Author: Cerreto, Scipione
Title: A Dialogue on music
Original title: Dialogo Harmonico.
Source: Bologna, Museo Internazionale e Biblioteca della Musica, MS C.131, 1-<220>

[Page numbers are given in accordance with the ones marked by Cerreto himself on each page of the treatise proper up until page 20 and continued thereafter. Roman numerals have been supplied for the first page and the Proem.]

[--] Jesus Saviour of Humanity. A dialogue on music, where one deals within a single discourse with all the rules of counterpoint on a cantus firmus and on a measured melody, and also with composing for several voices, as well with canons, proportions and everything else that is essential to the practice of music itself, written by Scipione Cerreto from Naples and set between a Teacher and his Pupil. What is organised lasts. Music is a harmonious discord. [--] Cerreto to the Reader. Gentle Reader, what are you looking at? Stop looking, but read intently What this book contains, and you shall become A wise and learned composer. Consider that if you do all this, And if you understand all of it with ease, I assure you and I promise That soon you shall be installed into a high position. The Reader to Cerreto. O wise Composer, whoever shall be able To understand your Muse, Without great study and difficulty, Since your book certainly requires it. I say more, and you shall see That I never fail to read it often, Because you told me and promised me [[who knows virtue well, sits in a high place]] That who possess such virtue is already rich. [--] Proem It is certain that when the Sublime Lord created our father Adam, He created him with every beauty and perfection and made him endowed with every virtue and knowledge. In fact, he had innate knowledge of every essence and was a great expert of the power of herbs, stones and of the fruits that contributed to his preservation and to the preservation of his descendents from generation to generation up to the deluge. Therefore, we shall say that after these first prerogatives were lost, they were recovered by future generations with extreme effort and trouble. They put all this knowledge into practice as a result of great application, as one can see clearly in the case of the science of music theory and in its practice, as proven by the variety of books written by so many music theorists and practical musicians, as one reads of Iubal son of Lamech who was the first who practice instrumental and vocal music through nature, but not in the case of the philosopher and astrologist Pythagoras, who discovered the musical intervals with the hammers. Then Ptolemy added the synemmenon tetrachord to the Greek system, while Aristoxenus displayed a whimsical attitude in his work and introduced the use of the intervals of the enharmonic genus. Didymus disregarded the chromatic and enharmonic genus and wanted to use only the diatonic, while Severinus Boethius and Franchino Gaffurio, who lived after them, discovered and illustrated [--] the whole truth about music, which was so true, that other theorists who wrote about it after them, such a Toscanelli, Zarlino and others, whom I do not mention to avoid being long-winded, have embraced and followed their opinion. Therefore, I say that now that I intend to discuss again the reasons that underpin music and counterpoint, or, rather, now that I have the opportunity to do so, I shall do it in the form of very short and easy answers given by the teacher to the pupil, in the form of a dialogue. I have considered it appropriate to employ my simple and native Neapolitan language in this third work of mine, as I did in other occasions in my other printed works, namely, the Musical Practice and the Musical Tree, both of which were written on the subject of music. Therefore, to avoid being prolix, I recommend this treatise of mine to the Omnipotent God, maker and creator of all things. I do not want to fail to write herewith an ottava where I explain who was the first man to practise music. First Ottava You must read further, as I tell you Who was the inventor of the intervals. I shall say it, and prove with arguments That he first singer was Iubal. Genesis states it, and tells the story. It is true and I am not mistaken. Let those who do not believe me search in another way, And thus they shall find that they are mistaken. [-1-] A dialogue on music, where one deals within a single discourse with all the rules of counterpoint on a cantus firmus and on a measured melody, and also with composing for several voices, as well as with canons, proportions and everything else that is essential to the practice of music itself. As I do not want to spoil the excellence of music which I practised since the beginning of my youth up to now that I have reached the age of eighty years, and thanks to the grace of my Creator who has allowed me the enough time and the strength to be able to write even now for the common benefit of inquisitive young people who desire to learn about this skill, I have agreed to return to write the present dialogue on the occasion of a request put forward to be by a new pupil. I say ‘a new pupil’ because this very treatise was taken from me without my knowledge. This occurred while some of my musical compositions were being sung in my Academy, when modern musicians and others of the profession were present. However, let it be useful to the person who stole it, since perhaps he needed it. Therefore, since it has not been returned to so-far, and in order to [-2-] let it be known to the world that it is my own work, should it be published in print under someone else’s name after my death, I was prompted to go back and to write it anew, especially since I have a new occasion to do it for this new pupil, since his pleas to me have been so strong that they convinced me to return to take up this task once again. Now, pupil of mine, since you have come to me yearning to understand and learn the reasons and the difficulties that prevent you from understanding this musical science, put forward your doubts with good cheer, so that I, with the help of the grace of God, may clarify them and help you to understand everything. Pupil. Before I start to ask you what I wanted to understand from you, I shall say just a couple of words. Firstly, I shall say that I am very sorry to hear that you lost your Dialogue, but more with myself in mind, since said work would have spared me effort and time. However, when I think about it, I am comforted and content because I shall gain some other pieces of good advice that were not contained in that Dialogue. Therefore, my dear Signor teacher, abandon so much sadness and melancholy, and listen to me with cheerful disposition to answer all the questions that I am about to ask you. Teacher. Pupil of mine, I am comforted by these words of yours. You have guessed what I was about to say. [-3-] In fact, when I realised that my book went missing, I decided to add to this one another treatise on the proportions and other instructions that are necessary to said practice of music. Therefore, I am now quiet and listening, so, carry on and ask me about what you want to understand, since I shall enjoy hearing about it. Pupil. Since this is what you want and require, I want to disclose to you that I am eager to know the true rules to write a counterpoint on a cantus firmus, and then the rules to write one on a measured melody, since you will do me the favour next to deal with the other more important rules both on composing for several parts, as well as covering what I need to know to achieve some degree of perfection. Teacher. Come on, perceptive pupil of mine, what you ask for is very beautiful and necessary for a beginner. In order to learn to write counterpoints both on a cantus firmus, as on a measured melody, it is necessary to know what are the consonances and dissonances. The former are four, namely, the third, the fifth, the sixth and the octave. They are called simple consonances because they born from themselves without the addition of any other number, as you shall be able to observe with greater ease from the following example and from its ottava. Second Ottava I shall say it herewith, and I do not want to delay any further discussing the consonances. They are four and always sweet When one sings them, unlike the dissonances. However, if you join them artfully, Their mixtures shall prove sweeter. This is true and you can experience it for yourself Since their artful application is much more advantageous. [-4-] [Cerreto, Dialogo Harmonico, 4, 1; text: Essempio delle prime Consonanze dette semplici.Terza, Quinta, Sesta, Ottaua] There are also three simple dissonances, which are also indispensible in order to build counterpoints and other musical compositions. They are the second, the fourth and the seventh. They are called simple because they are not produced by another number. However, everything is explained in this following ottava and example. Third ottava If you have learned already, perceptive and dear Reader, What the consonances are and how many they are, I do not want to appear miserly And avoid dealing with such dissonances. Although these have a somewhat bitter taste, They can prove sweet when they are mixed with consonances. This is their illustration, as you see herewith that there are three, and I am confident that you believe me. [Cerreto, Dialogo Harmonico, 4, 2; text: Essempio delle primo Dissonanze dette semplici Seconda, Quarta, Settima] [-5-] Pupil. I was convinced that this practice of counterpoint was extremely difficult, but, from the rule that you gave me above, I can see that you helped me understand it in the blinking of an eye, since you have answered me in a very satisfying way. Please, carry on and tell me about the rest. Teacher. Easy, easy, my little son, as I shall explain to you some important matters. Listen. I say that from these first simple consonances and dissonances others consonances and dissonances are derived that are called by musicians compound consonances and dissonances. They are named thus because they are created when the number seven is added to each of the simple consonances in this way, namely: By adding seven to the third, one creates the compound consonance called the tenth. By adding seven to the fifth, one creates the compound consonance called the twelfth. By adding seven to the sixth, one creates the compound consonance called the thirteenth. By adding seven to the octave, one creates the compound consonance called the fifteenth. Then, by adding seven to the second, one creates the compound dissonance called the ninth. By adding seven to the fourth, one creates the compound dissonance called the eleventh, and, by adding seven to the seventh, one creates the compound dissonance called the fourteenth. However, this is better explained through the example and its ottava. [-6-] Fourth ottava Reader, now read of the learned invention Discovered by the expert composers And illustrate it with true reasons. They were right to take the seven and abandon the six. Thus they created comparisons With utterly new reasons, And thus they created the compound intervals And called them in this way. [Cerreto, Dialogo Harmonico, 6,1; text: Essempio delle prime Consonanze Composte Decima, Duodecima, Terzadecima, Quintadecima] [Cerreto, Dialogo Harmonico, 6, 2; text: Essempio delle prima Dissonanze Composte Nona, Undecima, Quarta decima] Pupil. My sweet teacher, since you have discussed the four compound consonances and the three compound dissonances, I would like to know if there are in music other intervals apart from those that you mentioned above. [-7-] Teacher. I reply to the question you put to me and I say that learned theorists wanted that all the species of the intervals should be fourteen, namely, unison, semitone, tone, minor third, major third, fourth of the triton, or major fourth, fifth, minor fifth, also called false fifth, minor sixth, major sixth, minor seventh, major seventh and octave. In order that you may understand them better, I shall write herewith its ottava and its example with the names of the interval both in Greek and in Latin or Italian. Fifth Ottava Read, gentle Reader, with how many names Musical intervals are called, Both in Greek and in Latin, And hear their name, as they are all contained in this last illustration. I do not deceive you, nor am I mistaken, But I tell the truth without any excuse. Herewith is the example. You shall learn them And see which ones they are and how large their number. [Cerreto, Dialogo Harmonico, 7; text: Cerreto, Dialogo Harmonico, 4, 2; text: Essempio di tuttj l'Interuallj della Musica, Unisono, seconda minore spatio, seconda maggiore Tono, terza minore Semiditono, terza maggiore Ditono, Quarta Diatessaron, Quarta maggiore Tritono, Quinta Diapente, Quinta falsa Diapente falso, Sesta minore Essachordo minore, Sesta maggiore Essachordo maggiore, Settima minore Eptachordo minore, Settima maggiore Eptachordo maggiore, Ottaua Diapason] [-8-] Pupil. Now I remained satisfied with the illustration of the intervals that you supplied above. Why did you tell me that there are two dissonant intervals are not suited to contrapuntal music. Will you tell me which ones they are? Teacher. Now I reply to your question and I say that the two intervals that are not suited to music are the tritone and the false fifth. In fact, they cannot be used in musical compositions as their sound is unpleasant to our ear, because the exact octave cannot be created from those two intervals, since they form the false octave. This is true, but I warn you, pupil of mine that, the false fifth can be used in composing, as long as the composer can use it by stepwise motion, which cannot be done in the case of the tritone, or major fourth, as it is too dissonant an interval. Pupil. Since you told me that one is allowed to use the false fifth in composition and in counterpoint, I would like to see a short example of this, so that I may use it and apply it in my musical compositions. Teacher. I shall write it herewith, but first I shall write its relative ottava. Sixth ottava It is right that we should discuss herewith A false interval, but one that is good. In fact, the composer is permitted to use it And it produces a sweet sound when it is used. The Muse orders expressly That those who use this interval, use it correctly. This interval is the minor fifth, And it can be used without mistake. [-9-] [Cerreto, Essempio come si può usare la Quinta falsa. a due uoci. Dialogo Harmonico, 9, 1; text: quinta falsa] [Cerreto, Dialogo Harmonico, 9, 2; text: Essempio come si può usare la Quarta falsa a 3 uoci, et a 4. uoci, a 3. uoci, a 4. uoci] Pupil. I understood everything that you have told me and exemplified above, but I would like to know, dear teacher, if it is not too much effort for you, if one can create a number of consonant and dissonant intervals that is larger than the one that you showed me. Teacher. You will be able to form as many intervals as you like by adding the number seven, and they shall also be called compound or derivative consonances or dissonances. [-10-] Now, please, do not omit to discuss other important and necessary matters concerning the practice of counterpoint. Teacher. You want to have me apply myself more than I thought that I would have to do, but I do not want to fail to provide you with this satisfaction. Therefore, pay attention. I say that, since I said above that counterpoint is built on consonances and dissonances, it is appropriate to see which of the four consonances are perfect and which ones are imperfect. Hence, we say that the fifth, the octave and their compound consonances are perfect, while the third, the sixth and their compound consonances are imperfect. The fifth, the octave and their compound dissonances are called perfect because nothing can be added or removed from then as they are created simple, while the thirds and the sixths and their compound and derivative consonances can be altered and reduced without any harm to the compositions and to the nature of the consonances. So, the consonances that are major can be made minor and the minor ones major, but that major and minor quality cannot occur in the perfect consonances. Although some ancient theorists maintained that the unison should be considered among the other consonances, this opinion is not true, because consonances and dissonances are created from proportions of equality. This is not an interval but the origin of the interval, as I shall show at the appropriate place, when I deal with them. Therefore, pupil of mine, pay attention to what I am explaining to you: you need to concentrate because the reasons that lay behind music are complex. Pupil. Therefore, please, do not fail to tell me how the imperfect major consonances can be made minor and the minor ones major. Teacher. The question that you raise, dear son of mine, is very easy, at first sight, but I shall ensure that you understand it with ease by explaining it succinctly. Therefore, you must remember that I said at the beginning that imperfect consonances can change their nature without detriment for the composition. Moreover, this is why practical composers say and maintain that there can be an infinite gradual series of similar imperfect consonances both in ascending and in descending. This does not hold true in the case of perfect consonances, and this is why I shall show you now how imperfect major consonance can be turned into minor ones and the minor ones into major ones, in the case of the natural thirds and sixths and in the case of the altered ones. Here is its ottava and the illustration. Seventh ottava How powerful is my Muse, Since the attentive musician can employ Various consonances without mistake. I say moreover that, when the melody is mixed, The singing will be more successful, And when you try this out, You will see what great advantage you will gain. [Cerreto, Dialogo Harmonico, 11; text: 3. minore fatta maggiore] [-12-] Next, I shall show you that the major thirds can be made minor and the minor ones major in the lower part. [Cerreto, Dialogo Harmonico, 12; text: 3. maggiore fatta minore] Pupil. I understood well how the consonances of the major and minor third are altered. Please, continue to show me how the consonance of the sixth can be changed from major to minor and from minor to major, in such a way that they are illustrated with ease, as you have done with the previous ones. Teacher. Such request is not too inquisitive, since they are easy to [-13-] illustrate. In fact, the same process that we have seen involved in altering major and minor thirds can be followed also in the case of the major and minor sixths, as one can see herewith, not only with its own ottava but also with its example. Eighth ottava It is good to deal also with the hexachord, Either major or minor, as it may be. This interval is always in tune with the third or with the octave. I have tried out everything on the monochord, And I discovered what my heart desired, Namely, that both intervals have this habit, That they sound agreeable either raised or lowered. [Cerreto, Dialogo Harmonico, 13; text: Sesta maggiore fatta minore dalla parte di sotto dalla parte di sopra] [-14-] Therefore, now that you have seen the rule to alter the aforesaid intervals of the major and minor thirds and sixth, you shall be able to compose your compositions for several voices and counterpoints both in writing and at sight, not only on the cantus firmus, but also on a measured melody. Pupil. I understood everything with great ease, and, since I have a doubt left in my mind, I would like you to explain it to me before you move on to discuss more important matters, so that I may have perfect knowledge of the principles that underpin music. Teacher. Please, tell me what you mean, and I shall not fail to satisfy your curiosity. Pupil. When you discussed the number of the intervals you told me that the unison is not an interval and that it is not considered a consonance. Can you clarify this issue? Teacher. I shall endeavour to solve this doubt in the ways that shall be available to me on the strength of my weak intellect supported by the opinions of learned writers. I state [- 15-] that the unison is not considered a consonance in music nor an interval. However, it is the origin of one and of the other, since the unison in music has the same function as the number in arithmetic or in counting or as the dot has in geometry. The ottava written herewith clarifies further its nature and property. Ninth ottava Happy Music, who are counted Among the sciences and the liberal arts, You are a harmony so well endowed, Even with essential intervals! I know that you are well regarded By the learned and most important composers. The reason for this is only the unison, That creates every interval, be it good or of medium quality. Pupil. The aforesaid octave explains very clearly what belongs to the function of the unison. However, do let us move a little further. Tell me, please, since the semitone and the tone are counted among the intervals, this signals to me that both of them are both necessary in our practical composition. Teacher. I answer now your question and I state that the semitone is called by music theorists the span of an interval and the vocal tone is called dissonant interval or major second. Conversely, the semitone is called minor second. In fact, the first consonance is the third. The major third consists of two tones and the minor third of a tone and a semitone. Therefore, the distance called a semitone is part of the tone and the tone is part of the consonance. [-16-] Also, although the tone is also an interval, they call it in this way because it can be divided. In the middle of it one finds a semitone and its span is contained within three keys, as one can see easily on the monochord or on the harpsichord. Therefore, we conclude that said semitone is absolutely necessary in music, both to alter and to reduce the size of the intervals. The vocal tone called a major second is equally necessary, as one can see from these two ottave that explain its nature more easily. Tenth ottava. On the Semitone. I shall not refrain from saying That the semitone is not an interval nor a consonance. Nobody can prove me wrong, As I tell the truth and I do not contradict it. It is called a distance, and it can always be used To alter an interval, and that is its function. I ensure you that every sweet sound Is enlarged with this semitone. Eleventh ottava. On the vocal tone [[O Composer, listen, pay attention: never include in your music This mistake, of which I want to talk to you on the subject of music]] Now, let us talk about the vocal tone, Which is called an interval. Every other consonance can be created by it in such a way, That it can provide sweetness to one’s singing. From it every other essential sound Is perfected through its changing. Therefore, Reader, I told you what I feel, And these are good reasons and not words in the wind. [-17-] Pupil. The two octaves recited above have answered my questions, as they have unveiled to me all the function that these intervals have in music. However, since there is something left for you to explain to me on the subject of the tritone, please do not fail to discuss it at some length. Teacher. I can tell you nothing but that said interval cannot and must not be used in musical compositions, not even in two-part counterpoint, because it is a very dissonant interval and it is avoided by every composer of music. It cannot be used even in the cantus firmi, therefore, it must be avoided and not used. As proof that this is true, read this ottava herewith, that explains its nature to you with ease. Here it is. Twelfth ottava. On the tritone. Composer listen and pay attention To what I want to tell you about music. Never use in one of your compositions An interval that would make it harsh and bad. I warn you now briefly, To avoid this bad method as much as you can, As it shall make your singing dissonant. Pupil. Now, I have realised that you were right not to provide me with an example of the semitone, tone and of the tritone, since you have explained and illustrated them to me with ease in the discussion on the intervals. However, now I desire to understand whether I am capable from now on to start to compose a written counterpoint with these few rules that you have explained to me. Tell me please frankly and without adulation, since you allow me to be continually under your guidance and supervision, as someone who has been chosen to be your obedient pupil. [-18-] Teacher. I cannot give you leave to do so, because first you must have a good knowledge of the hand of Guido of Arezzo, which other music theorists called musical Introduction, since one can achieve through its application the goal to be able to sing through all of the three clefs perfectly and to make the mutations of the six notes used in singing, namely, Ut Re Mi Fa, Sol, La, Pupil. I thank you dear teacher, as you have informed of what I need to learn. However, since said Introduction is necessary to me, I would be eager to obtain from you an example, so that I may understand it, as my first music teacher did not provide me with a written example. There is no doubt that one needs to know the explanation of Guido’s Introduction, but, before we write it down, I want to tell you a few details about said Guido, since he was a man of great reputation in music and in the field of plainchant, since he wrote in plainchant the Gradual and other books necessary for the services of the Holy Church. The Holy Pontiff Pope John XX was informed of this and sent for him to come to Rome. He obeyed, and he appeared in front of His Sanctity to show him all the works that he had composed at the service of the Holy Church. The Holy Pontiff was very pleased with this and ordered that he should reside in his court as a way to honour him, since he was a monk. Said Guido thanked him for this, but replied that he had other works to complete in the service of the Holy Church, but, before he left, he showed the Holy Pontiff and the whole of the Roman court the invention of the six syllables. Truly that was not the work of a man but of God. [-19-] Pupil. I would like to understand how Guido created the six syllables, namely, the sixth notes called Ut, Re, Mi, Fa, Sol, La. Teacher. I tell you, so that you know, that I have dealt with this topic in my Musical practice, that I published thirty years ago in print. However, to be succinct, I shall explain it with a few words. In fact, while the learned Guido was singing the Hymn of the feast of Saint John the Baptist, he noted, by divine virtue, that the six syllables could be extracted from said hymn. He did so, as one can see clearly by considering the words. In fact, from the first verse that says Ut queant laxis, he extracted the first syllable ut; from the second verse, Resonare fibris, he derived the second one, namely, Re; from the third one, that says Mira gestorum, he derived the third syllable, Mi; from the fourth one, that says Famuli tuorum, he took the fourth syllable, Fa; from the fifth one, that says Solue polluti, he took the fifth syllable, sol, and from the sixth verse, that says Labij reatum Sancte Ioannes, he took the sixth syllable, La. Thus, he formed all of the said six syllables, from which he created later on the hand called musical Introduction that is called Guido’s hand up to this day and shall last until the end of this universal machine. I add to this that, since Guido wanted to show that he held the ancient Greek musicians in high regard, [-20-] he placed a Greek letter at the start of his Introduction, in this way [gamma], which corresponds to G in our language. So, he started it with said Gammaut and Are and followed them with his other letters, as one can see in his illustration. He also added three clefs and everything that is necessary for the practice of singing, counterpoint and composition for several parts. I warn you that I just wanted to provide an outline of this learned invention, so that future generations may rate virtuous musicians, and especially Guido, who was a famous man. Here is the illustration. I shall write after it first the ottava that explains who was the inventor of said Introduction [[and then the hand of said Guidone]] Space for the thirteenth ottava [[signum] add. in marg.] [Cerreto, Dialogo Harmonico, 20; text: Mano di Guidone Aretino, Chiaue, C, A, F, D, B, G, E, la, sol, fa, mi, re ut, [sqb]] [-<21>-] Pupil. In truth, pupil of mine, everyone who considers this Introduction admires it. In fact, it has brought great pleasure to my heart and it has encouraged and lent me hope that I shall reach the desired harbour and conclusion of this practice of music thanks to it. Teacher. I am very pleased that you have been left contented and happy with what I told you and shown to you with the examples. Therefore, I want that now you understand these other few words about said Introduction. So, I state that there are seven hexachords essachordi [essachor ante corr.] twenty-one tetrachords, three clefs and six musical syllables, that are these: Ut, Re, Mi, Fa, Sol, La. I shall show you here the illustration with the three clefs and all of the mutations, both ascending and descending, through all of the lines and the spaces, as wel as the spaces of said clefs and the sixth notes that are sung naturally, with the flat sign and with the square [sqb]. However, I want you to read this ottava that I wrote in praise of Guido, the author of said Introduction. Thirteenth ottava Blessed Guido, you had the knowledge To discover the first principles of singing. Firstly you created the hand And you added the notes for the practice of singing. You offered this invention to the Holy Pope, So that the world would be able to adopt it, Hence, the invention is learned and holy, And it allows any music to be sung with ease. [This octave is placed above the Introductions where there is this [signum] hand of Guido add. in marg.] [-<22>-] [Cerreto, Dialogo Harmonico, 22; text: Essempio delle tre Chiaui, e delle mutationi di essi cosi ascendenti come discendenti, Queste sei note si cantano per natura, Queste per [sbq] quatro. Queste per natura, Queste per b molle, Ut, re, mi, fa, sol, la, Chiaue di G sol re ut, Chiaue di C sol fa ut, Chiaue di F fa ut] Pupil. Since we have to discuss the three clefs and the six notes, it is good that I should obtain an answer to the doubt that I have in my mind. In fact, I would like to know why the clefs are three and no more than three, since the entire of Guido’s Introduction contains twenty-six letters and six notes. Please explain all of this to me. Teacher. I do not know if I can explain very quickly such a topic, which is immensely wide. Nevertheless, I shall say some things, referring you as to the rest to the books of learned writers [-<23>-] who have written about this topic. Therefore, I state, that the number of the clefs that are marked in the aforesaid Introduction cannot be smaller or larger than three, namely, F, C and G. The clef that is marked on F fa ut warns us that the Ut in the F is sung with the b flat; the clef that is marked on C sol fa ut warns us that its six notes are sung naturally, while the clef marked on G sol re ut informs us that the six notes are sung with the square [sqb]. However, the clef used in singing is not just one, but there are two ones that carry accidentals. One of them is based on the b flat and the other one on the square [sqb]. Moreover, this term clef has been invented by not very expert musicians who called them in this way to compare them to a key that can close and open a door. Without it, in fact, one cannot enter or exit a room while it is closed or locked, as we want to call it. This is precisely why they called it clef in the practice of singing, which means a sign that enables the singer to sing the six notes ascending and descending without making a mistake in the mutations, while music theorists have called them clefs or signs that enable the singer to sing the six notes, as I showed in the aforesaid example. Nevertheless, some other musicians say that the clefs are as many as the letters of said Introduction. This opinion is not true, but false. In fact, this would be so if the three clefs themselves were created accidentally either through the b flat, the square [sqb] or the [- <24>-] semitones, but these clefs shall be the same as the other ones that we have illustrated. Pupil. [Teacher. ante corr.] You have reassured me with such learned arguments and I have understood everything with utter ease. Therefore, will you be able to move on and discuss other matters that are more important and more advantageous for me? Teacher. I can see clearly that you are seeking to keep be busier that I believed that I would have been, but I do not want to fail to fulfil my duty and to explain to you the most fundamental notions for the practice of counterpoint and composition for several voices. Therefore, I say that I want to write here for your benefit a numerical table through which you shall be able to write with ease an extemporaneous counterpoint on whichever melody and that shall be also useful to compose a composition for whatever number of voices you prefer in the blinking of an eye. Pupil. I shall be glad to see it, so that I may fulfil my desire to learn the art of counterpoint. I thank you for considering my need. Teacher. I want you to know that I want to write for your benefit this illustration that I call numerical table because you shall be able to profit from it in a short time. In fact, you shall have to consider in it [-<25>-] nothing but the distance from a clef to the other through all the lines and spaces of said clefs, whether they be those marked with the b flat, those marked with the square [sqb] or the natural ones. This will also benefit the composers who are not very familiar with the Introduction of the hand of Guido and even to someone who cannot sing, as long as one keeps to the aforesaid rule. Hence, in a short time and with little effort one shall produce good results. I write said illustration herewith for you, preceded by its ottava praising its author and explaining the benefits of its application. Fourteenth ottava Dear Reader, pay a little attention, As I want to show you now an illustration Which, I am sure, will satisfy you, And shall enable to compose without fear. In it you shall find an instruction whereby (I can tell you) if you apply yourself, Not only you shall compose a strict counterpoint, But you shall also become a perfect musician. [-<26>-]> [Cerreto, Dialogo Harmonico, 26; text: Figura, detta Tabola numerale Composta dal Cerreto, Terzadecima., Undecima, Nona, Settima, quinta, Terza, Unisono, 1, 2 5, 7, ij, 13] Pupil. My sweetest teacher, I see that you have drawn me an illustration or a table, as you call it, which I cannot understand at sight without your help or explanation. Therefore, I beg you to explain it to me, please, so that I may be able to relay it to others in our profession. [-<27>-] Teacher. In truth, I believe that you do not understand it at first sight. However, it will not be so if you consider it closely. In fact, from the first clef of F fa ut that is marked on the fourth line above to the second clef of F fa ut there is the distance of a third. Equally, from the position of each one to the position of other of the following keys there shall be a third, both in ascending and in descending. Moreover, from the first clef of F fa ut to the last one of C sol re ut there is the distance of thirteen notes, to the clef of C sol fa ut on the first line there is a distance of eleven notes, to the once o Csolfaut on the second line the distance is of nine notes, while the distance one of Csolfaut on the fourth line is of five notes, as you can easily learn from the aforesaid example. Therefore, my perceptive pupil, be content and cheerful because, if you adhere to what I told you and I have explained to you, you shall benefit both in writing counterpoints and in your compositions in general. Pupil. I am pleased, in fact, that you have solved succinctly all my doubts on the aforesaid illustration or table. However, please, do explain to me another easy rule which is necessary for my needs, so that I may begin to write counterpoints, since this is precisely what I desire, as long as I am now ready to start learning about it. Otherwise, I am content with obeying your will. [-<28>-] Teacher. These are all truly beautiful and interesting questions, and, consequently, they require beautiful answers and I shall not fail to answer them. Therefore, with the strength of my weak mind aided by the opinions of the learned writers who wrote about this sort of music, I shall strive to provide you with the rules and answers to your doubts that are necessary to you and within my grasp. However, since I know that what you need now is to learn about the eight essential rules of counterpoint and of composing for several voices, I shall start from them in this way. Therefore, you must know that the first rule to write a written counterpoint or an extemporaneous one says that it can be done in three ways, namely, free, with ties or syncopated. Free counterpoint can be done in two ways: the first one, when the notes move only from a consonance to another consonance, and the second one, when the counterpoint ascends and descends by step through consonances and dissonances. The counterpoint with tied notes occurs when the consonances are tied with the dissonances and these are resolved on to their closest consonances. Thus, the seventh resolves on the sixth and the fourth on the third. The syncopated counterpoint occurs when the notes progress from a consonance to another one, but they occur against the beat. However, one must consider that the skill of laying out well the consonances is no less important that the skill of laying out the dissonances, because, as learned writers say, opposita iuxta se posita magis elucescunt (Opposites placed by one another are more apparent). However, so that your questions may be fully answered, I shall write for you the ottava first and then the example. [-<29>-] Fifteenth ottava Pupil of mine, I know that you understood well What I taught you about counterpoint. Now I want to explain further to you what you have heard, So that you may compose a good composition with strict rules. I answered your question with an ample explanation, So that you may not fail to make it perfect. Now pay attention and consider what you do, So that you will not say that you have wasted time. [Cerreto, Dialogo Harmonico, 29; text: Essempio della Prima Regola del Contraponto, Procedere sciolto, Procedere ligato, Procedere sincopato, sciolto, ligato, sincopato] Pupil. May the Lord be praised, as you have reassured me with these examples and with your easy instructions. However, if it is not too onerous, I would like to have another easy explanation of the second rule of counterpoint, so that we may proceed with order. Teacher. To satisfy your eagerness to learn, I shall explain and illustrated the second essential rule of counterpoint. Therefore, I say that, according to the teaching of old musicians, the second rule of counterpoint says that the contrapuntist must ensure to provide easy, weak and slow movements at the beginning of his counterpoint. In fact, such kind of progress is lauded not only by the ancient theorists, but [-<30>-] also by the modern ones, as well as by philosophers who say that à facilioribus etst incoandum, which means that one must start from what is simpler. I also state that one may start the counterpoint with imperfect consonances, as also the learned Franchino Gaffurio confirms at the end of the third chapter of his Practice of Music. I shall write the illustration of all of this for your benefit, but first I shall write the respective ottava, as it deals with the same subject. Sixteenth octave Carry on reading, Reader, and pay attention To what you have to do to obey the rules. Start the counterpoint with a sweet beginning And proceed slowly with it. This is the rule that I entrust to you, my pupil, So that your singing may be slow. Therefore, abide by what I told you now, So that your counterpoint may be perfect. [Cerreto, Dialogo Harmonico, 30; text: Essempio della Seconda Regola del Contraponto, Principiare per Consonanza imperfetta, e finire per Consonanza perfetta] Pupil. Since I understood you the second rule of the counterpoint commands, I would like to hear another instruction, namely, the one of the third rule. [-<31>-] Teacher. It is certain that this is absolutely necessary because one must pay attention and listen to what the learned music theorists teach us. Therefore, the third rule says that the countrapuntist cannot employ (in his counterpoint or in any other musical composition) two or more similar perfect consonances that rise or descend by step, namely, two or more fifth, two or more octaves or two or more of their compound or derivative intervals, because the listener who listens to that progression does not receive pleasure or satisfaction. The reason for this is that compositions are pleasing to the ear when they proceed with a variety of intervals. This inconvenience does not occur when two or more imperfect consonances ascend or descend in stepwise motion, because one can move from a minor imperfect consonance to a major imperfect consonance, or, conversely, from a major imperfect consonance to a minor imperfect consonance, both in the case of the thirds and of the sixths, or, equally, in the case of their compound or derivative intervals. Pupil. This is the greatest pleasure I have felt all day, since I have learned so many learned rules about counterpoint. Therefore, you can write the example for my benefit, so that, if there is something that I cannot understand, if I practice them they shall make a stronger impression on my mind. Teacher. I shall be pleased to do so, but I shall write first its respective ottava and then the example, since the example is more powerful than the words. [-<32>-] Seventeenth ottava Indeed it is a great thing, o Learned, what I say, That what is good sounds bad and is never accepted By the wise composers. Rather, it is shunned, Because it produces an ill effect in singing. What I want to say is quite interesting and intricate, As the perfect interval must be subordinate. The rule says it clearly, As the good pupil has had the opportunity to read above. [Cerreto, Dialogo Harmonico, 32; text: Essempio della Terza Regola del Contrapunto. Quinte uietate ò le loro deriuate Ottaue uietate ò loro deriuate] Pupil. The arguments put forward in the aforesaid third rule pleased me greatly. However, please, move on to discuss the fourth essential rule of counterpoint. Teacher. Your are quite confident in asking, but I do not know if I shall manage to reply. I state that the fourth essential rule of counterpoint is that, when the contrapuntist writes a counterpoint on a cantus firmus or on any other subject, if he wants to write it in such a way that it is sweet and pleasant, he will do well to have it move often [-<33>-] by contrary motion. He will be allowed on occasion to employ two different perfect consonances, going from the fifth to the octave or from the octave to the fifth, but it will be better if one ascends from a major imperfect consonance to a minor perfect consonance, or to a perfect major consonance, namely, from a major third to the fifth or from a major sixth to an octave. Therefore, conversely, the counterpoint shall be better and more respectful of the rules when one descends from an imperfect minor consonance to a minor perfect one, namely, from the minor sixth to the fifth or from the minor third to the unison. The same shall apply when one proceeds in the same way with compound or derivative consonances. Pupil. This is the greatest pleasure I enjoyed today, since I learned so many learned rules on counterpoint which have left me satisfied. Teacher. For this reason, I want to write for you herewith a simple example so that you may remember it better. However, to maintain the sequence that we have started I shall write its ottava first, so that one may understand it all with greater ease. [-<34>-] Eighteenth ottava I do not want to fail to tell you, Reader of mine, How you must write your composition. The rule states it and so do I, But pay close attention when you write it So that the parts may murmur against each other. Mix the sounds in your counterpoint Always with a pleasant fashion, Until you reach the end. [Cerreto, Dialogo Harmonico, 34; text: Essempio della Quarta Regola del Contraponto. Proceder non troppo uago, Proceder più dolce, e uago] Pupil. You explained it well, but you have satisfied my curiosity better with the ottava and with the example. In fact my mind is jubilant from the contentment that I feel. On the basis of this good will I want to beg you that you want to explain herewith the fifth essential rule of the counterpoint. Teacher. I share your satisfaction, dear pupil of mine, because I know that you draw some benefit from it and you are not wasting time. I tell you briefly that the first essential rule of counterpoint states that, if the countrapuntist wants to make his counterpoints [-<35>-] beautiful and pleasant, he must place two or more imperfect consonances between two perfect consonances of the same kind. This is done to ensure that the imperfect consonances differ as to their interval. Moreover, it is good to intersperse the imperfect consonances among the perfect ones. This opinion is confirmed by learned theorists, especially by the knowledgeable Franchino Gaffurio in the third chapter of his Practice of Music. The example is herewith together with its ottava for greater ease. Eighteenth ottava You must remember, refined Reader, What was said about the consonances, namely, That if they are perfect and similar, they clash. Therefore, you must always balance everything And you must be correct like a set of scales When you compose, so that you always place Some imperfect consonances between two perfect ones. [Cerreto, Dialogo Harmonico, 35; text: Essempio della Quinta Regola del Contraponto. Consonanze imperfette, D'altro modo di Consonanze intramezate con due perfette simili, perfette tramezate] [-<36>-] Pupil. I considered closely the example written above and also its ottava. Both of them have pleased me. However, will you not do me the favour to move forward in order to deal with the sixth essential rule of counterpoint? Teacher. Learned music theorists declare that these eight rules of counterpoint and of writing for several parts not only are essential, but also that no composer can omit to observe them, since they have the dignity of a law approved by ancient and modern musicians. Therefore, we shall say that the sixth essential rule of counterpoint and of composing for several voices entails that the contrapuntist will be able to employ in his counterpoint several perfect consonances of a different sort both in ascending and descending, as long as the low part is held and is maintained on the same line or in the same space. This means, that the composer is allowed to move from a minor perfect consonance, which is the fifth, to a major perfect consonance, which is the octave. This motion will be upwards, while the downward motion shall take place when one moves from a perfect major consonance to a perfect minor consonance, namely, from the octave to the fifth. This rule [-<37>-] is more suited to writing canons than counterpoints because said way of proceeding does not produce a beauty of a kind that inspires pleasure in the listener. To prove that this is so, I shall write the musical example, so that you may recognise that this is true. However, I shall illustrate this better in the following ottava. Twentieth ottava I shall speak herewith about the obedience That counterpuntist must observe, Because the law is like a set of scales: It can be forced or also adapted. The aforesaid rule is so important, That the composer must not fail to observe it, He must do what you have learned earlier From my writings and he must stop being doubtful. . [Cerreto, Dialogo Harmonico, 37; text: Essempio della Sesta Regola del Contrapunto, Note contra note, e non è uago, Et è buono per far Canonj] Pupil. You were correct to enlighten me on the aforesaid counterpoint, and I shall employ it in the canons, as you have mentioned. Therefore, you will be able to move on to discus the seventh essential rule of counterpoint. [-<38>-] Teacher. I inform you, pupil of mine, that the seventh rule of counterpoint states that, when the contrapuntist employs the descending major sixth, it must be followed by the major third. The ascending major sixth must be followed immediately by the octave, while the minor sixth must descend to the fifth, as it is its adjacent consonance. One must observe this rule more closely in the counterpoints than in other musical compositions. In fact, in the counterpoints for two parts on a cantus firmus or on a measured melody the composer must proceed with greater adherence to the rules and avoid certain consonances that do not produce a good effect. In other words, where one finds the fifth, there must not be the octave, and where one finds the octave, there must not be the fifth. Instead, the contrapuntist must employ the imperfect consonances, either major or minor, according to the need. This is what can be said on this seventh rule. I shall write the ottava and the ensuing example herewith for your own instruction. Twenty-first octave While I talk about the Muse, I am all cheerful and I am always happy; But when I see this virtue in disarray, I become all angry and I am unhappy. I wish it was not so, namely, that everyone should apologise, Because they are not worthy of such talent. But my hope rests only in this That my examples shall soon bear fruit. [-<39>-] [Cerreto, Dialogo Harmonico, 39; text: Essempio della Settima Regola del Contraponto. Come si battono le Consonanze imperfette maggiori, e minorj [minore ante corr.] ascendendo, e discendendo] Pupil. This seventh rule is very important and essential so that the major and minor sixth may produce a sweet and pleasant effect. Teacher. There is no doubt that you tell the truth. Moreover, I want to mention here that you must ensure (both in your counterpoints and your compositions for several voices) that, when the minor consonances, such as thirds and sixths, ascend, they must be made major, and when the major ones descend, they must be made minor. If the counterpoint is woven beneath the cantus firmus or beneath a measured melody, the thirds, the sixths or they compound intervals must be made minor. This rule is also essential. Therefore, if one proceeds in this fashion, the counterpoint and the composition become beautiful and pleasant. Pupil. You have explained to me the aforesaid seventh rule well. [-<40>-] Therefore, you may continue to discuss the eighth essential rule of counterpoint. Teacher. This eighth rule is the most necessary one in all the counterpoints and other musical compositions because the contrapuntist must conclude all his compositions always with a perfect consonance, namely, an octave, a fifteenth, a twenty-second, and sometimes with the unison, although the unison is not a consonance, as we said on other occasions. It is an essential rule and a law established by all learned theorists, because the end of any composition must be perfect, so that the listener remains satisfied and content. Nevertheless, one can conclude a composition with a fifth or with its compound or derivative intervals, however this way of proceeding does not abide with the strict rules and it is not worthy of praise. We shall show you the example and also the ottava that deals with such topic. Twenty-second ottava They say that every ending must end With every perfection and great satisfaction. This is my Muse, and I can say so, As to my technical skill and as to what I feel about it. This can be proven by hearing The sounds and compositions that are pleasant to the ear. This is what this Muse of mine states, Who says that every ending must be perfect. , [-<41>-] [Cerreto, Dialogo Harmonico, 41, 1; text: Essempio dell'Ottaua Regola del Contraponto, Fine per unisono, per Ottaua, per Quinta decima, per uigesima Seconda] Although this that I want say now is not an important rule of practical composition, nevertheless I state that the contrapuntist can observe the practice of employing two similar octaves or fifths upwards or downwards, but one immediately after the other, since, otherwise, they could not be employed. Pupil. I would be glad to see a short example of it, so that I may employ them myself, if the occasion arises. Teacher. I shall write it herewith with a few notes, since it is something of little importance. [Cerreto, Dialogo Harmonico, 41, 2; text: Come si posseno battere due consonanze perfette simili cosi ascendendo come discendendo] [-<42>-] Pupil. Now that I have heard and understood everything on the eight rules of counterpoint, will it be now time to be able to start a counterpoint on a cantus firmus? Teacher. I reply to you and I say briefly that we shall be able to begin to look at what you require, but one must learn and understand certain other precautions that are also necessary to write a counterpoint respectful of the rules, whether written or improvised. In fact, the contrapuntist must see and consider with the eyes of the mind what sounds he wants to produce, and it must avoid exceeding the interval of the fifth both above and below the notes of the cantus firmus. In fact, if we add seven to the first note, the product is an octave, if we add it to the second, it ninth, if we add it to the third, the result is a tenth, and if we add it to the fourth, it is an eleventh. Conversely, if we proceed a second below the octave, the result is a seventh, if we proceed a third, the result is a sixth, if a fourth, it is a fifth. Similarly, if we proceed below the unison and we add seven, the result is an octave, the lower second produces a ninth, the lower third a tenth, the lower forth an eleventh, and so on ad infinitum. Pupil. You did really well to teach me this other rule. However, dear teacher, if anything else is left for me to learn, please do not fail to instruct me. Teacher. Listen to me and I shall conclude this topic with the truest rules. [-<43>-] Therefore, I state that if the contrapuntist wants to compose a counterpoint in a choir where there are several singers singing in counterpoint, he must ensure that he employs free counterpoint. This is of two sorts, either note against note or with minims and semiminims, quavers or semiquavers. He must take care to avoid the sixth between semibreves and minims. In fact, if they encounter a part that sings a fifth, the dissonance of a second would ensue. This is tolerated in the case of semiminims, quavers and semi quavers because they are quick. This rule is given not for the benefit of learned contrapuntists, but it is for beginners. Also, because of the variety of the passages and of the notes of the cantus firmus, for this reason we shall start to demonstrate certain passages on an ascending and on a descending cantus firmus, both with the top and with the bottom part, as you shall be able to consider with ease herewith. However, first I shall write its ottava, which explains the whole matter with beautiful words. Twenty-third ottava Now is the time, my clever student, To say something about the counterpoint That occurs in a choir and also ex tempore. Who listens to it must be clever and ensure Never to use the sixth, So that it may not clash with the fifth. Abide by this rules and, as to your motion, And you can make as many motions as you want. [-<44>-] [Cerreto, Dialogo Harmonico, 44; text: Essempio el Contraponto che si fa in Choro sopra Canto Fermo senza batter Sesta per consonanza, mà per Dissonanza può usarsi cosi in ascendendo, come discendendo. Tenor, Basso, Saggio Cantore Canta perch'appresso, L'istesso cantarai molto diuerso.] [-<46>-] Pupil. If there is no impediment, let us consider the counterpoint composed below the cantus firmus, as you promised me Teacher. Stop, my dearest pupil! I want to write it herewith. The parts shall be inverted, so that the cantus firmus shall proceed at the octave higher. One shall be able to sing the same counterpoints at the lower fifth, as long as the clef that carries the counterpoint is marked with the flat sign on bfa. You can see its form here as well as its ottava. Twenty-fourth ottava I talked above about the counterpoint That is composed by the choir on a plainchant. I want also that you consider this other sort That is more distant from singing. You can see where the cantus firmus has been added: It is here in the soprano clef. The part of the cantus firmus and of the counterpoint are inverted, And the bass sings the counterpoint, in that way that it is notated here. [Cerreto, Dialogo Harmonico, 46; text: Essempio del Contraponto riuoltato per Quinta sotto fatto sopra l'istesso Canto fermo riuoltato per Ottaua sopra. Alto, Basso, uedi Cantor come la Musa dotta. Te fa cantar diuerso in una botta] Pupil. I believe to have understood well the rule concerning both sorts of counterpoint written above and below the cantus firmus, and I have found that if one writes the part of the counterpoint in sixths below the cantus firmus, one produces dissonances instead of consonances. Therefore, I would like you to show me another counterpoint written with the lower part on the same cantus firmus, as I would be very glad to consider it. Teacher. Listen, pupil. The practice of counterpoint is very subtle and contains within itself many other recondite rules. Therefore, you must know that, if the same cantus firmus is sung a fifth above, one may be able to sing the same passages an octave lower and they will produce a good result. You can ascertain all of this from the following example, but read first its ottava, which shall please you. [-<49>-] Twenty-fifth ottaua Now it is time to show you, Gentle Reader, how powerful is our Muse, And how many kinds of counterpoint one can employ. I wrote this for you in three ways, As you can see in this third version, that I have added. Here is the example, and you must be sure That in time you also shall be able to compose a similar one. [Cerreto, Dialogo Harmonico, 49; text: Essempio del primo Contraponto riuoltato per Ottaua sotto sopra l'istesso Canto fermo che canta una Quinta alta del primo Canto fermo. Horsi ch'io dico il uero, e n'è buggia, Mentre che canti st'altra Simfonia.] Pupil. In truth this practice of counterpoint [<-50->] improvised in a choir on a cantus firmus is such that not all practical contrapuntists can employ it. I had this thought when I tested myself in the same counterpoints. Therefore, please, be kind enough, dear teacher, to deal with the counterpoint that one writes by oneself apart from other singers, in order that I may learn all of this and I may not be deprived of its knowledge. I shall listen to you. Teacher. You had a good idea, and you do need it. However, one must consider first that now it is not the time to deal with the above request. In fact, you must know, pupil of mine, that one usually writes a counterpoint on a cantus firmus that it has a larger quantity of notes both on the lines and in the spaces. Hence, it is good that we do not move on to provide you with other counterpoints composed on other cantus firmi, but on the same ones with the double number of notes both on the lines and in the spaces. Therefore, I shall write one herewith to satisfy your curiosity and to show you that you can write the same passages that can be inverted with the cantus firmus at the octave and at the fifth, as long as you do not use the sixths in the same passages both ascending and descending, because, when the counterpoint is sung in the lower part, they produce a dissonance. Pupil. Since you have obliged me by writing the same cantus firmus so that there is a greater number of notes in the spaces and on the lines, I shall be very pleased to see its example and to learn it. Teacher. I shall write its relevant ottava for you, and then the example, for your greater satisfaction. [-<52>-] Twenty-sixth ottava Consider again, Reader, this delight, As there are more notes to be sung In this cantus, and it displays greater talent, So that this work is worthy of great praise. Every singer would want to sing it, Even if there were a hundred notes. Hence, I warn you, do as I say, And regard your application as your trusted friend. . [Cerreto, Dialogo Harmonico, 52; text: Essempio del Contraponto [che add. supra lin.] si fa in Choro col Canto fermo raddoppiato di figure, Quanto più aggiungi legna al tuo foco: Tanto più senti caldo nel tuo gioco.] [-<55>-] Pupil. You have handled this counterpoint learnedly, my sweetest teacher, and I have understood it with the greatest ease. Moreover, since you have told me that the parts of this very cantus firmus and its counterpoint can be inverted, please do not fail to provide me with an example. Teacher. I want to show you the beginning of it for my own satisfaction. I shall write it herewith, so that the cantus firmus is sung an octave higher and the counterpoint is woven at the lower fifth with the key of F faut and the flat sign. I shall write its ottava here for your greater satisfaction. Twenty-seventh ottava There is no need to discuss Any other composition or sort of music, Since we are considering the same style of singing And the same method of composing. As far as one can see, there is no difference, since the counterpoint in the lower part moves in the same way. Hence, sing assuredly and pay attention, And you shall gain more satisfaction in your singing. [Cerreto, Dialogo Harmonico, 55; text: Essempio del Contraponto, e Canto fermo riuoltato, per Quinta, [[e per Ottaua]] sotto il Contraponto, et il Canto fermo per Ottaua supra,Chi impara stà uirtu può dir di certo. Ch'in breue tempo poi n'haurà il merto] [-<57>-] In order to complete the sequence started above, I do not want to fail notate here an other example for your benefit, where the same counterpoint can be sung in such a way that cantus firmus proceeds at the fifth above and the counterpoint at the octave below, as one can see herewith. It will consist of just a few notes, since it is short. I shall write its ottava as well, for the Reader’s greater satisfaction. Eighteenth ottava See, Reader, how clearly you can consider The learned counterpoints That are improvised and sung By wise and prompt singers. This is the composition. I write herewith The cantus firmus and the added counterpoint. Reader, come on, sing it, if you like, And behave as a good, learned and daring singer. [Cerreto, Dialogo Harmonico, 57; text: Essempio del Contraponto riuoltato, che canta Ottaua sotto, et il Canto fermio riuoltato che canta Quinta Sopra, Te dico il uer Lettor, dhè non lasciade, dè dir de stà Uirtù quel che te pare. qui basta] [-<58>-] Teacher. Now that you have considered the secrets of the counterpoint composed in the choir above the cantus firmus (above it, below it and invertible) I believe that the aforesaid examples shall be sufficient to illustrate that composing practice. Pupil. I thank you very much for making this effort on my behalf. Therefore, if it is not too much trouble, will you agree to deal with the topic of counterpoint written by a single composer on the cantus firmus and to teach me all the instructions and rules that one has to obey in this matter? Teacher. I do not want to fail to meet your request and, so that you may be more satisfied with it, I shall write a counterpoint for you on an antiphon of the first tone, since it is the first counterpoint on a cantus firmus we present. However, so that you may be more satisfied with it, I do not want to fail to write its ottava as well and, after it, its illustration. Twenty-ninth ottava Since we have completed our discussion On the counterpoint that is composed by the choir, It is right that we should show next Another one that is composed with great beauty. I have already written it here and I have ensured That it is entirely perfect, and the result of good work. This is the strict counterpoint That one writes alone and then perfects in detail. [-<59>-] [Cerreto, Dialogo Harmonico, 59; text: Contraponto osseruato [[che si]] tutto sopra l'Antifona del Primo Tono, Deus in nomine tuo Saluum me fac et in uirtute] [-<60>-] Teacher. Since the antiphon of the second tone is next, we shall write it herewith, preceded by its ottava that explains many rules and restrictions of this type of composition. Thirtieth ottava I have already discussed and told you The rules of counterpoint, How the sort that one writes alone can be perfect, So that who hears it and then may understand it. This is what the law and the rule requires That is observed down to the last note. The following one, already made, is of the second tone, While the first one was of the first tone, and entirely good. [-<61>-] [Cerreto, Dialogo Harmonico, 61; text: Contraponto osseruato che si fà sopra il Canto fermo del Secondo tono, e della sua Antifona, del secondo tono. Voce mea ad Dominum clamaui ad Deum et intendit mihi] [-<62>-] Teacher. Up to now I have notated for you two examples of counterpoint written on the antiphon of the first tone and also on the one of the second tone. Therefore, I shall add nothing else, since both counterpoints have been composed in accordance with the due rules and instructions, as their law requires. In order to avoid being long-winded in my discourse, consequently, it is appropriate that I show you another counterpoint that should be composed on the antiphon of the third tone, so that we may follow the sequence of the antiphons of all the eight tones in order. Pupil. I am pleased with all of this, dear teacher, but ensure that the part that sings the counterpoint is written with the same clef without extending too far in the lower register, so that it may be comfortable for me to sing. Teacher. I know very well that said two counterpoint that I wrote above for your benefit would be sufficient, however, since I do not want to save myself effort when I can be of service to you, I am happy to notate them all, as we said above. However, before I write the third example for you, I want you to read its own ottava, for your amusement. [-<63>-] Thirty-first ottava Listen, dear, refined Reader of mine: What power our music has To make the counterpoint perfect and preciously written, As it suits the contrapuntist! When you write your own, make it refined, Since its writing reflects on your reputation. Therefore, I said it all, Do not fail to avoid what sounds bad and pursue what sounds good. [Cerreto, Dialogo Harmonico, 63; text: Contraponto osseruato sopra l'Antifona del Terzo tono, IN te Domine speraui non confundar in e libera me] [-<65>-] Pupil. Who does not know, my refined teacher, that one cannot emulate the beautiful passages and graceful and learned observance of the rules of these three counterpoints that you have shown me so-far? In fact, not only I have learned from them the way to compose them, but I have also how to set the words to them. For this reason, I beg you to continue the sequence that you started with the counterpoints that are left and their antiphons. Teacher. There is no doubt, pupil of mine, that you tell the truth, because you are able to understand from these few examples all the rules and laws according to which they need to be written and that they must obey. However, since it is the case that I have already composed the rest of them, it is best not to leave them aside. Therefore, I shall write herewith for you the counterpoint of the fourth tone composed on its respective antiphon also of the fourth tone, but I shall not fail to write its ottava first, from which I know that you shall learn something good. Here it is. Thirty-second ottava I want to tell you in this fourth explanation That, when you write passaggi and when you break the words, The words must be pleasant to hear, And avoid that the listener should complain. If you do so, you will prevent Those who criticise you from talking behind your back. Therefore, abide by what I taught you know, And singers shall praise you. [-<66>-] [Cerreto, Dialogo Harmonico, 66; text: Essempio del Contraponto fatto sopra l'Antifona del Terzo [terzo ante corr.] tono Miserere mei Deus secundum magnam misericordiam tuam] [-<67>-] Pupil. This counterpoint written on the antiphon the fourth tone has surpassed the other three, since it has followed the nature of that tone with its notes. Therefore, will you be able to continue and to show me the counterpoint on the antiphon of the fifth tone, if you please? Teacher. Indeed you did not stray from the truth, since the progress of the fourth tone has a very sad character and the composer must sustain it and make it more spirited by employing major consonances. One shall see that the opposite occurs in the following counterpoint written on the antiphon of the fifth tone, since it has a haughty and self- assured character. However, I shall not say more about it before I write out its ottava. Thirty-third ottava Our Muse’s order says That, when one writes in the fifth tone, One must proceed sweetly up to the end, So that the composition may be entirely good. However, this counterpoint does not require justification, Since it is written on a tone that has an imposing sound. You shall know this with ease, When you shall hear it sung by a good singer. [Cerreto, Dialogo Harmonico, 67; text: Conttraponto Osseruato fatto sopra l'Antifona del Quinto Tono. Laudate dominum omnes gentes laudate eum omnes populi Alleluya] [-<69>-] Pupil. I can see clearly that the composition of these counterpoints shall impress some authoritative musician, not only as to the way it is woven, but also because of the imitations and answers that it contains. However, will you continue with the rest? Teacher. I shall not fail to do so, since I owe it to you. Since the following antiphon is the one of the sixth tone, I want to write it, so that it sounds a little sweeter than its authentic. I shall not fail to write its ottava herewith, from which, I am sure, you shall gain pleasure and enjoyment. Here it is. [-<70>-] Thirty-four ottava Remember, Reader, when you were told About the counterpoint written on the fourth tone, That they should be sweet and provide a good effect, As this would gain praise for the good student. This order is appropriate in this other subject That follows it in the sixth tone, And one must ensure That one never deviates from the character of the tone. [Cerreto, Dialogo Harmonico, 70; text: Contraponto osseruato fatto sopra l'Antifona del Sesto Tono.Laudate pueri dominum laudate nomen domini.] [-<71>-] Pupil. I considered said counterpoint and reviewed its progress. I have learned many rules and instructions from it, so, will you be able to write a counterpoint on the antiphon of the seventh tone, so that the part singing it is written with the clef of G sol re ut, since the antiphon is authentic? Teacher. You were clever in thinking that the clef that carries the counterpoint should be written as authentic, so that the counterpoint may proceed comfortably, as we can note afterwards. However, read the ottava, as it will explain some of its essential features. Thirty-fifth ottava Reader of mine, it is good that I should tell you How to write you composition. The rule says it, and I say it myself, But be very careful when you write it, So that the notes may murmur One against the other in sweet music. Also, mix and vary the counterpoint Until you reach the end. [-<72>-] [Cerreto, Dialogo Harmonico, 72; text: Contraponto osseruato fatto sopra l'Antifona del Settimo Tono. Beati quorum remisse sunt iniquitates quorum recta sunt peccata] [-<73>-] Pupil. O, how much you have pleased me with this other counterpoint, especially in the passages that proceed cheerfully! Therefore, since all that is missing is the counterpoint on the antiphon of the eighth tone, I beg you to provide me with it and not let me be deprived of it. Teacher. I shall do so and I shall be brief, as it is true that, since I have shown you many examples of counterpoint, they shall suffice. However, in order to complete what is left to complete, I shall not fail to do so, as you can gather from the following example with ease. However, firstly I shall write its ottava, as it is interesting to read. Thirty-sixth ottava Since all I have left is to discuss The eighth counterpoint, I should say What the good Reader should do in this respect, Before anyone starts to work on it. I warn everyone who wants virtue to be Their friend that they should tend to this counterpoint, And I promise you, That you shall reap a reward for your efforts. [Cerreto, Dialogo Harmonico, 73; text: Contraponto osseruato fatto sopra l'Antifona dell'Ottauo Tono. O Uirgo Uirginum Maria stella maris succurre cadenti] [-<75>-] Pupil. Let the Lord be praised, as He as allowed me to reach the goal of understanding with ease the rules of the strict counterpoint on a cantus firmus. Therefore, I would like (if no obstacle is in the way of my dear Signor teacher) to understand the rules and study some examples of the counterpoint woven on a measured melody, since I realise that I still need to learn it. Teacher. You have been very eager in asking me what I planned to illustrate and explain to you. Therefore, you must be aware that, in the case of these counterpoints written on a measured melody, their rules is not different from those that you have seen composed on the cantus firmus, as to their counterpoints, however, in order to give you fuller satisfaction, I shall start from the first counterpoint on the bass part of the madrigal Fammi pur guerra Amor by Archadelt. Its respective ottava will help to explain any peculiar detail of this subject. Here it is. Thirty-seventh ottava Although earlier we have discussed and explained The rules of counterpoint, Nevertheless these other ones follow The same rules as the examples that I prepared and showed earlier. These following ones, however, have different effect, Produced by imitations and by words sung note against note. They are composed on a measured melody, That forces the composer to obey the rules. . [-<76>-] [Cerreto, Dialogo Harmonico, 76 text: Contraponto osseruato fatto sopra Canto figurato con la Parte del Soprano, Fammi pur guerr'amor quanto tu uuoi Che gli occhi di costei pace mi danno come ueder tu puoi Che stimo poco di tuoi lacci'il danno] [-<77>-] Pupil. I realise, dear teacher, that this practice of writing strict counterpoint is very subtle and that great knowledge is required to know how to write it. Although so-far I have understood some of the rules that concern them, nevertheless, please, to not fail to write another counterpoint herewith for my benefit, but one woven by the part of the bass on the same madrigal, to keep to the same work. Teacher. Since you are preparing yourself to ask me to solve some doubts that have to be solved for your own benefit, therefore, I shall strive to satisfy you request by providing you with an example and its respective ottava. Thirty-eighth ottava Ottaua xxxuiij We shall discuss now the counterpoints That are made by the bass against the subject That is sing by the soprano, at the same time, And we shall see who is more successful and who sings better. However, I want to demonstrate with ready arguments That the bass adds greater weight to its subject, Because its gravity is so powerful, That it can sustain a deadly weight. [-<78>-] [Cerreto, Dialogo Harmonico, 78; text: Contraponto osseruato fatto sopra Canto figurato con la Parte del Basso. Occhi benigni il cui ualor eccede ogn'altro uiuo raggio uiuete lieti si di me curate lumi santi, e diuini la cui alta beltate mi mostra sù dal Ciel qual sia il uiaggio Uoi hauete mercede cosi di me nel mio intenso ardore Che poco curo le fiamme d'amore] [-<81>-] Pupil. This counterpoint woven with the bass has amazed me, and you have shown in it great skill both in the passaggi as in the answers and in the fughe. So much so, that, if I didn’t think that you find it easy, my sweet teacher, to show me an infinite number of examples, I would say that these two counterpoints would suffice to teach me what I need in this matter. Therefore, if it is not too onerous, will you be able to show me another strict counterpoint woven by the contralto on the tenor of the same madrigal, in such a way, that it may be rich in beautiful passaggi and imitations of fughe and answers? Teacher. I now realise that you are eager to ask your questions and you do not think or consider that, because of my old age, I am not always ready to be able to deal with so many rules on music and to write about them. However, your words are so sweet that they prompt me exceedingly to put into practice what you require of me. Nevertheless, I desire first of all that you read its relevant ottava, so that you may find it easier to understand the rule of said counterpoint. Thirty-ninth ottava Let us see these other parts that we have written With the contemplative beauty of our counterpoints. In fact, the tenor has subscribed the pact That those who sing it must certify. And since the parts are in agreement, Let he who weaves this counterpoint be ready to sing. We shall see soon in practice If the ending is made with our Muse. [-<82>-] [Cerreto, Dialogo, 82; text: Contraponto osseruato fatto sopra Canto figurato, con la Parte del Contralto sopra quel del Tenore, dell'istesso madrigale.Fammi pur guerr'Amore quanto tu puoi Che gli occhi di costej pace mi danno Come ueder tu puoi Che stimo poco di tuoi lacc'il danno] [-<83>-] Pupil. Are you going to fail to write for my benefit the strict counterpoint that the tenor must weave above the part of the contralto? Teacher. This is not so at all. Pupil of mine, do you think that I intend to fail to write it down? On the contrary, since this that is the last counterpoint, I shall endeavour to render it beautiful and pleasant as much as I can, and that it contains fughe and answers, as one can consider herewith. However, I shall not fail to write out an ottava on this type of this counterpoint as well, since I find that I have already composed it. Fortieth ottava Consider the beautiful weaving of parts That one can see in the singing of the alto and of the tenor, While everyone believes to be the best In making passaggi to enhance their own variety. What I like is that none of the two admits defeat, Since both of them are skilled in their proceeding, And they do well to do so because their music Proves sweet to the ears of the listener. [Cerreto, Dialogo Harmonico, 83; text: Contraponto osseruato fatto sopra Canto figurato con la Parte del Tenore con il Contralto. seconda parte, Occhi benigni il cui ualor eccede ogn'altro uiuo raggio uiuete lieti si di me curate lumi santi,e diuini la cui alta beltatemi mostra sù dal Ciel quel simil quiaggio quel simil uiaggio Uoi hauete mercede cosi nel mio intens'ardore Che poco curo le fiamme d'Amore] [-<87>-] Pupil. How skilfully you have conducted these four counterpoints, wise teacher, from which I gained much profit and knowledge. Therefore, I hope to be able to proceed further, and to understand the method of composing for several voices with the appropriate rules. Teacher. This question that you put to me so abruptly requires an answer, but it also renders me somewhat suspicious, as you appear so cocky, that you believe to have reached perfection in the art strict counterpoint, while you do not realise that this practice of strict counterpoint requires long and continuous study. Nevertheless, I do not want to discourage you and tell you that today you are going to hear and understand the rules of composing for several voices, but slowly, slowly, since I want to start from the easiest ones, so that you may learn everything with ease. I shall start with a duo, so that you may understand everything with comfort. I shall compose it strictly on the same madrigal by Archadelt entitled Che più foco al mio foco, to avoid that any learned and expert musician may murmur against me and accuse me not to have written it in a strict style. I shall notate it herewith, but first I shall write its ottava, so that you may understand it better. Forty-first ottava How good it is to discuss herewith, To what is due the perfect art of composing, And what is bestowed by Music So that the compositions may achieve their effect. Music says, with express instruction, That composing for two voices is very strict, But if the intervals are interwoven, They shall be sweeter and easier to compose. [-<88>-][Cerreto, Dialogo Harmonico, 88; text: Madrigale à 2 uoci, fatto à imitatione, Fammi pur guerr'Amor quanto tu uuoi che gli occhi di costei pace mi danno come ueder tu puoi Che stimo poco di tuoi lacc'il danno] [-<90>-] Pupil. I examined very closely your duo, or madrigal, however we want to call it. You have composed it with really great doctrine and knowledge, not only as an imitation of the original composition, but also as to the fughe of Archadelt’s madrigal, without departing from its specific tone, both in the part of the soprano as in the one of the contralto. Therefore, I beg you to explain to me herewith how I should write a trio, not only in imitation of another work, but as a free composition. Teacher. You demand a lot of me, and you do not consider that I am tired and worn out by now because of my age. Moreover, you should be satisfied with so many examples and rules that I showed you. However, so that I may keep my promise to you, I want to write it herewith, in order that it may be written as for the rest on the same madrigal, without straying from the imitation of it, in the same way as we proceeded in the aforesaid composition for two parts. However, before I write it, I want you to read its ottava, which, I hope, will please and benefit you. Forty-second ottava If it was said in the first stanza That composing for two voices is very strict, I want to say here what is left to say That was not mentioned before. I shall give you instructions herewith and you must trust The examples and the doctrine that you read. Therefore, I say that, if you abide By what I told you, everything you write shall be good. [-<91>-] [Cerreto, Dialogo Harmonico, 91; text: Madrigale à 3 uoci, fatto ad imitatione. seconda parte, Occhi benigni il cui ualor eccede ogn'altro uiuo raggio uiuete siete lieti si di me curate Lumi santi, e diuini la cui alta beltate Mi mostra sù dal Ciel qual sia il uiaggio Uoi hauete mercede Cosi di me nel mio intenso ardore, Che poco curo le fiamme d'Amore] [-<93>-] Pupil. This example written for three voices, as far as I can tell, cannot be improved, both as to the proceeding of the fughe, as well as to its imitation of Archadelt’s madrigal. Moreover, I have noticed that, you always avoid writing the fifth straight after an octave, [-<94>-] but that you intersperse between them some imperfect consonances both major and minor. Teacher. If you remember correctly, pupil of mine, I told you several times that good music comes from the mixture of imperfect consonances, either major or minor. This effect is not achieved when the composer fills its compositions only with perfect consonances. In fact, although the composition is not dissonant, nevertheless, it does not produce a sweet and graceful effect. Therefore, learned musicians are right in saying in this respect that imperfect consonances and the dissonances are the condiment of music. Moreover, I add that it is easier to write a composition for four or more voices than a duo or a trio, for the reason adduced above. Pupil. Since you have talked about composing for four or more parts, I would like to have an example of this. Teacher. This technique is not very difficult because the composer lays out the four consonances as he prefers both in ascending and in descending and renders the minor consonances major and the major ones minor according to the rule that I gave you at the beginning. I shall not fail to inform the composer that in all his compositions he must maintain the tone with which he has started them, however the number of voices. He must not abandon the tone unless he is [-<95>-] forced to do so by some idea contained in the text. Also, so that you may observe all these recommendations of mine, I shall write here for you an easy example in four parts. It will be written as an imitation of the same madrigal entitled Fammi pur guerr'Amore, albeit just its beginning and, so that you may find it easier to compose it, I shall write first its octave and then its example. Forty-third ottava Now, Reader, pay attention a while To what I want to say at this point, So that you may be satisfied in the end And, little by little, you may understand what I say. When you write your composition in four parts, Make sure that the parts develop independently And that every interval is placed in the right position, So that the listener may be pleased. [Cerreto, Dialogo Harmonico, 95; text: Madrigale à quattro uoci fatto ad imitatione, Fammi pur guerr'Amor quanto tu uuoi Che gli occhi di costej pace mi danno Come ueder puoi Che stimo poco di tuoi lacc'il danno.] [-<98>-] Pupil. I would be very keen to hear if now I shall be able to compose a piece for five parts, since I have understood the rule to compose for four parts. This is all the more true, since the consonances are four and the dissonances are three. Therefore, what consonance shall I place in the fifth part? I am not clear about this. I reply to you now, pupil of mine, that this doubt that you have raised with me will be very useful to you. It is going to be hard for me to explain it to you, so be patient and concentrate. This is the rule you must observe. When you desire [-<99>-] to write a composition for more than four voices, you must remember that at the beginning of our discussion it was said that, if a composer wants to employ more consonances than the first four or more dissonances than the first three, he should add to each the number seven, and thus he shall create as many other consonances as he desires. These shall be the same consonances or dissonances as the ones from which they are derived, and they shall be called compound or derivative. Therefore, if you want to add a fifth part, you must use the compound consonances and dissonances, and with this beautiful order you will be able to compose a piece for more than four voices or for as many as you like. It is true that, when a fifth part is a tenor or another alto, said parts will be able to proceed by contrary motion without availing themselves of compound consonances and dissonances. Thus, one shall be able to compose for as many parts as one likes and also or two or more choirs, and, if you want to see an example of this, it will be easy for me to write it. Pupil. You must not bother to supply me with an example, since I shall study it by myself. Therefore, if you please, you may discuss now some easy rules on the subject of canons, since they are important in music, and I am so eager to learn them. I shall deem this a blessing and a special favour. [-<100>-] Teacher. Pupil of mine, you have been very prompt in asking me to provide you with other rules concerning practical music, and especially regarding the subject of canons. Therefore, I reply to you and say that their rules are infinite. Also, to start with those that are composed at the unison, it is necessary to ensure that, as the consequent part rests for two beats or more, you will have to make said consequent part shorter than the leader by the same number of notes, so that they end at the same time. If the ending is made in the proper note of the tone in which the canon was begun, the will shall be called stricter, all the more so, as it proceeds with the same movements of notes and with the same intervals. One must also avoid in these canons to use rests longer than half a bar in the body of the canon, and to write the leader too high or too low. However, if one writes a canon at the unison in a mass or in a sacred composition, one can use as many rests as the composer likes, with respect towards the fughe and towards the other singing parts. It shall be good to observe the rule that states that, when the leader sounds a major or minor note, the composer must ensure that the consequent itself does the same, in order to vary the progress of both of the parts. [-<101>-] Pupil. I thank you for the instructions and for the rules that you have given me, but, in order for me to be entirely content, I would like you to provide me with another example to aid my understanding, so that I may exercise myself in it more easily, should I wish to compose some similar to these. Teacher. You acted wisely in asking me for an example, since I know that you need it; So much so, that canons are hard to compose especially since you are a budding composer. I shall write it herewith in such a way that you can repeat it from the beginning as many times as the singers prefer. I shall also write an ottava about it. Forty-four ottava I must tell you now something else On composing perfect canons. I shall say it in verse rather than in prose, Supporting it with arguments untold by anyone else. The rule is not so recondite, That there are no perfect examples of it. This is the first example that I composed for you, So that it may be sung at the unison at sight. [Cerreto, Dialogo Harmonico, 101; text: Canone all'Unisono.Guida, Conseguente] [-<102>-] Pupil. I examined that aforesaid canon and, in truth, I have found in it more observance of the rules that I believed I would, since it proved to be very pleasant to sing. Therefore, you may proceed and deal with the canons that one writes at the second above, so that the sequence that was started may be preserved. Teacher. Composing canons at the second above differs from composing canons at the unison because the movements of the consequent differ from those of its leader. Therefore, before I [-<103>-] notate the relevant example, you must be aware that the canon is written with the square [sqb] and that the leader must not descend by step from A la mi re to E la mi with these notes, namely, la, sol, fa, mi or la, mi, because, if its consequent sings a second above, it will produce a harsh tritone both by stepwise motion and by leap. Were this to occur, the proceeding of the composition would be unpleasant and harsh to the ears the listener. So that you may understand and exercise yourself on this matter, I shall write herewith an easy example together with its relevant ottava for the greater satisfaction of the Reader. Forty-fifth ottava Reader, listen to this beautiful thought: When the leader sings its part, The consequent will do its job, Since the consequent sings a whole tone above it, It is not worth one but a hundred. This is the example, as you can see here, And everyone who sings it, I know, will believe me. [Cerreto, Dialogo Harmonico, 103; text: Canone alla Seconda alta. Guida, Conseguente] [-<105>-] Pupil. In truth, every musical professional marvels at your compositions, especially those who delight in writing canons. I have already understood the rules that you observed in the aforesaid canon, so, all is left is to instruct me as to what I should do if I want to compose a canon a third above the leader. Teacher. I shall make you understand what you need to know with a few brief words. In fact, you must know that, if you want to write a canon at the third above, you must write the clef of the consequent part a third above, so that you may proceed appropriately through all the lines and the spaces of those melodies and, also, so that the each singer may sing comfortably his part. Moreover, one must ensure that the fughe are written in the species of the tone in which the composition was started. This rule holds true for the leader, rather than for the consequent, because the latter is not bound to it. I shall write the example of it for you and especially its respective ottava. Forty-sixth ottava I do not want to forbid us to discuss these rules and of the precepts, and to consider how one should write a canon. I have already explained the rule that deals with it, And I have already said how they must be written. Therefore, I have already done it, And the canon must be A third above the said melody. [-<106>-] [Cerreto, Dialogo Harmonico, 106; text: Canone alla Terza alta, Guida, Conseguente] Pupil. Since the canon written above was so short, I have noted much artistry both in it fughe [-<107>-] as in its capacity to please, when it is sung. I must praise it all the more because it was written in front of me in the blinking of an eye. Therefore, you may carry on explaining to me how to write a canon ad the fourth above. Teacher. Composing canon at the fourth above has its rule, which is not difficult. In fact its consequent proceeds almost through the same intervals as the leader, but one must pay attention only to this, namely, that the clef of the consequent must be written a fifth above the one of the leader, so that both parts can be sung with ease through all the lines and the spaces. One must never fail to preserve the tone, especially in this type of canon, as it proceeds through the same intervals. That all that I say is true, one may realise it from the example notated herewith. However, I shall not fail to write its own ottava before it, knowing for sure that it shall please whoever reads it. Forty-seven ottava I marvel and I am always worried When I discuss this music of mine. Since canons and other compositions Shall be based on its instructions in their hundreds. I want to speak and I am very happy, Since now I open up my imagination. I shall speak of the fourth canon, that I have already written, So those who want to sing it can sing straight away. [-<108>-] [Cerreto, Dialogo Harmonico, 108; text: Canone alla Quarta alta.Guida, Conseguente] [-<109>-] Pupil. Among the main features of the aforesaid canon, I say that an important one is the fact that you have ended it on the same note from which the leader started to sing, although I leave aside the learned adherence to the rules in writing the fughe and in maintaining the tone. Therefore, I do not want to fail to ask you to provide me with a rule on how I may compose a canon at the fifth above. Teacher. Your words are so sweet that I am drawn very strongly to please you by meeting your request. Now I shall write herewith an easy example that you may use as a model to write others similar to it, but first of all I want to write its own ottava so that one may understand it fully. Forty-eighth ottava The following canon has already been written With artistry, intelligence and with the knowledge Of what our Muse has ordered, As one can see well here beneath. I shall say so because I wrote it here as an example, Because the consequent can have all the same notes, So that it may be sung more easily. [Cerreto, Dialogo Harmonico, 109; text: Canone alla Quinta alta, Guida, Conseguente] [-<110>-] Pupil. My dear and sweetest teacher, I am frightened to tell you the truth, since I know that in the past you were angry with me. However, I ensure you that all of these five canons had me marvel not only at their fughe, [-<111>-] but also at their conclusions, and at the very important principles that I have noticed in them. However, this is not an obstacle for me to ask you to write out for me the rule and the example of a canon written at the sixth above. Teacher. I told you several times that I shall not fail to provide satisfactory answers to your questions on the practical rules of music. Therefore, I want to compose for you herewith a canon at the sixth above so that it may be easy for you to write some similar ones, although they are a little limited in the encounters between the two parts because their intervals do not proceed with the same sort of notes, as we have seen in the other ones written at the unison, at the fourth and at the fifth. To prove that this is true, you shall be able to note their difference from the example that I shall write herewith. First of all, I must write the ottava that deals with this subject, and then I shall write what follows. Forty-ninth ottava If this example herewith is different, Because the instruction proceeds in a different way, Nevertheless you shall be very firm here, While the haughty consequent proceeds. I have great regard for this rule, Because I know very well that it is not harsh. This is what you see in the following canon, That its consequent sings at the sixth. [-<112>-] [Cerreto, Canone in Sesta alta, Dialogo Harmonico, 112] [-<113>-] Pupil. Since you the canon that you are going to write out for me is the one at the seventh above, I do not want to fail to ask you to do me the favour to do so, but in such a way that it is done with the ease and mastery that shone through in the previous ones. Teacher. Since the entire sequence of canons proceeds upwards to the octave above and downwards to the seventh below, and, since its consequent proceeds with opposite intervals to its leader, you must ensure not to employ tritones or false fifths. I shall write the example here, preceded by its ottava. Fiftieth ottava Come on, we must discuss now The progress of the consequent That wants to sing at the seventh, So that you may be aware of it. The composer can compose it all, And make its composition learned So that the leader and the consequent May sing with sweet and sonorous voice. [-<114>-] [Cerreto, Dialogo Harmonico, 114; text: Canone alla Settima alta, Guida, Conseguente] Pupil. I have drawn great benefit from this canon at the seventh above, as to my practice of composition. I noticed in it [-<115>-] many instances of observance of the rules both on the matter of the fughe and of their answers, but also in the species of tone, since the leader started and finished on the note of G sol re ut. Therefore, you may write the last canon at the octave above for my benefit, so that I may understand all the rules of the canons that instruct us on how they are to be written on a given leader. Teacher. I shall not fail to meet your request, since I owe it to you to do it, so that your needs may be satisfied, although it is not very difficult to write the canons of which you ask now, because both of their parts proceed with the same intervals, altered and natural, and are similar to the canons written at the unison. I shall say no more. I omit to tell you about maintaining the same tone because I am sure that you will make no mistake, although I remind you that the canon shall proceed at the octave higher. I shall write for you the example preceded by its ottava. Fifty-first ottava I want to pray you, sweet Muse of mine. You are the queen of singing, The mother of composition And of those who sing and play. I have composed this composition of my invention. This is the example, and pay attention here, Since the consequent sings at the octave above. [-<116>-]> [Cerreto, Dialogo Harmonico, 116; text: Canone all'Ottaua alta. Guida., Conseguente.] [-<117>-]> Pupil. My sweetest teacher, when I have considered and examined the aforesaid canon written at the octave above, I found that you wrote it with great doctrine, in the middle as well (and even better) in its conclusion. I also find that you wrote it in the eighth tone, if I am correct in identifying the species of the tones. Teacher. My dear pupil, since you have mentioned the species of the tones, I want to let you know that I have written all of the above eight canons in each of the eight tones. I constructed the first in the first one, the second in the second one and so on the rest of them. I am pleased to say that now you have become aware of it. Pupil. I have remembered another curious question that I wanted to put to you, namely, now that I have understood with ease all the rules concerning the composition of canons up to an octave above the leader, I would be very pleased if I could hear from you the other rules on composing the other canons written under the leader [-<118>-] down to the lower octave. Please, if you rate my devotion, do not fail to tell me, as I cannot wait for you to start your answer. Teacher. Pupil of mine, I believed that the eight canons written above would suffice for your compositional practice, but, since this is your will, I do not want to fail to meet it. On the contrary, for your greater satisfaction, I shall compose them with different species of tones following the same orderly sequence of the earlier canons. I shall start with those written at the second below. This is the example and its respective ottava. Fifty-second ottava You two parts, as you are two sisters, who sing now so close to each other, since the Muse created beautiful things, sing them in the evening or in the morning. Inside the fughe are so agile, That the listener then may be satisfied. Second canon at the second below. [Cerreto, Dialogo Harmonico, 118; text: [[Conseguente]], Guida, Conseguente] [-<119>-] Pupil. In truth these compositions of yours are worthy of admiration. When applied myself to the aforesaid canon at the second below, I discovered that you composed it with the greatest artistry, especially as it is written for two high voices. Therefore, can you notate for me an example of canon composed at the third below, so that we may follow the order that was begun? [-<120>-] Teacher. I shall do that gladly, and I shall compose it in such a way that the leader is written in the third tone, because the consequent proceeds with different intervals, as one shall be able to consider more closely in the example and in its corresponding ottava. Fifty-third ottava In truth it is appropriate to talk again Of the sweetness and of the suave sound Produced by this canons when one listens to them, Because the parts sing well. It is right that we should seek satisfaction In the song that will be written in the third tone: The learned composer promised To make it sweet and graceful, and he notated it here. Canon at the third below [Cerreto, Dialogo Harmonico, 120; text: Guida, Conseguente] [-<121>-] Pupil. Since I have exercised myself with the help of the aforesaid canon, and I considered closely how strictly it follows the rule on which it is based, also in relation to weaving of the fughe and to the adherence to the tone. Therefore, you may proceed to illustrate a canon at the lower fifth and to provide me with its rules on how to compose it. [-<122>-] However, I would like the example to be written with the b flat and that composed in the fifth tone. Teacher. I am pleased, because what you require from me now is reasonable and important. Therefore, I do not want to fail to provide it. Moreover, it is good that the remaining canons should be written with the b flat, so that you may able learn to compose in all the transposed tones thanks to this variety. I shall write the canon at the lower fifth herewith, preceded by its ottava. Fifty-fourth ottava It pleases me a great deal That our senses derive greater nourishment and pleasure from variety. I am even more pleased when one sings With beautiful devices without contravening the rules. All this can be seen in this song, Therefore, it is appropriate to praise it author. [Cerreto, Dialogo Harmonico, 122; text: Canone alla Quinta bassa. Guida, Conseguente] [-<123>-] Pupil. Since I have read and considered closely the aforesaid canon at the fifth below, and I was very pleased with its progress, therefore, I shall be extremely delighted if you were to write for me the canon at the sixth below, but in such a way that it may be written with the b flat sign. Teacher. Since you told me that you were pleased with the canon at the fifth below and with its progress, I shall compose the sixth canon at the lower sixth in the same style. I shall make it short, but I warn you that, since the consequent proceeds with different intervals, one must be careful not to write in it false fifths or tritones, as I told you elsewhere in relation to the other canons that are written at the second, at the third or at the seventh both above and below the leader. To be succinct, I shall write the example, preceded by the ottava written on it. [-<124>-] Fifty-fifth ottava As one can see, this composition Is written with great art and with observance of the rules. Therefore, I say (and I know that everyone believes me) That this canon holds its own in comparison with others. My Muse shall support my claim, That everything that I explain is true. This is the form and the progress of the composition That follows herewith. [Cerreto, Dialogo Harmonico, 124; text: Canone alla Sesta [Settima ante corr.] bassa. Guida., Conseguente.] [-<125>-] Pupil. Dear teacher, these compositions of yours excite great marvel and admiration not only in me, a mere beginner in the practice composition, but in all the learned practitioners of this art, all the more in this example at the lower sixth, since you have written it in the blinking of an eye, and you concluded it in the very note on which you started said canon. Therefore, will you be able to write the canon at the seventh below for my benefit, so that I may work on it and employ it as a model to write others myself based on it? Teacher. Not only I want to write the canon that you mentioned for your benefit, but a thousand more, as long as you do not fail to exercise yourself on them, because you need to. Moreover, I want to show you the ottava that I wrote on this matter, from which I know that you shall gain pleasure and satisfaction. Fifty-sixth ottava When I think about what I promised to you, I decided, not to be proven a liar, to write a canon at the distance of a new interval, but in such a way that it is well written throughout, because my Muse as allowed me to follow the common practice. Therefore, I have done so, And this is my composition, Who follows it at the seventh shall be pleased with it. [-<126>-] [Cerreto, Dialogo Harmonico, 126; text: Canone alla Settima bassa. Guida, Conseguente] Pupil. All is left to do is to consider the last canon at the octave lower. I would like it to be written in the eighth tone altered with the b flat sign. Please do not fail to satisfy my request, as I am an obedient pupil. Teacher. I understood you straight away and I shall not fail to write it herewith, so that it may be of the eighth tone transposed, just as the above canon is of the seventh tone. I want to write here its ottava for your benefit. [-<127>-] Fifty-seventh ottava Now I can speak as an artist, Because I want tell you about the sort of composition, Whose part is written at the interval That is the smallest that there is. This is the octave and it is divided entirely Up to where one encounters the seventh. This last composition is written in this way, So that the number eight may be employed successfully. [Cerreto, Dialogo Harmonico, 127; text: Canone all'Ottaua bassa, Guida, Conseguente] Pupil. Dear teacher of mine, it is good that we should both say [-<128>-] Benedicta sit Sancta Trinitas (Blessed be the Holy Trinity) after we concluded the discussion on the canons. We should also repeat Benedicta sit Sancta Trinitas (Blessed be the Holy Trinity) because we have abided by three elements of perfection in this last canon, namely, in the fughe, in maintaining the tone and in the learnedly written conclusion. Teacher. Dear pupil of mine, we say correctly in that proverb that who has little believes to have a lot. You are a beginner in this practice of music, therefore, you cannot know what artistry is involved in writing canons according to the rules. In fact all the canons that you have seen and practised so-far are nothing in comparison to the ones that learned musicians are able to compose. Pupil. Please, tell me. Are there any other rules concerning the composition of canons? If it is so, please do not fail to make me understand your rules and how they are written, so that I may not lack preparation in this matter. Teacher. You are moving ahead too fast and you ask to know topics that are exceedingly hard and difficult, such as writing a canon on top of another one. Not all musicians of this world are equipped to write such compositions, or indeed able to do so. Pupil. Therefore, I dare to beg you with confidence that you may consider it worthy to explain them to me, since I know that you have written an infinite number of them and had them printed. Hence, it will not be hard for you to notate some examples of them. Teacher. Come on, since I cannot fail you, I shall write a canon written above the canon at the unison, but first I shall write for you the octave that deals with this subject. [-<129>-] Fifty-eighth ottava. [[On the canon above the canon at the unison]] Listen, Reader, how powerful the Muse is In composing. The composer Cannot put forward as an excuse The fact that he does not know the best style of composing. This rule is not confused, Because it deals with what is true, rather than what is a lie. Consider this double composition that I wrote So that you may learn to write one in the shortest time. [Cerreto, Dialogo Harmonico, 129; text: Canone all'Unisono fatto sopra al sotto Canone allUnisono. Guida, Conseguente, Canone all'Unisono] [-<130>-] Pupil. Dear and sweet teacher, I have been left besides myself when I considered the canon at the unison written above. You have written it with such artistry that it amazes every excellent musician and especially me, since you have written it in front of me. Teacher. It is such an arduous and obscure matter for those who are not well versed in it, because not all composers study this subject. I can tell you for sure that in our city of Naples, which is one of the main cities in the world, there are many musicians of high repute who do not follow these difficult and important rules, but only those that achieve the provision of some earning. They do not go beyond this, because they are satisfied with writing a simple motet or a catchy villanella in imitation of some little Spanish canzonetta. They have abandoned the practice of the past when [-<131>-] one always saw and heard, both in works written on Latin text for use in the cathedrals and in popular works on an Italian text, that they were composed and sung by various different musicians in a serious style and full of perfect doctrine, as it is clear without naming the authors of the musical works. Pupil. I understood everything, and all what you say is true. If no obstacle intervenes, I would like you now to provide me with another rule on this same subject of writing a canon above another canon, but in such a way that is different from the first one. Teacher. It is my task to do so, since I know that you need to know this. I can telly you that Nemo dat qui non habet (Nobody who is without can give anything) and it is easy for me to do so. I shall write for you herewith a canon at the octave below written above a canon at the octave below and, so that you may able to learn it more quickly, I shall write its respective ottava from which you shall learn a beautiful detail. Fifty-ninth ottava These examples are not as amazing As you regard them, Reader of mine, Because you can complete something that is already Rich with ease, just as I have done myself. Here you must consider, That few people have this desire, But, if they went to school and studied how to do it, They would be able to sing this verse. [-<132>-] [Cerreto, Dialogo Harmonico, 132; text: Canone all'Ottaua bassa, sopr'al Canone all'Ottaua bassa. Guida, Conseguente] [-<133>-] Pupil. Let the Lord be praised, who has allowed me to reach a level where I can exercise myself on the example of musical compositions of such difficulty. I am aware that not all those who are music professional understand them, and, if I am not mistaken, the close contains even greater artistry. Therefore, I do not want you to fail to provide me with another rule, if there is one, on how to write three canons at the same time. If there is one, I would like you not to fail to tell me about it. Teacher. I told you several times, pupil of mine, that the rules that preside over this matter of canons are infinite, just as they have been demonstrated for your benefit with innumerable examples. Therefore, I shall teach you how other canons, which proceed by contrary motion, are composed, and this is also a difficult rule. [-<134>-] I warn you that you must not have any tied dissonances in the leader, because, since the consequent proceeds by contrary motion, they sound wrong. Moreover, you must not rise too high or descend too low with the leader, but limit yourself to whole of the five lines and spaces, so that the two parts can be sung comfortably, as you shall be better able to gather from the example written herewith and from its ottava. Sixtieth ottava Reader, you must here ensure That the leader does not contain Tied dissonances, as it sounds wrong With what the consequent wants to sing. Do not exceed upwards or downwards The lines of the written part. This is what reason wants and commands, While capriciousness is left on one side. [Cerreto, Dialogo Harmonico, 134; text: Canone per contrarij moti, Guida, Conseguente] [-<135>-] Pupil. I am in awe, my dear teacher, of this canon that you wrote for me just now proceeding by contrary motions. I noted in it that the rule is somewhat difficult, but this is not sufficient reason for you to refrain from proceeding any further and from discussing some other substantial rules for my benefit, as I want you to be certain that I am fond of all of them, because I hope to benefit by studying them assiduously. Teacher. Pupil, you must know that, before I move forward to discuss other canons, I want to disclose to you a secret that is unknown perhaps to other musicians of our time. In fact, the aforesaid canon can be sung in such a way that the consequent part becomes the leader and the leader the consequent, but with the same rests that were employed by the consequent, [-<136>-] as you shall be able to gather from the following example, and, even better, by reading its ottava written herewith. Sixty-first ottava Consider, Reader, and pay attention, Because our Muse has devised a game Which is the complete opposite of the first composition, As you can see here below, where it is. I do not worry about this, And I do not ask anyone to unveil the truth, But if you desire to see this passage, The consequent la has given checkmate to the leader. [Cerreto, Dialogo Harmonico, 136; text: Canone per contrarij moti riuoltato con ambi due parti del Canone superiore. Guida, Conseguente] [-<137>-] Pupil. This rule that you have given me above is truly amazing, where one can see that the consequent can become the leader and the leader the consequent. I assure you that I can speak freely for the entire world and say that, in all the books that deal with the discipline of music, I have not so many learned secrets, as there are here. However, do not consider me to be a fawning student, because I am telling you the truth. Nevertheless, let us not move on, so that I may not forget what I wanted to ask you. Yesterday I witnessed a discussion of professional musicians and singers where someone said that one can also find certain canons that are called cancrizans. [-<138>-] I would like you to explain to me this other rule, so that this topic may not be left in the shade, as far as I am concerned. Teacher. You are enticing me to explain what you desire to know with sweet words. However, this is not a good reason for me to deprive you of the teachings that are necessary for a practical musician, so I want to do you the favour of explaining them, as I do not deem it onerous. Nevertheless, I do not want to refrain from telling you that you should not abandon your continuous practice, especially on the subject of the canons. Therefore, I want to write herewith a canon that is sung in a cancrizans way. It shall be brief and substantial. However, be careful that you cannot write passaggi when you compose in this way, neither ascending nor descending, because, since the consequent will have to sing from the end of the leader, the passage shall sound wrong, which is something that would go against the rules of composition. So, in order for you to experience in practice what I taught you, I want to write down the ottava that deals with this topic for your own benefit. Sixty-second Canon Listen, dear reader, now I tell you Of this beautiful, intricate musical topic. It is a matter very worthy of being heard, Although the mind finds it confusing. It is important that the composer should learn it, So that you may not have to justify yourself in front of the world Because you do not know it. The example Written is cancrizans, and it starts from the beginning and from the end. [-<139>-] [Cerreto, Dialogo Harmonico, 139; text: Canon Cancorizando à due Uoci] Pupil. Dear teacher, I found through experience that it is true what you have told me, namely, that in this sort of canons divisions and passaggi are forbidden, both ascending and descending. The reason for this is that the consequent proceeds in contrary motion to the leader. Therefore, while I am curious to know everything on this practice of writing canons, I shall want to know if it is possible to write another canon above the aforesaid one, which seems to me to be the case. I understood what you have asked me, and in order not to fail to answer your question, I shall strive to fulfil your request. However, I must warn you first that the canon written on top of this one must follow the same rule that we mentioned above, namely, it must not proceed with ascending or descending passages, because, when they are sung or played, they do not allow the parts to be heard properly, as one can gather from the example notated below and also from the information contained in its ottava, as you can read herewith. [-<140>-] Sixty-third canon The intricacy is not over yet, Because the Muse is always searching, The knowledge grows from an hour to the next, And the composer always makes mistakes. For this reason that it would be better, To talk further on the subject of music, Because composers are lazy and slow And want to learn everything without hard work. [Cerreto, Dialogo Harmonico, 140, 1; text: Sopra Canone al Canone Cancorizando a 2. Uocj] [Cerreto, Dialogo Harmonico, 140, 2; text: Canone Principale Cancorizando a 2 Uoci] Pupil. One cannot deny, my sweetest teacher, that you conducted yourself learnedly in the addition of this canon. Therefore, [-<141>-] I was convinced that it would have been impossible to write it. However, tell me, please, if you deem it worthy of teaching me it, can anyone write in music another sort of canons? Teacher. I told you several times that you must remember well that the rules of the canons are infinite. Therefore, apart from the ones that I showed, you there are the canons called enigmatic, that are more obscure than the other ones, both those that are accompanied by Latin words and those that contain descriptions in Italian. However, if you want to learn how they are composed and how they are resolved, you will be able to use my own canons (printed in my book entitled Musical Practice at the end of the third book, or in my second book for two parts in the section entitled enigmatic canons) as models for your own practice. Pupil. I say in reply that if, God willing, I found myself in such a position where I can study and understand fully what music theorists have written, I ensure you that I would not dare to disturb you by asking you about musical technique. Therefore, I do not want to fail to beg you to do me the favour to provide me with those other examples. Teacher. I do not want to fail to write it down in order to meet your request. However, you must understand that the resolution of the canon and the instructions on how one should sing the other parts are obtained from the description without any other demonstration or any other sign employed in other canons. For this reason music theorists have called it enigmatic. However, so that you may understand it better, I want to write its relevant ottava. [-<142>-] Sixty-fourth ottava I have told you several times, Reader of mine, That it would be too long-winded to deal With the canons. However, listen to what I say, It would be better to stop talking about them. However, since I always have this deep desire That prevents me to mind discussing them, These are the enigmatic canons, And they are more obscure than the other ones that you have seen. [Cerreto, Dialogo Harmonico, 142; text: Canone Ennimmatico, Sequere me] Pupil. The resourcefulness of these canons is remarkable and I was left amazed all the more because this branch of composition is bound and governed by so many sorts of rules, especially in this matter of canons. Therefore, after I read and examined the words of the riddle in said canon, they speak very clearly as to the meaning of the words in that they say that the consequent part must follow its guide, although they do not say how. In fact, every singer who wants to sing it must be clever, so that he may solve that difficulty. This is all the more so, because there are no signs that indicate where the consequent may start to sing, nor has it been subdivided into bars, as it was the case with the earlier canons. [-<143>-] Teacher. It is true that these enigmatic canons are not solved very easily, especially those that are written as a single part without sign to indicate where the consequent must start to sing. An inexpert and ignorant musician would not have been able to make sense of it, but the leader says: ‘follow me’ to its consequent, which means that it shall have to follow it after the rest of one of semibreve, while the consequent itself comes to a rest a bar of a semibreve before the end of its leader. If you go back and verify it, you will find that this is the truth. Pupil. In truth, I had an inkling that what you have taught me was the case, but, since I have understood the previous canon completely, it would be good if you could compose another canon, still of the enigmatic variety. I would be very grateful if you did so. Teacher. You are asking me to explain many matters that it is not necessary for a beginner composer to know. Therefore, leave aside these difficulties and attend to what is of greater importance for you. In fact, with time and continuous study you shall reach perfection in all that you need to know. However, since I do not want to leave you dissatisfied, I want to write for you another enigmatic canon composed above said enigmatic canon in such a way that the its rests are in answer to the words of the first canon. I shall not fail to write out its octave first, from which you shall draw benefit and pleasure. Sixty-fifth ottava Now I want to satisfy you fully, Dear Reader, as to what you asked me, So that you may unravel this composition, Since it cannot be done if it is left unresolved. The wind will carry away all the efforts of the composer, If he does not know what I said. Therefore, I want to inform you fully about it, So that you may proceed always quickly in your studies. [-<144>-] [Cerreto, Dialogo Harmonico, 144, 1; text: Sopra Canone Ennitmatico, fatto sopra al sotto scritto Canone Ennitmatico Sequere me. Si legis me obserua mandata] [Cerreto, Dialogo Harmonico, 144, 2; text: Canone Principale Enitmatico, Sequere me] Pupil. Now it is the case that I can tell you freely that I am satisfied with what I need to know on the subject of canons, and I assure you, dear teacher of mine, that a pupil, however ignorant one may be, when he reads the aforesaid rules and examples cannot help but being able to account for it to anyone of the profession. Now, I want to ask you to consider it worthy to discuss some of the principles behind the proportions, if you please, that are used in counterpoint, since I know that [-<145>-] they are necessary for the practice of music and because they are employed nowadays by almost all composers in any composition that they write. Teacher. I am pleased that your reasoning is correct and that you have benefited from what we have discussed. Therefore, allow me the pleasure to move on to discuss what you require, and especially the proportions, as you requested. I warn you that these issues are not understood, since practical musicians consider them just as meaningless and almost foreign labels, because practical musicians only care about what they employ in their music, and the proportions are based on subtle considerations and speculations that require someone who is good at arithmetic rather an a simple musician, who needs that its subject is easy, familiar and of everyday use. Pupil. I say in reply to what you told me now that the speculations are the remit of speculative theorists. However, I am interested in understanding only their practical application, since I shall be able to gather all the rest with time and application. Teacher. Since this is what you require, I do not want to fail provide you with this satisfaction. Now, so that a beginner may have good knowledge of the species and genera of the harmonic proportions, we shall start by explaining what [-<146>-] what the dupla, the tripla, the quadrupla, etcetera are, and we shall deal of the meaning of certain terms that are not well understood by everyone, even the terms species and genus, by themselves and in their actual meaning, since I shall have sometimes to refer to such species calling them genera. The first three simple genera are these, namely the simple genus, the superparticular and the superpartient. The other two genera, the multiple superparticular and the multiple superpartiens, are compound genera and they derive from the first three. Therefore, I inform you that there is not species that is not contained by some particular genus and, since the dupla, the tripla and the other ones are used in composition, we say that all the comparisons and oppositions of the numbers in use are all embraced by a particular genus that is called multiple, whose being and essence consists in nothing but containing and embracing all the opposed and in comparing the numbers to the unit, if musicians wanted to compare them up to the number one thousand. Pupil. Therefore, if you like, can we come to the facts, so that I may understand the matter better? [-<147>-] Teacher. Since you are eager to know, you must realise that a proportion in our music practice is nothing but the convenience and habit of comparing numbers together. One is called proportion of equality and has its numbers equal between each other, while the one called proportion of inequality has different numbers, as one will be able to gather more clearly from this example notated here below. [Cerreto, Dialogo Harmonico, 147; text: Proportione di Equalità 2, 3, 4, Proportione di Inequalità] Pupil. Please, help me to understand the difference between the proportion of equality and the proportion of inequality. Teacher. I reply by saying that this is the difference. When one compares two equal numbers a species called rational proportion of equality is generated, which is not suited to music. Conversely, if one compares two unequal numbers, the second species called rational proportion of inequality is created. It consists of five genera, or five species named [-<148>-] as we said above with the addition of the prefix sub, namely, submultiple, subsuperparticular and subsuperpartient. The same occurs in the other two compound genera. One must also note that in the proportions of larger inequality the larger number is placed above and the smaller one below, while in the proportions of smaller inequality the smaller number is placed above and the larger one beneath. Since we said that that the proportion has five genera, namely, five species, for this reason, it will be good to start from the first species, which si the multiple one. Therefore, the first species will be the dupla proportion that occurs when the number two is compared to the number on. This is done by way of this comparison, 2/1, which indicates that, because of that number two, two of the note values, one of which used to be contained within the whole span of a bar, have to be contained within the bar. Therefore, since ordinarily a single semibreve is contained within a bar, because of the position of the number two, it will be worth half a bar, as one can gather better from the example and from what is said in its ottava. Sixy-sixth ottava Therefore, we must discuss The musical proportions. It will be best that I leave aside Their subtle speculations, As they are for the use of the experts of arithmetic. In fact we only we deal with even numbers From an even to another one, and this is its form. [-<149>-] [Cerreto, Dialogo Harmonico, 149; text: Essempio della Dupla] Pupil. I have realised that the number above indicates the action of the present and the lower one the action of the past. Teacher. You have understood this passage correctly. In fact, when there are two different numbers, the number above indicates the quantity of the notes that must be contained within the span of a bar. Moreover, all the different juxtapositions of numbers are made in relation to the note value that spans the length of the bar, so that the other figures may agree in some part of their value, as in the case of the numbers four and eight that create a dupla proportion in the same way. In fact, these species of juxtaposed numbers have been found only because, just as naturally a single not value fits a bar, thus on the base of the indication of the numbers we have to place two, three or four of them, or as many as said numbers indicate. Pupil. I understood well your explanation on the creation of the dupla, but I would like you to explain how the subdupla is created, so that I may employ it in my musical compositions. [-<150>-] Teacher. You can see it easily by reversing the numbers so that the number two is below and the number one si above, thus 1 2, as you can gather from this other example. [Cerreto, Dialogo Harmonico, 150; text: Essempio della Sub Dupla] Pupil. I understood the formation of the subdupla with ease, therefore you may move on to discuss the other proportions that follow. Teacher. So that the first simple genus of inequality may not be incomplete, we must deal with the tripla proportion. I shall say that it proceeds in a similar way to the other proportions that spring from the same multiple genus. In fact, one can understand the tripla and quadruple proportion on one’s knowledge of the dupla. The tripla is the species that is closest to the dupla. So that we remember well the species of the tripla, which is formed by the comparison of these numbers 3 1, we shall show a little example to make it clearer, as well as it respective ottava. [-<151>-] Sixty-seventh ottava Reader, concentrate and pay attention, Since I want to show you another example next, Of the same genus (which will please you) And you shall know that I am not a dishonest. This proportion, this composition, Shall be the tripla with no other error. It is written here beneath, you will see it, And you shall learn everything from it. [Cerreto, Dialogo Harmonico, 151, 1; text: Essempio della Tripla. Tripla] Pupil. It remains for you to show me now the example of the subtripla so that it may be imprinted in my mind. Teacher. The learned writers say that cognito de uno cognoscitur de reliquis (if you know about one of them you will know about them all). Therefore, I shall illustrate it to you with ease, and everything shall be clarified by the example of the subdupla. If you place the smaller number above, and the larger one below, the result will be this 1 3, which will constitute the subtripla. Here is the demonstration. [Cerreto, Dialogo Harmonico, 151, 2; text: Essempio della Sub Tripla. Tripla, Subtripla] [-<152>-] Pupil. Will you continue and deal with the formation of the quadrupla, if you please? Teacher. Pay attention and soon I shall show you the constitution fo the quadruple, since it is created in the same fashion and with the same species that we have seen in the case of the dupla tripla and of the first multiple genus of inequality. Therefore, I do not want to refrain from writing the quadrupla for you in the example written below, so that you may understand with ease what you may not have understood. Moreover, we shall say that the numbers that constitute the quadrupla are juxtaposed in this fashion [4 1 add. supra lin.]. Here is its example and its octave demonstrating the nature and quality of said proportion. Sixty-eighth ottava It remains for us to unveil, dear Reader, The true form of the proportion Called quadrupla with good reason. The proportion is established herewith, Since I wrote it with a clear example, So that I may that I am kind, rather than stingy. [Cerreto, Dialogo Harmonico, 152; text: Essempio della Quadrupla. Tripla Sub Tripla Quadrupla] [-<153>-] Pupil. You have helped me to understand how the quadrupla proportion is created with just a few words, but I need to hear about the subquadrupla. Teacher. I shall enable to master all of this in a few words. Therefore, you must note that the subquadrupla proportion is also formed from the first species of the proportion of greater inequality which corresponds to the multiple genus of inequality. It occurs when the smaller number contains the larger one four times. Said smaller number is placed above the larger one with the addition of the prefix sub and we shall call it supquadrupla proportion, consisting of these numbers compared together thus 1 4. I shall write its example herewith. [Cerreto, Dialogo Harmonico, 153; text: Essempio della Sub Quadrupla, Sub Quadrupla] Pupil. I understood very well how the proportions that spring from the first simple genus of inequality called multiple. Hence, you may proceed to illustrate the second genus of inequality, if it is convenient for you to do so, please. [-<154>-] Teacher. I said above that other proportions are derived from the dupla, tripla and quadrupla species and that different numbers are juxtaposed in them. Therefore, pay attention and listen to this subtle theoretical explanation. Remember that I showed you some aspects of the first multiple genus with some examples, so, now I shall tell you about the second genus, the superparticular. Therefore, I state that, although we have considered and examined very diligently the juxtaposition of simple numbers, I shall not fail to order them appropriately and to say that the multiple genus is created by comparing simple numbers to the unit in particular, namely by comparing the number two, the number three and so on. However, because, when one compares a simple number to another compound one, one moves from a genus to another one, we say that those juxtapositions do not belong any longer to the multiple genus, but to the superparticular, because the numbers are not compared to the number one, as it was the case earlier. Therefore, when the juxtapositions are made in the aforesaid way, one enters with them into other different genera. Therefore, since these two first forms of juxtaposition are very clear and easy because of their simplicity, therefore we shall move on to discuss the compound ones. Hence, [-<155>-] one must know that, if one wants to form different sorts of juxtapositions, the species, as well as the genera, shall be different. This is done by subtracting from the larger number the number of times it exceeds the smaller one. The denominator of said species will consist of the smaller number and the numerator of the larger one. Therefore, to come to the practical explanation of the second genus, which is called superrparticular and it Is the proportion of greater inequality, it occurs when the larger number contains the smaller one with the remainder of a smaller part that is called aliquota, in such a way that the smaller of these two parts shall be the same, as a number, to the larger one, as in the case of two and three and four and three, juxtaposed in this way 3 2 and 4 3. Pupil. I understood well the theoretical explanation. What is left now is for you show me a practical example. Teacher. I like your request, because the example has a more powerful effect on the intellect than words have. I shall write it herewith together with the example of the sesquiottava and of the sesquiterza, since they belong to the same genus. I shall not fail to add its respective ottava. Sixty-eighth ottava Read, Composers and do not fail to do so, As it is worth you knowing everything That our Muse requires. Do not delay, Since everything is explained here and not hidden. You must do so for the proportions Because they are learned and desired. The proportion placed herewith Is the one that belongs to the second genus. [-<156>-] [Cerreto, Dialogo Harmonico, 156, 1; text: Essempio della Sesquialtera, e sesquiterza. Sesquialtera, Sesquiterza] Moreover, pupil of mine, to avoid boring you and being long-winded, I shall write herewith the example of the subsesquialtera and of the subsesquiterza. Pupil. I shall like to look at it, since I am convince that I shall understand the rule better, if I run my eye across it. Teacher. However, first of all I want to remind you how and on the basis of which rule both these proportions are created. This happens when the larger number is placed beneath and the smaller one above, in this way: 2 3, for the subsesquialtera proportion, and in this one: 3 4 for the proportion sesquiterza. I write its example herewith. [Cerreto, Dialogo Harmonico, 156, 2; text: Essempio della Subsesuiqltera, et Subsesquiterza, Sesquialtera, Sub Sesquialtera, Sub Sesquiterza] [-<157>-] Pupil. I cannot deny that, since you have written the aforesaid example for my benefit, you have allowed me to understand everything in the blinking of an eye. Therefore, will you deal with the other proportions next? Teacher. As to the superpartient proportion, I shall say that it springs from the third simple genus or from the third species of the proportion of greater inequality, which occurs when the numbers are different and the larger number contains the smaller one once and the remainder is two, as in the case of 5 and 3. Said proportion is called superbipartient terza. However, if the larger number contains the smaller number once and three parts are left over, the proportion shall be called superbipartient quarta, in this way: 7 4. I am sure that you shall be able to understand all of this in practice with this easy example, especially because it shall be accompanied by its ottava that deals with the same topic. Sixty-ninth ottava Reader, since you were shown What belongs to the second genus, Because nothing was amiss And I have done everything for your convenience, Therefore, Reader of mine, be ready: This is the example, so that you may Defend it in front of other composers. All I said is true, and this is its rule. [-<158>-] [Cerreto, Dialogo Harmonico, 158, 1; text: Essempio della Proportion Superbipartiente terza, Super bi partiente terza] Pupil. What is left now for me is to see now the example of the subsuperbipartient terza proportion. Teacher. I shall write it briefly. It is created in this way and it occurs when the smaller number is placed above the larger one together with the addition of the prefix sub in the name. For instance, it occurs when these numbers are juxtaposed: 2 5, and it will be called proportion subsuperbipartient terza, and also in the case of these numbers 4 7, in which case the proportions shall be called subsupertripartient quarta. Here is the example of its structure. [Cerreto, Dialogo Harmonico, 158, 2; text: Essempio della Proportione Sub superbipartiente terza. Sub superbipartiente Terza] [-<159>-] Pupil. You have helped me to understand everything about the third superpartient genus with very brief explanations. Therefore, I shall be very pleased to move on and to deal with the fourt compound genus, but as briefly as it is possible. Teacher. You must know that the fourth compound genus, or the fourth species of the proportion of greater inequality is the multiple superparticular genus, which contains different numbers and occurs when the larger number contains the number several times - this is understood as to its multiple character – while, as to the superpaticular aspect, it occurs when there is an aliquota part of the smaller number. Therefore, first one has to see how many times the larger number contains the smaller, as its multiple, and then, as its superparticular, if that aliquota part is half of smaller number. Music theorists have called said proportion dupla sesquialtera in this way if the aliquota part is one half of the smaller number, and if it is a third they call it dupla sesquiquarta, thus: 9 4. Therefore, by the same process one can create the other proportions of the same genus, a wellas the proportion submultipla superparticular. Herewith is an easy example of one and of the other, but I do no want to fail to write for you its ottava, since it deals directly with such a proportion. [-<160>-] Seventieth ottava O learned composer, I want to explain to you here The great difficulty that one can see In this fourth genus as to what it must do, Since, if I do not provide evidence, I am not believed. This is the mixture of this genus, As the rule says, if you allow it. Hence be cheerful, for this is its form that does not deviate from reason. [Cerreto, Dialogo Harmonico, 160; text: Essempio della Proportion dupla, e sub dupla Sesquialtera. Dupla sesquialtera Sub Dupla sesquialtera] Pupil. Thanks to your learned explanations and your easy examples I have understood all of the aforesaid rules on the four genera of the proportions. However, since the fifth and last genus remains to be illustrated, I would like to beg you to be brief and substantial. [-<161>-] Teacher. As to being succinct in my explanation, this is more naturally convenient to me, being old, than to you, who are a young man. However, I shall do so as a duty of affection, all the more so, since you need to hear all the essential principles of the practice of music. Therefore, you must know that the fifth compound genus, namely, the fifth species of the proportion of greater inequality is the multiple superpartient genus, whose numbers are different and occurs whenever the larger number contains the smaller one several times, as it is its multiple, but, as superpartient, it will be when there is a remainder of two, three, four or five parts above that number. Said proportion is called dupla superbipartiente terza, and it is written in this way: 8 3. However, when the smaller number is placed above and the larger one beneath, such proportion shall be called submultiple superpartient terza, and thus one shall proceed ad infinitum. I shall show you the example of both proportions, but I shall also write its ottava which shall prove useful and pleasant. Seventy-first ottava We must not fail to say everything, And we must not leave unfinished This discourse on the observation Of the rules that our Muse has given us. Therefore, we must deal with the fifth genus And exemplify its rule. Its proportion is written here With its numbers, and it has been examined closely. [-<162>-] [Cerreto, Dialogo Harmonico, 162; text: Essempio della Dupla, et Sub Dupla Superbipartiente Terza, Sesquialtera, Dupla superbipartiente terza, Sub dupla Superpartiente Terza] Pupil. My sweetest teacher, I remember that at the beginning of this discussion on the proportions, you said that you needed to deal with the topic with subtle speculations. Indeed I have found in it more that I imagined. However, I thank the sky, for I understood everything without becoming stuck in music theory issues. Nevertheless, I shall not refrain from begging you, to do me the favour to resolve another doubt that has remained in my mind, which is this one. Teacher. Pupil of mine, consider that, if you require to have all the obscurities of this discipline of music explained and to discuss everything that is not absolutely necessary, it would be the precisely same [-<163>-] as if one wanted to go back to the beginning and start to discuss everything that is not essential to music itself. Anyway, unveil to me what you are thinking, as I shall listen gladly. Pupil. This is what I wanted to know. A few days ago I happened to be present at a discussion between singers and musicians. After some musical words for five and six voices were sung, among which was a wonderful madrigal for five voices by a composer whom I do not want to name, where there were some tripla or hemiola, however we want to call them, because of the difficulty that occurred in singing it, an irredeemable controversy arose. It was impossible to get them to agree. Some said something, others something else, some believed that it was a major hemiolia, others a minor one. Teacher. To tell you the truth, pupil of mine, that disagreement is similar to the one recounted by the ancients, as to whether the egg came before the chicken or the other way round. Therefore, I shall resolve this doubt with a few words. I state that some theorists believe that when a composition I written with black breves or semibreves, then the hemiolia is major, while, if it is written with semibreves and minims, then the hemiolia is minor. They say all this because they consider the quantity and the quality of the note values, rather than the time, and they are wrong. In fact, learned theorists believe that a hemiolia consists of breves and semibreves or of semibreves and minims, all of them black, [-<164>-] which are sung with the same length of the bar, since it is considered hemiolia when it is sung under the sesquialtera proportion, under the tripla or under the perfect proportion and with whichever sort of note values. However, it is true that there is some difference between them because the hemiolia is always notated in black, and the note values are imperfect because of their blackness. Although you say that modern theorists call the one type of hemiolia major and the other minor, distinguishing the one written with the semicircle, which they call minor, from the one with the halved semicircle, that they call major, nevertheless, both of them have the same value because of that altered sign, so that the one with larger note values is equiparated to the one with smaller note values. Therefore, they are the same thing, because a leaden cantaio weighs as much as one of cotton wool, although the latter occupies a more space. Hence, to give you greater satisfaction I shall write a simple example herewith preceded by its ottava. Seventy-second ottava My wise singer, do not have any doubts On what I want to disclose to you presently, Since you differentiate in your singing Between the tripla and the hemiolia. I want to answer briefly and tell the truth: Avoid the opinion of the majority, As you will not make much progress by speaking against the truth. [-<165>-] [Cerreto, Dialogo Harmonico, 165; text: Essempio della Emiolia] Therefore, pupil of mine, you have now seen that there is no difference at all between one and the other hemiolia, because they are both sung under the same length of the bar. Therefore, these adjectives of major and minor referred to the hemiolia are employed falsely, because these terms are reserved for the major and minor modus, and are used to indicate that their note values are perfect or imperfect, as we shall see at the appropriate place, and this is how both ancient and modern music theorists have interpreted it. Moreover, one must note that the ancient compositions were written with black notes, which are sung in the same way as the hemioliae, as I shall write here with a short example. Also, so that you obtain greater satisfaction, I have set out to write its ottava, that is really worthy to be read. Here it is. Seventy-third ottava In order that we conclude successfully our discourse, Whether you are a composer or a singer, Do not seek anything else on the triple, As we said many amazing things. Therefore, it is good to deal with other matters And never to talk about tripla again. It will suffice to show an example of them, So that everyone may say that I am not wrong. [-<166>-] [Cerreto, Dialogo Harmonico, 166; Essempio delle Triple ] Pupil. My dearest teacher, I have been left satisfied with what you have taught me and illustrated with examples, particularly those concerning the five genera of the proportions. Teacher. It is no small feat to have understood a good portion of the practice of music up to this point, especially the part concerning with the proportions, as there are some composers nowadays who are barely able to write a tripla or a sesquialtera in their composition. Moreover, they hold in little consideration the rules of said proportions, convinced that it is not necessary to know them. This be as it may, I am content with the fact that you understand them. Therefore, I considered that now you must be familiar with the quantitative genus, which contains almost the entire practice of music. I tell you more, the composer rules and balances all of the musical compositions through it and, if a composer is not knowledgeable about it, he cannot compose anything of worth. [-167-] Pupil. Alas, dear teacher, what do I hear? You make me feel besides myself, and, since you have mentioned this rule, please, do not fail to explain it to me, as it is so essential. Teacher. I shall make myself understood little by little. Therefore, I tell you that the quantitative genus is nothing but what shows to us the perfection and imperfection of the five essential note values, namely, the maxima, the longa, the breve, the semibreve and the minima. In order to facilitate the singing of measured compositions, both ancients and modern musicians wanted that some notes should be sung and that others should be rests, which derive from the symbol of the breve. They ascribed to them the name of tempus to which they assigned two numbers, one perfect and the other one imperfect which shall measure each of them with two different signs, namely, the perfect and the imperfect one. The perfect is ternary in value and the imperfect is binary. Their value has been attached only to three note values, namely, to the longa, to the breve and to the semibreve, because the maxima was given its own particular signs, to distinguish its ternary or binary number, so that it might be understood as perfect or imperfect according to the need. This derives from the quantitative genus, as this ottava demonstrates. [-<168>-] Seventy-fourth ottava How great is the power, happy Muse, That you exercise on the learned composers, So that nobody can find an excuse For something not to be what it must be. I have included this genus So that everyone may possess that I want them to possess. Hence, everyone shall say in haughty tones, That they carry the flag of the Muse. Pupil. In truth, when I read the ottava written above I understood many matters that are important for the practice of music. Moreover, you have highlighted in a learned fashion the qualities that the good composer must possess. Among many other important elements, it says that it is necessary that the composer masters what is contained within the quantitative genus. Therefore, do not fail to write me a sort example of this. Teacher. I want to meet your request and I shall start from the first perfection that is the major perfect modus, but first I shall write its ottava, which shall please you when you hear it. Seventy-fifth ottava Come on, do let us talk of the major modus, Which is not only major, but perfect. Its sign provides you with great rigour, Since it makes the maxima perfect, as it was said. Therefore, I say without mistake, That it is very powerful in the case of the longa, Since this modus is so effective, That it can alter the value o the longa. [Cerreto, Dialogo Harmonico, 168; text: Essempio del Modo maggior perfetto, Modo maggior perfetto 12, 4, 8] [-<169>-] Pupil. It is convenient that you show me now the example of the minor perfect modus, so that I may be able to write it when I need to. Teacher. I shall be happy to write it. Moreover, since the major perfect modus is indicated by writing in the singing part the circle with two number threes, as we have seen above, therefore, we shall notate the minor perfect modus only with the circle and one number three, because such signs indicate the perfection of the longa and the alteration of the last breve. I shall write the example preceded by its own ottava, from which you will gain benefit and instruction. Seventy-sixth ottava I want also tell you about the minor modus. When it is perfect it is very powerful And dominates the breve As long as it is close to it. What I say, I say it gladly, Namely, that the excellence of this more Consists in altering the breve, By rendering it larger by a half. Pupil. I understood the content of the aforesaid ottava, but it does not say when and where the longa becomes perfect and the breve altered. Teacher. Slowly, slowly, pupil of mine, since it is not possible to say and to everything in one instant, because, when the occasion arises, you will understand everything. Therefore, consider closely the example of these sing of perfection, so that you shall be able to master them with greater ease by perusing them. Here is the example. [-<170>-] [Cerreto, Dialogo Harmonico, 170, 1; text: Essempio del Modo minor perfetto. Modo minor perfetto, 6, 2, 4] We shall say next that the same can be said and can occur in the perfect tempus, as we saw in relation to the maxima and to the longa. In fact, the breve can be made perfect and the semibreve can be altered. Here is its example and also its ottava on the subject of the perfect tempus. Seventy-seven ottava Since we mentioned what is the power Of the minor modus when it is perfect, We shall describe the power of the tempus And what it can do when it wants to. When it is perfect, it is very powerful, And gives value to the breve when it appears. This is what its rule declared, When it is subject to the perfect tempus. [Cerreto, Dialogo Harmonico, 170, 2; text: Essempio del Tempo perfetto, Tempo perfetto, 3, 1, 2] It remains for us now to illustrate the fourth perfection of the quantitative genus, which consists in the perfect prolation. It is indicated in practice with the circle or with the semicircle with a dot in the middle and it represents the perfection of the semibreve and the alteration of the minim, as it will be show at the right time and on the appropriate occasion. [-<171>-] All these is supported by the relevant ottava. I am sure that you shall benefit from reading it. Seventy-eighth ottava Listen, refined Reader, to what I want to say. Now that the perfection Of the semibreve ensues, I want to Complete my discourse by telling you about the prolation. Nobody can prove me wrong, When I say that the point and the time Show that such proportion is perfect, And as such it has been defined by the Learned. [Cerreto, Dialogo Harmonico, 171; text: Essempio della Prolatione perfetta, [[Prolatione perfetta, 3, 1, 2]] Prolatione perfetta 3, 2] Pupil. Now that I have heard and understood the four sorts of perfection that spring from the quantitative genus, it will be good if you show me next the four sort of imperfection of the same genus. Teacher. Everyone knows that you have asked me intelligent questions on what you need in the practice of music, especially on the important topics. Therefore, pay attention and remember what was said above, when we discussed the major perfect modus, namely that the maxima could be perfect and the longa altered, while under the minor perfect modus the longa can be perfect and the breve altered. Finally, in the perfect tempus, the breve can be perfect and the semibreve altered, while under the perfect prolation, the [<-172>-] semibreve can be perfect and the minim altered. Nevertheless, one must assume than when a composition is inscribed at the beginning with a semicircle that it is understood that that composition is sung under the imperfect tempus. The major and minor perfect modus can originate from said imperfection, if we a semicircle either halved or not before the numbers, as one can gather easily from the example below, starting from the major imperfect modus and from its ottava, which tells some something beautiful. Seventy-ninth ottava Now we must talk of you, major modus. I want to tell you that, now that you are imperfect, You do not govern the longa any longer, Nor you can contrast the imperfect. Since you have lost your vigour, You can go away with the other songs, and you have to sing the maxima and the longa with the time that you sustain. [Cerreto, Dialogo Harmonico, 172; text: Essempio del Modo maggior'imperfetto. Modo maggior'imperfetto, 8, 4, 4] The perfect minor modus can be turned into imperfect by placing a semicircle at the start of the composition. Such imperfection has the effect that the longa is not perfect and the breve is not altered. The note values are sung accordingly, as one can gather better from the example notated underneath and from its ottava. [-<173>-] Eightieth ottava The learned Muse wants and also says That in the imperfect minor modus The cleaver singer cannot sing The longa as imperfect, as I said. The learned composer does not Contravene reason and the rules, But he reinforces and desires That all that is written is true, and not a lie. [Cerreto, Dialogo Harmonico, 173; text: Essempio del Modo minor imperfetto. Modo minor imperfetto, 4, 2, 2] Pupil. Shall we see next how one should indicate the imperfect tempus at the beginning of the melody? Teacher. The imperfect tempus can be notated not only at the beginning of the composition, but also in whichever part of it, since this manner of placing different mensural sign is left to the judgement of the composer. However, now we are dealing only with the rules and principles of different sorts of perfection and imperfection and of the essential note values used in singing. We shall say immediately that, when one places a semicircle at the beginning of a composition, the breve is sung as imperfect and it is worth two semibreves, as one can see better from the example and by reading the relevant ottava, which shall be also beneficial in some measure. Pupil. I am keen to hear not only the example, which benefits my practice, but the ottava, since it deals with the same rule. Teacher. I shall write the ottava herewith to provide you with greater satisfaction. [-<174>-] Eighty-first ottava We shall also talk about the imperfect tempus. I say that the rule states that it breve Must be sung for two semibreves, And this must be observed by the good singer. The learned composer himself is also forced Not to oppose reason. This is the example, and who wrote it here, Has thought about it very deeply beforehand. [Cerreto, Dialogo Harmonico, 174; text: Essempio del Tempo Imperfetto. Tempo Imperfetto, 2, 1] To avoid being long-winded in this topic of the different sorts of perfection and imperfection, I want to show you an example of how to write the mensural sign that indicates the imperfection of the imperfect prolation. This occurs when one writes a semicircle in the composition without a dot in the middle. In that case the semibreve is sung in such a way that it corresponds to two minims. Pupil. You have give me great satisfaction, not only because you have explained succinctly the substance of the rule of the perfect prolation, but also because you have made me understand it with ease. Therefore, will you provide me with a bit of an example, if you can, just enough so that I may understand the substance of said rule Teacher. There is no need to be so long-winded. I shall write it with a few notes, but it shall be preceded by its ottava and followed by its example, as you can gather herewith. [-<175>-] Eighty-second ottava Come on, let us conclude our review of the types of imperfection That spring from the quantitative genus. Let us not fail to explain other principles, So that the discourse may more expedite. Let the perfect prolation prompt us still To conclude its explanation: its semibreve has to be sung As two single minim without alteration. [Cerreto, Dialogo Harmonico, 175, 1; text: Essempio della Prolatione imperfetta, Prolatione imperfetta 2 minime] I warn you that sometimes it occurs that the sign of the imperfect time is removed in favour of the one indicating the minor modus by placing a number three before the one of the perfect tempus. In that case we say that those note values are sung under the minor perfect tone and the perfect tempus, as we consider herewith with the example and with its ottava. Eighty-third ottava Since the Muse wants to demonstrate The great power that she exercise on our compositions, I wanted to write herewith Two mensural signs with different inventions. Not only do they alter their singing And their perfection occurs in different ways, One belongs to the minor perfect modus, While the other one is of the tempus, as I said before. [Cerreto, Dialogo Harmonico, 175, 2; text: Essempio del Minor perfetto, et Tempo perfetto, Modo minor perfetto, et Tempo perfetto., 3] [-<176>-] Moreover, I shall say that in practice composer write in their composition the imperfect tempus with a number two. This shows that the composition is sung under the minor imperfect modus and with imperfect tempus. Therefore the longa and the breve are sung as imperfect, notwithstanding the fact that the tempus is halved. I shall write a small example together with its ottava, which highlights some useful detail. Eighty-fourth ottava We shall also speak of the different sorts if imperfection Of the tempus and also of the minor modus. The tempus sings with its principles, And the minor modus with its rigour. You must pay quiet attention to what I explain, As it is all true. Hence, the example shall prove it clearly, As its notes are sung in pairs. [Cerreto, Dialogo Harmonico, 176; text: Essempio del Modo minor imperfetto, e Tempo imperfetto, Modo minor'imperfetto, Tempo imperfetto, 4, 2, 2] Since I had the chance to show you the aforesaid example of the minor imperfect modus and of the imperfect tempus, I remembered that it is not a good not to fail to deal with the major and minor modus, perfect and imperfect, which was used with great competence by our ancient musician, which is the true spring of practical and speculative music. This consists in placing [-177-] the circle [O] and the two number threes at the beginning of the composition. As to what follows in relation to the other sorts of perfection and imperfection, they wrote two rests of a circle and two number threes to indicate the perfect major modus and, as to what follows in relation to the other sorts of perfection and imperfection, they wrote two rests of perfect longae. In the case of the minor perfect minor modus they wrote the rest of a perfect longa; when they wanted to indicate the major modus was imperfect, they wrote two rests of imperfect longae and so that the minor modus may be understood as imperfect, they wrote a rest of an imperfect longa in this way, as you can see that they are written herewith. However, so that all these concepts may be understood with ease, in the first place I have written the ottava, from which you may derive some benefit. Eighty-fifth ottava Our Muse wants to show you still How its value is rendered perfect, And wants that the rest may render The note value perfect, if it is major. I do not want to fail to show The other imperfect modi Are reinforced if the imperfect rest is placed before them. This is how reason has ordered it. [Cerreto, Dialogo Harmonico, 177; text: Essempio del Modo Maggior, e minor perfetto, e del Modo maggior, e minor imperfetto usato dagli Antichi musici, Modo maggior perfetto ò uero cosi Modo maggior imperfetto Modo minor perfetto Modo minor imperfetto 12, 4, 8, 2, et Tempo perfetto, et Tempo imperfetto] [-<178>-] Pupil. I was exceedingly content, my sweetest teacher, because you have helped me to understand this new practice, namely, that the rests have the power and strength to render the two values of the maxima and of the longs perfect and imperfect, and also to alter the breve in the minor perfect modus. Teacher. Now, I want to move forward and for you to know that when ancient composers used to write these two signs at the beginning of their compositions, namely, C 2, they wanted that their compositions should be sung under the imperfect tempus and under the minor imperfect modus, while those inscribed thus, C 3, were meant to be sung under the imperfect tempus and the minor perfect modus, and those that had this mensural sign, O 2 had to be sung under the perfect tempus and the minor imperfect modus. They also wanted that their rests should be counted in a similar way according to the perfection and imperfection of the mensural sign and of the numbers. These principles were observed with extreme diligence because they believed that such law had been discovered learnedly by those ancient musicians. The proof that this is true is in the fact that the learned musicians of our day employ them and regard them highly. Pupil. In truth, when one considers these rules of the quantitative genus, they appear to be obscure and difficult. However, since they have been explained with such simplicity, they became easy to understand. I have already understood all of the most substantial and fundamental elements contained in said quantitative genus, [-<179>-]. Therefore, now you may proceed to discuss the rest.. Teacher. Slowly, pupil of mine! We have not yet finished our discourse, as you shall realise soon. Therefore, you must consider that it is necessary to discuss another rule of the tempus, which is defined in our practice as being nothing but a certain particular form or quantity of note values considered under the value of a breve, which is subject either to the perfect tempus or to the imperfect tempus, as it is shown in this example written herewith and also as the way its ottava explais it. Here it is. Eighty-six ottava Happy tempus, since you are they measure Of the note value of the breve and of the others. The composer determines the speed of his music Thanks to you and only you he observes. Whether the tempus is perfect or imperfect, The breve shall he always your mistress, Never let the tempus stop being your leader and protection, Since without the tempus all music is dead. [Cerreto, Dialogo Harmonico, 179; text: Essempio del Tempo perfetto, et imperfetto mediato, e senza medio. Tempo perfetto, imperfetto, mediato, Breue, perfetta, imperfetta] [-<180>-] Pupil. You told me above, if you remember correctly, that the perfections and imperfections of the quantitative genus are four, but up to now we discussed only three of them. Therefore, please, do not fail to provide me with some rule on the fourth perfection and imperfection. Teacher. You are correct in saying that what remains to be discussed is very important for the practice of music. Therefore, consider what ancient and modern learned musicians have observed on the subject of the prolation, which they define simply as the number of minims ascribed to the value of a semibreve. It is indicated in two ways with the sign of the circle and with the semicircle. They called one of them perfect and another one imperfect. The one based on the number three is called perfect prolation, while the one based on the number two is called imperfect prolation. In music they are written in two ways, namely, with the dots, thus [Od] [Cd], and without the dots in the middle, thus [O] [C]. The time signatures with the dots in the middle, the prolation shall be called perfect, while those without the dots will be called imperfect prolation proceeding with two minims. Similarly, one notes that under the perfect prolation the rest of a semibreve is perfect and it corresponds to three minims, while in the imperfect prolation it corresponds to two minims. Therefore, pupil of mine, consider very carefully this last rule of the perfection and imperfection, because I can tell you, and I tell you the truth, that nowadays there are some composers who do not know what a perfect prolation or an imperfect prolation is, but they employ them in their composition. What I said is enough. I shall notate a comprehensive example of this and its relevant ottava, since it is necessary to understand this topic. [-<181>-] Eighty-seventh ottava I want to explain everything that Concers the prolation called perfect with ease. The composer cannot prove me wrong, Since our Muse has spoken thus. I do not want to fail herewith to describe The prolation called imperfect: The semibreve must be sung According to the time signature. [Cerreto, Dialogo Harmonico, 181; text: Essempio della Prolatione perfetta, et imperfetta, Prolatione perfetta, imperfetta, 3 in 3, 2, Tempo imperfetto, perfetto] In addition, we shall say that composers write the perfect prolation in their harmonies in this way [Od] [Odrvd]. Therefore, we shall say that, since said circles represent the perfect tempus, whether halved or not, when they are used we consider the breve is perfect and corresponding to three semibreves, and that every semibreve corresponds to three minims, both in the halved tempus ans in the whole one. Here is the example accompanied by its ottava. Eighty-eighth ottava It was also said above very well What concerns the prolation, Whether it is perfect or not, and what It suits it, as it has been shown with reason. We shall say herewith what it contains Here, two tempora and the perfection. And the breve and the semibreve are perfect, Because the dot provides them with what they require. [-<182>-] [Cerreto, Dialogo Harmonico, 182, 1; text: Essempio della Prolation perfetta in Tempo perfetto, Prolation perfetta in 3, Tempo perfetto, mediato] Composers also write said perfect prolation with the halved semicircle, thus [Cdrvd], so that the breve is sung as imperfect and comprises two semibreves, while the semibreve is sung perfect and contains three minims. Here is the example together with its ottava. Eighty-ninth ottava Our Muse has explained The length of the semibreve In the imperfect cut time With the dot added in the middle. Hence, I have taught it to you, My Reader, as far as I could and it is my task. As to its time, the example Provides a reliable illustration of it. [Cerreto, Dialogo Harmonico, 182, 2; tempo: Essempio della Prolatione perfetta in Tempo imperfetto mediato. Prolatione perfetta in 2, 3 Tempo imperfetto] However, in order that you may understand everything on the subject of the perfect prolation, which one can write in the perfect and imperfect tempus and in [-<183>-] the halved and not halved, I do not want to fail to notate an example preceded by the octave that discusses the matter. Eighty-ninth ottava Lucky breve and also semibreve, Our Muse has thought you worthy To be made perfect, as it must be done, So that each of you may be well grounded. Each one that receives the other perfection From the perfect tempora is already well grounder. The example that is written here beneath Has illustrated everything easily. . [Cerreto, Dialogo Harmonico, 183; text: Essempio della Prolation Perfetta in Tempo perfetto, et imperfetto. Prolation perfetta, 3 semibreui, Due semibreui, In tempo perfetto, imperfetto] Pupil. Next, I would like to know why it has not been assigned another different sign to the other note values, namely, to the minim, semiminim, quaver and semiquaver, as it was done in the case of the other four notes. Teacher. I tell you in reply that ancient musicians who invented the theory and practice of music did not want to assign them or create for them other sign than the one that was ascribed earlier, which is the tempus, perfect or imperfect. This does not occur in the case of the other four note values mentioned above, [-<184>-] since the maxima in the major perfect modus is worth three longae (just as its perfect rests) and the long in the minor minor perfect modus is worth three breves, while the longa in the minor imperfect modus corresponds to two breves. The rests follow the same rule, as long as the last number is two. Therefore, the minim, the semiminim, the quaver and the semiquaver cannot have a particular tempus, but they are subject to the first tempus mentioned above, whether it is perfect or imperfect. It is true that the minim under the perfect prolation can be altered. Also, it is an agent note value, rather than a patient, and it cannot be made perfect, as it occurs, conversely, in the case of the maxima, because it does not have a note value greater than it is. Therefore, as I said about the quantitative genus, learned musicians, both ancient and modern, have observed all of these rules. I will say more: as to the fact that we regarded the minim as an essential note value, that name suits it, because, in the perfect prolation, it produces something that can be altered, as we stated above. Pupil. I understood well what you say, but, please, resolve this other doubt of mine: why do some music professional say that the perfect prolation notated in the perfect tempus must be called major perfect prolation, while the one written in [-<185>-] in the imperfect time must be called minor perfect prolation? Teacher. I shall reply by telling you something good. In fact, this opinion helf by some theorists is not shared by all those who profess the art of music for the reason that I told you earlier when we discussed the hemiolia. In fact this qualification of major and minor pertains only to the major and minor perfect and imperfect modus and not to the tempus as such persons maintain. Therefore, it is necessary to disregard these tales of musicians of little experience. If these persons were to read Gaffurio at chapter nine of this Practice, or the sixth opposition in the second book of Pietro Aron’s Lucidario, they would discover that what I maintain is the truth. Pupil. You have given me satisfaction as to the doubt that I put forward to you, but, if you please, I require that you tell me if I need another rule to write some pleasant composition. Teacher. I do not want to fail to tell you the truth on the question that you asked me, to avoid making you sad, but, since I told you many times that the rules of music are infinite and, therefore, it is necessary for a beginner as you are to study with consistency and to begin by composing something in an easy style, because consistency fosters ability, since we have dealt in this last part with a few rules of the quantitative genus, it will be very appropriate now of how the musical notes can be made perfect. Therefore, we shall say that under the modus, tempus [-186-] and prolation, many factors cause each of the note values mentioned above to vary according to which one of them (there are several) accompanies them. Hence, some have been called agent and other patient, as I explained a little earlier when I said that the minim is an agent note because it cannot receive any perfection, although it can cause the other note values that we mentioned to become imperfect, because it is smaller than any other note value, albeit it can be divided into two semiminims and into four quavers. I also said to you that the maxima could not be altered, but it could be made perfect. For this reason it is called patient, as a note value, because, since it is the largest note value of all, cannot suffer being made imperfect. They also say that the other three essential note values, the longa, the breve and the semibreve, are called agent and patient, because they can be made perfect and imperfect. The perfect note value corresponds to three of the notes that are its immediately smaller portions. For instance, the perfect maxima will be worth three longae, the perfect longa three breves and the perfect breve three minims. [-<187>-] That perfection of note values shall not ensue, however, when a note value shall be placed in front of a similar one, either white or black, namely, the maxima in the major perfect modus, the longa in the minor perfect modus, the breve in the perfect tempus and the semibreve in the perfect prolation. All this matter has been well considered both by ancient and modern composer, because something cannot be rendered imperfect by something that is similar to it. One can note that the same happens in two subjects that are equal virtually and potentially one cannot surpass the other or be surpassed by it. This is understood with regard to the form of the note rather than to its colour, because the form is what confers essence to the subject. Therefore, the fact that the note is black does not deprive it of its shape, as for instance, the fact that someone is black does not render him devoid of reason, since the colour is only accidental and, although sometimes it can be separated from the subject. Therefore, no note value can be rendered imperfect by another one larger that it is, but by a smaller one, because the larger note value is always patient in comparison to the smaller and the smaller note value is always agent in relation to the larger one. Moreover, when the perfect note value is placed [-<188>-] before the rests of its denomination under the signs of perfection, those very rests produce the same perfection that their respective notes would produce. Also, we say that, when a maxima is placed before a ligature of the value of two longae, or a longa in front of a ligature of the value of two breves, or a breve in front of a ligature of the value of two semibreves, or a semibreve in front of two minims or in front of the rests that correspond to those note values, as long as said rests are placed on the same line, those note values shall be perfect, because said ligatures or rests placed in that fashion have the power to unite. However, if those rests are employed separately, then that rule is not valid. Pupil. You have spoken very well. However, they say that the examples are more beneficial than words. Therefore, shall you do me the favour of writing me an illustration of what you have discussed accompanied by its respective ottava? Eighty-ninth ottava We shall talk again of the imperfections That the maxima has in music, Who patient as to the perfection And also agent in music. The maxima itself has the added feature, That it is only agent in music. This is true, as learned singers have found When they added them up. [-<189>-] [Cerreto, Dialogo Harmonico, 189, 1; text: La prima figura di ciascuno essempio è perfetta] Those note values can be made perfect by placing a dot next to each of them as long as there are the signs of perfection, without placing any other note in front of them. I show you an illustration of them herewith together with the ottava that provides some detail on this matter. Ninetieth ottava O what a great power has the Dot, Who can make every note value perfect. However, one must ensure That the signs of perfection take care of it. Such Point is not always united, Since sometimes the notes are against it. Therefore, I said what I can say of it, In such a way that the Muse cannot disprove us. [Cerreto, Dialogo Harmonico, 189, 2; text:Tutte queste ffigure sono perfette per rispetto del Punto] [-<190>-] The aforesaid larger note values can achieve perfection under the same signs of perfection when they contain in between two or three smaller note values which are their immediate subdivision. The same can be said of the note values and of the rests of a same value placed together in the same way. Moreover, when one places between two larger note values five smaller immediate subdivision, the first larger one shall be perfect and the last smaller one shall be altered. When one places six smaller immediate subdivisions under the same sign of perfection, the first larger note value shall be perfect, but one does not alter the last smaller one. I shall produce the example with its relevant ottava. Ninety-first ottava Consider the power of the mensural signs, Especially when they indicate perfection. In fact, often the make their note values Sing with perfection according to the rule. They can alter the smaller values, When it is required by their laws. The composer must always pay attention to this, In order that his composition may be perfect. [Cerreto, Dialogo Harmonico, 190; text: La prima figura di ciascuno essempio è perfetta 3, 2] [-<191>-] [Cerreto, Dialogo Harmonico, 191; text: La prima figura di ciascuno essempio è perfetta, è l'ultima minore è alterata, 3, 2] Pupil. I considered all the perfection that the larger note values can achieve and the alterations of the smaller ones, therefore, I would be very keen to discuss the imperfection of the same note values next, so that I may be knowledgeable of one sort and of the other. However, I would beg you to explain them in a short and substantial manner, so that it shall not be so arduous and we may save time. Therefore, you may start, while I shall be intent on listening to you. [-<192>-] Teacher. It is appropriate that we should deal with this topic, therefore pay attention and listen, because, since we have talked about the essential imperfections, now we shall talk about the imperfections, which are also essential, of the four not values, naely, the maxima, the longa, the breve and the semibreve, but also those of the minim, since it is a principal note value. Therefore, you must note that the maxima is considered imperfect under the signs of perfection when it is worth two longae; the longa is considered imperfect when it is worth two breves; the breves when it is worth two semibreves, and the semibreve when it is worth two minims. However, said imperfection occurs when said four note values are not accompanied by the accidental signs shown above. It is true, however, that the note value that suffers that imperfection shall be in this condition, when it will be larger than the note value that causes the imperfection, and, conversely, when the note value that causes the imperfection is of a smaller value. Therefore, the condition of imperfection is judged on two criteria: first of all as to the whole, and, secondly, as to the parts in relation to the whole. In the first case one considers a note value that is rendered imperfect by an immediate subdivision, and this is the greatest imperfection that can be conferred to it and it occurs when a maxima is rendered imperfect by a longa, a longa by a breve, a breve by a semibreve and a semibreve by a minim. The second one occurs when a maxima [-<193>-] is rendered imperfect by a breve, a longa by a semibreve, a breve by a minim, and the semibreve by a semiminim, and one says that such note values are rendered imperfect by a remote note value. Then, when a maxima is rendered imperfect by a semibreve, the longa by a minim, the breve by a semiminim and the semibreve by a quaver, then we say that said note values are rendered imperfect by a note subdivision that is more remote. Finally, when a maxima is rendered imperfect by a minim, a longa by a semiminim, a breve by a quaver and a semibreve by a semiquaver, then we say that said note values are rendered imperfect by a subdivision that is very remote. I draw your attention to the fact that, although rests are not subject to imperfection, since they are agent values instead of patient, nevertheless they have the power to render a note value imperfect. The same is achieved by dots and coloration, which is the filling-in of the note. Pupil. I would never have imagined that the quantitative genus was so rich in so many detailed rules, but, since you have explained it to me with such ease, I have those rules imprinted in my memory. Therefore, all that I am missing is their practical illustration. Teacher. While you ask for it, I am keen to provide it. Moreover, I shall add to it its relative ottava, which shall give you satisfaction. [-<194>-] Ninety-second ottava Reader, I do not want to fail to tell you Of the imperfection of the note values. The Muse cannot prove me wrong on this matter, Although it is a very obscure topic. However, so that I may speed up this discourse, So that the singer may not be concerned about ir, The larger note is the one that suffers the imperfection, And the one that confers it is the smaller one. [Cerreto, Dialogo Harmonico, 194; text: La prima figure di ciascuno essempio è imperfetta. 8, 4, 2, 1] [-<195>-] In order to conclude this discussion of the quantitative genus, I do not want to fail to provide you with some other rules concerning the dot, which is an essential element of music. Therefore, one must note that the dot in our practice of music is considered in the same way as an expert of geometry defines it, namely, that it does not have any dimension and that it is indivisible, or in the same way as philosopher explain it when they say that it is a unit furnished with position. However, in music it is defined as nothing by a particle, a quantity or a very small sign that is placed as an accidental next to the note values in different ways, namely, after the note, above it or between one and another one. Practical musicians have ascribed to it four functions: as a sign that confers perfection to said note values, as a sign that enlarges them, as a signs that divides them and a sign that doubles their value. Therefore, since said point has four functions, as we said above, for this reason they named it in four ways, namely, dot of perfection, dot of enlargement, dot of division and dot of alteration or doubling dot. Therefore, the dot of perfection is the one that is placed immediately after the note that can be made perfect under the signs of perfection and it is written so that the perfection of said note value may be preserved, as one shall be able to ascertain with greater ease from the example noted herewith and also from its ottava. [-<196>] Ninety-third ottava Tell me, Muse of mine, what will I have to do To demonstrate your great power? Since you see now what topic I am dealing with, Allow me to explain it with every excellence. I shall have to demonstrate the perfection Of the first dot in front of you. This is the dot of perfection, Which renders the note values perfect with great reason. [Cerreto, Dialogo Harmonico, 196; text: Essempio di Punto di Perfettione] The point of enlargement is the next one. It occurs when the dot is placed after the note that cannot be made perfect in any other way, but that it is subject to the signs of perfection. Said dot is employed in the ligatures and in separate note values. Here is the illustration of it with its ottava. Ninety-fourth ottava O Muse, you know great art And great value, since you make so much of a single dot, that the entire world still employs it, While I sing it in verse and not in prose. I cannot find an excuse to do so, Since they are matters very demanding. This is the point of enlargement, which always pleases the good singer. [-<197>-] [Cerreto, Dialogo Harmonico, 197; text: Essempio del Punto di Accrescimento] The following topic is the third dot called dot of division, which occurs when it is placed between two similar smaller note values that are next to each other and located between two larger note values under the signs of perfection. The only function of this dot is to divide and render imperfect the first and the last larger note value, and it is written in the music above the two smaller notes and iin the middle, so that said dot separates one of the smaller note values from the other and unites them with the two larger ones. Said dot has the same function when it is placed between a rest placed first and a note value placed after it. The illustration of it is notated here beneath, preceded by its ottava. Ninety-fourth ottava O how very loving are you Muse of mine, In separating the smaller note values, And by separating them you do a great favour To the other two larger ones. Listen to me and be kind to me while I pray you. In fact, if a great noise is made about this intricate matter, The rests still want their prerogatives, So that they may all be happy. [-<198>-] [Cerreto, Dialogo Harmonico, 198; text: Essempio del Punto di Diuisione, 2] The fourth dot, called of alteration or doubling dot occurs when the composer places it in front of two smaller note values that have in front of them a note value that is immediately larger. Its function is to highlight if the perfect tempus is considered between said smaller notes. However, it is necessary to place said dot of alteration in the previous tempus and at the beginning of the following one. It is called dot of alteration or doubling dot because it is marked to indicate that, since the first note value is equivalent to the number one and the second one to the number tow, it is appropriate that the number two is placed after said number one. We shall illustrate how it is notated above the smaller notes, as it is not sung, in its example together with its ottava, Ninety-fifth ottava This other dot deserves great attention, Since the smaller value can be altered, But with the signs of perfection So that they can be sung in double time. There is no contradiction in it, And the Muse wants that we observe That the dot is not sung, but it is placed To indicate the alteration. [-<199>-] [Cerreto, Dialogo Harmonico, 199; text: 8, 4, 2] Pupil. Thanks to your doctrine you have explained to me these proportions and alterations of the dot and you have clarified them with such ease, that I have been left satisfied. Therefore, you shall be able to discuss other rules that I will find necessary. However, do explain them in such a way that I may be able to understand them. Teacher. You were right to ask me that I should tell you what you need to know, which shall conclude what one can observe on the subject of the major and minor perfect modus, of the perfect tempus and of the perfect prolation under the signs of perfection. We shall also say that it is possible to produce alterations and to double the minor values without employing the dot in this way. When two smaller immediate subdivisions are placed betwee two larger note values, in that case the first larger value shall be perfect and the last smaller one shall be altered. The same can occur when two smaller note values are placed between two rests corresponding in value to the two larger notes, or when a rest of the value of the first larger note is placed near the two smaller [-<200>-] note values. In this case the first larger note value shall be perfect and the last smaller one shall be altered. Also, when a rest equivalent to the smaller note value is placed between the two larger ones, the first larger note value shall be perfect and the last one shall be altered. All of this can be done only when the signs of perfection are involved, as we said earlier on anoter occasion. The example shall be notated herewith accompanied by its ottava. Ninety-sixth ottava Here are the tempora and what they can do, Especially when they are perfect. Often they make their note values Sing with perfection and following their rules. They alter the smaller note values, When it is required by their rules. The composer must be always alert to this, So that his composition may be perfect. [Cerreto, Dialogo Harmonico, 200; text: La prima figura di ciascuno Essempio è perfetta, e la seconda delle due minori è alterata. 3, 2] [-<201>-] Pupil. From what I understood through the rules and through the examples, I believe that I understood everything. Nevertheless, I presume that I need some other essential rule. Therefore, most sweetest teacher of mine, if you think I am correct, please, do not fail to present me with it, as I shall listen to you gladly. Teacher. Pupil of mine, I believe that up to this point we have covered a little less than half of the entire subject matter of music. However, if you are eager to ask me question, I want to be as fast as I can in answering. Therefore, you must ensure that you have knowledge of the tones on which musical compositions are based, because you cannot reach a degree of perfection without this knowledge. Therefore, the main tones or modes, as the ancient called them, are no more than eight, although modern theorists consider them to be twelve. I refuted this claim as clearly as possible in the second book of my printed book Musical Practice. Therefore, I shall not be long-winded in discussing this topic, but I shall say what you need to know to compose for several voices, and I shall avoid the topic of the ecclesiastical tones. So, since the tones are eight, we shall start discussing the first one. Since the first tone starts from the low D sol re and spans from said note to the high D la sol re an octave higher and the whole of its body goes through a fifth and a fourth both ascending and descending [-<202>-] it is called authentic, because the fourth is placed above the fifth. Conversely, we shall see that the second tone is based on the same note of the low D sol re ut, although it has the fourth below and the fifth above, hence it is called a plagal tone by theorists. However, both tones consist of a fifth and a fourth both ascending and descending. Moreover, we shall say that both the first and the second tone consist of the first species of the diapente and the first species of the diatessaron, where diapente means fifth and diatessaron means fourth. The third tone is based on the low E la mi and ascends an octave up to the high E la mi. Similarly, it contains a fifth and a fourth and it is called authentic for the same reason mentioned above, namely, because it has the fourth above, namely from the note [sqb] fa [sqb] mi to the high E la mi. Since the fourth tone consists of the same fifth on which it is based the third one, which is its relative authentic, however, because the fourth is below the fifth, it is called plagal, as we said in relation to the second tone. I add that the third tone and the fourth have been created from the second species of the diapente and from the second species of the [-<203>-] Diatessaron. The fifth tone is base on the low F fa ut and ascends by the interval of an octave up to the high F fa ut. It is authentic because it has the fourth above the fifth. As to the sixth tone, although it consists of the same fifth, because it is plagal, it is built with the fourth beneath, namely, from low F fa ut to the first C fa ut. These fifth and sixth tones are created from the third species of the diapente and from the third species of the diatessaron. Finally, we say that the seventh tone occurs between the note of high G sol re ut ascending by an octave to the highest G sol re ut. It is called authentic because it has the fourth above the fifth, namely, between the D la sol re and the highest G sol re ut. As to the eighth tone, it is based on the same high G sol re ut, but, because it is plagal, its fourth is located between high G sol re ut and the low D sol re. I add that when the composer writes a polyphonic composition, he must conclude it on the note on which the octave of the tone is based, as long as the composition is not divided into two or more sections. These seventh and eighth tone are created from the fourth species of the diapente and from the first species of the diatessaron. Therefore, pupil of mine, I have made you understand all of this easily [-<204>-] and with a short explanation. However, so that you may understand better the constitution of all said natural tones, I want to write an example of them herewith preceded by its ottava, which will deal with them in a fruitful way. Ninety-seventh ottava How mistaken are the composers, Who believe that the tones Are twelve. However, I would like Us to say this with true arguments, namely, That the tones are eight, not seven, not six, Because the extra four have improper names. The Holy Church has always said so, And so say I, speaking with respect. [Cerreto, Dialogo Harmonico, 204; text: Essempio dell'Otto Toni naturalj, Primo, Secondo, Terzo, Quarto, Quinto, Sesto, Settimo, Ottauo Tono, Autentico, Placale] Pupil. My sweetest teacher, I cannot deny that you have explained to me the structure of the tones with the greatest succinctness. I gather clearly from it that their number cannot be greater than eight, since you have told me that their species consist of four species of fifth and three species of fourths. Therefore, since the species are only these, it is true what you have told me. Teacher. Moreover, pupil of mine, I want you to know that this other form of tones called transposed or acquired tones cannot consist of more than eight tones. They shall be written with the accidental of the b flat and are transposed by musicians a fourth above or a fifth below. They consist of the same four fifths and three fourth, as the natural ones illustrated above, and with the same species. I shall show you an illustration of them, but first I shall write the ottava that deals with this matter. Ninety-eighth ottava O wise Ptolemy, you were able To find the principle of our music. You added the flat sign to the systems, In order to vary the melodies. You called the names with different names In your learned and beautiful inventions, So that they were called later on With the name of acquired or transposed tones. . [-<206>-] [Cerreto, Dialogo Harmonico, 206; text: Essempio degl'Otto Toni Trasportatj, ò uero acquisiti, Primo, Secondo, Terzo, Quarto, Quinto, Sesto, Settimo, Ottauo Tono, Autentico, G sol re ut, A la mi re, B fa, C sol fa ut] Pupil. I understand clearly that this practical music springs from speculative music, because its principles are governed by music theory, which does not stray from the truth. Therefore, I want to remind you not to fail you to do me the favour of providing me with other rules that you know I might require, if there are any, and I shall not fail to listen to you with my usual attention and obedience. Teacher. I want to reply to what you mentioned just now namely that Theorici, [[uero]] est considerare, Prattici uero essercere (speculation belongs to the theorist, and action to the practical composer) and say that there is no doubt that what good exists in practical music, it all [-<207>-] derives from speculative music called theory. Therefore, since we have the chance, I do not want to deal herewith with some principles of the chromatic tones. It is all the more necessary to say something about them because it is common practice nowadays to compose chromatic composition, which cannot be done if one does not go through the constitution of the tones of said chromatic genus. Therefore, the tones of this genus are built on the same natural notes, but with the addition in those of the accidental sign of the square [sqb], or of the semitone (#) or of the b flat that are written in front of the natural tones, so that the compositions are transposed. These tones belong to the chromatic genus because this word chroma means the transfiguration of an object, which is the function of this genus. Pupil. In truth, this explanation that you supplied to me now not only appears to me to be necessary, but I state that it is one of the principal rules of thi music. Therefore, do not fail to continue it, as I shall listen to you very intently. Teacher. I shall not fail to do so, but I hope to complete it within a short time. Therefore, one must know that said chromatic tones are chromatic tones are also eight, of thich four are authentic and four are plagal. They are created with the help of the accidents. The first and the second are based on the note of low D sol re with [-<208>-] their altered fifth and fourth, which, added together, create the first and second chromatic tone. The third and the fourth one are also found through the accidentals and are based on the low E la mi. The fifth and the sixth are created in the same way through the accidentals, but on the low F fa ut, while the seventh and the eighth follow the same sequence by adding the necessary accidentals to create them, both in the case of the fifths and of the fourths, but on the chromatic G sol re ut. Said eight tones are also based on four fifths and three fourths, as we saw at the beginning. I add that four of these eight chromatic tones are authentic and four are plagal. The first, third, fifth and seventh are called authentic because they are created with the fourth above the fifth, while the second, fourth, sixth and eight are created with the fourth below the fifth, hence they are called plagal. I also warn you that when these eight tones are used in musical compositions their final notes must be the same as those at the beginning, whether it is a polyphonic piece or a plainchant, because it is appropriate to do so and by doing so one does not make a mistake, this being a rule established by learned musicians both ancient and modern. [-<209>-] Pupil. I wonder how it is possible that these ending may occur in other places that are natural or transposed. Teacher. If you allow me the time to answer, I shall reply and answer your doubt, although it is a difficult matter. I said that, when the budding composer wants to conclude a composition written in this chromatic genus, he shall be able to do it easily by using the notes that are good and suited to said purpose, since he can find the positions of all the notes in the chromatic hand, including those with the b flat sign, those with the square [sqb] sign and those with the semitone sign (#). Pupil. Alas, I am left besides myself when I hear this new method of composing. It is all the more new, since I cannot find this variety of notes in any musical instrument commonly used, whether they be wind instruments, string instruments or instruments with strings of steel. Teacher. Listen to me and do not worry, since I shall tell you how these compositions can be sung and played. If I am not mistaken there are instruments in our city of Naples that are built with the addition of chromatic keys. They are good and suited to playing these sorts of compositions, since these harpsichords have three sets of strings. I shall add [- <210>-] that there are other string instruments, such as lutes, archlutes, thiorbos, lyres and others of this kind that are suited to this function. Therefore, if you want to become acquainted with them in practice, it will be all the more easy for you to do so since there are excellent players who shall be able to answer all your questions about them. Therefore, it shall not be easy for you to practice such style of music. Pupil. You have explained these principles with ease. All that I need now is to have a short example. Teacher. I shall show it to you, but it cannot be done by employing just a few notes, since it needs to contain the notation of all the body of the eight tones. Firstly, I shall write the ones altered with the square [sqb]s and semitone sign, as they absolve the same function. I shall also add the relevant ottava, which will satisfy you more than the earlier ones. Ninety-ninth ottava How learned you are, o sweetest Muse of mine, since you draw from the chromatic such strength and vigour, so that you change the sweet composition to black, white or to another colour. This is the great virtue, this is the way That you always show with true love. In this example everything is unveiled, As you allow us to draw fruit even from the slightest thing. [-<211->] [Cerreto, Dialogo Harmonico, 211; text: Essempio dell'Otto Toni Cromatici incitati per [sqb] quatri e Semituonj, Primo, Secondo, Terzo, Quarto, Quinto, Sesto, Settimo, Ottauo Tono, Autentico, D sol re Cromatico, E la mi Cromatico, F faut Cromatico, G sol reut Cromatico] Pupil. Since I have exercised myself in the aforesaid example and I have noted that all the notes of the fifths and of the fourths are transposed a semitone higher from the ones that are find elsewhere in their natural position, therefore, I believe that when I compose some composition in this genus, I shall be forced to move all the parts that sing in the same order. Nevertheless, although it seems difficult to me to be able to lay them out, I hope to reap some fruit of my work after long practice. Therefore, you may move on and deal with other necessary instructions. [-<212>-] Teacher. I am pleased that you have understood everything that I explained above. This gives me the chance to explain to you also what rules one should observe in writing a composition of the same chromatic genus, but with the b flat. Therefore, you must note that when one wants to show the distribution of all the eight chromatic tone altered with the b flat sign, one must consider that, because the flat sign occurs in all the six notes that have to be sung in its position on the note fa, it is clear that, if one wants to build the first and the second tone in the place where it says fa, it shall be necessary that the note fa becomes re. Therefore, one can show clearly in this way that the eight tones have to be created with the aid of accidentals and that the note fa becomes re. Thus, all the eight tone altered with the flat b signs can be created, and, in order to b e succinct, I want to write their illustration for you, preceded by the ottava that deals with the ame topic. I assure the Reader that one shall gain greater satisfaction by reading the ottava that by examining the illustration. One-hundreth ottava I said above, if I am not mistaken, That you, my Muse are so able That your actions are well known. You illustrate this already through you good practice. Therefore, I beg you, show your strength, Since I know that you can learn it, Place you accidentals in front of my tones, So that you may write all sorts of things in your compositions. [-<213>-] [Cerreto, Dialogo Harmonico, 213; text: Essempio dell'Otto Toni [nini ante corr.] naturalj, Primo, Secondo, Terzo, Quarto, Quinto, Sesto, Settimo, Ottauo Tono, Autentico, D sol re, E la mi, F fa ut, G sol re ut] Pupil. I thank God that I achieved the goal of understanding this explanation of the chromatic genus, so that I may employ such knowledge in future. Therefore, my sweetest teacher, if you agree to do so, you shall be able to continue your discourse and discus the other rules that I need to know. However, let all this be said with humility on my part, because, the fact that I am aware of your loving nature has emboldened me to ask you many questions on the subject of this discipline of music, but always with respect. [-<214>-] Teacher. I cannot be more pleased, pupil of mine, than when you begin to address me by naming and thanking the name of the good Jesus. I ensure you that, when you do so, then my desire to discuss further this practice of music increases. Therefore, pay attention, because now I want to teach you through this discourse everything that you shall need on the rests. The rests are eight, namely, the rest of the maxima, of the longa, of the semibreve, of the minim, of the semiminim, of the quaver and of the semiquaver. However, not all of them correspond to the value or their notes. In other words, the rest of the maxima corresponds to two rests of the longa, four rests of the breve, eight rests of the semibreve etcetera. The rest of the longa is equivalent to two rests of the breve, four of the semibreve and eight of the minim. The rest of the breve corresponds in length to two rets of the semibreve, four rests of the minim and eight of the semiminim. The rest of the semibreve has the same vaoue as two rests of the minim, four of the semiminim and eight rests of the quaver. The rest of the minim is equivalent to two rests of the semiminim, four rests of the quaver and eight rests of the semiquaver. This occurs when said rests, namely, those of the maxima, of the longa, of the breve and of the semibreve, are not subject to the signs of perfection, as in that case the rest of the perfect maxima corresponds to twelve semibreves the one of the perfect longa to six semibreves, the one of the [-<215>-] perfect breve to three semibreves, and the one of the perfect semibreve to three minims. Therefore, said rests are counted in this way. Pupil. Please stop, my dearest teacher. In fact, before you conclude your discourse, I would like you to explain to me why it says in that printed book of yours entitled Musical Practice that the rests are no more than seven, while you counted eight of them just now in front of me. Teacher. You have done well to ask me this question as a conclusion to what we have dealt with in our discourse, and pointing out an issue whose cause has not been understood or considered by all practical musicians. In fact, I want you to know that ancient musicians did not want to ascribe a rest to the maxima because there was no way that it would suffice to indicate the quantity that was necessary to said maxima, as one can gather well from the five lines in measured compositions. Proof of this is that the rest of the longa occupies three lines, the one of the breve two and the one of the semibreve one. Therefore, if one were to write the rest of the perfect maxima it would be necessary [-<216>-] to write it in such a way as to cover all of the five lines of the pentagram used in measured composition. In such a way such sign would indicate the end of the composition. Therefore, two rests of a longa are used to indicate the value of the maxima, since it covers four lines when it is perfect and three when it is imperfect. Pupil. You have explained these principles in a learned fashion and your opinion is really worth of praise and devoid of contradiction. Moreover, I am not the only one who subscribed to it, but others of the profession have done so. Therefore, it will suffice to for me to have a short example for my understanding. Teacher. I shall be pleased to notate it, and I shall not fail to write its relevant ottava before it, which shall please who reads it. One-hundred and first ottava It is now appropriate that at the end we should deal Of the so called values of omission, By the learned composer, quite correctly. They are the rests, and their number is no greater than seven. We must not count the maxima, As the Muse forbids us to count it. This is what the Muse wants and commands, And when you require the rest of a maxima, you borrow it from other values. [Cerreto, Dialogo Harmonico, 216-217; text: Essempio di tutte le Pause, Pausa di massima, Di lunga., Di breue., di Semibreue., di Minima, Pausa di Semiminima., di Croma., di Semicroma] [-<217>-] Pupil. Since you mentioned above that there are other rests in practical music that are counted in a different way, I would like you to explain them to me. Teacher. I shall help you to understand them now. I tell you that, usually, in the compositions that contain signs of perfection, where such perfection has to be shown both with the note values and with the value of the rests, then it is necessary that the composer should write two signs of rest that cover four lines both in the major perfect modus as in the minor perfect modus. Therefore, there is no other method of indicating the rests. So, we say that this is why ancient and modern musicians did not discover other ways to mark the rests of the maxima, as one can gather more clearly from the example written herewith. [-<218>-] [Cerreto, Dialogo Harmonico, 218; text: Pausa di Massima perfetta, Di lunga perfetta, Di Breue perfetta, Di Semibreue perfetta] Pupil. You have explained everything on the subject of the rests with ease, but, tell me, please, is there anything else that you should tell me? Teacher. In order to conclude our discussion, we shall explain some principles on the matter of indicative rests, which are written in the compositions beneath the signs of perfection, which ones are written, and provide an indication that the four essential note values are made perfect, namely, the maxima, the longa, the breve and the semibreve. However, they are not counted or written before the tempora, while, if they are written after the tempora, said rests are counted and indicate the perfection. Here is their illustration with the ottava that explains some detail of said indicative rests. One-hundred and second ottava O learned Muse, I have to speak to the world Of your value of the perfection And of your so ancient law And of the observation of the rests. I know that you are so fond of all of them, And of the singer who sings advisedly. Therefore, the rests, even the indicative ones, are necessary to the compositions, [Cerreto, Dialogo Harmonico, 219; text:Essempio delle Pause Indiciali, Che non si numerano Che si numerano] Finally, the budding composer must ensure that, when he wants to use the aforesaid rests, especially to indicate the perfection of their note values, particularly in the case of the breve and of the semibreve, he must write the two rests of a semibreve on the same line. Similarly, if he wants the semibreve to be perfect with the perfect prolation, if said two rests have been placed separately on two lines, said perfection cannot follow. This is what the rule that is observed by all expert musicians requires. The example is written above and I shall speak no more about it. Therefore, pupil of mine, you can rejoice that now I grant you permission to compose at your leisure, as long as you continue to study and to continue to read the works of learned theorists. If you do so, I can assure you that you shall be considered as one of the good practitioners of this virtuous occupation. I apologise profusely because, if my examples and also my rules have not been expressed with the eloquence [-<220>-] and doctrine that would have suited this subject matter, I am sure that if my efforts are considered not only by you who have been my pupil, but also by other persons of sane judgement, if I do not deserve praise and to be considered among the other learned practitioners of said discipline, I shall be confident that, thanks to the kindness of everyone, I shall be more appreciated than detested, since it is necessary that those who teach virtuous subjects are appreciated. Also, as we have concluded our discourse by talking about the rests, it is appropriate therefore that now we stop talking and that we rest entirely. [[However, one shall be better able to understand the conclusion of our discourse thanks to these two ottave therefore…]] One-hundred and third ottava I thank the Almighty God, refined Reader, Who has enlightened me in the art of Music, Since what I said, I said entirely without error, And he has led me in everything that I wanted to explain. Now it is your turn to study with true passion, Since everything shall bear good fruit. These are the rules that I obeyed and that you must also follow, If you want to preserve your knowledge. One-hundred and third ottava Come on, let us conclude, pupil of mine. Now it is time to rest. Listen, if you want, to what I say, Since we have dealt with the topic of rests. We must thank the Almighty God, Who has allowed us to come to the end of our discussion. Therefore, united and with good heart, Let us give thanks to Christ the Redeemer.