 9. 14. 5. 10. 15. under the supposition that the preceding chords B 5 # 3 # are employed as representing the natural chord B 5 3 and, consequently, as artificial chords of the tone A with the minor third. [-439-] 23. D # 5 3 [sqb] C # 5 3 and 24. D # 5 3 # C # 5 3 contravene the fifth canon. In this case as ell the preceding accompaniment D # 5 3 # of the passage number 24. is considered as representing the natural chord D 5 3 and as artificially belonging to the minor tone A. 25. F 5 # 3 E 5 3. In order that the augmented fifth C # of the preceding accompaniment F 5 # 3 may rise to the note D, as the third canon prescribes, it is necessary to add the seventh to the consequent chord E 5 3 of the minor third and fifth, so that it takes the form E 7 5 3. Now, said chord does not enjoy the privileges of the chord E 7 5 3 # of the major third, fifth and minor seventh by a long stretch, by which privileges the augmented fifth would have been able to ascend to the minor seventh in the passage number 25. F 5 # 3 E 7 5 3 and please the ear. Therefore, one can see the reason why, after I allowed the passage number 26. F 5 # 3 E 7 5 3 # in the previous paragraph, I now forbid the passage number 25. F 5 # 3 E 5 3. 27. G 5 # 3 F 5 3. In order to satisfy the requirements of the third canon, it would be necessary to ascend from D #, augmented fifth of G, to E, major seventh of F. Since this is forbidden, as I shall demonstrate when I deal with the seventh, consequently, the practice of said passage must be banned, quite aside from the other defects contained in it. 33. A # 5 3 [sqb G # 5 3 and 24. A # 5 3 # G # 5 3. These passages contravene the fifth canon, which requires that one should cadence from the fourth artificial note A # to the fifth B of the tone E with the minor third, to which the preceding chords belong. [signum] 10. The passages of the third downwards and upwards must follow the passages of the second upwards and downwards, and they must precede those mentioned in the first place as more perfect than their inversions. [Riccati, The laws of counterpoint, 439; text: Passaggi artificiali rappresentanti il naturale C 5 3 A 5 3, E 5 3 C 5 3. F 5 3 D 5 3. G 5 3 # 5 3. A 5 3 F 5 3. B 5 3 G 5 3. 5 # 3, 5 3 #, 5 3 [sqb], 5 3, 5 # 3, 5 [sqb] 3, 5 [sqb] 3 [sqb], 5 [sqb] 3 #, 5 # 3 #, 5 #, 3 [sqb], 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20.] [-440-] 1. C 5 # 3 A 5 3 #, 2. C 5 3 A # 5 3 [sqb] and 3. C 5 # 3 A # 5 3 #. These three passages, which leave one tone to move to another one in the very harsh chord of the major third and augmented fifth, must be used very rarely. The consequent chord of te first passage can belong to the tone D or to the tone E with the minor third, but also to the tone G with the major third. The consequent accompaniments of the second and third passage belong to the minor tone E. The examples shall illustrate how such passages may be employed in music. [-441-] [Riccati, The laws of counterpoint, 441; text: Basso continuo. Fondamentale, 6 4, 5 3 #, 7 5, 6, 6 #4, 6 3, 5 3 b, 5, 7 5 # 3 #, 6 # 5 3, 5 # 3 #, 6 [sqb] 4 #, 6 3 #, 10 9, 6 # 4 #, 8 5 # 3 #, 7, 6 5 3 #, 5 3 #, 5 # 3, 3 b, 5 4, 3 #, 7 5 3, 5 3 [sqb], 1. 2. 3.] 4. E 5 3 C # 5 3, 5. E 5 3 # C # 5 3. If the fourth passage has to contain a modulation, the preceding chord must belong to the tone of A minor and the consequent one to the tone of D minor. In the fifth passage the preceding accompaniment belongs to the minor tone A, while the consequent can be ascribed to the minor tone D, to the minor tone E and also the the major tone G. our passages are good, both because they are of the third downwards and because a cadence can conclude on the first chord. [-442-] I invite the Reader to take a look at the examples. [Riccati, The laws of counterpoint, 442, 1; text: Basso continuo. fondamentale, 5 3, 6 # 3, et cetera, 75, 6 4, 5 3 #, 7 b 5 [sqb], 5 3, 7 5 [sqb], 6, 4 5 3, 7 [sqb] 5 [sqb] 3, 7 5 [sqb] 3, 7 5 # 3 #, 4. 5.] 6. F 5 # 3 D 5 3 #, 7. F 5 # 3 D # 5 3 [sqb], 8. F 5 # 3 D # 5 3 #. the consequent chord of the sixth passage cannot belong to the minor tone A and to the major tone C, just as the consequent chord of the similar passage number 1. C 5 # 3 A 5 3 # belongs both to the minor tone E and to the major tone G. Since I did not provide an example of this last case, I place one here where the consequent chord of the passage 6. F 5 # 3 D 5 3 # belongs artificially to the tone C with the major third. [Riccati, The laws of counterpoint, 442, 2; text: Basso continuo. fondamentale, 5 3 #, 5 # 3, 7 [sqb] 5 3 # 5 3 # 7, 3 #, 6.] [-443-] The passages number 7. F 5 # 3 D # 5 3 [sqb] and 8. F 5 # 3 D # 5 3 # are similar and they correspond totally to the passage number 2. C 5 # 3 A # 5 3 [sqb] and 3. C 5 # 3 A # 5 3 # as to their modulation, hence, I omit their examples. 9. G 5 # 3 # 5 3 #. The preceding chord of our passage belongs to the tone of E minor, while the consequent one belongs to the tone of A minor, just as the preceding chord of the passage number 1. C 5 # 3 A 5 3 # belongs to the tone of A minor and the consequent one can be assigned to the tone D with the minor third, because the first example of the first chapter corresponds to the ninth passage. 10. A 5 3 # 7 5 [sqb] 3 and 13. A 5 3 # F # 5 [sqb] 3. the passage number 10. would be similar and corresponding to the passage E 5 3 # C 5 [sqb] 3 mentioned at chapter 5. [signum] 13., were the preceding chord considered as artificial of the tone D with the minor third. If one takes it as artificial of the tone G with the major third, the passage is disallowed on the basis of the fifth canon. Therefore, we are left with the option that it may be assigned artificially to the tone E with the minor third, as to which C # is the sixth artificial note. The extremely subservient nature of the sixth artificial note, I shall say, renders the tenth passage of very limited use. However, I have tried to render it more tame in the following example. [Riccati, The laws of counterpoint, 443; text: Basso continuo. fondamentale, 6, 7, 6 [sqb], 7 5, 6 5, 3 #, et cetera, 7 5 3 #, 5 # 3 #, 3 [sqb], 7 5 3, 5 3 #, 5 [sqb] 3, 5 3, 10.] [-444-] The second example of the fifth passage E 5 3 # C # 5 [sqb] 3 applies to the passag number 13. A 5 3 # F # 5 [sqb] 3 whenever the preceding chord is employed as artificial of the minor tone A. The first accompaniment itself can be ascribed to the tone D, while the second one to the tone C with the major third. The possibility of the preceding chord belonging to the major tone G is rejected on the basis of the fifth canon, but it can be ascribed to the minor tone E, in which case one shall modulate to the major tone C or to the minor tone A according to whether the consequent accompaniment is used as artificial accompaniment of one or of the other of the two aforesaid tones. The example that I adduce presumes that the first of the two chords is artificial of the minor tone E and the second one also artificial of the tone C with the major third. [Riccati, The laws of counterpoint, 444; text: 6, 7 3, 6 #, 7, 6 4 # 3, 7 [sqb], 7 3 #, 3 #, 7 5 3 #, 5 # 3 #, 3 [sqb], 7 5 3, 3 #, 7 5 [sqb] 3, 7 [sqb], 7 5 3 #, et cetera, 13.] 16. B 5 3 G 5 # 3, 17 B 5 # 3 G 5 # 3. These passages must be employed rarely and with the greatest care, since they conclude on the very harsh chord of major third and augmented fifth, where the modulation occurs. In the passage number 16. the preceding accompaniment is also consonant by representation; in the passage number 17., instead, it is truly consonant, but it contains the artificial sixth note F # of the tone A with the minor third, to which it is presumed to belong. After such chords, it modulates clumsily. I have been careful to ensure that the chord E 5 3 # should precede the chord B 5 # 3 in the second example, so that the former may be ascribed logically to the tone A with the minor third. In bother of the examples I have prepared [-445-] the chord B 6 3 # of the third and minor sixth by employing the device explained at [signum] 7. [Riccati, The laws of counterpoint, 445, 1; text: Basso contnuo. Fondamentale, 6 3, 6 3 #, 6 # 3, 5 # 3 #, 6, 6 #, 6 4, 5 # 3 #, 5 4, 3 #, 5 # 4, 3, 5 3, 5 # 4, 3 #, et cetera, 5 [sqb] 3, 5 # 3, 8 5 3, 7, 8 5 # 3 #, 17.] [signum] 11. The following passages do not deserve to be accepted in counterpoint. 11. A # 5 3 [sqb[ F [sqb] 3, 12. A 3 5 3 # F [sqb] 5 3, 14. A # 5 3 [sqb] F # 5 [sqb] 3 [sqb], 15. A # 5 3 # F # 5 [sqb] 3 [sqb]. They contravene the fifth canon. 18. B 5 # 3 # G 5 # 3, 19. B 5 # 3 # G 5 # 3, 20. B b 5 3 G 5 # 3. The same canon excludes the passages number 18. e 19., if the preceding chord belongs to the chord A with the minor third. Were it to belong to the tone of E minor, the passage would begood and similar to the passage E 5 3 # C 5 # 3, discussed at chapter 5. [signum] 13. the passage number 20. is established as faulty by the sixth canon. [signum] 12. I introduce to the Reader the passages of the third upwards that are the opposite of the ones contained at [signum] 10. [Riccati, The laws of counterpoint, 445, 2; text: Passaggi artifficiali rappresentanti il naturale A 5 3 C 5 3. C 5 3 E 5 3. D 5 3 F 5 3. E 5 3 G 5 3. F 5 3 A 5 3. G 5 3 B 5 3. 5 3 #, 5 # 3, 5 3 [sqb], 5 # 3 [sqb], 5 # 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18.19. 20.] [-446-] 1. A 5 3 # C 5 # 3. Apart from being a passage of the third upwards, this one contains the defect that the sound C # of the preceding chord A 5 3 #renders the augmented fifth of the consequent chord C 5 # 3 more bitter. The preceding chord can belong artificially to the tone D and to the tone E both with the minor third. Since three cadences of the tone of D minor end on the accompaniment A 5 3 #, such circumstance renders our passage not entirely worthy of condemnation, whenever A 5 3 # belongs to said minor tone. In the example that I provide the chords A 5 3 # and C 5 # 3 do not mix very much because a musical idea ends with the first one and another similar idea begins with the first one. If the preceding accompaniment is ascribed to the tone of E minor, since no cadence concludes on said chord, I have not been able to find a suitable device in order to render the first passage tolerable when it is employed in this fashion. I invite the Reader to look at the promised example. [-447-][Riccati, The laws of counterpoint, 447, 1; text: Basso continuo. fondamentale, 6 3 #, 5 3, 6 5 3 #, 5 3 #, 6 [sqb] 3 #, 6 5 3 [sqb], 5 3 #, ett cetera, 5 # 3, 7 5 b 3 #, 7 5 [sqb] 3 #, 1.] 4. C # 5 3 E 5 3, 5. C # 5 3 E 5 3 #. Albeit the passages discussed in the present chapter must modulate from one tone to another tone, this cannot occur in the passage number 4., if C # 5 3 is not assigned to the tone D with the minor third, or to A with the minor third or to the tone C with the major third. Apart from the fundamental movement of the third upwards, our passage contains in itself the fault consisting in the fact that G, minor fifth of C #, remains minor third of E in the following accompaniment. Therefore, I am not surprised that I struggled to lay it out in such a form that it may not be unpleasant to the ear. [Riccati, The laws of counterpoint, 447, 2; text: Basso continuo. fondamentale, 5 3, 6 4, 6 # 3, 5 4 , 3, 5 3 #, 5 3, 7 5 3 #, 4.] The preceding chord C # 5 3 of the passage number 5. C # 5 3 E 5 3 # can be assigned to the tone D or to the tone E both with the minor third. Therefore, said passages modulates either from the minor tone D or from the minor tone E to the minor tone A, to which the consequent chord E 5 3 # belongs. Were the natural note G involved in such accompaniment [-448-] instead of the artificial note G #, the minor fifth G of the preceding accompaniment would become the third of the consequent accompaniment with an inverse preparation, as I noted with regard to the passage number 4. The artificial note G # remedies such defect and allows our passage to be introduced occasionally in musical compositions under the two aforesaid forms. I have strived to achieve this in the best possible way in the following examples. [Riccati, The laws of counterpoint, 448; text: Basso continuo. fondamentale, 73, 6 #, 5 3 #, et cetera, 5 3, 6, 5 3 #, 6 # 4, 6 # 4 #, 7 5, 6 # 5 3, 5 # 3 #, 9 5 3, 8, 8 3 #, 7, 7 5 3 #, 7 5 3, 5.] 9. # 5 3 # G [sqb] 5 # 3. In the present passage the preceding accompaniment belongs to the tone A with the minor third and the following to the similar tone of E. therefore this passage correspond to the passage number 1. A 5 3 # C [sqb] 5 # 3, when the first chord is assigned to the minor tone D. The mentioned example, which can also be adapted to the passage number 9. E 5 3 # G [sqb] 5 # 3, conforms to this premise. 10. F 5 3 A 5 3 #, 11. F 5 3 A # 5 3 [sqb], 12. F 5 3 A # 5 3 #, 13. F # 5 3 A 5 3 #, 14. F # 5 3 A # 5 3 [sqb], 15. F # 5 3 A # 5 3 #. If the passage number 10. has to contain modulations, the consequent accompaniment [-449-] A 5 3 # must be considered as artificial of the major tone G or of the minor tone E. I employ it in the example placed herewith as belonging to this latter tone. [Riccati, The laws of counterpoint, 449, 1; text: Basso continuo. fondamentale, 6 3, 6 5 3, 7 5 3 #, 5 3, 6 5 3 #, 7, 5 # 3 #, 7 5 # 3 #, 10.] The second and third example present to us the passages number 11. and 12., which modulate from the tone A to the tone E both with the minor third in the aforesaid examples. [Riccati, The laws of counterpoint, 449, 2; text: Basso continuo. fondamentale, 3 #, 6, 7, 5 3, 6 # 3, 5 # 3 #, 6 5, 6 # 3, 5 # 3 #, o pure, 6 3 #, 7 5 # 3 #, 7 3 #, 8 5 3 #, 7, 5 3 [sqb], 8 5 # 3 #, 5 3 #, 11. 12.] In all three of the adduced examples I employed the device of terminating the cadence E 5 3 # F 5 3 from the fourth of the fifth note of the tone B derived from the tone A with the minor third in the preceding chord F 5 3 of the passages number 10., 11, and 12. Since said cadence contains within itself some sense of conclusion, it attracts the attention of the ear. Therefore, the juxtaposition of F 5 3 with the following chord A 5 3 # or A # 5 3 [sqb], or A # 5 3 # of the three mentioned passages is as obscure as the comparison between E 5 3 # and F 5 3 is clear. I warn the Reader that the passage number 12. F 5 3 A # 5 3 # is sung among those [-450-] that produce the idea of an unlawful modulation from one tone to another one not linked by reciprocal subordination. U leave it to the judgement of the Reader to decide if I have hidden sufficiently the discrepancy between the two accompaniments F 5 3 and A # 5 3 #. Were the preceding chord F # 5 3 of the passages number13., 14. and 15. to be considered as artificial of the tone C with the major third, one would infringe the fifth canon,. Therefore, it can be assigned only as an artificial chord to the tone A with the minor third. I employed as such in the examples that I place herewith. In the passage number 13. the consequent accompaniment A 5 3 # can belong artificially to the tone D or to the tone E with the minor third and also to the tone G with the major third. The first form appears more unexpected than the other two because of the preceding chord F # 5 3, which appears to require that A 5 3 # should be assigned to the tone E or to the tone of G major, whose scale also contains the note F #. In the examples number 13., 14. and 15. A sort of cadence E 5 3 # F # 5 3 from the fourth natural note to the fifth artificial one of the tone B derived from the tone A with the minor third ends on the preceding chord F # 5 3 of those passages. The aforesaid cadence is nevertheless not very conclusive, not only because the artificial note F # removes the natural semitone E F, but also because it renders the accompaniment F # 5 3 consonant by representation. [Riccati, The laws of counterpoint, 450; text: Basso continuo. fondamentale, 6, 3, 6 5, 5 4, 5, 3 #, 6 #, 6 4, 5 # 3 #, Oppure, 6 #, 3 #, 3, 5 3 #, 6 # 3, 5 # 3 #, 6 3, 5 3, 6 [sqb] 4 #, et cetera, 7 5 3 #, 8, 7, 8 5 # 3 #, 8 5 3 #, 7 5 # 3 #, 5 3 [sqb], 13. 14.] [-451-] [signum] 13. The following passages must be avoided in musica composition. 2. A # 5 3 [sqb] C 5 # 3, 3. A # 5 3 # C [sqb] 5 # 3. They remain excluded because they contravene the fifth canon. 6. D 5 3 # F [sqb] 5 # 3. If one considers the preceding chord as artificial of the tone ofC magior, the passage number 6. contravenes the fifth canon. However, if one ascribes it to the minor tone A as artificial as well, I said at [signum] 12. on the subject of the similar passage A 5 3 # C [sqb] 5 # 3 that the major third of the preceding accompaniment renders the augmented fifth so bitter that the ear cannot stand it, principally because of the preceding chord which does not conclude any cadence. In fact, no cadence of the tone A with the minor third ends on the chord D 5 3 #, which is presumed to belong artificially to said tone. 7. D # 5 3 [sqb] F 5 3 #, 8. D # 5 3 # F [sqb] 5 # 3. These passages are declared faulty on the basis of the fifth canon. [-252-] 16. G 5 # 3 B 5 3 [sqb], 17. G 5 # 3 B 5 # 3 [sqb], 18. G 5 # 3 B 5 [sqb] 3 #, 19. G 5 # 3 5 # 3 #, 30. G 5 # 3 B b 5 3 [sqb]. The passages number 16. 17. 20. infringe openly the third canon, because in their consequent accompaniment there is no D #, which forms an augmented fifth with the base of the preceding accompaniment, or E, to which said sound D # must ascend. The same canon makes us reject the passage number 18. as well, because, albeit the consequent chord B 5 [sqb] 3 # contains the note D #, it is so harsh that it proves unbearable to delay ascending to E in such way. As to the passage number 19., since the chord B 5 # 3 # is common to the minor tones A and E, and since it comes after the chord G 5 # 3, which belongs to the tone E, the ear assigns it to this tone. As to the passage C 5 # 3 B 5 # 3 # belonging to the minor tone E, I discussed it at chapter 5, [signum] 17, where I produced an example. In the example placed here beneath the preceding chord G 5 # 3 makes the ear assign the consequent chord B 5 # 3 # to the minor tone E, as I stated just now. However, if this is followed by the chord E 5 3 # belonging to the tone of A minor, the ear changes opinion, and regards it as belonging to A minor. I short, the chord B 5 # 3 # is employed as based firstly on the fifth note of the minor tone E, then as based on the second note of the minor tone A. In this last capacity, it requires that the cadence B 5 # 3 # E 5 3 # from the second to the fifth note, which contains the ascent from D # to E (as required according to the third canon by the accompaniment G 5 # 3 of major third and augmented fifth already heard) should be realised according to the fifth canon. [Riccati, The laws of counterpoint, 452; text: Basso continuo. fondamentale, 5 # 3 #, 6, 7 5 #, 6 5 3, 5 4, 3 #, 6 # 4 # 2, 6 3, 7 5 3, 5 # 3, 7 5 # 3 #, 7 5 3, 5 # 4, 19.] [signum] 14. I conclude this sixth chapter by discussing the passages that consist of two artificial chords [-453-] representing the same natural ones. These passages modulate from one tone to another one that do not share the same scale in as much as indicated by the artificial notes. I place the aforementioned passages in order. [Riccati, The laws of counterpoint, 453; text: Passaggi formati da ue accordi artificiali, che rappresentano il naturale C 5 3. F 5 3. G 5 3., 5 3, 5 # 3, 5 [sqb] 3, 1. 2. 3. 4. 5. 6.] 1. C # 5 3 C [sqb] 5 # 3. The preceding chord C # 5 3 representing the natural one C 5 3, can belong to the tone of D minor and to the tone of E minor. Were one to ascribe it to the tone of G with the major third, one would infringe the fifth canon. Therefore our passage will move lawfully from the minor tone D to the minor tone A or from the minor tone E to the minor tone A mentioned before. The unprepared augmented fifth C 5 # reaches the ear harshly, and it is rendered prominent by the memory of the sound C #. I have managed to mitigate the passage by employing it in the following way, namely, E 6 # 3 E 6 3 #, by placing the harshest chord E 6 3 # on a weak beat and by juxtaposing together only melodically the sounds C and G #, which form a diminished fourth in the aforementioned chord. [-454-] [Riccati, The laws of counterpoint, 454; text: Basso continuo. fondamentale, 7 3, 6 #, 6 [sqb] 3 #, 7 5 3, 6, 5 3 #, 6 3, 6 [sqb], 6 [sqb] 3 #, 5 3, 5 3 #, 9 5 3, 8, 5 # 3, 9 5 3 #, 1.] 3. F # 5 3 F [sqb] 5 # 3 and 5. G # 5 3 G [sqb] 5 # 3. In the passage number 3. the preceding chord must not be considered as artificial of the tone C with the major third, since such presumption contravenes the fifth canon. Therefore, it can only belong artificially to the tone of A minor. On this basis, the passage number 3. is similar to the number 1. C # C [sqb] 5 # 3, when the preceding accompaniment is assigned to the minor tone E. One should deduce that the second of the last two examples is referred to it. The first example refers to passage number 5., whose preceding accompaniment belongs to the tone of A minor, because it is similar with the passage number 1., were the preceding chord to be ascribed to the tone D with the minor third. [signum] 15. The discipline of counterpoint does not allow the passages written herewith. 2. C 5 # 3 C # 5 [sqb] 3, 4. F 5 # 3 F # 5 s[qb] 3, . G 5 # 3 G # 5 [sqb] 3. these passages infringe the third canon, because the augmented fifth cannot be resolved by ascending by a second. [-455-] Seventh chapter. On the artificial passages that represent the natural ones and move from accompaniment to another one belonging to two tones, one principal and the other subordinate, or vice versa, sharing the same scale. [signum] 1. I have discussed in the third chapter of the natural passages that modulate from the principal tone C major or A minor to the subordinate ones that do not share the scale, or vice versa. I ordered them according to eighteen species and six classes and I reflected at length on how to employ them well according to their different character. I shall follow the same structure employed in the quoted section in dealing with the artificial passages that represent the aforesaid natural passages. Our artificial passages originate from substituting artificial chords that represent the natural ones, whose function they perform, instead of one or the other natural chord or instead of both. These artificial accompaniments are borrowed from the principal or subordinate tone to which the natural accompaniment represented belongs. For instance, if a passage contains the chord G 5 3 b as belonging to the tone F with the major third and to its relative D with the minor third, I shall be able to substitute instead of G 5 3 b all the artificial chords that the two mentioned tones supply to me. As I have not considered as a passage the application of a particular natural accompaniment firstly as belonging to one tone and then as belonging to another one, thus, I shall not class as passages the repetitions of the same chord, which is employed firstly as natural of the previous tone and then as artificial of the following tone, or vice versa, or as artificial of both tones. This double character of the same accompaniment shall be allowed when it does not infringe any of the canons established in the fourth chapter. For instance, I am allowed to use the chord B b 5 3 firstly as natural of the relative tones F major and D minor and then as artificial of the tone A with the minor, [-456-] because I can fulfil the requirement of the sixth canon by producing the cadence B b 5 3 # 5 [sqb] 3 # from the second to the fifth note, thanks to which said artificial accompaniment has been introduced into the discipline of counterpoint. To presume that the chord B b5 3 is first artificial of the minor tone A and then natural of the relative tones F major and D minor would go against the mentioned canon. [signum] 2. Without abandoning the order kept in the third chapter, I shall discuss first of all the artificial representing the natural ones that consist of two accompaniments whose bases are correspond to each other at the unison. [Riccati, The laws of counterpoint, 456; text: Passagi artificiali rappresentanti i naturali G 5 3 G 5 3 b, D 5 3 # D 5 3 [sqb] della prima spezie. G 5 3 b G 5 3 [sqb], DD 5 3 D 5 3 #, seconda. E 5 3 E 5 b 3, B 5 # 3 B 5 [sqb] 3, terza. E 5 b 3 E 5 3, B 5 3 B 5 # 3, quarta. 5 3, 5 3 b, 5 3 #, 5 3 [sqb], 5 b 3 [sqb], 5 b 3 #, 5 [sqb] 3 #, 5 # 3 #, 5 [sqb] 3 [sqb], 5 [sqb] 3, 5 # 3 [sqb], 5 # 3, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 2. 21. 22. 23. 24. (1.), (2.), (3.), (4.), (5.), (6.), (7.), (8.), (9.), (10.), (11.), (12.), (13.), (14.), (15.), (16.), (17.), (18.), (19.), (20.), (21.), (22.), (23.), (24.)] 2. G 5 3 G # 5 3 b, 2. G 5 3 G # 5 3, 3. G # 5 3 G [sqb] 5 3 b, 4. G # 5 3 GG [sqb] 5 3. 5G # 5 3 G # 5 3 b. All these passages can prove useful in composition. They are employed to modulate from one and from the or from the other of the relative major tones C major and A minor to one or the other of the relative F major and D minor. Instead of the accompaniment G # 5 3 b, one shall employ more elegantly the derivative accompaniment B b 6 # 3, while in the passages number 3. and 4. containing an inverse preparation of the fifth, it shall be necessary to substitute to the fundamental chords the derivative ones of the third and sixth, so that said passages will assume the following form: 3. B 6 # s B b 6 [sqb] 3 4. B 6 # 3 B 6 3 [sqb]. The passage number 3. is very apt to express tender emotions because of the double flattening of the notes from B to B b and from G # to G, which I believe to have achieved in the third example. I warn the reader that in the fourth passage, 4. G # 5 3 G [sqb] 5 3, the consequent chord can perform the role of artificial chord of the tome D with the minor third or of the tone F with the major third. I have employed in this double form in the fourth and in the last example. L [Riccati, The laws of counterpoint, 457; text: Basso continuo. fondamentale, 6 3, 6 # 3, 5 3 #, 5 3 b, 6 4, 6 #, 5 [sqb], 7 3, 6 #, 6 [sqb] 3, 7 5 3 #, 7 b 5 3, 5 3, 3, 7 5 3, Perchè così mi strazj? O Dio che langue il core. O pure, et cetera, 6 5 3, 8 5 3 #, 7 [sqb], 7, 3 #, 6 4 2, 5 # 3 #, 6 # 4 # 2, 5, 5 3 #, 9 5 3, 5 4, 3, 5 3, 8 5 # 3 #, 1. 2. 3. 4, 5.] [-459-] 6. G 5 3 b G # 5 3 [sqb] and 7. G 5 3 G # 5 3. Ifthe principal tone is C major or A minor, as one always presupposes, The passage number (6.) D 5 3 D # 5 3 # shall be employed more easily than the passage 6. G 5 3 b G # 5 3 [sqb], which is similar to it, because two cadences of the subordinate mode D with the minor third end on D 5 3, while no cadence of a subordinate tone ends on G 5 3 b. Therefore, in the first example I prefer to employ the passage(6.) D 5 3 D # 5 3 # than the similar one 6. G 5 3 b G # 5 3 [sqb]. [Riccati, The laws of counterpoint, 459, 1; text: Basso continuo. fondamentale,, 6 5 3, 7 5 3 #, 7 b 5 3, et cetera, 7 5 3 #, (6.)] [-460-] Were one to employ the preceding accompaniment G 5 3 of the passage number 7. G 5 3 G # 5 3 as artificial of the tone F with the major third, one would infringe the fifth canon. Nevertheless, one can consider it as artificial of the minor tone D, as long as one part moves from C # to B, namely, from the artificial seventh note to the artificial sixth note of the aforesaid tone, as one can see in the following example. [Riccati, The laws of counterpoint, 460; text: Basso continuo. fondamentale, 6 b 3, 7 b 3, 6, 7 3, 7 5 3, 6 3, 6 4, 5 3#, 9 b 5 3 #, 8, 9 5 3 #, 7.] 11. E 5 3 # 5 b, 12. E 5 3 E 5 3 #, 13. E 5 3 # E 5 3 [sqb], 14. E 5 3 # E 5 b 3 #, 15. E 5 3 # E 5 b 3 #. The passage number 14. is the best of the ones written above, and it is used to modulate with great elegance from the tone A to the tone D both with the minor third. The passages number 11. and 15. prove harsh because of the consequent chord of the major third and minor fifth. Since the chord A 5 3 # must follow necessarily the consequent accompaniment E 5 3 #, which is presumed artificial of the minor tone D, the ear suspects that these two chords, albeit common to the major tone D, belong to said tone what is not considered among the ones that are subordinate to the principal tone C major or A minor. Therefore, one has to be very skilful to ensure that the ear is pleased with the series of accompaniments E 5 3 # A 5 3 # D 5 3, since it the minor third of the last chord is hear as rather strange. The Reader will judge from the following example how successfully I have managed to accomplish this. [-461-] [Riccati, The laws of counterpoint, 461; text: Basso continuo. fondamentale, 6 3, 7 5 3 #, 5 b 3 #, 5 3 #, 6 [sqb] 3, 5, 5 # 3 #, 6 5 3 #, 6 # 5 3, 5 # 3 #, 6 # 4, 6 #, 3 #, 7 5, 5 3 [sqb], 5 3, 6, et cetera, 5 b 3 [sqb], 6 5 3, 5 b, 7 5 3 #, 7 5 3, 8, 7, 8 5 # 3 #, 5 3, 6 5 3, 8 5 3 #, 7 [sqb], 8 5 3, 11. 12. 13. 14. 15.] [-462-] 16. E 5 3 E b 5 b 3, 17. E 5 3 # E b 5 b 3. the passage number 16., and even more the passage number 17., consist of chords that are so far apart that appear to move from a tone to another tone not linked by mutual subordination. Although I exclude almost completely such passages in the eighth canon, nevertheless I place the example of our two. In order to show that they can achieve, I adapt the words 'Stop, o God, what terrible death; is there no pity in you?' to the first example containing the passage number 16. which is less faulty. [Riccati, The laws of counterpoint, 462; text: Basso continuo. fondamentale, Ferma o Dio che fiera morte nè si trova in te pietà? 6 3, 6 b 3 b, 4 # 2, 4 2, 7 5 3, 8 5 3, 7 5 3 [sqb], 3 #, 5 3 #, 6 b 3, 7 5 [sqb] 3 #, 5 3, 64, 5 3 #, 5 b 3, 5 [sqb] 3 [sqb], 16. 17. et cetera] [-463-] 18. E 5 b 3 E 5 [sqb] 3 #, 19. E 5 3 E 5 3 #. Here is how these two passages can be employed. [Riccati, The laws of counterpoint, 463; text: Nasso continuo. fondamentale, 6 3, 6 3 b, 5 [sqb] 3 #, 6 5 3, 7 5 3, 5 3, 5 4, 3 #, 3, 5 3 #, 5 b 3, 5 [sqb] 3 #, 8 5 3 #, 7, 18. 19.] [signum] 3. Of the passages that represent other natural passages consisting of two chords whose bases are correspond to each other at the unison, the following ones are rejected from musical composition. 8. G # 5 3 b G [sqb] 5 3 [sqb], 9. G # 5 3 b G # 5 3[sqb], 10. G # 5 3 G [sqb] 5 3. These passages, representing the natural passage G 5 3 b G 5 3 [sqb], do not abide by the fifth canon. The passage number 9. also infringes the seventh canon. 20. E 5 3 #, E 5 3[sqb], 21. E 5 b 3 # E 5 [sqb] 3 [sqb], 22. E 5 b 3 # E 5 [sqb] 3 #, 23. E b 5 b 3 E [sqb] 5 [sqb] 3, 24. E b 5 b 3 E [sqb] 5 [sqb] 3 #. The passages number 20. 21 and 22. contravene the fifth canon; the passage number 22. contravenes the seventh canon as well, while the passages number 23. and 24. infringe the sixth canon. [signum] 4. If we follow the order observed in the third chapter, we must turn to consider the artificial passages representing the natural ones that move a fifth upwards or downwards. [Riccati, The laws of counterpoint, 463; text: Passaggi artificiali rappresentanti i naturali composti da due accordi, le cui basi si corrispondono in Quinta presa all'insù, o all'ingiù. E 5 b 3 B 5 3, B 5 3 F # 5 3 della quinta spezie. B 5 3 E 5 b 3, F # 5 3 B 5 [sqb] 3, sesta. 5 b 3, 5 # 3, 5 [sqb] 3 #, 5 # 3 #, 5 3, 5 [sqb] 3 [sqb], 5 b 3 #, 5 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. (1.), (2.), (3.), (4.), (5.), (6.), (7.), (8.), (9.), (10.), (11.), (12.), (13.), (14.), (15.), (16.), (17.), (18.), (19.), (20.), (21.), (22.), (23.), (24.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.) (39.) (40.) (41.) (42.) (43.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.) (39.) (40.) (41.) (42.) (43.) (44.) (45.) (46.) (47.) (48.)] [-265-] 1. E 5 b 3 B 5 # 3, 2. E 5 b 3 B 5 [sqb] 3, 3. E 5 b 3 B 5 # 3 # and 4. E 5 b 3 B b 5 3. All of these passages are employed very rarely. The first and the third one appear to move from one tone to another tone that are not reciprocally subordinate. The fourth one is similar to the diatonic passage B 5 3 F 5 3, which was forbidden from a base to a base because it contains three imperfections (chapter 2. [signum] 6.). Finally, the second consists of two chords that are both consonant by representation, where the consequent very harsh chord of the major third and minor fifth is introduced without preparation. I try to mitigate our passages. I set the passages 1., 2. and 3., which are in fact very suited to express from an plangent emotion to an active and strong one, to the verses 'Hear! My pain cries revenge and threatens you, unjust monster,' where the tender words la pena mia follow the words expressing high cries and revenge. [Riccati, The laws of counterpoint, 465; text: Basso continuo. fondamentale, Senti; la pena mia Grida vendetta, e te Minaccia o mostro iniquo, 3 #, 6 3, 5 b 3, 6 [sqb] 3 #, 6 3, 5 3 #, 5 3, 6 #, ovvero, 6 [sqb] 3 [sqb], 5, 6 b 3, et cetera, 8 5 3 #, 7, 5 3 [sqb], 8 5 [sqb] 3 #, 5 # 3 #, 8 5 3, 1. 2. 3. 4.] 5. E 5 3 B 5 3, 6. E 5 3 B 5 # 3, 7. E 5 3 B 5 [sqb] 3 #, 8. E 5 3 B b 5 3. If the chord E 5 3 has to be considered artificial of the minor tone D, it must be preceded by an accompaniment that contains the artificial seventh C # of said tone. Accomplished this in the examples below, which allows also to know that the chords belong artificially to the tone A with the minor third because they are followed by the chord E 5 3 #. [Riccati, The laws of counterpoint, 466; text: Basso continuo. fondamentale, 5 4, 3 #, 3, 10 6 5, 5 3 #, o pure, 3, 6 # 4 3, 6 3, 5 3 #, 6 b 3, 5, et cetera, 7 5 3, 8 5 # 3, 5 3 #, 8, 7, 7 5 [sqb] 3 #, 7 5 # 3 #, 8 5 3, 5. 6. 7. 8. 9.] [-467-] 25. B 5 3 E 5 3, 26. B 5 3, E 5 b 3 #, 27. B 5 3 E 5 3 # and 28. B 5 3 E b 5 b 3. Of the four passages that I present to the attention of the Reader and that represent the natural passage B 5 3 E 5 b 3, which modulates from the major tone C or minor A to the major tone F or minor D, the passage number 26. is very harsh on the ear, because it introduces the chord E 5 b 3 # of the major third and minor fifth without preparation. The passage number 28. proves strange because it appears to move from one tone to another one, both of which are not linked by reciprocal subordination. I employed such a passage in the last example to express the sentiment of these words: 'It shall happen, therefore, beloved son, that you may abandon me?' [-468-] [Riccati, The laws of counterpoint, 468; text: basso continuo. fondamentale, 5 3, 4 2, 6 3, 6 4 # 2, 6 5 3 b, 5 3 #, 6 5 3 b, 6 5 3, 5 b 3 #, 5 [sqb], 10 9 5, 8, 6 b 3 b, 5, 4, 3 #, 5 4, 3, E fia dunque o Figlio amato che tu possa abbandonarmi, 7 5 3, 7 5 3 #, 7 5 b 3, 8 5 3 #, 7 [sqb], 5 b 3, et cetera, 25, 27, 26. 28.] 29. B 5 # 3 E 5 b 3, 20. B 5 # 3 # 5 3, 31. B 5 # 3 E 5 b 3 #, 32. B 5 # 3 E 5 3 # 33. B 5 # 3 E b 5 b 3. Our passages are harder to employ that the four last ones because of the F # introduced into the previous accompaniment B 5 # 3. This F # is employed as sixth artificial note of the minor tone A, and it must always follow or precede the seventh artificial note G #. There is so much harshness in the passage number 31. and such extravagance in the passage number 33., that I do know how the examples that I present may prove successful and may be met with approval. [-469-] [Riccati, The laws of counterpoint, 469; text: Basso continuo. fondamentale, 5 3, 3 #, 5 # 4, 6 3 b, 5, 7 5 3 #, 7 5 3 b, 7 5 3 #, 5 # 4, 6 3, 5 3 #, 5 b 3 #, 6 b 3 b, 4 # 2, 5 [sqb], 4 2, 7 5 4, 11 9, 10 8, et cetera, 7 5 b, 8 5 b 3, 7, 8, 7 5 3, o pure, 29. 30. 32. 31. 33.] [-470-][signum] 5. All the passages between number 10. and number 24. deserve to be banished from counterpoint under the supposition that they represent the natural passage E 5 b 3 B 5 3, because ten contravene the fifth canon, and five contravene the sixth canon. Similarly, the fifteen passages that represent the natural passage B 5 3 E 5 b 3 from number 34. to number 48. inclusive are subject to the same fortune because they are their opposite. The ten passages between number 34. and number 43. contravene the fifth canon, while the remaining five contravene the sixth canon. Note that I have forbidden the thirty passages mentioned above under the supposition that they represent the natural passages E 5 b 3 A 5 3 and B 5 3 E 5 3 b. If this condition changes and they represent some other natural passage, some of them will be allowed. For instance, such are the passages number 15. E 5 3 # B 5 3, 16. E 5 3 # B 5 # 3, 17. E 5 3 B 5 [sqb] 3 #, 18. E 5 3 # B 5 # 3 # and 19. E 5 3 # B b 5 3, if they represent the natural passage E # 5 3 B 5 3, which I discussed at chapter 5. [signum4.], and of whom I provided some examples. One may also employ the passages number 35. B 5 [sqb] 3 # E 5 3, 37. B 5 [sqb] 3 # E 5 3 # 10. B 5 # 3 # E 5 3, 42. B 5 # 3 # E 5 3 # and 47. B b 5 3 E 5 s[qb] 3 #, when they represent the natural passage B 5 3 E 5 3. I discussed these at chapter 5. [signum] 7. 5. 9. 10., and I did not decline to illustrate them with examples. [signum] 6. I continue by examining the artificial passages that represent the natural ones descending by a third. I discussed them in the third chapter. [Riccati, The laws of counterpoint, 470; text: Passaggi artificiali rappresentanti i naturali di Terza all'ingiù. naturali B b 5 3 G 5 3 [sqb], F 5 3 D 5 3 # della settima spezie.G 5 3 b E 5 [sqb] 3, D 5 3 B 5 # 3, ottava, G 5 3 E 5 b 3, D 5 3 # B 5 [sqb] 3, nona, B 5 3 G 5 3 b, F # 5 3 D 5 3 [sqb] decima. 5 3, 5 3 [sqb], 5 3 #, 5 [sqb] 3 #, 5 3 b, 5 [sqb] 3 [sqb], 5 3 [sqb], 5 # 3 #, 5 # 3, 5 # 3 [sqb], 5 b 3 #, 5 b 3, 5 b 3 [sqb], 5 3 b, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. 1.), (2.), (3.), (4.), (5.), (6.), (7.), (8.), (9.), (10.), (11.), (12.), (13.), (14.), (15.), (16.), (17.), (18.), (19.), (20.), (21.), (22.), (23.), (24.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.) (39.) (40.) (41.) (42.) (43.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.)] 1. B b 5 3 G # 5 3 [sqb], 2. B 5 3 G 5 3 and 3. B 5 3 G # 5 3. In the passages number 2. and 3., which represent the natural passage B b 5 3 [sqb], the preceding chord B 5 3 cannot be considered as artificial of the major tone F, because in that case one would contravene the fifth canon. [-472-] However, it is legitimate to assign it artificially to the minor tone D. I put it into practice in this way in the second and thir example, where the seventh artificial note C # is followed by the equally artificial note B. [Riccati, The laws of counterpoint, 472; text: Basso continuo. fondamentale, 6 # 3, 6 3, 6 [sqb] 3, 6 b 3, 6 4, 8 5 3, 5 3 #, 7 5 3, 6, 7b 5 3, 6 #, et cetera, 7, 5 3, 1. 2. 3.] 4. G 5 3 b # 5 [sqb] 3 #, 5. G 5 3 E 5 3and 6. G 5 3 E 5 3 #. the fifth canon prevents us from employing the preceding accompaniment G 5 3 of the fifth and sixth passage as artificial of the tone F with the major third. No law prevents us to assign it artificially to the minor tone D. I employed in this form in the second and third example. [-473-] Although the first example contains the passage number 4. G 5 3 b E 5 [sqb] 3 #, I must not omit to inform the Reader that one shall encounter the passage number (4.) D 5 3 B 5 # 3 # with greater success under the supposition that the major tone C or the minor relative tone A is the principal tone, for the reason explained at length at chapter 3. [signum] 5. [Riccati, The laws of counterpoint, 473; text: Basso continuo. fondamentale, 6 3, 5 3 #, 5 3 b, 6 3 [sqb], 6 3 #, 5 3, et cetera, 6 b 3, 7 b 5 3, 6, 7 5 3, o pure, 5, 5 3 [sqb], 8 5 3 #, 4. 5. 6.] 11. G 5 3 E 5 3, 12. G 5 3 E 5 b 3 #, 13. G 5 3, E 5 3 # and 14. G 5 3 E b 5 b 3. The passages number 11. and 13. are very good even under the present supposition, namely, that they represent the natural passage G 5 3 E 5 b 3. In order that the sound B, sixth artificial note of the minor tone D, may be used logically and with good reason in the consequent chords E 5 3, E 5 3 #, it is necessary to rise from it to the seventh artificial note C #, which one sees occurring in the first and second example. The very harsh chord of the major third and minor fifth is introduced unprepared into the passage number 12., while the passage number 14. appears to modulate from one tone to another one without the link of a reciprocal subordination. Our passage can be useful to move from [-474-] a strong emotion to another one fraught and extremely plangent. [Riccati, The laws of counterpoint, 474; text: Basso continuo. fondamentale, 5 3, 6, 5 3 #, 6 3, 6 5 3, 6 # 4 2, 5 3 b, 5 3, 3 #, e ti sfida a giusta morte ma o Dio lo sposo esangue, 6 b 3 b, 4, 7 b 5 3, 5 4, 3, 5 3, 7 5 3, 7 5 b 3 #, 8 5 3 #, 7, 5 3 b, 8 5 b 3, 7 b 5 3, 11. 13. 12. 14. et cetera] 15. G # 5 3 E 5 b 3 [sqb], 16. G # 5 3 E 5 3 #, 17. G # 5 3 E 5 b 3 #, 18. G # 5 3 E 5 3 # and 19. G # 5 3 E b 5 b 3. Of the five passages notated above representing the natural passage G 5 3 E 5 b 3, the passage number 17. proves harsh because of the consequent chord E 5 b 3 # of the major third and minor fifth. One must not overlook the consideration that the sound G #, which originates the harshness [-475-] of the mentioned accompaniment E 5 b 3 #, must be prepared. In the passage number 19. G # 5 3 E b 5 b 3 the chords are even further removed than in the passage number 14. G 5 3 # b 5 b 3. In order to avoid that the three sounds G, B b and E b prove too harsh on the ear, when the composition moves from preceding chord to the consequent one, I add the ninth to said consequent chord, so that one may hear first only the two sounds G and B b, and, after the resolution of the ninth, one may hear the sound E b as well. I invite the Reader to consider the examples of our five passages. [Riccati, The laws of counterpoint, 475; text: Basso continuo. fondamentale, 5 3, 6 4, 7 5 3, 6 5 3 b, 6 4 # 2, 8 6 3, 5 3 #, 6 5 3, 7 5 3, 6 5, 6 # 5 3, 6 # 4 3, 6 5 [sqb] 3, 5 3 b, 5 4, 3 #, 6, 7 5 4, 3, 7, 6 b 3 b, 5, 6 4, 8 7 5 b 3 #, 8 5 3 #, 9 5 3, 8 6, 7 5 [sqb] 3 #, 15. 16. 17. 18. 19.] [-476-] 20. B 5 3 G 53, 21. B 5 3 G # 5 3 b and 22. b 5 3 G # 5 3. All three these passages are good. In the consequent chords of the passages number 20. and 22., the sound B is employed as sixth artificial note of the minor tone D, from which one must ascend to the artificial seventh note C #. The example contains the accompaniment G # 5 3 b ordered in its best form. [Riccati, The laws of counterpoint, 476; text: Basso continuo. fondamentale, 7 5 3, 6, 5 4, 3 #, 6# 5 3, 6 4, 5 3 #, et cetera, 6 #, 6 3, 5 [sqb], 7 5 3, 7 5 3 #, 7 5 3 b, 8 5 3 #, 3] 23. B 5 # 3 G 5 3 b, 24. B 5 # 3 G 5 3, 35. B 5 # 3 G # 5 3 b, 26. B 5 # 3 G # 5 3. Albeit the sound F #, sixth artificial note of the minor tone A confers the passages number 23. and 25. the appearance of modulating from one tone to another tone that are not mutually subordinate, the ear shall not listen to them unwillingly once it understands clearly that F # is an artificial note of the aforementioned sound A introduced into counterpoint thanks to the seventh equally artificial note C #. [-477-] [Riccati, The laws of counterpoint, 477; text: Basso continuo. fondamentale, 5 4, 3#, 5 # 4, 3, 6 3, 7 5 3 #, 6 5 3 b, 5 4, o pure, 6 [sqb] 3, 6 5 3, 5 # 3, 6 # 3, 8 5 3 #, 10 [sqb] 9 5, 8, 6 #, 5 [sqb], et cetera, 5 3 b, 7 5 b 3, 5 3, 23. 24. 25. 26.] [signum] 7. The canons established earlier in the fourth chapter forbid the following passages. 7. G # 5 3 b E 5 [sqb] 3 [sqb], 8. G # 5 3 b E 5 [sqb] 3 #, 9. G # 5 3 E 5 3 [sqb] and 10. G # 5 3 E 5 3 #. They are banished on the basis of the fifth canon. In order to avoid any misunderstanding, one must be aware that the passages number 9. e 10. are not admitted under the supposition that they represent the natural passage G 5 3 b E 5 [sqb] 3, and that G # in the previous accompaniment is the fourth artificial note of the tone D with the minor third. [-478-] In fact, were they to represent one or the other of the natural passages G 5 3 E 5 3, G 5 3 E 5 3, one would have no need to reject them. If we consider the in the first form, I discussed them at chapter 5 [signum] 13.; If we consider them in the second form, I have dealt with them at [signum] 6. of the present chapter. One may also employ the passage number 10. G # 5 3 E 5 3 # as artificially belonging to the tone of D minor and as representing the natural passage G 5 3 b E 5 b 3. I invite the Reader to consider what I said on the similar passage D # 5 3 # B 5 # 3 # belonging artificially to the tone A with the minor third at chapter 5. [signum] 13. 27. B 5 [sqb] 3 # G t [sqb] 3 b, 28. B 5 [sqb] 3 # G 5 [sqb] 3, 29. B 5 [sqb] 3 b, 30. B 5 [sqb] 3 # G # 5 [sqb] 3, 31. B 5 # 3 # G 5 [sqb] 3 b, 32. B 5 # 3 # G 5 [sqb] 3, 33. B 5 # 3 # G 5 [sqb] 3 b and 34. B 5 # 3 # G # 5 [sqb] 3 b. the fifth canon does not allow to admit this passages under the supposition that they represent the natural passage B 5 3 G 5 3 b. If we change this premise, some of them will be able to be employed, as for instance the passage number 32. B 5 # 3 # G 5 [sqb] 3 and the passage number 34. B 5 # 3 # G 5 [sqb] 3, when they represent the natural passage B 5 3 G 5 3. I have discussed the passage E 5 3 # C 5 [sqb] 3, similar to the passage number 32., at chapter 5. [signum] 13. I presented an example of it by Padre Calegari at chapter 2. [signum] 19. One finds three examples of the passage E 5 3 # C # 5 [sqb] 3, similar to the passage number 34. B 5 # 3 # G # 5 [sqb] 3 as representing the natural passage B 5 # 3 G 5 3 at chapter 6. [signum] 10. 35. B b 5 3 G 5 3 b, 36. B b 5 3 G 5 3 [sqb], 37. B b 5 3 G # 5 3 b and 38. B b 5 3 G # 5 3 [sqb]. These passages are banned on the basis of the sixth canon, on the supposition that they represent the natural passage B 5 3 G 5 3 b, so that B b is the second artificial note of the tone A with the minor third. Were B b 5 3 G 5 3 b considered as natural, and the other three as representing them, they would prove similar to the passages F 5 3 D 5 3, F 5 3 D 5 3 #, F 5 3 D # 5 3 [sqb], F 5 3 D # 5 3 #, which I described with approval earlier on, namely, the first one at chapter 2. [signum] 18. and the other three remaining ones at chapter 5. [signum] 13. One may also take as natural the passage B b 5 3 G 5 3 [sqb], which would be represented by the artificial passage B b 5 3 G # 5 3 [sqb] <.> I mentioned the first one at chapter 3. [signum] 3. and 5., while I discussed the latter one in the present chapter [signum] 6. [signum] 8. The natural passages that descend by a third are followed in the third chapter by the passage that move by a minor semitone upwards or downwards. Now I set out to discuss the artificial passages that represent them. [-479-] [Riccati, The laws of counterpoint, 479, 1; text: Passaggi artificiali rappresentanti i naturali di Semituono minore all'insù, e all'ingiù. B b 5 3 B [sqb] 5 3, F 5 3 F # 5 3 della undecima spezie, B 5 3 B b 5 3, F # 5 3 F [sqb] 5 3, duodecima, 5 3, 5 # 3, 5 [sqb] 3 #, 5 # 3 #, 5 [sqb] 3, 5 3 [sqb], 5 [sqb] 3 [sqb], 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. (1.), (2.), (3.), (4.), (5.), (6.), (7.), (8.), (9.), (10.), (11.), (12.), (13.), (14.)] 1. B b 5 3 B [sqb] 5 # 3, 2. B b 5 3 B [sqb] 5 [sqb] 3 # and 3. B b 5 3 B [sqb] 5 # 3 #. the passages number 1. and 3. engender the suspicion of a forbidden modulation from one tone to another one that are not reciprocally subordinate. This imperfection is not contained in the second passage, therefore, I would be less loathed to put it into practice. [Riccati, The laws of counterpoint, 479, 2 ; text: Basso continuo. fondamentale, 6 b, 6 5 [sqb], 4 # 2, 6 3, 5 3 #, o pure, 8 6 b 3, 6 [sqb] 5 3 [sqb], 5 3 #, 6 5 3, 6 [sqb] 5 3 #, 7 5 # 3, 7 5 3 #, 7 5 3, 7 5 [sqb] 3 #, 8 5 3, 7 5 # 3 #, 1. 2. 3.] [-480-] B 5 3 B 5 # 3, 5. B 5 3 B 5 [sqb] 3 #, 6. B 5 3 B 5 # 3 # and 7. B 5 3 B b 5 3. the passages 4., 6. and 7. contain an inverted preparation of the minor fifth. In order to hide it, it is necessary to employ our passages in those secondary forms and in those ways that render it less prominent to the ear. The passage number 5. is better than the others because it lacks the aforesaid imperfection and because the diminished third D # F is prepared before it is introduced into the consequent chord. [Riccati, The laws of counterpoint, 480; text: Basso continuo. fondamentale, 6 3, 6 5 3 #, 5 3 #, et cetera, o pure, 5 3, 6 5 3 [sqb], 6 b 3, 5, 7 5 # 3, 7 5 # 3 #, 8 5 3, 7 5 [sqb] 3 #, 8 5 3, 7] [-481-] B 5 # 3 B b 5 [sqb] 3, 9. B 5 # 3 B 5 [sqb] 3. The passage number 8. appears to modulate from one tone to another one not bound by the link of mutual subordination. Therefore, if one wants to put it into practice, it is necessary that F # follows G #, so that the ear can comprehend clearly that the preceding chord B 5 # 3 belongs to the tone A with the minor third, which can be followed lawfully by the accompaniment B b 5 3, naturally belonging to the relative tones of F major and D minor. So that the consequent chord B 5 3 may be employed in the passage number 9., as in the second example, as an artificial accompaniment of the tone D with the minor third, it is necessary that the sixth artificial note B is followed by the seventh artificial note C #, which occurs demonstrably in the mentioned example. [Riccati, The laws of counterpoint, 481; text: Basso continuo. fondamentale, 7 5, 6 4, 5 3 #, 5 2 #, 6 3 #, 6 b 3 [sqb] 5, 6 b 4 #, 6 3, 5 [sqb], 6 4 # 2, 7 5, 3 [sqb], 6 # 3, 6 5 3, et cetera, 5 # 4, 3, 8 6 5 [sqb] 3, 7, 7 5 b 3 #, 8 5 3 [sqb], 7 5 3 #, 7 5, 5 [sqb] 5 3, 7 5 3, 8. 9.] [signum] 9. the following passages must not be allowed: 10. B # 5 # B b 5 3 [sqb], 11. B 5 [sqb] 3 # B 5 3 [sqb], 12. B 5 # 3 # B b 5 [sqb] 3 [sqb], 13. B 5 # 3 # B 5 [sqb] 3 [sqb] and 14. B b 5 3 B [sqb] 5 3, representing the natural passage B 5 3 B b 5 3 because they contravene, the first four the fifth canon, and the last one the sixth canon. Were we to assume that the passages number 12. and 13. [-482-] represent the natural passage B 5 # 3 B 5 [sqb] 3, they would be similar to the two passages E 5 3 # E b 5 b 3 [sqb], E 5 3 # E 5 b 3 [sqb] discussed by me and illustrated with some examples at [signum] 2. If the passage number 14. B b 5 3 B [sqb] 5 3 is employed as a natural passage, it is one of the two that belong to the eleventh species of the passages described at 3. [signum] 1. and following. The consequent chord of the passage number 14. can also be employed as representing the preceding chord. In that case said passage is similar to the passage F 5 3 F # 5 3 mentioned by me at chapter 5. [signum] 19. [signum] 10. If I follow the sequence of the third chapter, I must discuss the artificial passage that represent the natural ones that ascend by a third in the aforementioned chapter. [Riccati, The laws of counterpoint, 482; text: Passaggi artificiali che rappresentano i naturali all'insù. Rappresentanti, G 5 3 B b 5 3, D 5 3 # F [sqb] 5 3 della tredicesima spezie. E 5 3 G 5 3 b, decima quarta, E 5 b 3 G 5 3 [sqb], B 5 3 D 5 3 #, quintadecima, G 5 3 b B [sqb] 5 3, D 5 3 F # 5 3, decima sesta. 5 3, 5 3 #, 5 3 b, 5 # 3, 5 3 [sqb], 5 # 3 #, 5 b 3, 5 b 3 #, 5 [sqb] 3 #, 5 # 3 #, 5 [sqb] 3 #, 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35. 36. 37. 38. (1.), (2.), (3.), (4.), (5.), (6.), (7.), (8.), (9.), (10.), (11.), (12.), (13.), (14.), (15.), (16.), (17.), (18.), (19.), (20.), (21.), (22.), (23.), (24.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.) (39.) (40.) (41.) (42.) (43.) (25.) (26.) (27.) (28.) (29.) (30.) (31.) (32.) (33.) (34.) (35.) (36.) (37.) (38.)] [-483-] 1. G 5 3 B 5 3, 2. G # 5 3 B b 5 3 and 3. G # 5 3 B 5 3. If our passages represent the natural passage G 5 3 B b 5 3, the preceding chords of the passages number 2. and 3. need to be used as artificial of the tone A with the minor third, and the consequent chords of the passages 1. and 3. as artificial or of the major tone F or of the minor tone D. Aside from the imperfection of the fundamental movement of the ascending third, which is common to all three these passages, the passages number 2. and 3. contain an inverted preparation of the minor fifth, which I have tried to hide as much as possible in the second and third example. Nevertheless, said passages are unimportant and must be put into practice extremely sparingly and with the greatest circumspection. [-484-] [Riccati, The laws of counterpoint, 484; text: Basso continuo. fondamentale, 10 6 4, 6 # 3, 6 5 3, 7 5 3 #, 11 9, 10 8, 6 3, et cetera, 5 3, 6 4 #, 6 b 3, 7 b 5 3, 6, 7 5, 6 # 3, 7 5 3, 5 3, 7 5 3 #, 8 5 3 #, 8 5 3, 1. 2. 3.] 4. E 5 3 G 5 3, 5. E 5 3 G # 5 3 b, 6. E 5 3 G # 5 3, 7. E 5 3 # G [sqb] 5 3 b, 8. E 5 3 # G [sqb] 5 3, 9. E 5 3 # G # 5 3 b and 10. E 5 3 # G # 5 3. In the consequent accompaniments of the passages placed above representing the natural passage E 5 3 G 5 3 b, the artificial notes must achieve the aim for which they have been introduced into the discipline of counterpoint, which one shall see occur in the following examples. [-485-] [Riccati, The laws of counterpoint, 485; text: Basso continuo. fondamentale, 5 4, 3 6 3, 6 5 3, 9 5 3, 3 #, o pure, 6 [sqb] 3, 6 # 5 3, 5 [sqb], 9 5 3, 6 # 5 3, 8, 7 4, 6, 6 # 3, 6 #, et cetera, 5 3, 7 5 3 #, 8 5 3 #, 7 [sqb],5 3 b, 4. 8. 6. 10. 5. 9.] The Reader can note the bad relation of the fourth augmented in the last two examples between the sound E contained in the first bar and the sound B b at the beginning of the basso continuo of the second bar. I had no difficulty in allowing it because the harsh accompaniment B b 6 # 3 covers it so completely that the ear does not notice it. The passage number 7. E 5 3 # G [sqb] 5 3 b is not contained in the adduced examples, since I dercided to take the example of said [-486-] passage or, rather, of the similar passage (7.) B 3 # D [sqb] 5 3 [sqb] from the very beautiful duet by Monsignor Steffani entitled Occhi perchè piangete? The double reduction of the sounds is very apt to express sadness, while the singers move from D # to D [sqb] and from F # to F [sqb]. [Riccati, The laws of counterpoint, 486; text: Basso continuo. fondamentale, perchè piangete, et cetera, 5 3 #, 4, 3 #, 3 [sqb], 5 # 4, 5 3 [sqb], 8 5 3 #, 5 4, 3, 7.] 11. E 5 b 3 G # 5 3 [sqb], 12. E 5 3 G 5 3and 13. E 5 3 G # 5 3. In the preceding accompaniment E 5 3 of the passages number 12. and 13., representing the natural accompaniment E 5 b 3, the sound B, fifth of E, is the sixth artificial note of the minor mode D. Therefore, it must be preceded by the seventh artificial note C #, as one can see realised in the [-487-] examples that I present to the Readers. [Riccati, The laws of counterpoint, 487; text: 6 3, 6 3 b, 7 5 3, 5 3 #, 5 3, 3 #, 3, 10 6 4, 10 6 4 #, 5 b 3, 11. 12. 13.] 20. G 5 3 b B [sqb] 5 # 3, 21. G 5 3 b B [sqb] 5 [sqb] 3 #, 22. G 5 3 b B [sqb] 5 # 3 # and 23. G 5 3 b B b 5 3. The passages number 20 and 22 appear to modulate from one tone to another tone without the link of a reciprocal subordination. The entire artistry consist in letting the ear know that the consequent accompaniments are artificial of the tone A with the minor third and in avoiding, especially in the bass, the movements that render the remoteness of the chords that constitute the aforesaid passage too apparent. The passage number 23 proves very good. In fact, albeit the consequent accompaniment s employed as artificial of the minor tone A, it belongs naturally to the relative tones of F major and D minor, to whom the preceding chord G 5 3 b belongs. [-488-] [Riccati, The laws of counterpoint, 488; text: Basso continuo. fondamentale, 6 3, 5 3 #, 5 3 b, 6 [sqb] 3 #, 6 3 [sqb], 5, 6 5 3, 5 3 b, 6 [sqb] 3 #, o pure, 3 b, 5 [sqb], 6 [sqb] 3 [sqb], 6 b 3 b, 6 b 3, 5 [sqb] 3 #, et cetera, 5 # 3, 5 3 [sqb], 8 5 [sqb] 3 #, 7, 8 5 3 #, 5 # 3 #, 8 5 b 3, 7 [sqb], 8 5 [sqb] 3 #, 5 [sqb] 3 #, 8 5 3, 20. 22. 21. 23.] 24. G 5 3 B 5 3, 25. G 5 3 B 5 # 3, 26. G 5 3 B 5 [sqb] 3 # and 27. G 5 3 B 5 # 3 #, 28. G 5 3 B b 5 3.IF the preceding accompaniment of our five passages is employed as representing the natural accompaniment G 5 3 b belonging to the relative tones F major and D minor, and if it is followed by a modulation, the fifth canon forbids us to employ it as artificial accompaniment of the tone F with the major third. It can be ascribed nevertheless to the tone D with the minor third. Moreover, so that the sixth artificial note B may be [-489-] employed logically and with good reason, it is necessary that it is preceded by the artificial note C #. [Riccati, The laws of counterpoint, 489; text: Basso continuo. ffondamentale, 5 3, 4 2, 6 3, 7 3, 6, 6 5 3, o pure, 5 # 3, 5 # 3 #, 9 5 3, 8, 5 [sqb] 3 #, 7 5 b 3, 8 5 3 #, 7 5 3, 8 5 3, 7, 7 5 3 #, 7 5 b 3, 5 # 3, 7 [sqb], 24. 28. 25. 27. 26.] [signum] 11. The following passages are forbidden on the basis of the canons established at chapter 4. [signum] 14. and following. 14. E 5 b 3 # G [sqb] 5 3 [sqb], 15. E 5 [sqn] 3 #, G # 5 3 [sqb], 16. E 5 3 # G [sqb] 5 3, 17. E 5 3 # G # 5 3, 18. E b 5 b 3 G 5 3 [sqb] and 19. E b 5 b 3 G # 5 3 [sqb]. If we presume that these passages represent the natural passage E 5 3 G 5 3 [sqb] moving from one or from the other relative tone F major and D minor to one or the other relative tone C major and A minor, the first four passages contravene the fifth canon, which prescribes that, if the fourth artificial note G # of the tone D with the minor thirds occurs in the preceding accompaniment, one must not modulate, but it must be followed by the accompaniment A 5 3 # or A 5 3, which are based on the fifth note of the aforesaid tone. The last two contravene instead the sixth canon, which requires that one must move from the accompaniment E b 5 3 , based on the second artificial note of the tone of D minor, to the accompaniment A 5 3 # of the fifth note. If this premise is changed, the passages number 16. 17. 18. 19. can be considered. As to the passages E 3 # G [sqb] 5 3 and E 5 3 # G # 5 3 as representing the natural passage E 5 3 G 5 3, I have discussed them at chapter 5. [signum] 16. One finds the same passages as representing the natural passage E 5 3 G 5 3 b discussed in the paragraph immediately preceding this one. Finally, if the passages E b 5 b 3 G 5 3 [sqb] and E b 5 b 3 G # 5 3 [sqb] represent the natural passage E b 5 b 3 G 5 3 b, they are similar to the passages F 5 3 A 5 3 # and F 5 3 A # 5 3 # representing the natural passage F 5 3 A 5 3. I adduced the examples of these at chapter 6. [signum] 12. 29. G # 5 3 b B [sqb] 5 3, 30. G # 5 3 b B [sqb] 5 # 3, 31. G # 5 3 b B [sqb] 5 [sqb] 3 #, 32. G # 5 3 b B [sqb] 5 # 3 # and 33. G # 5 3 b B b 5 3. These passages are declared faulty on the basis of the fifth canon. 34. G # 5 3 B 5 3, 35. G # 5 3 B 5 # 3, 36. G # 5 3 B 5 [sqb] 3 #, 37. G # 5 3 B 5 # 3 # and 38. G # 5 3 B b 5 3. these passages are banished on the basis of the same canon under the [-491-] supposition made earlier that they represent the natural passage G 5 3 b B [sqb] 5 3. Were they to represent the natural passage G 5 3 B 5 3, they would have to be allowed, but with care. See what I wrote about them at chapter 5. [signum] 17. The passage G # 5 3 B 5 3 can represent the natural passage G 5 3 B b 5 3. I have considered it in this form in the previous [signum] 10. [signum] 12. In the chapter 3. [signum] 3. the passages of the third upwards are followed by those that descend or ascend by a minor fifth. Therefore, all I have left to do is to deal with the artificial passages that represent the aforesaid natural passages. [Riccati, The laws of counterpoint, 491; text: Passaggi artificiali, che rappresentano i naturali di Quinta [[diminuita]] [minore add. supra lin.] all'ingiù, e all'insù contenuti nel [signum] 3 del chapter 3. rappresentanti, B b 5 3, F 5 3 B 5 # 3 della spezie diciassettesima, E 5 3 B b 5 3, B 5 # 3 F [sqb] 3 diciottesima. 5 3, 5 [sqb], 5 3 #, 5 # 3 #, 5 # 3, 1. 2. 3. 4. 5. 6. (1.), (2.), (3.), (4.), (5.), (6.)] 1. B b 5 3 E 5 [sqb] 3 #and 2. B 5 3 E 5 3 #. The first passage is employed to modulate from one or from the other relative tone of F major and D minor to the tone A with the minor third. The fifth canon forbids us to ascribe the preceding accompaniment of the second and third passage [- 492-] to the tone F with the major third. Nevertheless, said chord can be assigned artificially to the tone F with the major third. Said chord can be assigned artificially to the tone of D minor, as long as the sixth artificial note B is preceded by the seventh artificial note C #. [Riccati, The laws of counterpoint, 492; text: Basso continuo. fondamentale, 8 5 3, 7 b, 7 5 [sqb] 3 #, 7 5 3, 5 3 #, et cetera, 6 3, 7 5 b 3, 5 3 #, 6 b 3, 6 [sqb] 4 # 2, 5, 3 #, 7 5 3 #, 5 4, 8 6 3, 7, 3, 3 #, 1. 2. 3. ] [-493-] 4. E 5 3 B 5 3, 5. 5 3 # B b 5 3 and 6. E 5 3 # B 5 3. The consequent accompaniment B 5 3 of the passages number 4. and 6. representing the natural accompaniment B b 5 3 can represent the artificial of the tone F with the major third or of the tone D with the minor third. In the following first and third example I employed it in the second form. Also, so that the sixth artificial note B may be introduced correctly, it is followed by the seventh artificial note C #. In the fifth passage the natural consequent chord belongs to the relative tones of F major and D minor. In the second example said chord belongs to the tone of F with the major third. [Riccati, The laws of counterpoint, 493; text: Basso continuo. fondamentale 5 3, 3 #, 3 [sqb], 6 3, 6 # 3, 5 3 b, 6 4, 5 3 #, et cetera, 5 3 #, 7 5 3, 6, 8 6 b 3, 7 5 b 3, 3, 6 4 [sqb], 8 6 3, 6 4 #, 7 5 3 b, 6 3 [sqb], 5, 6 5 3, 8 5 3, 8 5 [sqb] 3 #, 7, 4. 5. 6.]