Epistola -- Girolamo Mei -- Vincenzo Galilei -- Giovanni Bardi

Speranza A Translation of Girolamo Mei's Letters to Vincenzo Galilei and Giovanni Bardi Keywords: opera greca -- tragedia greca, opera italiana. Camerata, Early Opera, Giovanni Bardi, Girolamo Mei, Shaked, Vincenzo Galilei, Zarlino Letters 2-6 [Letter no. 2] [122] [fol. 43r] To Sir Vincenzio Galilei [from] Mei Very magnificent sir, your letter of November the fourth made me understand, finally, what you called coma. I see that you think that the major semitone, which (as I imagined before) you think is the proportion eleven-tenths, you place in the lowest interval of the diatonic tetrachord, and you put the minor tone which you think is the ten-ninths in the central interval [of the diatonic tetrachord], and that tetrachord put in this order, you called the “syntono diatono” that according to this form descends from the highest note towards the lowest one through the nine-eights, the ten-ninths and the sixteen-fifteenths and backwards ascending from the lowest note towards the high one through the sixteen-fifteenths the ten-ninths and the nine-eights. Now, in principle you must know, that this is not Ptolemy ‘s syntono diatono, although the intervals of both have the same names and the same measures, because those of Ptolemy ascend from eleven-tenths to nine-eights and to ten-ninths and after descend from ten-ninths to nine-eights and to sixteen-fifteenths, so that the highest interval of the tetrachord of Ptolemy is the ten-ninths while the other [tetrachord’s highest] interval is the nine-eights instead. In Ptolemy’s [tetrachord] the central interval is the nine-eights and the other [tetrachord] is the ten-ninths. The proportion sixteen-fifteenths is common to both of them, in the lowest interval of the tetrachord. This is not a major semitone, nor a minor semitone, but it is the major part of the minor semitone, that is approximately 24/2048 and the minor [part] that is a little less than the major part is approximately 11/2048. It is true that he who can be satisfied only by the sense of hearing, and is not upset by not understanding the truth of things, the difference is so little and won’t be meaningful to him because the sense of hearing cannot notice it. And this [i. e. the other] way to distribute the steps, according to what is the meaning of the name of syntono according to Ptolemy not only that it is not syntono, but is of an opposite nature, because the meaning of syntony according to him is: “that between the higher and bigger intervals”, when [in the other] the one that is the highest is smaller and more tight [teso]. This isn’t quite true in your case: the clue is that in Ptolemy’s writings all the forms that have the nine-eights in the highest [interval], are called by him tones, and according to his way of thinking can’t be called tone no other proportion than the nine-eights, that is the result (as I told you in one of my precedent [letters]) of a perfect fifth [in Latin], called fifth [in Greek], that is in the proportion of three-halves, distributed in two tones with some nine-eights and also it is in a minor semitone less than a perfect fourth and a fourth that is in a four-thirds proportion distributed in two tones and some nine-eights, and also in a minor semitone. Therefore, the main thing, as I have said [124] before, is that the distribution of this kind is not at all like the sintono diatono of Ptolemy, having the highest pitched interval of the tetrachord, larger than that in the middle and so it is in contrast with the real nature of the sintono. Also, it is completely against the definitions of Ptolemy who firmly declared this imperfection as unfit for the highest note, and most of all for every kind of music with an equal distribution of intervals, as I think, is in this one, where the interval [fol. 43v] ten-ninths is in the center and not to the first one [i.e. the lowest], as it appears in the margin, following the numbers that indicate the steps. Moreover must be considered well that Ptolemy with his new way of distributing the steps, with so much care and so fine taste and skill, shows his own systematic demonstration in order to take away the reputation and the heritage from the old diatoniea that shows clearly the imperfection of the last and the lowest interval of the tetrachord, because it is not in a superparticolare proportion, and his force is not enough to overcome it [the old diatoniea], already as you can see in the following period of time, starting, I didn’t say from Ptolemy, but from [125] Plato and going on up to our times, following very much the testimonies of the most noble ancient and modern writers of this faculty until Josef Zerlino from Chioggia wanted to interfere and to use his authority again, as I have heard said, and also to put in dispute such kind of steps distributions non really taken from Ptolemy, but from Didymus, and very much rejected by Ptolemy himself for so many troubles caused. I told you what I heard from others, because really I have never read, as far as I remember, in the works of Zerlino about this kind of distribution of the steps, since when I read, I did it in no other place, but where it deals with tones and when I found it to be following Glarean’s ways of dividing harmonically and arithmetically the octave to make tones as he liked, I preferred to avoid to get tired in reading the remaining things, having no other aim and so I had enough and I left off the practice of modern harmonies entirely to the performers. To the other questions left unanswered that you made on your other letters, now that we understand each other [much better], perhaps my answer will be much more clear for you. You asked me in your letter of August the 17th how did it began that those who are performing don’t comply exactly with the theorist‘s designs, as should be done, because the theorist has the reason of things. I‘ll answer you that is quite different to think and understand, and another to do things and put in performance, since to the first belongs the intellectual judgment and the second to the judgment of the senses, and [the senses] are not so perfect to perceive as are the mental faculties and so the reason and other circumstances are needed always to accompany it, because the performer must simply satisfy his senses, and it is not [126] necessary for him to care much and use refinement as it is for a theorist and so he doesn’t esteem so much the reasons as do a theorist and he is pleased when his performance proceeds well enough to satisfy him, and he has with no other aim. In short, the one that in a different way takes in more consideration and studies more accurately the right angle, the circle, the triangle and the other figures with respect to their different purposes, is the mathematician more than the carpenter. The same happens between the music theorist and the singer. Because to the first is important to understand exactly and to second it is enough to perform [well] what can be heard. In your letter dated October, the 19th. you asked me [fol. 44r] if I know how many comas the minor semitone contains, and how many the major. Starting from the fact that you told me that you understand that coma is the excess left by the proportion of the nine-eights interval, usually called: tone by the ancients. It becomes clear that the major tone contains nine comas and the minor, eight. Because if we find a common number, in which is whole and contains eight and ninth, as is the number 72, whose division for nine, gets as result 9, and if it is divided for nine, 8 is the result obtained; compared with nine parts the longer part is the eighth part, with 8 the short part is the ninth, really one seems different and bigger from the other and so the height of nine is bigger than the eight makes the whole number minor. The result is that it is the major tone of nine comas, as seen in our research to find how many comas contains the minor semitone and lemma and how many the eleven-tenths, that you knew as major semitone, and how many the apotome which really is called a major semitone by all the other ancient musicians and all the others that I knew, with the exception of Zerlino. The lemma is the part of the tone that is the rest of the four-thirds less two compound tones. The eleven-tenths is the proportion of that, plus the reminder of the nine-eights interval, and the reminder of the ten-ninths interval is needed to [127] make a whole four-thirds. The apotome is the remainder of one whole tone deducted the lemma, and a minor semitone. Therefore, to find these kind of things it is necessary to find a whole number that can be divided into parts without any fractions to avoid the trouble of dealing with the odds, and linked together so that you can get three uninterrupted nine-eights one after the other. These three nine-eights and the tones are bigger than the four-thirds, composed by two nine-eights, and a lemma exactly as an apotome and a major semitone of not Zerlinians musicians. To be able to find correctly the lemma and the proportion eleven-tenths is equally necessary to find such a whole number that or divided or added can grow also rightfully and create a four-thirds proportion. Now, to find such numbers my calculator makes me to proceed in this way: in the first place I multiply eight by itself, and I get 64, this 64 I re-multiply by 6 and I get 512 and the number 512 re-multiplied by three gives 1536. I’ll take this 1536 for the first step with the highest sound. Once this first is in its place, dividing it by 8, the result is 192 that added to 1536 makes 1728, and I take it in the place of the second step with a lower sound than the first, and makes with it a nine-eights. I divide the same 1728 by eight and I get 216, this 216 added to 1728 makes 1944. This I’ll take [fol. 44v] as the third step with a lower sound than the second, and with it a nine-eights is made. After, I divide the highest of all these three first steps, that is the 1536 by three and I get 512, that with 1536 makes 2048. This I'll take as the fourth step and lowest on the tetrachord that matches well with the first one. The difference shown as the interval between the third step 1944 and the fourth with the lowest sound [128] than all the four that is 2048 is: 104/2048, and that much is the proportion lemma. So, once the step 1944 is divided by eight, we get 243, that added to1944 makes the third nine-eights and the tone between them is 2187. Now subtracted from their difference 243[!] the 104, as above-mentioned, is the lemma portion, and remains the apotome 139/2048. To find the quantity of the eleven-tenths, I turn back to the first step 1536 and from the start I divide it, as done before, in eight and I get again 192, that once added to it in the same way, makes 1728 that I use as the second step. I divide this by nine to obtain the ten-ninths portion for the middle interval and I get again the same 192 that added to 1728 makes 1920 that serves me for the third step of the Zerlinian tetrachord, or rather of Didymus. Finally, I divide 1920 by fifteen and I get 128 that with 1920 makes 2048 that I use as the fourth step of the tetrachord with the lowest sound, which similar to the one in the ditonieo tetrachord, matches well with the first one and with higher sound 1536 and eleven-tenths with the third [step] 1920[?]. The difference that is in this interval, between the third and the fourth steps, is 128/2048, being so the lemma 104/2048, the eleven-tenths 128/2048, and the apotome 139/2048[!], we get that the lemma is smaller than the eleven-tenths by 24/2048 and this is smaller than the apotome 11/2048. To see now how many comas contain each one, I proceed this way by searching the value obtained by the eleven-tenths part of the nine-eights and after multiplying eight by fifteen to have a whole number without fractions so to fit the two divisions, I obtained the number 120 that, divided by eight, gives as eight 15ths, and its division by 15, gives fifteenth eighths. An 8 fifteenth of 120 compared with 15 eighths of the same 120, and following the proportion sixteen-fifteenths the 8/15 of nine eights. Now, once proved that what I said before is the truth, if the whole nine-eights long 15 comprises nine comas, how many will be in an eight fifteenths of it. And so, following the law of proportions, I will find clearly that it worth 4 4/5. Done this, I ask again if 128/2048 is an eleven-tenths proportion that comprises 4 4/5 comas, how many will be in 104/2048 that is a lemma portion. And so using [129] the same law of proportions, I found that evidently it must be worth 3 29/32, the distance of the nine comas that form the tone and the nine-eights 3 29/32 that comprises the lemma and the major [fol. 45r] semitone that is the remain of the nine-eights and tone less the lemma and minor semitone. The lemma so, is smaller than the eleven-tenths and comprises 3 29/32 comas. The eleven-tenths is smaller than the apotome and receives 4 4/5 comas. The apotome is bigger than that of the lemma and the eleven-tenths, and remains with 5 3/32 comas, and nothing more I know. About what you ask on the authority of finding among the step mi [square] flat and the step b fa , the major semitone, I replied to you before, also with my demonstration. My intention was [to let you understand], why I used the name of major semitone for the apotome and not the eleven-tenths, like did all the musicians following Zerlino. Because [130] this, never was held by them as an imperfect interval like are the lemma and the apotome, as the meaning of their names is clearly expressed in the Greek language used by the major writers that flourished in this science, It doesn’t signify any kind of well- known proportion; but the first means – “reminder”; meaning that this interval contains a reminder beside the two nine-eights of the whole four-thirds and a reminder almost in a rough reckoning, showing in a certain way that a fragment of it was torn up. Now, as we want to place in the third interval not the lemma, but instead in its place the eleven-tenths that you call in the Zarlinian tetrachord the major semitone. Changing the terms and increasing its interval, is not the same. And according to the result that is drawn out from my calculator the interval between mi [square] flat and b fa came out to be smaller than that between b fa and a` , as it is from 49 to 63. Finally, you ask me again about the origins of the ten-ninths tone. The proportion ten-ninths like all the others, was created by nature, servant of God, as far as I can understand, but, if you for this (as I believe) you want to say and learn who was the first, that I know, to make use in his music of this interval, really I cannot say. I see very well that before Ptolemy it was used by Didymus the well renowned musician, as can be seen before in his diatonic distribution. Now I want to get ridden of my old debts with you and satisfy at least the less old things that you asked me on your [letter] dated 9th. What you imagine of the origins of the enharmonic and chromatic tetrachords of Ptolemy is incorrect, as you can see on the penultimate chapter of the first book of his musica, where is it disclosed what were the ways and reasons that ruled in all the kinds of the distributions of his intervals, in all the genera. To your second question, half of me wants to laugh, seeing what happened on the same day that I smiled to myself infinite times. And this when [131] I was busy in some of my thoughts. I felt the need to blow my nose, I searched for the handkerchief here and there, without being aware that I had it in my hand. And this because when you are preoccupied of believing that our music has different principles and different nature [fol. 45v] than the ancient, you are not aware of the handkerchief that you have in your hand. Now, every time you go to church and put your mind to the intonations and chant of the psalms, of the hymns, and of the antiphons, and their airs, you cleanse yourself of everything, because they were made in antiquity as far as at times of S. Gregory, and are made according to the practice of that times, if good they are all in the diatonic genus, and you can not wave the conjecture that like this also is made in the enharmonic, and in the chromatic. Except because they have different steps, they could not raise or lower their air and respond entirely to the diatonic. And the answer to the inquiry that in certain way you asked me, with saying that if the ancients, as you want to say [second person singular] all sang, for much that may be together, only the same air and always the same one [solo], and like today is said a plainchant, why was it necessary that the ancient musicians in their books made a lot swarming all around to their consonances? To you I respond that the science has a different aim and a different way of acting from the art. Science searches the truth of the accidents and all the property of their subject and their causes, having for aim the inner truth of their cognition and no more: and the art has for aim the performance, which is a thing entirely different than to understand. The arithmetic searches all the properties and qualities of numbers, if are equal, if not similarly equal, if are squares, if are cubes, what proportion they have one with the other, how they are produced in a certain way and thousand of other of their rules. Who uses the calculator, does not use any of up mentioned thing, but only pay attention to multiply and divide and add the numbers, and to the parts derived from them and considered them like measure or value of certain subjects and matters. And because of this you do not need to marvel if the ancient musicians [132] did not pay attention when dealing with singing, to consider the nature and virtue of the consonances. The interval of the tone, that is of the nine-eights made (like you said) properly of the Diatonic, justify by the name, calling it diatonic that equals when proceeds by tones. Like this, the Diesi Enharmonic that is the almost fourth part of the tone and almost half of the minor semitone, made properly in the Enharmonic, and the minor and major semitones of the two most low pitched intervals of the chromatic tetrachord, according to those that distributed the steps of the genera with similar intervals. I say this because Ptolemy’s followers did not have these names and not these ways of intervals of diesi [enharmonic], and semitones, because the diatonic, having (as we know) the minor semitone in the lowest sound of the three intervals of the tetrachord, is not their arrangement but is a very old one as was in use even in Plato’s times, as we know also by his own testimony in the “Timaeus”. The ancients did not make perfect (in a manner of speech) nor make so imperfect any consonance [fol. 46r], nor their nature, like those that sing solo song, like is said and heard made in the plain song [canto fermo] hundreds sung together and they did not need to do things in this way, because the virtue of their music consisted in making the air explain well every feelings that they wanted to express with their words, and not quite by matching tunes or fugues or diminuations or other similar things. It is an certainly marked by the fact that among them can’t be found any of the names equivalent to those that you use [today] to distinguish between your different parts: bass, tenor, contralto, canto, soprano, or what ever is the name you want to use for it. All their words were so clear, and also their verses, that consequently their ideas were too, without any accidental interruption that may divert their minds from those virtues. Also this helped mostly to give them strength to penetrate better, especially when they were all accompanied by much industry to move [be touching] forcefully. What was the reason of the mutation of the synemmenon, is profusely examined and explained by Ptolemy in the sixth chapter of his second book. And on [133] Dorian tones or Phrygian tones or of others, I have to do this in another way and not in writing a letter. To finish, really they were seven in number, although some counted at least eight, some else thought thirteen, or even fifteen, For everybody all the shapes were based according to the high and low sounds in the system and for others, instead, they were based rather on their own nature than on properties of the octave that can be raised up or down following the natural system of the voice of anyone, giving high or low sounds. The Mixolydian was endowed with the highest sound and according to Ptolemy’s followers, for its own shape, was an octave lower. The Lydian was with a lower sound, and second in power for its shape with a lower octave, and so we can go on and find that the highest octave of the natural system came out from of the lowest sound of all, the tone Hypodorian, compelling down the natural system. Now, if you want to explain and take into account the circumstances and prove why the notes were no more than seven and on the contrary the reasons kept by those who though that the notes were more - it is a thing too long to explain in a letter. Ptolemy disputed [this] in many and many chapters of his second [book]. Please keep my advice in mind and make fun of those who, using the harmonic and arithmetical divisions on the octave form, think that the notes are twelve or even more, because they are all vanity and have no contact with the real things of this world in its different aspects, so they don’t match with the world, and for them (the octave), was made without any principal or final steps and no effort was made to recognize them, except those that clearly fit to the octave form, taken from its natural level to an higher or a lower pitch and consequently all its system. It is true that the singing voice remains several times near the level of the central step of the octave, sometimes ascending very much [fol. 46v], sometimes descending, but always returns back to its precedent middle level. For the middle of the octave intending the fourth starting from the lowest [tone] [134]. Nothing more in this matter I know to say. I consider it my debt to answer your letter received this week, but today I am dead tired. I ‘ll make up for it next week. Meanwhile, love me as I do you. I send you my best love, From Rome the xxii of November 1577. A[ll] Y[ours] G[irolamo] M[ei] To say what is the particular name of the middle interval in the chromatic tetrachord, will take a lot of time because each distribution in the ancient musicians’ writings is so different in this matter one from another that it gives a lot of troubles. The usual (distribution) says a major semitone. The difference is minor than the apotome by a tiny quanitity, as you can see when you compare the numbers one with the other, showing the way they are, in Boethius’s fourth book at chapters 5, 6, 7, 8, 9 and 10, where he divides the steps and distributes them and assigns them according to the different genera of any tetrachord. [Fol. 47r] All the quantity which is compared one with the other or with itself alone, like as for instance, when we compare 12 [135] with 8 and then we can say that 12 is three-halves of 8. In reality, there must be taken in consideration and compared the results produced or the factors of the computations. Following the first way, we see that 25 is the five-quarters of 20, a proportion bigger than 24 that is the six-fifths of the same number 20. Secondly, we can see that the portion of 30 obtained from the calculation of its three-halves, is bigger than the portion derived from the four-thirds of 30. In the former case examined, it can be said that 25 is one twentieth bigger than 24 so that 25 is 5 twentieth bigger than 20 so as 24 is bigger [than 20] by 4, and so we see that 5, a fraction of 20, is bigger than 4, also a fraction of the same 20. Therefore, it can be said that 45 produced by 20[!] portions and half of 30 is bigger than 40 produced by 20 portions and one third of 30, or rather [is bigger] by 5 fourtieths, the result obtained by 1/8 [of fourty]. In the same way we deal with the nine-eights proportion, that includes one whole [number] 40 plus its eighth part. Another kind of quick comparison, I don’t know, because either we must consider the parts from the aspect of quantity, following in this way, find the whole number where they hide, or find the whole number they produce, and like this as plain scattered portions almost whole numbers, or together with other numbers that are the factors or the results. Now we can see what is the proportion between the ten-ninths and the nine-eights following the up mentioned ways. So, we have a step (we catch a step to be able to see by ourselves and really understand) that must be put between these extreme endings AB. The end point A is taken for the higher sound and B for the lower one. We divide this [136] in ten equal parts, nine of these left by the highest side and one-tenth by the lowest one. The high part is named CA. We divide the part CA in four. Three lean towards the end point A, and the last one towards the end point C, so that we have as the highest sound DA and as the lowest one CD. Then we divide the part CD in twenty equal small parts. We enlarge from the side CB a small part EC so that the part ED becomes twenty-one-twentieths part of CD. We extend the part DA so much that the fraction added makes all together a six-fifths including the whole DA and one fifth more and its increase will be in the point F and so FA will be six-fifths of CA. Once this is done, we can say that the step (and so also the line CA), includes the whole line DA plus one third of it, is now its four-thirds and consequently the interval between the perfect fourth [in Latin] and the fourth [in Greek]. Moreover, since the line CD is twenty equal small parts long, obviously DA must be sixty similar parts long. If DA sixty, then FA, its six-fifths will be 72 parts long. Since CA is 80, EA will be 81. So it is clear that EA will be nine-eights of FD[!], and for the same reasons CA its ten-ninths. EA will be 9 small parts more [from FD], and CA 8 [parts more]. If you compare CF with EF, you can see that EF exceed by a small part, the ninth[?] part of it. The excess is called coma as agreed. So, once compared the separate quantity of the interval ten-ninths, with the quantity of the interval nine-eights, in the interval nine-eights there [is need to] add really 9 equal small and so [these are] 9 comas. After we compare the whole EA, result of the nine-eights, with the whole CA the result of the ten-ninths will be obviously EA eighty-ones-eightyths of CA [fol. 47v] and like this is eightyth bigger than it, that is a similar small part to each one of the 8, that CA is longer than FA by. Finally, if we compare DF[!] a nine-eights interval and CA[!] a ten-ninths with FA (both AC and DF derived from it) we can see that CF[!] is one seventh - two’s part bigger than a ten-ninths fraction of the same 72, hence it follows that the ten-ninths part of [137] DF[!], when DF[!] that is of 72 small parts, became 8 small parts major of it and so joint together 1/9 with 1/72 it turns into an eighth named the interval EA[!], that is made of 9 small parts. Now like you can saw all these ways that always appears that the interval nine-eights exceeds the ten-ninths by a ninth part of its, and so obviously is formed by 9 comas and also that the ten-ninths is formed by eight. I go now. [Letter no. 3] [fol. 48r] None of the ancients had even mentioned of any other consonance of those that the modern call perfect, of which only six were found in all the perfect system: but some wanted to receive no more than five, that are, as you must know as I do, the Fourth that is in proportion four-thirds, the fifth in three-halves, the octave in double, the octave and fourth, because these are not in multipication superparticolare but falls in multipication superparziente like 8 to 3 the Pythagoricans never wanted to accept for consonance, the octave and fifth in [138] triple and the double octave in four-fold. Those, that later increased the system, when according to them could extend longer and for a distance between the high and very low pitch of the voice that was, as also today is in use the last tetrachord separated and an higher pitch of all, they moreover added in the double octave and fourth that is of the steps D. d. la sol. 1728 with A. re. 9216, that goes in proportion five fold with four-thirds and the double octave and fifth in six-fold with the step Ee, the 1536 with the same A.re. Of no other type of consonance I have never found or read about in any of any ancient musician’s [writings]. The intervals of all those, as well demonstrated to you, make the two steps fall in proportion one with the another of multiplication or superparticolare or multiplied superparticolare , exception for this is the octave and the fourth that as was said above it falls in multiplication superparziente , and for this reason, the Pythagoricans did not want to receive it as one of their consonances. Against them Ptolemy did all his very best and fought with hands and feet and all he knew to preserve it. Not at all with the simplicity of senario [comprised of small numbers from 1 to 6], or little things like this, but making it in any piece to demonstrate that really according to his demonstration, it falls in proportion multiplied superparticolare and not in superparziente. If it is really true or not, in these days, anyway, it is not necessary to argue. The imperfect consonances have this name because they are [139] apparent consonants that have not a so delicate measure and are not able to harmonize well as the true ones, and you can use them only when they are near the true consonances and only then, they appear to be consonances and this, for the imperfection of the sensing elements with the help of them [the near real consonances] the sense is forced to understand them and maximally want to judge them as similar [plain] objects. This is why the eye understands what is its proper object: the variety of colors, perfectly, when is not being hindered by various circumstances that happen sometime, and so the ear [understands] the high and low pitch of sounds, as the taste [understands] sweet and bitter and the other tastes, but the eyes do not understand the size, nor the forms and if they are equal or much bigger and many other things that are not their own characteristic, easily and for a little error they can make a big mistake and so confirm easily the similarity instead of as really they are. So is the ear of our musicians and its imperfection and not other cause, makes them defend these consonances. You can see from here that the perfect fourth is not received by them among the accords but conditionally, because if it is not with under the fifth they consider it as dissonance, and they do not approve of it, even if it is also superparticolare and also one of the two approved by all the ancients. It is so much untrue that the proportion according to our fellow [musicians] is the esteemed true cause of consonance, because they only measure these with their own senses. [fol. 48v]. Now, clearly, it can appear to you that the true reason of the imperfect consonances was really the imperfection of the sense which make us judge according to him and it isn’t enough objective and is not distorted in these matters according to its own virtue, and not because of it they must be considered as really true consonances. And if also appears, is faraway from the truth, the belief that the ancient musicians did not esteemed them, because of the imperfections, and its possible to proceed infinitely and nobody can put any determined end a specific reason for a final conclusion. These elements were introduced since the pleasure of the sense has overcame the virtue of the intellect and was the reason that people start to sing these many aria songs together without understanding the power of the words and their meaning while in spite of the action almost of the nature ministered by God who gave [140] to man, for his own perfection, the speech for the purpose to understand the concepts of others and make clear his intentions, and on the contrary the man wants by any means and way to imitate the shriek of the birds and the howl of the other animals without intending them to have force to help to achieve his meaning. But let us leave these complaints to the legislators and turn back to our purpose. At the end (if I am not wrong) I will make clear if the kind of songs that we sing today is the Ditono syntono or the Ditonnieo. It is not necessary to reach such oppositions, because the same distribution of the steps indeed can be a evidence without any doubts. Because if you wind up over a lute (of which, as bigger can be, it will be better to compare by ear [the song] to what you are searching for) two middle steps or side by side steps or use any name you want, so equal in length or size as can be, together they can produce unison and after your correct underlining of the keys according to the distribution of the intervals of each of the two genera: sintono and ditonieo, and after you’ll manage to check the keys of any, observing each step, one by one, of the tetrachord which one of the two, truly corresponds to the step that is played today. So, with no doubts, easily, can be clear to any one, if not yet became real clear before, when I figured it to myself a lot of times, following more my own convictions than facts for that it is not necessary for now to apply any other argument. And this is what I can say in reply to your questions made on yours two letters. I would like to think that I have satisfied you. If I could, I’ll take it as a precious [thing] done, if not, excuse me, this incomprehension is caused by my age and by my slight illness in this season that is very hostile to the old [141] and more for the difficulties caused by the necessity to put in writing the rules of this subject and explain them, so well as it is necessary, to be clearly understood. And more, once neglected, it is necessary to remind me of them back. My best wishes from Rome, January 17th, 1578 to the birth [of Jesus]. A[ll] Y[ours] G[irolamo] M[ei] [Letter no. 4] [148] [fol. 55r] Illustrious Sir, and my most honorable Sir, Ptolemy wanted in this occasion to give a possible explanation to the reasons why the system of three tetrachords connected, called commonly of b. flat, was held some time among the ancients as a perfect system, and therefore he needed to demonstrate it to the writer. And it becomes clear that he brought with him alterations principally of four types of alterations and mutations that could be considered in the harmony, that were: of a true change of genus, like from an Enharmonic to Chromatic, and of their kind like from an diatonic syntonic to a diatonic delicato; otherwise of changing of tone like from Dorian to Phrygian: or for a variation according to their custom , like from quiet to moved[rimesso], or from this to largo and almost splendid, or otherwise only of change of order and almost-air[melody] of the system and that of the constitution of the steps, having left the custom to play on one of the sides like an old preceding habit that clearly can be seen very different from what was in his hands. He demonstrated that it was neither a change of tone, because the whole system did not became nor more or less high note pitched, or have more or less of low or high sounds: nor the same change of genus because in the tetrachords the distribution of the steps cannot be changed at all; and so because stable or mobile, all maintain [149] the same intervals between one to another, but rather in a certain way it was like a change of rising or by lowering the singing: and so because it was only a change of the order of the tetrachords. All four that are in the perfect system usually are so well pasted together, that only two remained connected with one common step on the high pitch side; and two other connected, in the same way, on the low pitch side, being separated by an interval of nine-eights that separated the two lower pitches connected together, from the two other higher pitches connected. So, in joining three together, can be changed the usual form of the system from that point were usually it is customary to place the interval of the separation that is between a and the b, because it is usual to rise from the step a. to the following step with the interval of one nine-eights. One, could rise with a lot smaller [interval], according to the tolerance of distribution of the Enharmonic or the Chromatic, or the Diatonic, in the lower interval of the tetrachord (that in the Diatonic was a minor semitone) and likewise in going lower, so that it can have in this place a change in the system, and so in the going down and or in the rising for almost the greatness of a large step, whose clinging together or lowering if used with due mode and time proportioned to them and fit to the song, manage with this his mutation to be graceful and in order. But if used too often or in un proper occasion or place it was fully useless and could be more harmful. Now, such alteration in the system where there are four tetrachords, could be done for the same reason, connecting, in the same way, the three highest pitches as the way connecting the three lowest ones, because nothing prevented to move comfortably and without disturbance, the distributions of different genera or the nature of the low and high pitches of the whole system. The interval of seperation is under the three highest tetrachords, as well as above the three lowest ones: since this or that inflexions are caused by the same reasons, and the reason is that the interval is not related to the distribution of the steps of tetrachords - on the contrary, as an usual thing for all the perfect systems of any type and kind of distribution, can be found between them [150] and only it is used on the tetrachords to separate them, and also if it is not taken into high consideration, in any way its work is done also in parting the three lowest from the fourth, the highest of all, and also in parting the three highest from the fourth, the lowest of all ones. Because if it was alright to put between the highest two tetrachords and the lowest two, it can not be because of the reason, that all the seven different species of the octave can be found in the system; cannot appear elsewhere, although for the ancients it could not be moved [fol. 55v] along this place, because they had no knowledge nor use for it there, but only about the three tones like: the Dorian, the Phrygian and the Lydian and they have no desire for any different forms. In case, that the [disgiunzione] is only one and is moved, it links in this way, at his usual place towards the high side, the highest between the two lowest tetrachords joined together with the lowest of the two highest, from the lowest side are well joined together the three tetrachords. of which, the lowest one of the two united highest pitched, divided from the others is moved towards the lowest two, it is changed into the highest of all three. So when it is linked in direction of the low side, after the interval, the lowest of the two connected with the higher with the lowest ones and are put together again, in direction of the highest pitched side, the three tetrachords together, from of them moved, becomes the lowest of all three. [151] These two kinds of distributions and the positions of tetrachords successfully made like this is a practical demonstration done by Ptolemy who aimed to give it in this way. It is system and the tone AF. Starting from the highest side of it and proceeding towards the low side, the tetrachord AB is placed, and is connected with the following BC, immediately after this over the tone and nine-eights of the interval [disgiunzione], and under it, again two more tetrachords follow, well connected together, of them, the first will be DE, and the second EF, the lowest of all. And in the same way kept in direction of the high side for as much as is the interval of one four-thirds and a fourth an interval similar to the CD, the: GH, and again, the two tetrachords HI and IM are to be connected to it, in direction to the lowest sound side. In the same way, is kept in direction to the lowest sound side, far as much as is the interval of a four-thirds [that is ]a fourth another interval [disgiunzione] similar to the CD. This will be NO, and again, connected to it will be the two tetrachords OP and PQ in the direction of the high sound side. [152] [fol. 56r] Also, then the step H is similar to the step D, nevertheless each one of them result to be the lowest sound between the other two kept together (in whatever point are taken the tone and the nine-eights of the two intervals[disgiunzioni]) it will be of a higher sound then the second for the length of one fourth, and of a much higher sound then the step I. Then D and the step I become a perfect unison in the same way obtained by connecting step D to the highest part of the tetrachord IH, and so can be obtained in the system also the tone AF composed by the continuously linkage of the other three tetrachords FE, ED, DH, one after the other, with the result that DH will be the highest sounding one. And again, for the same above mentioned reasons, the step H is similar to the step D, and so happen to the step O with the step C, being both the highest note then two kept between the tone and nine-eights of the two intervals, will be for the interval of a fourth a lower note then it, and the same, even would be lower then the step P. Then the step P and the step C will be in unison, in such a way that it will be possible to connect the step C with the tetrachord OP from the low sounding side, and so we have joint again in the system and in the tone AF the three continuous tetrachords AB, BC, CO one after the other, and the CO will be lowest of all three. And this is, as I believe to be the topic you described on the last letter, that Your Excellency wrote to me on the ninth of December, that I did not interpret word for word, but, on the contrary, at the end, in order to understand the text as I could, and with smaller difficulty, I broadened and arranged it as I wanted, to make it more clear. This is not because the writer is not clear for himself in his own language, but many times, the way of speech in one language doesn’t have an equivalent in another. What is properly and clearly said in one, when is converted to another [language] becomes very unclear; except that at times when one is writing so many times always on the same things so that they become very much stale matters and when arguing with whom that has continuously these matters underhand, when its certainly not necessary anymore to dwell on these terms, but on terms that you cannot do without them. Now, again I need to remind Your Excellency, that I am half-blind and old man and not so fit to do the hard work. So by all means, you must excuse me if I cannot do what [153] that can well satisfy you, and especially for me is of great inconvenience to write by hand. So, the best suitable thing for you is to spare me as much as you can. The same must do our Sir Vincenzio , to whom, as you can see, I wrote a book as long as the bible to satisfy some of his inquiries; because really, the hard writing with so much assiduous attention required by these material is the capital enemy of my indisposition, but if still You want to take advantage of my knowledge and of my doing, something that I can do to satisfy Your Excellency is that you can come and stay here for fifteen days. In this time I will make you capable to understand many things that you can not read on one of my long letters, for there they are certainly long and of difficult nature, and for me, it is harder to write almost impossible. For this reasons I don’t need anymore things, kissing your hands, From Rome, January 17th 1578 to the birth [of Jesus] At the service of Your Excellency ready as much as I can be, Girolamo Mei [154] [fol. 56v] As you can see, on one side there are the modes according to Aristoxenus, showing the two keys used by his disciples in addition to those thirteen else used by him. Under are the modes according to Boethius, and near by the ones according to Ptolemy. I didn’t make any effort to measure the intervals since I thought that it was possible to avoid an unnecessary labor because the step names marked by letters will provide you with all their peculiarities. All the intervals of the systems are Diatonic Ditoniei. When you see the mark 0/1 signed on, it’s means that there, between these two steps, there is nine-eights interval or as you say of a whole tone, and when you see this mark 1/2 the meaning is that there are between the two steps an interval named lemma, or as you want a minor semitone, [Letter no. 5] [155] [fol. 32v] Very Magnificent Sir Vincenzo I send you this in response to your [letter] dated May the fourth, including in my handwriting a copy of the characters of the steps according to Alypius in tones that you desire. Arrange them in order as you like, following the demonstrations you sent me, and I return back to you. The order was to put above the first of those two character that are united, the one which shows the voice, and below, the second that shows the steps of the instrument playing together with it, in this mode [???/??C] etc. and so it was possible to sing and to play together in solo, also the air [melody] of the voice, and of the counterpoint [156] of the stringed instrument (because wind instruments it was impossible to use) that was necessary to play with. Put them above any syllable of the song, as you can see in the airs I sent you times before. But over these, no other characters were marked on, but only those of the voice because in the examples that I had before, those of the [instrumental] steps were not on. I believe, if I remember well, that I copied them from an example that I had fifteen or sixteen years ago, when I followed those home tales in blessed memory of cardinal Sant’ Agnolo: or really those from the library of the Cardinal da Carpi that was in the Music of Aristides Quintilianus or of Brennio. The library of Carpi, as I think I heard, was donated to A. the G.D [Grand Duke] by Sir Lionello da Carpi’s brother and heir of this Sir. I beg and ask you to spare me as you can, about having to copy writings and [especially] where it is necessary to do this outside my room; because I’m old man and badly fit to the hard work, especially when it is accompanied by the inconvenience of unfitness. In the characters of Alypius, as I think, there are also some mistakes, but not so many as in Boethius, because I find in it differences in writing. However, [157] those things are not in use today, but only as ostentation or pomposity to show to the world, and it is not a big thing to care about. Even if it is not worth a rap to know their use, we have in Boethius’s or in those of Alypius or of Gaudentius’s (because all that can be found in them, also can be found in the writings of Aristide Quintilianus’s) if it is accurate [fol. 33v]. Concerning the order of the octave according to the Latins, if you understand the Latins as I do, following Boethius as you can see on the 14 chapter of the 4th [book] he starts to count from the a` [in Boethius’s term that is a` in Mei’s terms] and ends with the B [in Boethius’s term that is B in Mei’s terms] and for the first specie count the octave that is between the a` and the a for the second that between the g` and the g. and so this, step by step, going down always in direction of the lowest pitched step of all the four tetrachords of the separate system, leaving outside the A, because when you put the letter A to mark the B, and the B to mark the c And the C to mark the d[!], and consequently up to fourteen letters to mark the fourteen steps of the four tetrachords mentioned above in the following mode A, B, C, D, E, F, G, H, I, K, L, M, N, and O. Then, when you name the different species of the octave, start to count: OG the first, NF the second, ME the third, and LD the fourth, KC the fifth, IB the sixth, and HA the seventh, the octave is not taken in account because it is like the first one, as the diatonic distribution keeps the diatonic semitones in their same places namely in the second and the fifth interval, and not composed of four [158] tetrachords pending the addition of the A and in the other divisions can be found the same intervals right in the same places as before, named in the same way. About the order used by the modern Latins I do not remember them and I don’t have them ready. You can see them easily by reading their works. I sell it cheaply in this way, because in similar matters, I don’t care much of their opinions when they make up their mind to deviate from their own doctrine. About the four-thirds, and three-halves of Diatonico incitato mentioned by Aristoxenus, if you want to know them exactly, it is necessary to form all the system. In this way, scruples aside, as we can see the truth, I would form it with perfect and separate [disguinto] starting from the a` and descending [fol. 33v] to include the A. We start with a step with the highest sound of the four [159] tetrachords made of ninety equal small parts and after, we order all the remaining interval by filling it with thirty similar small parts in such a way necessary to make a whole four-thirds. The fourth of the tetrachord hyperboleon is in this way and after to form the following tetrachord I would like to say that, if for ninety (parts) twelve are in a tone, how many are for one hundred and twenty, using the proportional rule. I‘ll say: sixteen. To the b adding the eighth of one hundred and sixty for the interval [disguinzione] that must be a perfect nine-eights, that is of twenty, makes the a long all together 180. And after to make the remaining steps of the following and low sounding tetrachord, I‘ll tell you that if for ninety, 12 are for a tone, for 180, I‘ll find: 24 and I‘ll go on saying: [160] [fol. 34r] If for 90, 12 are per tone, how many for 240, and I’ve found a 32. I will go on up to finish with the nine-eights and, to find at the end the A, I'll add to 320 one eighth of it, formed by other 40 small similar parts that added to 320 make 360 complete the A. So is the entire perfect system. [161] Once this is done, all the differences that you search, are easily seen, almost all in front, because it can be found in the perfect system of the diatonico incitato, of Aristoxenus as in all other perfect system twelfth fourths. These start from the highest pitch step in it, and go down to the lowest pitched 90 with 120 [fol. 34v] 102 with 136, 114 with 152, 120 with 160, 136 with 180, 152 with 204, 180 with 240, 204 with 272, 160 with 228, 228 with 304, 240 with 320, 272 with 360. Of these, in total there are eight four-thirds of which two are short and two plentiful. The two short are 136 with 180 that go short of 4[?] and 272 with 360 that turns short of eight[?]. Of the two plentiful 152, with 204 turns greater four[?], and 160 with 228, turns greater 24[?], so good that, this, in all the nature of these arrangements turns grater then the nine-eights of the interval[disgunzione]. The fifths are eleven 90 with 130, 102 with 152, 114 with 160, 120 with 180, 136 with 204, 152 with 228, 160 with 240, 180 with 272, 204 with 304, 228 with 320, 240 with 360. Of these, five disposition are exactly three-halves 120 with 180, 136 with 204, 152 with 228, 161[?] with 240 and 240 with 360. Two dispositions are plentiful 90 with 136, with two[?] left, and 180 with 272 with 4[?] left. The others, that are four, all are short 102 with 152 are short of two[?]. 114 with 160 became smaller 22[?], but it turns also imperfect in the other distributions, 204 with 304 became short of four[?] and 228 with 320 became shorter 44[?] that in the same way became imperfect in the other distributions. And this is my reply to your letter dated the fourth of the [162] present [month]. I remain in debt to you, to tell you about the plectrum and where it can be found. You have to know the friend told me well known things, especially that in the Cardinal Santa Croce’s home a pillar can be found in which there are sculptured Muses and one of them is seen keeping in one hand a chiseled copy of it [a plectrum] and near her a musical instrument. Likewise, it seem to me that another I saw lately, also an ancient sculpture, is in a high niche of the courtyard of the palace once of my master and today owned by the (well known) Ceoli, in the hand of a woman statue with an instrument for [accompanying] song. But since sometime I see wrong, I ‘ll not try to say [fol. 35r] that I saw it clearly and well. This reminds me of the tibias, but I’m not satisfied with my understanding, and also I have an occupation that keeps me so busy that hardly I could even think to answer to your on this matter. After you make use of Alypius’s writings, I’ll ask you please, to send them back. And if you or others would, for a chance, make a copy of them, is not important, use them as pleased. I sent it in its [original] language because it seems to me too hard to translate them. [163] In this matter, easily could undertake the trouble to help, are some of those friends to whom no less than Master Lorenzo Giacomini can address you to. I'll take this opportunity to ask you to send him my best regards, a hundred times. To our “well known” Sir Giovanni [Bardi] I’ll kiss your hands. I am all yours for as much as I worth. I pray God to send you His best. From Rome, May 15th, 1579. Always when you like, Girolamo Mei The reason why, as read before, we used to differ the steps of the instruments from those of the voices with different characters, was especially in order not to mix up the air of the [instruments], with that of the human voice. And this is why, if you sing the same words with a different air of human voice than the air of the [instruments’] sound and mark up each syllables using all the characters the one and of the other following the composer’s order, and the characters may be alike, easily a confusion could come out, and particularly in those passages where one of them is silent and the other follows, or the opposite. [Letter no. 6] [165] [fol. 56v] To Galileo I will respond to your doubts as I will be able to do. To those that are originated just from the name or perhaps from the theory, or from the report made on some studies either in the language in which the problems were written, or from the speculations on this science and from reading on so many writers as I can handle and whose arguments on this matter arrived to me. By chance I‘ll be able to tell you something that could open the road to some remains of understanding. If you find something that doesn’t satisfy you, wherethe doubts are originated from a plain [practical] experience, try to be patient with your error, calling for help to whom is forceless, since even you know that I cannot sing or play any instrument or dance. But let us leave up these excuses and go to the facts. I‘ll start first with the names. It seems to me that the names that you don’t understand and are an impediment for you are especially these: Magadeggiare, Antifono, Antistrofo, Catastrofe. The first [term]: when the ancient musicians made the monochord and wanted to find the correct places for sure in each step, and to know the quantity of the intervals that remain from one to another, as you know, usually they screw up only [166] one very long cord, over a wooden board in a way so that each head can be fixed over a small bridge that, in equal height as the other one, have also a semi-circular form and placed in a point that the longest line is made at right angle with the level of the wood, over which the cord came, pulled and stretched. All this space left between the two, wide as the length of the cord, could be changed in different way according to the proportion between one cord to another; and after with a third similar mobile small bridge only more high than the two others already fixed up, that can hold firmly the cord in a way that can put at one painted point or at another and hold so firmly that with his help, the cord can nearly be cut when is beaten on over the part from which the sound can be played as wanted by the experiments done [fol. 57r] and as was needed. Now, the little bridges like these were called by the Greeks magadi and by moving and by changing the place of magade, that they called mobile, up or down, for finding the positions of the steps the verb magadeggiare was put in use. The meaning of this, is like to that effect done by the sound from the key instruments when somebody research and find, and finally in someway touch them. About the antifono. Three were the simple consonances for the ancients. The four-thirds, the three-halves and the double. that are originated among the nearest cords, or among the remotest ones and now, I intend for remotest not only those, as it is clear, from their position in the system, but also the major distance from the high and from the low pitch. What came out further from other three ones, is called the double, commonly named the octave, that, [167] nevertheless, for the virtue of its proportion like can hear any healthy ear is really the “queen of the consonances” because it unifies them more, and thus, or for being every step of his side nearly up to the last and farthest border of high pitch or down to the lowest pitch that can come out; and the same is in simple consonance or for being mixed together so much that apparently can be heard in certain way as they became only one; or, as it seems, for one or another quality, but only it of all the consonances was called antifono, and equally its step antifone, almost equally answering its proof to their [other intervals] inequality, being one precisely double of the other. With the word derived from their term “????”[“anti”, opposite, against] that corresponds to our contra, and to the name ”????”[uttering in sound or speech], that means voice. From this must be known that their word “????”, was forged by some different names, for sure with the meaning of “contrary”, but yet many times meant responds and in certain way functions as an accompanist. Regarding antistrofo: the meaning of this name according to the ancient musicians is observance and servitude to the poetical form named ode, in which it always happened that in the verses and in the songs and in the rhythms one side responded to another in accordance to certain determined conditions, which are in part respected by our poets in their own songs, where each of their stanzas should be similar in number and in quality and lines, and for a chance (like easily can be proved by listening to so many airs that still remain) the same must have happened to the singing, before the time that was introduced and used a new form of singing in a mixed manner in harmony with so many airs together. The ode was divided in ancient times into three parts: the first one was called strofe, the second antistrofe, and the last one – epodo. The strofe and the antistrofe were of equal number and of the same quality of verses, like are all the stanzas of our songs, except when we have a [168] refrain in it or in a more usual way when it serves for the ending. The epodo was different, and when it happened that the ode, distinct in all these three parts, was made longer, because it was played again and again in the same order, the strofe and the antistrofe, also were made equal and similar and corresponding to the former ones, and all the epods to the first one. Calling these parts with different names according to the impression made in singing them, as a multitude of singers was singing the ode at the sound of wind or stringed instruments, or both of them, dancing in circle, or in such order (in all part very similar to what is known now at our times: dancing in a ring , or in pairs or in triplet). And all this was called choro. The [fol. 57v] strofe that was, like was said before, the first, and was to be danced changing places, flexing forward, to the left, and coming back to forward. On the contrary the antistrofe - flexing from the left to the right and returning to the left. And the epodo - always standing in the same place. With the strofe they wanted to represent the movement of the first mobile from east to west returning to the east. With the antistrofe, the movement of planets from west to the east and returning to the west. With the epodo, they signified the stability of the earth around which the other planet’s movements are made. Now all the observances and servitudes to answer each other in this condition, was called - antistrofo, almost (in a manner of speech) in opposite way. If you want to see an image of how was the form of the lines fit one to another, (however without the rime) in poems like this, look among Luigi Alamanni’s first poems, in the second volume, where there are still together poems on the forests and tragedies, these can be read really very similar and they imitate the Epiniesi of Pinadro, those called by our “friend”: Hymns. The first part of each -ballata, the second - contraballata to express the word antistrofe and the third - stanza, whose servitude in the ode, was altered in part, Later, finally in names first, and later in ditirambi was left out [the structure] entirely. For, it was enough to leave out [169] the antistrofe or follow all other undetermined form, but [later] the names were used so freely that later the verses were no longer similar. And so, a resolution came out as regard of this kind of poems which became more and more imitative from hand to hand and in the long run have almost blocked up any form of action, and so, in order to have a good result, its poets resolved to free themselves completely from any obligation and servitude that prevented them. Now the antistrofare (in a manner of saying) made it [to them] uncomfortable to follow the obligation to correspond with the same form of verse or of singing or of rhythm to the old stanza of the song. Many times, for sure, it prevented them from expressing themselves freely with actions and new concepts and full of effects, so that opposition [arose], and [they] completely left those odes and started to violate the rules introduced and held by the ancients, whenever an opportunity offers itself today or tomorrow. About the catastrofe: with this term the musicians expressed the end of the “so called” song, if I understood well what I observed, called desposizione by our musicians. Almost painting with the force of the word, what will happen, because the instruments’ sound came out, during the remaining part of the song, in a certain comic way, always with the singers’ voice in chorus, almost fighting against itself with the [singers] difference in consonances, with no taking care to follow the same steps in another way and, at least, for peace sake, to be transformed and hold by force to join it when the song [canzone] is about to finish or one of its principal parts. This was done using only the means of an octave and in this case this was in order to express the word power. For your better understanding I’ll enlarge more by telling you the following partial example. The new comedy, was divided, as you can rely on the testimony of the ancient grammarians, who wrote of those of Terentius, in three parts. The first called protasi, almost a prologue of the act: the second epitasi, almost his extension and development: and the third catastrofe which was the issue and the purpose when almost it got untied and made peace, and finally a total overturn of the action which all the acting characters [170] have to submit to. [fol. 58r] The pleasure of everybody as they become calm and happy. This usually happened always owing to the natural octave, namely of marriage, and in conclusion of union of husband and wife. By a chance I got through a lot of those declarations but I did it to help you reach a better understanding of what is necessary in order to solve the doubts you proposed , and also, if you have a lot of them, please, leave out the unnecessary ones and keep with you the others. Now we arrive to your questions, that rise from the seven problems: according to my book: the 7, the 12, the 13, the 18,the 19, the 30 and the 39. According to my book, if you wrote well, the 40, and we will see what I know to say. I believe that it will be very little. In the 7th problem you show that you have difficulty with the words (in this sentence): So that the ipate expresses better the antifono than the nete. I don’t see from where you take it. If we want still to hold firmly the point that virtually in the lowest step can be included the highest one; because it would be better to keep the more important (in a figure of speech) of the two, and in virtue represent more the force antifono, when the low step or the high step is missing. Now, this was the hypate, and not the nete; because the [number] 12 contains the 6 but not the opposite. All the trouble comes from trying to understand the meaning of the word more. Even if it is a little word however, in this place it is very important, because the writer doesn’t say that the hypate absolutely renders the antifono, but that mainly the nete does not; as proved by those words of the 13th, where it is stated that the highest notes or the lowest ones can be played very fast: maximally when both are played together. But if you have to choose one of them, it is the lowest one, because it is the bigger as our proverb says: “the more you have the more you want”. I don’t understand [171] not only the words of the 12 that you sent me, but also the words in Greek, or those in the old translation. Theodorus (as he did many times) arranged his translation as he wanted without any respect to the original text and do things as our proverb says: at a rough guess [eyes at the cross]. In my opinion, the place where I have to read is in rags and I will not guess how to read it without any good help by an ancient example and I would not dare to lay hands on it, especially because this thing is bounded to a good practical method. I was made to believe that it is very wrong if I don’t want to learn any uncompleted matter, because as you can see clear, the old translation was subjected to other writings [=manuscripts], and that of Theodorus does not say himself in no way, that he followed the old one and not the one in use today. The old one says this: [172] “Se enim oportet dimitere quae est circa medium paramesem cum alia media, fit medium nihilo minus. Si autem medium utraque alta non fiunt.” For this clear reasons it is evident that different things could be read in this book instead of ours, using more and different words, because instead of ????”[?], that is: singing, he has ?????[????-to be?], that was translated dimitere. No trace of the words translated “circa mediam” [in approximation?] are after all in our well done translation. The two terms “????” and “????” [love, like?], are translated in his work as “?????” and “?????” [high] taking them as high, in which it is noted as an error (as I believe - of writing). I read in one printed papers that I saw in the first of the two places: “alia” [by another way]. The words of Theodorus must be read in this way: [173] “Nam si proxima quoque a media pulsanda sit, media tantum nichilominus reddi medium potest: at si media subjungenda est per proximam a media idem reddi non potest” Therefore who easily can be satisfied, can have a good and common feeling. If after all [fol. 58v] this is really what who proposed the problem left in writing, is a different matter. It is true that for the reasons produced everyone could believe that Theodorus granted that proposal, if it is not truly the same, it appears nevertheless that he took this way, but as I am not a brave person, I prefer to take the decision that I don’t understand it. In 13, you doubt the proposal that is born by a chance from the word antifono, that in this case must be interpreted not simply as such similarity of the steps playing together only in the octave and not in other consonances, but because the low pitch almost wins in virtue in comparison with the high pitch, I should almost say, became his master [174] and not the contrary, because he can overcome it. Where the high pitch has less power and doesn’t have the same possibility of action nor the same force as the low pitch, and they cannot counter- balance each other as equals, really the singing came out maximally from both of them together. But if you examine each one separately and by supposition now that both are not together, the song is in the low pitch, and never in the high pitch, because, in any way, the low pitch cannot be contained in [the high pitch], because as we said before, six does not contain the quantity of 12, but the opposite is possible. In 18, I don’t understand what bothers you with the meaning of the words magadeggiare, and antifone, that I see them underlined, or perhaps, what to be said on the one or on the other, that may be enough to satisfy you but I didn’t want to be with you disadvantaged avoiding to tell you that in effect is not to be considered superficially the force of the proposal in saying: “From what is born (the idea) that the consonance octave is sung alone?”, because this is magadeggiano and not other. Therefore, I come to a clear conclusion that a lot of people who liked to sing all together, nevertheless they were singing a solo air, because only the octave and no other was their difference, as explained in 39. Maybe because they needed to sing together and the reason was their ages or another natural impediments. Afterwards, once stated that the reason is not the voice but the stringed instrument, it may be enough if I can demonstrate that doubling the cords of the instruments, as you do, the lower pitches of lute with their octaves [175] equally was in use by the ancients, since they already magadeggiavano, a term that now I would like to interpret as “doubling”, and this with the octave only; since the word magadeggiare have the meaning of action on the keys and not on the voice. You have a crack in the proposal of 19th. This came, as I warned before, from the reason that your solution was accepted and for a chance was found untrue perhaps when I thought [something] that might be new, how the cords that make the consonance octave can be equally far from the middle. Because their steps are eight, and the average is “the fourth “ starting to count from the lowest pitched, and this has between itself and the ipate two steps only, and between itself and the nete have three, and more than the ipate, came the four-thirds of the average, and the average three-halves more than the nete. The rule on monochord easily will make you all clear, because if you take one step equaling AB. over two magadi, or firm small bridges, that can be used in this case and represent the e, this must be divided in four equal parts in the points CDE, and the result are the steps AB, CB, DB, leaving aside the other distance from one side to other, that is now superfluous: and after putting the magade, and a mobile small bridge on the point D, immediately with a strike on the step DB, can be heard in reply the high note, e’. of which the whole AB will be his doubled, and so will do the octave. But if you put the same mobile magade in the point E, and strike immediately [fol. 59r] the step CB, appears and can be heard the a` an that is exact average among the e and e`. And now, of all the interval AB, half of it is the interval AD, when fixing that the step DB, reaching an octave with the AB, becoming an higher pitch, in double. And the first C, dividing the space AD in two equal parts unavoidably falls right in the half between A and D, consequently came out the antifone AB, DB. Equally distant from the point produced by the CB, and consequently the same way of dealing with the “average” can be taken with the numbers that contain similar terms [176] and steps. How is the e: the fourth fixed from it to the middle make nine: and “the double” of it, that represent the e`, whose average obtained is three-halves, the right result will be: six. In the same way, then, all the numbers are in this mode 12, 9, 6. Now twelve is far from nine three points and the same between nine and the six, and also the same between the antipfone 12 and 6,equally distanced of the nine that can be found in the half way. [177] In the 30th you feel in trouble not understanding the word antistrofe, up mentioned beforehand in the part on the magadeggiare, and of the catastrofe that you have marked with an underline. About the 40th, here you are wrong (if I did not misunderstand you too) when you oppose at the conclusion of the problem the doubt that also the fifth and the fourth are voices one in contrast with the other, and you assume that the different and the opposite are simply the same thing. Now this is not true: because the opposite is always different: However, the meaning of diverse is not always the opposite. And then between these two different points cannot be found the half way, as, for instance, the red is well different from the white, but is not really its opposite, because its opposite is - black and “less” is the opposite of “more”. What is defined really as opposite, are those things of the same kind that are most far away one from the other. Now, for instance, the low pitch of the ipate is farther from the high pitch of the octave more then that of the fourth, or then that of the fifth. Hence, it is true that in the simple consonances only the antifone steps are truly in opposition to each other. Magadeggiandosi therefore with contrary voices means magadeggi in an octave that is the only step of antifone. And so it obviously happened that the octave, making only one [kind of] antifone step, can be damaged by the chaos of contrary voices. And I have no more answers left in my crossbow for the questions you put. I would like to please you, but if you are not satisfied by my good will, then try elsewhere, because nothing else I know. I directed the letter to you, because I imagined that all is mainly done principally for your own account. Also, if true that the Illustrious S[ir] G[iovanni Bardi], is the principal actor. So, if Your Lordship will be so kind to send me a letter in return again here, where I spend my holiday season, as I’ll send them [my letters] up to Vernio [an Italian country town], or where you [third person singular] can be found, and please excuse me with him if I could not answer in other way particularly to your letter but to tell the truth, I get very tired of writing today. I am looking with desire to receive your book [178] At a request of a friend, I began looking for an explanation why every passage of ancients’ music, so many as you can read, came out as a great work, and on the contrary our music, as always its appear, makes us look like idiots and unskilled, leaving no [strong] mark at all. Above all the answer leads to rhythms: but I’m tired of writing, and unable to keep [up my] mind and don’t want to give [fol. 59v] an obvious blow to my health when I go round thinking and am followed by the shouts and threats of the doctors. Now, they force me to stop again my work, and so all falls asleep. I have nothing more to tell you. I would like to know whether this letter had reached you. A[ll] Y[ours] G[irolamo] Mei [fol. 60r] Problem XLIX of Aristotle Of the Harmony Why the choirs in the tragedy do not sing according to the Dorian, nor according to the Phrygian? Maybe because these harmonies have very little melodies [179] of the type the choirs absolutely need. But the Phrygian has an active style; and so the Gerione closing part and exit were made by it. But the Dorian has the magnificence and the firmness and has a strong movement on the chitarra: and these two extremes are inappropriate for the choir, and appropriate to these of the stage. This because they are the imitators of the Heroes: All the leaders of the ancients were Heroes: instead the choir is made only by men from the People and its behavior and its melody weak and lazy as fit to them, because such are the people and we could find it in other harmonies as well: and no less than in the Hypophrygian. But this is furious and Bacchic. According to this then we are more moved by the feelings because weak people are more easily moved than the powerful. But this is fit to the choirs. But we operate according to the Dorian and the Phrygian, that is not appropriate to the choir; because the choir is a lazy writer, useful only to those it is presented. © 2003 * The Page numbers in brackets are those of Claude V. Palisca's book "Letters on ancient and modern music to Vincenzo Galilei and Giovanni Bardi", American Institute of Musicology, 1960) and the manuscripts pages mentioned there Hear Psalm 122 by the author in the background of photos of Jerusalem from www.JerusalemShots.com ----------------------------------------------------------------- Emails are gladly received Girolamo Mei's Biography The allegory of Monteverdi, Peri and Caccini's Operas on "Orfeo" (Orpheus) Johannes Ockeghem : Biography; S'elle m'amera-Petite camusete: A sophisticated game of meaning and structure; Polytextuality from Machaut to Ockeghem Josquin Des Prez : Biography; At the court of Louis XI; Two Textual layers in Josquin 's 'Tu Solus'; The Motet-Lament 'Absalon, fili mi' ABSTRACT: The painting "Libreria Musicale" (Musical Library) by Giuseppe Maria Crespi, as a source of information on the "Storia della Musica" (History of Music) by Father Martini The music of Abraham Casseres (Jewish Music) Music in the Bible Jacques Offenbach: The Tales of Hoffmann The harp as a hidden symbol in Bernini's 'David' Other articles by G. 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