Author: Bottrigari, Ercole
Title: <Marginalia ad Galilei, Dialogo della Musica antica, et della moderna>
Editor: Massimo Redaelli
Source: Bologna, Museo internazionale e Biblioteca della Musica, MS B.79

[Lower case Roman numerals have been supplied for the dedicatory letter and higher case Roman numerals for the concluding Index.] [--] line 31: page [28. add. supra line] 38. 62. 83. 127. 142. 146. [-1-] line 16: Zarlino, Chapter 2 of the third book of the Supplementi [-2-] line 26: Proposition line 46: Zarlino, page 86-87. [-3-] line 14: F faut and high [sqb] mi. line 15: low [sqb] mi and F faut. 2/1 line 45: Fogliano, part three Chapter 4. line 46: [[minor]] radical [-6-] line 25: These do not belong to the Diatonic, apart from those of the b fa [sqb] mj [mainly 135 to 128. add. in figura], or to the synemmenon, but some of them belong to musica finta, and some to the Chromatic. [-7-] line 13: because, once the sesquiottavo Tone is divided into two larger parts as large as possible, as it cannot be divided into two equal parts, the Lemma is smaller than the other Semitone, line 23: page 109. line 24: [[minor]] radical. The ratio 25/24 does not belong to the Syntonic Diatonic, but to Didymus' Chromatic, which is used in the thickening of that one. line 28: [[16/15 x]] 25/24 x 16/15 375/43 384/375 128/125 line 47: Euclid, book 7, proposition 2 [-8-] line 16: [[minor]] radical line 33: 25/24 16/15 [[384]] 400/360 line 43: 10/9 x 9/8 81/80 line 56: ancient Comma [-9-] line 15: [[smalle]] [smallest corr. supra lin.] line 16: Largest Semitone. line 23: Smaller Semitone. line 39: page 70 line 41: namely, 128/135 [-10-] line 1: 9/8 16/15 144/120 line 3: 9/8 256/243 [[2304/1944]] [[576/486]] 32/27 32/27 x 6/5 [[162/160]] 81/80. line 5: [[minor]] radical line 21: [Bottrigari, Marginalia ad Galilei, Dialogo, 10; text: 32/27, 6/5 errore] line 31: 25/24 x 9/8 8/ [[216/200]] 27/25 10/9 45/ [[270/225]] 6/5 line 37: Zarlino page 94. line 45: [[that]] line 47: Zarlino, Supplementi, page 94, Chapter 4 of the third book [-11-] line 1: [[eighth]] ninth line 2: Zarlino Chapter 4 of the third book of Supplementi, page 94. line 13: 12. 9. 8. 6. 4. 3. line 14: [Bottrigari, Marginalia ad Galilei, Dialogo, 11, 1; text: a, c, d, f, g, h, k l, m, n, o, p, 2, 4, 12, 7, 8, 6, 3, Zarlino Propositione 14. del secondo Ragionamento delle Dimostrationi, page 116.] [Bottrigari, Marginalia ad Galilei, Dialogo, 11, 2; text: Zarlino Supplementi page 95. A, B, C, D, E, F, G, H, I, K, L, M, O, 3. 4. 6. 8. 12.] line 20: [[unequal]] line 25: Ptolemy relates in that place that Elicona is the name of that ancient and square instrument, but he says that its parallelograms are unequal, rather than equal. He provides two Demonstrations which are both contained in the above mentioned, because there is no difference from one to the other, except for the external Triangle F D O, which is the same to the Internal one B F A. line 32: purpose line 39: 32/27 6/5 [[162/160]] 81/80 line 47: Very great Error 19/16 6/5 96/95 m. 32/27 19/16 513/512 p. line 48: [Bottrigari, Marginalia ad Galilei, 11,3; text: è falso 19/16 ma si bene 6/5. et però conuiene, anzi è lo istesso Semiditono, ò Terza minore perfetta. E tal’ è la dimostratione. 25/24 x 9/8 [[216/200]] 27/25 x 10/9 270/225 6/5 Trihemituono.] line 57: radical. line 58: [[minor]] radical. line 59: 9/8 16/15 2) [[144/120]] 3) [[18/15]] 6/5 9/8 x 19/16 [[10/9] x 19/16]] 8) [[152/144]] 19/18 19/18 9/8 [[9) 162/152 19/16 81/76]] 9) [[171/44]] 19/16 [-12-] line 5: [[minor]] radical. line 6. [[minor]] radical line 20: 6/5 25/24 [[150/120]] 5/4 [-13-] line 37: [[minor]] radical infra line 50: [Bottrigari, Marginalia ad Galilei, Dialogo, 13: M, s] [-14-] line 3: radical. line 4: radical. line 24: radical. line 25: radical. line 35: 729/512 cubic number, Beginning, ancient cubic number line 41: 9/8 10/9 ditone 90/72 9/8 9) [[816/576]] [[90/64]] 45/32] [-15-] line 14: 4/3 25/24 [[100/72]] 25/18] line 27: 9/8 x 81/10 648/720 9/10 72. line 28: radical line 29: radical line 30: page 149. line 40: such line 41: other cases [-16-] [this operation is not called sum, but subtraction. This one is. And this one is better 4/3 16/15 64/45 add. supra lin. 1] line 1: not this one: but this 4. 3 line 2: 16. 15 line 3: 64. 45. line 42: radical line 43: radical [-17-] line 28: radical line 29: radical line 44: radical. line 45: radical. [-18-] line 2: 40: 27 81:80 3240: 2160 1080 3 2 line 3: Diapente or imperfect Fifth lacking a Comma line 10: [Bottrigari, Marginalia ad Galilei, Dialogo, 18; text: m. M. This fifth is lacking because it has the smaller tone above the fourth both in the low register as in the high one.] line 24: radical. line 25: radical. line 33: radical. line 34: radical. [-19-] line 18: radical. line 20: radical. line 32: radical line 33: radical. line 46: radical. line 47: radical. [-20-] line 3: Tenor Clef corrected to Alto Clef. line 6: radical. line 7: radical. line 20: radical line 21: radical. line 31: radical line 32: radical. line 45: radical line 46: radical. [-21-] line 4: radical. line 5: radical. line 47: Eptachord. radical line 48: radical. [-22-] line 1: 3/2 6/5 [[18/10]] 9/5 [Bottrigari, Marginalia ad Galilei, Dialogo, 22] line 4: Eptachord line 5: [radical add. supra lin.] terms line 13: and it is, because it contains two sesquiottavi Tones. e line 38: Eptachord [-23-] line 1: Eptachord line 44: radical. line 45: radical. [-24-] line 1: Eptacord line 12: radical. line 13: radical. line 12: [Bottrigari, Marginalia ad Galilei, 24; text: major sixth 5/3 6/5, minor third [[30/15]] 2/1, octave, seventh, Eptachordo 16/9 9/8, 144/72 2/1, sixth, 8/5 5/4 40/20 2/1, Eptachord, 16/9 10/9 160/81, incomplete] line 21: dupla 2/1 81/40 [[2/1]] line 22: 81/80 comma. line 34: Eptachord. line 35: radical. line 36: radical. [-25-] line 50: radicali. line 51: radical. line 56: radical. line 57: radical. [-26-] line 5: [[seminore]] line 23: great blunder; it would be necessary to create a new sign which would indicate the semitone 135/128, and thus the fifth would be made really perfect. However, in order not to deviate from common practice of the others, one might use the asterisk [signum] [-27-] line 8: anzi hora se ne ha quantità maggiore assaj. uedi il mio terzo Dialogo del Trimerone. line 14: it is false, because the signs of the smaller Semitone 135/128 noted above are missing, and the other largest from 27/26 and also the one of line 26: [sqb] 9/8 16/15 144/120 9/8 [[1296/960]] 27/20 b. 16/15 9/8 144/120 10/9 [[1440/1080] 4/3 4/3 x 27/20 Comma 81/10 difference [-28-] line 17: radical line 34: 5/4 x 4/3 line 35: 16/15 line 36: radical line 39: one can say that that passage of Plutarch is corrupted, and that he meant to say the number three and the number one above the number three. See Zarlino’ s Supplimenti musicali, page 108, Chapter 8, book iij. See also my Dialogue entitled La Mascara, or on the Theatres and the Tragic-satyric-comic Scenes. line 41: Zarlino, Supplementi, page 108. line 43: page prima [10. 29. add. supra lin.] 38. 62. 83. 127. 142. 146. [-29-] line 1: Zarlino, Supplementi page 108. line 12: Zarlino, Supplementi, third book, Chapter 8, page 108. line 17: therefore, Tripla instead of sesquiterza. line 21: it is a tripla, e not a sesquiterza line 22: it is not a sesquialtra, but a dupla. line 24: it is of equality, and not of diplasia, or in the ratio of the double. line 28: page prima 10. 38. 62. 83. 127. 142. 146. line 53: He really says this, because there is no need for that Consideration on the size of the Tones in that context. line 59: The Syntonic of Ptolemy is not different by the System used nowadays in singing and playing. [-30-] line 6: Zarlino, Chapter 4, book four, page 131. line 9: [Bottrigari copied this passage by Galilei in his Melone add. m. sec. fortasse Martini] line 17: Il Desiderio, Dialogue line 33: Zarlino, page 132 line 34: page 80. line 38: 2/1 5/3 10/3; 3/2 3/2 9/4 3/2 27/8; 10/3 x 27/8 81/80 line 39: they mean, in practice line 41: 12/5 line 43: [Bottrigari, Marginalia ad Galilei, Dialogo, 30; text: by a sesquiottantesimo Comma, 2/1 6/5 21/5; 4/3 4/3 16/9 4/3 64/27; 27/18 18/12 12/8; 64/48 48/36 36/27] [-31-] line 13: Convergences of the modern Diatonic with Ptolemy’ s Syntonic. line 14: Zarlino, page 133. line 30: It is really so. If one subtracts the smaller semitone from 25/24 the remainder is 27/25; if one subtracts the larger semitone from 16/15 the remainder is 135/128 line 43: Zarlino, 132 line 57: 7 [seventh ante corr.] important difficulties put forward. first line 58: second line 59: third line 60: fourth line 61: fifth line 62: sixth [-32-] line 5: Desiderio, Dialogue [-33-] line 3: Zarlino, Supplementi, page 189. line 13: Desiderio, Dialogue, page 38. line 43: Zarlino, Supplementi page 190, 191. line 54: page 191. [-34-] line 24: Aristotle, Canons line 26: Zarlino, Supplementi, page 191. line 57: Zarlino, Supplementi, page 192. line 60: instument of the Author [-35-] line 1: roughly one hundred years [Bottrigari, Marginalia ad Galilei, Dialogo, 35, 1; text: 8. 9. 10. 15. 16.] line 6: Ptolemy, Chapter 13, second book, where he also adduces other reasons. line 20: [ancient add. supra lin.] line 26: Zarlino, Supplementi, Chapter , book . line 34:32/27 81/64 [[2592/1728] [[1296/864]] [[648/432] x 3/2 648/432 x 3/2 324/216 81/54 [[4/6]] 3/2 1296/1296] [Bottrigari, Marginalia ad Galilei, Dialogo, 35, 2; text: 4/3, 32/27, 81/64, 16/15, 10/9, 9/8, 2/1] line 38: Ptolemy in the seventh chapter of the first book [-36-] line 5: Plato line 9: Guido of Arezzo did not want to put mark the note b. fa in the [sqb], and why. line 18: [[of his]] of Guido of Arezzo. line 23: this is not true, because the singing styles of the Germans, of the Turks, of the Italian, of the French and of the Spanish are all different. line 39: Oddo in his [[Micrologus]] Enchiridion [-37-] line 2: taken from the first book, Chapter four of Don Nicola Vicentino’ s book and quoted without attribution, but a capriccio, because Giovanni de Muris does not say a word about it in his Music book entitled Opus de Musica et de contrapunto regali. line 21; Oddo in his Enchiridion [-38-] line 3: page 96. line 24: 7 6 5 4 3 2 1 28 line 27: Many numbers, which are not perfect, enjoy this privilege, consisting in being composed by a number and by all its parts. For instance, 10 is composed by 4 and by all his parts, 1, 2, 3, 4, which added together produce 10. Equally, 15 is composed by 5 and by all his parts. 21 is composed by 6, 36 by 8, and also 45 by 9. In short, the rule is that all the numbers which are called triangular have this property of being composed by their base and all the parts of it. line 32: [signum] line 36: page 82. line 38: page prima [8. 29. add. supra line] 62. 83. 127. 142. 146. [-39-] line 1: Zarlino, Supplementi, page 135, chapter 4. of the fourth book. line 8: Zarlino, Supplementi, page 86. line 15: An Instrument, with which Archita used to treat small children and protect them from dangers. It is called 'tamburino' nowadays in Italy. The Romans called it ‘Tintinnabulum’, or ‘Crepitaculum’. line 25: If Saffo invented the technique of hitting the strings of the Cithara with the Plectrum, this is a sign that Epigonius was not the first one who used to play the strings with his fingers, if Epigonius did not live before Saffo. And if Epigonius used to pluck the Strings with a plectrum, Saffo was not the person who invented the use of the Plectrum. [Bottrigari, Marginalia ad Galilei, Dialogo, 39; text: 3. 4. 5. 6. 7. 8. 9. VI. X. XV. XXI. XXVIII. XXXVI. XXXXV.] [-40-] line 1: ‘Above –Angle’ [literal translation of the Epigonius] [-42-] line 4: [[Around the second]] near two thirds line 5: Zarlino page 167, chapter 16, book 4. Aristoxenus, book one, towards the end. They were thirty, as one can gather from the passage quoted above, because he constituted the tone of xij. six twelve line 7: [[whole]] [[sixty]] thirty line 8: to the contrary, instead. line 11: six lin, 12: Tetrachords [[Tetrachord]] line 17: [Bottrigari, Marginalia ad Galilei, Dialogo, 42; text: 60. 12. 24.] line 25: It was Ptolemy, rather than Aristoxenus line 33: The reason was that he wanted whole numbers, so that the proportions might be more clearly apparent, as they cannot be seen from the fractions. line 34: 499/486 line 42: this is absolutely true. line 48: the Monochord. Line 50: Zarlino, Chapter 27 of the fourth book of the Supplementi, page 198. [-43-] line 2: (as I have told you and demonstrated) [Bottrigari, Marginalia ad Galilei, Dialogo, 43, 1; text: A, B, C, D, 18, 16, 15, Tuono, Semituono, Semiditono ouer Terza minore] line 4: (since the whole is divided into eighteen equal parts, of which it contains two) line 5: after ‘esse’ [18. add. supra line] line 5: Argument subtle and beautiful, but exposed in a crippled way. line 13: this is not according to Aristoxenus' opinion, but Ptolemy’ s. line 25: Supplementi, page 198. Zarlino, Supplementi chapter 27, book iiij. Ptolemy, chapter xi of the first book of his Harmonics line 27: This is denied. line 27: 10/9 10/9 100/81 100/81 10000/6561 10/9 100000/59049; 81/1/ 81/80 6561/6400 81/80 531441/521000; 10000/59049 531441/512000 53144100000 118098000 59049 295251 3023308800 line 29: Sesquinono [Sesquiottauo ante corr.] line 44: 6/5 6/5 36/25 36/25 1296/625 16/15 26/15 53144100000/30233088000 256/225 318862600000 2657205 1062882 13604889600000 151165440000 60466176 60465176 6802444800000; 1364889600000 6802444800000 Dupla infra line 57: [Bottrigari, Marginalia ad Galilei, Dialogo, 43, 2; text: Semiditones, or minor Thirds, or Trihemitones, as we call them, which fill all the seven species of the Diapason in the Lute. Ditones, or major Thirds, [of the 7. add. supra line]] [-44-] line 3: 5/3 5/3 25/9 25/9 625/81 line 4: 2/1 2/1 4/1 2/1 8/1 line 10: it is denied that they are Equal in their proportion. line 13: 5/4 5/4 5/4 25/16 [[25/16]] line 14: 125.64 [[625/256]] 2/1 128/125 remainder] line 27: or 8/5 8/5 64/25 8/5; 4/1 x 512/125 4) [[512/500]] 128/125. [-45-] line1: [[ 2/1 2/1; 4/1 4/1; 16/1 16/1; 256/16/1]] line 4: first 2/1 2/1; 3/2 3/2; second ones 4/1 2/1; 9/4 9/4; third ones 8/1 8/1; fourth 81/16 81/16; sixth 64/1 2/1; eighth 6561/256 81/16; seventh ones 128/1. twelfths 531441/4096; 128/1 x 531441/4096; remainder 531441/524288; 7153/524288 line 13: error 531441. [521441. ante corr.] line 13: very grave error lin 14: false. It is larger. line 15: error 531441. line 15: 81/80/ 531441/524288; 42515280/42467328 maggioranza cioè 47952/42467328; 524288 81/524288 1494301; 42467328 line 17: error 42467328. [-46-] line 5: 2/1 2/1; second ones 4/1 4/1; fourth 16/1 2/1; fifth ones 32/1 line 7: first 4/3 4/3; second ones 16/9 16/9; fourth 256/81 256/81; eigh th65536/ 6561 256/81; twelfth ones 16777216/531441 x 32/1; 32) 17996112/16777261 largest part; 531441/524288 largest in the smaller numbers line 13: 2187. 6827. line 17: Error 531441. [-47-] line 10: Harpsichords and Organs cannot be joined with Lutes and Viols in performance, because of the disparities in their tuning. line 16: Desiderio, Dialogue. line 28: Desiderio, Dialogue. line 46: [Bottrigari, Marginalia ad Galilei, Dialogo, 47] line 49: One must be aware that the b flat of alamire, and the lifting of the note, or diesis of dlasolre are not found in keyboard instruments. One must also know that between a diesis there is, in participated fashion, one of our modern Commas. This is the reason, respectively, of the languid and harsh nature of which Galileo talks about. Since the b flat in one and in the other place is more tense than this one is, and that Diesis is participated through a Comma in those keyboard instruments. This happens because the dlasolre and the b flat of elami, just as between Gsolreut and the b flat of alamire there is a larger Semitone, and between dlasore and its raised note, or diesis, as betweem Gsolreut itself and its Diesis there is the smaller semitone.] [-48-] line 47: this is false line 49: page 9. line 14: that, line 25: and line 34: point; line 63: [Bottrigari, Marginalia ad Galilei, Dialogo, 48; text: A, B, A re, B fa, [sqb] mi, C fa, ut, D sol, re, Ela, mj, F fa, ut, G sol, re, ut, A la, mi, re, b fa, [sqb] [sqb] mj, c sol, fa, ut, d la, sol, re, e la, mj, f fa, ut aa la, mi, re, cc sol, fa, ut, b fa, [sqb] [sqb] [sqb] mj] [-49-] line 39: Zarlino, page 201. line 45: one must note that the double of the square 9 is 36 instead of 18. line 45: this is false; in fact it is 36. line 50: this is false in Theory and little true in practice. That Aristoxenus says this is also false. line 52: Zarlino, page 203. line 57: Zarlino, page 203. line 59: Zarlino, page 203. line 59: It is a good, very good and very true point. Absolutely. line 59: Or rather, it is absolutely true and Euclid testifies to this. I am referring to the String though, rather than the bow. infra line 60: [Bottrigari, Marginalia ad Galilei, Dialogo, 49; text: 1. 2. 3. 4. 5. 6. 7. 8. 9. 1. 11. 12. A. c, d, e, f, g, h, i, k, l, m, n, o, p, 18. 17. 16 1/18. 15 53/324. 14 1873/5832. 13 55169/104976. 12 1467253/1889568. 12 2191985/34012224. 11 24i337089/612220032. 10 31390[<..>]6069/198359290368. 9 2147671268017/3570467226624. 9 4206546516673/64268410079232. 8 649926981496529/1156831381426176] [-50-] line 14: [Bottrigari, Marginalia ad Galilei, Dialogo, 50; text: difference, 24. 27. 13. 192, 216, 243 [46 ante corr.], 256, Tuono, Semituono, 12, 14, 17, 324., 13, 39] line 24: induced [induisse ante corr.] line 32: 192 Stable line 33: 228 Variable, Chromatic particular. line 34: 243 Variable, also in common with the Enharmonic and Diatonic. line 35: 256 Stable. [-51-] line 2: Boethius. Therefore, he was [Boetit. Therefore, he was ante corr.] line 3: Euclid, Harmonic Isagoge line 23: on cannot read even a word on this matter. [-53-] line 3: first line 4: Zarlino, Chapter 18, book iiij of the Supplementj [signum] line 4: of the [from the ante corr.] line 4: sound, line 5: contains, line 8: The frets on the neck of the Lute and of the viol became smaller going from the bridge to the extremity of the neck itself. line 15: Zarlino, page 168, Chapter 16, fourth book line 19: It is really the opposite. Lin 22: small note: [[&]] line 23: What fantasy is this? Aristoxenus never spoke about the Lute nor he would have ever been able to have any knowledge of it at all. line 30: page 49. m. line 31: second line 33: [[17/16 x]] 18/17 x 17/16 289/288 difference line 36: which [is add. supra line] not line 38: Zarlino, Chapter 16, book 4. of the Supplementi line 42: Zarlino, Chapter 18 [Chapter 16 add. supra line] of the fourth book of the [signum] line 43: This is not true. line 48: Great ignorance line 49: 1 ½ è 90; 3/4 è 45 line 50: third line 58: Aristoxenus wrote many volumes on Arithmethic, he was a pupil Aristotle’ s and he was acquainted with Theophrastus et cetera . Suida, page 112. [-54-] line 7: the Authority of Aristoxenus which supports Ptolemy is greater still line 12: according to Ptolemy: 12 – Semitone 24 – Tone 14 – Tone; 60 Diatessaron. According to Aristoxenus: 6 – [[12 ante corr.] Semitone 12 – Tone 12- Tone; 30. Diatessaron line 13: page 42. They were 30. They were doubled then by Ptolemy, because the number 60 was more comfortable and to avoid fractions in the sesquialtera Chromatic species. line 16: Who is not aware of this? line 57: This is denied, because of what has been noted above. line 60: It is, rightly, a sesquiterza, because it is composed by a sesquiquindicesimo semitone, by a sesquiottavo Tone and by another sesquinono Tone. line 60: It is, rightly, a sesquiottavo. line 62: It is truly so. [-55-] line 6: It is truly so. line 28: (as I have said) line 29: This is good. line 32: (as in the Lute and the Viol) line 43: Zarlino, Supplementi, page 251. m. Chapter four, book sixth line 46: Alypius said it himself, and he demonstrated the Characters one by one. line 50: diminished [tense, or smaller than perfect add. supra line] [-56-] line 8: Alypius in his Music [-57-] Demonstration of the thirteen Tones according to Aristoxenus’ intention, with two that were added by his followers in the higher register, which all together reach the number of fifteen [; and they are described by Alypius in his Isagoge add. infra] [-59-] line 5: Chapter 16. of the fourth book. line 13: page line 18: in this edition there is no demonstration of the Characters in that Chapter 14, but only a Table with lines which should have been used for pages and verses. How can it be that it is in bad condition and incorrect? line 38: Euclid, Isagoge [Bottrigari, Marginalia ad Galilei, Dialogo, 59; text: false] [-60-] line 7: [[Bottrigari, Marginalia ad Galilei, Dialogo, 60, 1; text: A, [Sqb], C, D, E, F, G, a, [sqb], c, d, e, f, g, aa, Proslambanomenon, Hypate hypaton, Parypate, Licanos, Lichanos Meson, Mese, Paramese, Trite diezeugmenon, Paranete, Nete hyperboleon, Synemmenon, mi, [sqb], La, re, a, D, sol, ut, G, C, fa, F, [Sqb] anzi fa, b] m. rec. fortasse Martini] line 32: only as far as it concerns the first low Diatessaron, as to the rest, no. line 41: Or rather, ascending, as Euclid demonstrates in his brief harmonic Institution. line 50: Boethius, Chapter 20 of the first book line 52: second line 55: third [-61-] line 45: it is not an instrument, but a semicircular bridge of the kind used in the Monochord, of which talks Ptolemy at Chapter 8 of the first book.. line 58: 'Archicimbalo' is called as sign of respect the harpsichord made by Don Nicola Vicentino, because it contains all the three harmonic genera according to the division which he made. [-62-] line 2: Zarlino, Supplimenti page 83. [28. 38. add. supra lin.] 127. 142. 146.] line 40: Then it is stable, since it is one of the stable Notes, in the Dorian Mode or Tone, as well as in the Hypodorian in all three of the harmonic Genera. [-63-] line 3: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 1; text: DORIO, E, a, e] line 23: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 2; text: FRIGIO, D, G, d] line 24: [[where]] [in the place, where add. in marg.] line 30: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 3; text: LIDIO, C, f, c] line 35: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 4; text: MISSOLIDIO, [Sqb], e, [sqb] [sqb]] line 44: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 5; text: HYPOLIDIO, F, [sqb] [sqb], f] line 49: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 6; text: HYPOFRIGIO, G, c, g] line 52: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 7; text: HYPODORIO, a, d, a di Euclide] infra line 61: [Bottrigari, Marginalia ad Galilei, Dialogo, 63, 8; text: Hypodorio, Hypofrigio, Hypolidio, Dorio, Frigio, Lidio, Missolidio, Mese.] [-64-] Demonstration of the seven Tones [[according]] [Against add. supra line] Ptolemy’ s intention. [But in a way which is very similar to the Description provided by Euclid add. infra lin.] [Bottrigari, Marginalia ad Galilei, Dialogo, 64; text: HYPODORIO. HYPOFRIGIO. HYPOLIDIO. DORIO. FRIGIO. LIDIO. MISSOLIDIO.] [-65-] line3: Supplementi, 243. line 18: Truly, in this way line 19: [[Phrygian]] [Lydian. corr. in marg.] line 20: [Bottrigari, Marginalia ad Galilei, Dialogo, 65; text: DORIO. LIDIO. t, s] [-68-] line 14: oh what a dream, what a vain thought. line 33: page 96. line 37: Chapter 10, book ij. line 38: [Bottrigari, Marginalia ad Galilei, Dialogo, 68; text: 1. 6. 4. 2. 7. 5. 3. Limma, Tuono, Missolidio, Lidio, Frigio, Dorio, Hypolidio, Hypofrigio, Hypodorio] [-70-] line 38: It was Euclid, not Ptolemy. On the contrary, Ptolemy created no application or distribution of those Species of the Diapason to the Tones, if not to show the position of those. He spoke about those Species clearly at the end of the fifth Chapter of the second [first ante corr.] book. However, he did say at chapter 9 of the same book that it would be a beautiful thing if the number of those Tones was not greater than the number of the species of the Diapason, adducing the demonstration, or the reason. In the same Chapter 9 of the second book he places the Mixolydian in the highest register, and the Hypodorian in the lowest one, assigning to the other five Tones their place in relation to their distance, namely, so that there be a Tone between the Hypodorian and the Hypophrigian, another Tone between the Hypophrigian itself and the Hypolydian, and a limma between the Hypolydian and and the [[Missolid]] Dorian. He put a Tone between the Dorian and the Phrygian, another tone between the Phrygian and the Lydian, and, finally, a Limma between the Lydian and the Mixolydian, so that a Tone was lacking to complete, as he says, a Diapason. At the end of Chapter 5 of the second book he places the first species of the diapason between the Hypatehypaton and the paramese; the second species between the parhypate hypaton and trite diexeugmenon, and thus, consequently the fourth, the fifth and the sixth. Finally, he put the seventh between the proslambanomenos, and the Mese and the Nete hyperboleon. Infra line 62: [Bottrigari, Marginalia ad Galilei, Dialogo, 70; text: A. Hypodorio. B. Hypophrigio. C. Hypolidio. D. Dorio. E. Phrigio. F. Lidio. G. Missolidio, prima seconda, terza, quarta, quinta, sesta, settima specie] [-71-] line 2: Euclid, I mean. line 22: book 2. line 24: book ij, chapter 10. line 50: Ptolemy, Chapter 10 of the second book of his Harmonics. [-72-] line 11: Bede, who lived 300 years earlier. The Authors quoted above lived around the years 1020, 300 and 720. [-73-] line 1: [Bottrigari, Marginalia ad Galilei, Dialogo, 73] line 41: Zarlino nel Capitolo 7. della 4. parte delle Institutioni [-75-] line 47: [[middle]] [middle add. in marg.] [-77-] line 32: [[doubt]] [ abuse add. supra line] line 43: Zarlino, Chapter 31, book 4. of the Institutioni line 50, addendum: [[In considering]] [-78-] line 16, in marg.: Dodecachordon [Dodecardon ante corr.] line 39, in marg.: [signum] [-79-] line 11: [signum] [-80-] line 18: [signum] line 26: 1581 150 1431 line 30: page 30. line 31: Modern style of singing for several voices has not been in use for more than one hundred and fifty years. line31: I have some Canzoni or Barzellette in books printed in Venice from 1480. line 36: Zarlino, Chapter 7, book 8. of the Supplementi, page 306. [-81-] line 13: [signum] line 38: [signum] line 45: Zarlino, page 309. line 46: from one of them [from one ante corr.] line 51: accompaniment [-82-] line 5: [signum] line 19: [signum] line 26: Desiderio, Dialogue [-83-] line 8: page 1, 28. [29. add. supra lin.] 38. 62. 129. 142. 146. line 38. Boethius, proem line 52, added note: Zarlino, page 311. [-84-] line 11: [regardless of Galilei’ s opinion, novelty is one of the most attractive virtues of modern Music, at least in our day add. Martini.] line 31: It is completely false line 36: page 80. line 51: [signum] [-85-] line 46: , and Cicero’ s eloquence. line 55: since Musical Aesthetics was not know at that time, it was impossible to achieve what Galilei would have still wanted in his wisdom. Martini [-86-] line 2: [signum] line 11: added note: 17. line 15: [by now he was performing more miracles that Saint Anthony!! nevertheless, commenting this passage one can find some truth in it. add. Martini] line 23: [the author trusts the lies of the Greeks too much. add. Martini] line 28: [I am surprised with how Galilei gives so much weight to Greek Mythology, and he does not limit himself to take from it just what it is necessary, [[aside]] leaving aside empty tales. add. Martini] [-88-] line 9: [Bottrigari, Marginalia ad Galilei, Dialogo, 88] line 29: the Example of this as well is at page 96. line 42: [Even nowadays the eye takes more pleasure than the ear in the fugues. add. Martini] [-89-] line 1: [signum] line 11; Cipriano Rore un’ altra volta ha Continenza line 45: Zarlino page 317. line 46: [signum] line 48: first line 50: second line 50: Instruction XV. line 51: third, fourth line 52: fifth, sixth line 53: seventh, eighth, ninth line 54: tenth, eleventh line 55: twelfth, thirteenth, fourteenth line 56: fifteenth line 58: Zarlino, page 317. [-90-] line 1: Zarlino, page 317. line 30: At Chapter 54 of the fourth Book he shows the eight Tones or Tropes, but only in the Diatonic Genus. [-91-] line 37: This is what I believe, therefore, I added the Tables of the three species of the Diatonic Genus, the two of the Chromatic and the single one of the Enharmonic according to Ptolemy line 39, added note: in the harmonic Isagoge line 40: in the proem of Alypius. See also Gaudentius at Chapter uiij. of his harmonic Institution. line 52: this is a great silliness, because one finds that the Characters of the Sound, as those of the Notes are transposed from a Mode or Tone to another. In my opinion, we must believe that those Characters are signs which indicate the Strings that need to be touched, as Alypius, Gaudentius and Boethius say, in the same way that we use signs to indicate the frets of the lute and also Its Strings. Boethius himself in that third Chapter says it clearly. Gaudentius notes it at Chapter 8 and Alypius at the beginning of his Isagoge. [-92-] [IN THE DIATONIC GENUS add. in marg.] line 11-13: Synemmenon line 22: note, string line 30-32: Synemmenon line 41: note, String line 49-51: Synemmenon infra line 57: NOTE, STRING [-93-] [ACCORDING TO THE DIATONIC GENUS add. in marg.] line 3; note, String line 11-13: Synemmenon line 22: note, String line 30-32: Synemmenon line 41: Uoce, Corda line 49-51: Synemmenon infra line 57: NOTE, STRING [-94-] [SECONDO IL GENERE DIATONICO. add. in marg.] supra line 1: NOTE, STRING line 4: , or Hyperdorian. [Alypius add. supra line] line 4: note, String line 12-14: Synemmenon line 23: , or Hyperphrygian. [Alypius add. supra line] line 23: note, String line 31-33: Synemmenon. line 50: they are fine as they are, so Galileo is wrong. line 51: Since there is no real difference. [-96-] line 9: Saint Gregory the first was the inventor of this kind of musical Characters, according to hearsay. Et esso Guido of Arezzo demonstrates this in His Micrologus with more than one Example. [Bottrigari, Marginalia ad Galilei, Dialogo, 96; text: [sqb] line 13: On the contrary, they are all there, proceeding as one has to proceed through the various species of the Diapason. line 22: Ptolemy says it clearly at Chapters 8, 9, 10, and 11 of the second book. line 25: So, Alypius lived before Ptolemy. line 35: page 37. [-97-] line 1: Primo line 2: [Alpha] line 19: Second. line 20: B line 36: [Gamma] line 58: 3. line 59: [Delta] [Bottrigari, Marginalia ad Galilei, Dialogo, 97, 1; text [Aeide Mousa]] [Bottrigari, Marginalia ad Galilei, Dialogo, 97, 2; text: [Khionolepharou]] [Bottrigari, Marginalia ad Galilei, Dialogo, 97, 3; text: [potamoi de sethen]] [Bottrigari, Marginalia ad Galilei, Dialogo, 97, 4; text: [Nemesin pteroessa, ï, M] line 75: this is the same clear Sign that Galileo could not read the Greek Language. [-99-] line 55: Instrument that is called Fagotto, which is demonstrated exhaustively by Father Don Teseo, Regular Canon, who was servant of Knight Ciro Spontone’ s. They used to sing with much elegance accompanying themselves with this instrument, which I did hold myself in my hands. There are also the bagpipes [with a bag add. supra lin.] the Bagpipe or Sordina, which also has a bag which is filled with air through a small pipe, and, once it is inflated, one holds it under the left shoulder, and thus this bag provides the air for the Pipe connected to it. And thus [verba quattuor] corna in [verbum unum]. line 60: the Blind man from Furli, Teseo from Ferrara line 61: you have been able to see infra line 62: Don Teseo Ambrosio, Regular Canon, in his book of the Introduction to the Chaldean Language and to other different ones, page 33 describes this instrument named Fagotto, and provides a perfect demonstration at page 179. [Bottrigari, Marginalia ad Galilei, Dialogo, 99; text: piua da bolza, ò Sordina.] [-100-] line 24: page 147. [-101-] line 28: Antigonus line 33: che [cha ante corr.] line 58: added note: see on the 5 book of the History of Mesochorus. They used this to tell the time. [-102-] line 36: Zarlino, Supplementi page 124, book 4, Chapter 2. line 49: Zarlino Supplementi page 125, book 4. line 58: Zarlino Supplementi, page 125 [-103-] line 2: Boethius, Proem of His Music line 10: Zarlino, Supplementi page 125, book 4. [-104-] line 33: [diapason queen of the Consonances add. Martini] line 43: [signum] [-105-] line 13: [He says the opposite in the discourse on the Works of Zarlino, page 102, and he is proved wrong by Bontempi, page 80 add. m. rec.] [-106-] line 10: transferring itself [trasferensi ante corr.] line 15: Chapter 14. of the second book line 59: This is result of scant diligence, since Ptolemy, at Chapter 14 of the second book of his Harmonics describes them all orderly and a little further he describes also their combinations with the Diatonic. [-107-] line 14: . Altri, [altri ante corr.] [Bottrigari, Marginalia ad Galilei, Dialogo, 107, 1; text: Tuono, 9/8, lemma, 192, 216, 243, 256, [sqb] [[6144.]] [[6912.]] [[7777.]] [[8192.]], 24. 27. 13. [[768.]] [[864.]] [[416.]] ANTICO ERATOSTENE] line 32: This has no consequence whatsoever. [Bottrigari, Marginalia ad Galilei, Dialogo, 107, 2; text: 21, 27, 8, 168, 189, 216, 224, [sqb.] 213. [293. ante corr.] i, ARCHITA] line 34: Boethius Chapter 12 and 15 of the fifth book del 5. line 35: it is completely false. [Bottrigari, Marginalia ad Galilei, Dialogo, 107, 3; text: 1, 2, 15, 17, 19, 20, 12. 16. [12 ante corr.], 6. un Tuono. Semituono. supertripartiente quindici 17/15, superbipartiente diciasette. 19/17, sesquidecimanona 20/19, ARISTOSSENO] [-108-] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 1; text: 5. 3. 2. 30, 35, 38, 40, ARISTOSSENO [[90.]] 30. 5. [[15]], 30. [[105.]] [[2.]] 3. [[114.]] 38 [[6.]] [[120.]] 40 [[2. Diesis Enharmonij]] [un Semituono. Add. supra line] 180. 210. 228. 240. sesquisesta 7/6 supertripartiente [superquadripartiente ante corr.] 35 38/35, sesquidecimanona 20/19] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 2; text: 24. 27. 30. [sqb.] 32. [[71.]] [[81.]] [[90.]] [[96.]] [[9.]] [[6.]] 3. 2. DIDIMO] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 3; text: TOLOMEO, [sqb.] 9. 10. 11. 12. [[90.]] [9. ante corr.] [[100.]] [10. ante corr.] [[110.]] [11. ante corr.] [[120.]] [12. ante corr.] 10. [1. ante corr.] differenza] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 4; text: [sqb.] 9, 10, 8. 15, 9, 16. 36, 40, 8, 45, 15, 16, 48] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 5; text: [sqb.] 7, 8, 9, 10, 20, 21, 63, 72, 80, 84] [Bottrigari, Marginalia ad Galilei, Dialogo, 108, 6; text: divided by 3. [[504.]] 168, [[567.]] 189, [[648.]] 216, [sqb.] 224 [[672.]] these numbers are precisely the same as those put by Ptolemy at the end of his fifteenth Chapter of the first book of his Harmonics. [[63.]] 21. [[81.]] 27. [17. ante corr.] [[24.]] 8.] [-109-] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 1; text: 16/19, 243/256, 64, 76, 81, 85 1/3, [sqb.] [[6144.]] [[7196.]] [[7776.]] [[8192.]] [[1512.]] [[486.]] [[416.]] 12. 5. 13. Cromatico ANTICO] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 2; text: 189, 224, 243, 252, [sqb.] [[1512.]] [[1792.]] [[1944.]] [[2056.]] supercinqueuentisettecima. superdiciannoueducenticinquantecima. sesquiuentottecima. These numbers are the same as those put into his Table by Ptolemy. [[280.]] [[152.]] [[72.]] 35. 19. 9. ARCHITA] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 3; text: 45, 56, 58, 60, [[90.]] [[112.]] [[116.]] [[120.]] [[444.]] [[8.]] [[12.]] [[4.]] 11. 2. ARISTOSSENO] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 4; text: 15, 18, 19, 20, [[F.]] [sqb.] [[90.]] [[108.]] [[114.]] [[120.]] [[16.][[6.]] 3. 1.] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 5; text: 60, 74, 77, 80, [[180]], [[226]], [[239]], [[240]], [[90.]] [[111.]] [[115 ½]] [[[115. ante corr.]]] [[120.]] Supertripartientesettantaquattresima [Supertripartiente115 ante corr.] supertripartiente settantasettesima [Sesquiuqntitreesima, ante corr.] [[21.]] [[4.]] 14. 3. Aristoxenus himself says it clearly in the second book of his Harmonics., adding there that the whole Dense, or Thick, namely, the first tow low Intervals added together are sesquialteri and the two lowest of the Enharmonic, because these are 9 and those 6.] [Bottrigari, Marginalia ad Galilei, Dialogo, 109, 6; text: this does not matter. 15, 18, 19, 20, [[40]], [[54]], [[57]], [[60]], [[90]], [[108]], [[114]], [[120]], E. D. C. [sqb.] [[1800.]] [[2160.]] [[2250.]] [[2400.]] [[360.]] [[190.]] [[120]] [[150.]] [[120.]] 3. i. ERATOSTENE] [-110-] [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 1; text: DIDIMO, 60. 72. 27. 80. 12. 3. 5.] [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 2; text: Tolomeo divided by 63, 66, 77, 84, 88, [sqb.] [[4158.]] [[4851.]] [[5292.]] [[5544.]] Sesquiundecima [Sesquiquindecima ante corr.], Sesquiuentunesima [Sesquiuentesima ante corr.] [[693.]] [[441.]] [[232.]] [[6.]] 11. [[12]] 7. 4.] [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 3; text: TOLOMEO i05 [105 ante corr.], [sqb.]] line 9: Enharmonic. line 9: [[used]] [placed add. supra line] line 10: I have not know this in relation to the proportions, but only as to the extreme Notes. [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 4; text: OLIMPO, [sqb.] [[644.]] [[7776.]] [[7984.]] [[8192.]] [[1632.]] [[208.]] 384. 486. 499. 512. 102. 13. divided by 16.] line 12: [[Enharmonic]] Diatonic. [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 5; text: ARCHITA, 84, 105, 108, 112, [sqb.] [[378.]] [[54.]] [[71.]] 21. 3. 4.] [Bottrigari, Marginalia ad Galilei, Dialogo, 110, 6; text: ARÍSTOSSENO, 30. 38. 39. 40. [[90.]] [[114.]] [[117.]] [[120.]] [[24.]] [[3.]] 8. 1.] [-111-] Bottrigari, Marginalia ad Galilei, Dialogo, 111, 1; text: ERATOSTENE, [[120.]] [[152.]] [[156.]] [sqb.] [[160.]] [[32.]] [[4.]] 8, 1, 30, 30, 39, 40, [[90.]] [[114.]] [[115.]] [[120.]] line 4: it is false, because, if it was convenient in the first two, it would be convenient necessarily in the remaining third one, and so it would be both Chromatic and Enharmonic. [Bottrigari, Marginalia ad Galilei, Dialogo, 111, 2; text: DIDIMO, [sqb.] [[120.]] [[150.]] [[155.]] [[160.]] 24, 30, 31, 32, 6. 1.] [Bottrigari, Marginalia ad Galilei, Dialogo, 111, 3; text: [sqb.] [[Super23partiente92.]] [sesquiquarta add. supra line] [words of someone who does not understand very well add. infra line], 2 ½, 4 53/60, 2 37/20 90. 0 112. 20. 117. 23. 120. 0 Numbers put in his table by Ptolemy in the fifth Column at Chapter 14 of the second book in his very Enharmonic, and at Chapter 15 of the first book, thus: 63756. 79695. 83160. 85008. 4/3, 23/ 24, 45/46] [Bottrigari, Marginalia ad Galilei, Dialogo, 111, 4; text: INCERTO [[4620.]] [[5775.]] [[6050.]] [sqb.] [[6160.]] [[1155.]] [[275.]] [[110.]] 231, 55, 22, 924, 1155, 1210, 1232] line 5: It is definitely a great gift. It is something derived from the Tables put by Ptolemy at Chapters 13, 14, and 15, of the first book and repeated at Chapter 14. of the second book. [-112-] line 13: Quinta parte line 14: Martianus Capella line 17: Aristoxenus pupil of Aristotle’ s, and page 53 line 33: It is not convenient to doubt of this. line 41: Not this, because in the Chromatic of Didymus which is employed nowadays it can be used uncompoundedly, singing from Elami to raised Ffaut, because there is the sesquiquindicesimo Semitone between E lami and F faut, and between F fa ut and et raised F faut there is the sesquiventiquattresimo semitone. These added together contain the sesquinono Tone and smaller. This happens in descending but never in ascending. Example: [Bottrigari, Marginalia ad Galilei, Dialogo, 112] [-113-] [Bottrigari, Marginalia ad Galilei, Dialogo, 113; text: Hypate, Parhypate, Lychanos, Mese.] [-123-] line 51: [However, hot is it possible that Terpander invented the Lyre with seven strings, if it had been used by Orpheus and by others? add. Martini.] [-124-] line 8: [Completely untrue. The inventor of something is always the inventor of it. If someone makes some improvements to it he will be someone who perfects it add. Martini.] line 45: shell. line 53, added note: [[Interpretatio]] [Explanation add. supra lin.] line 55, added note: [[around]] [on the add. supra line] [-126-] line 15: Benedetto Egio, page 127. [-127-] line 5: ire [collera ante corr.] line 17: Censorinus. line 19: Nicomachus. line 26: Briennius. line 30: page [28, 29. add. supra lin.] 38, 62, 83, 142, 146. line 30: [signum] line 33: Diocle, Suida. Words of Suida in its Historical matters. Firstly, at the entry DIOCLES: “Diocles of Athens of of Phlius. They say that he invented musical proportions from vases of terracotta called Oxybapha which he hit with a small stick.” Then, at the word [Oxylyphion]: “Diocles of Athens was the first one to invent musical proportions from terracotta vasis, which he used to hit with a small stick.” And also at the word [Oxybaphion] one reads: “They say that Diocles of Athens invented musical proportions from [Oxybapha], namely vases of terracotta, which he hit with a stick.” line 35: [The story of the invention of Diocles is more natural than the one involving Pythagoras, which provokes laughter and nothing else. add. m. rec.] line 36: [signum] line 43: Benedetto Egio on Apollodorus, page 126. [-128-] line 49: 28. 29. 127. [-130-] line 5, added note: canto [chapter ante corr.] line 19: [What infantile words Galileo uses to name and explain the plectrum! add. man. rec.] line 29: From the monuments or paintings from Herculaneum one fints that the Lyra was not placed on the chest, but one the knees. add. man rec.] [-131-] line 19: [signum] [-132-] line 28: 6. 8. 9. 12. line 30: Zarlino line 35: 12. 9. 8. 6. line 54: [signum] line 55: what great ignorance! No learned person would state this. line 60: exterior, rather than interior greatness. See what Galilei wrote later on in his Discourse on Zarlino’ s Works at page 104, where he deals with the Weights that Pythagoras attached to the Strings to compare them to the proportions of the musical Consonances found thorough the Hammers. [-133-] line 9: instruments, line 9: air, line 11: that, line 17: tensed, line 18: intelligible, and line18: then, line 19: measures, line 21: distinct line 23: water, line 24: sounds, line 24: strings, line 25: numbers, line 25: order; line 25: concave, line 26: that, line 27: to [a ante corr.] line 27: it is very true, and people make songs on it line 28:[Con simili strumenti acustici oggi si danno anche dei concerti add. m. rec. line 36: [signum] line 46: they call it Tympanum. [-134-] line 15: page 145. [-135-] line 22: according to the ancients this is a Diapason, namely from Mese to Nete hyperboleon. line 45, added note: [[second]] third. line 56: A. line 56: Zarlino, page 299. line 61: notions [notion ante corr.] [-136-] line 14: 24. 12. 9. 8. 6. line 16: B. 23: Zarlino, page 300. line 29: [Bottrigari, Marginalia ad Galilei, Dialogo, 136, 1; text: 16. 8. 4. 2. 36. 12. 16. 3.] line 29: [[The greater part of the whole is the half]] [false corr. supra line] line 38: C. line 40: [Bottrigari, Marginalia ad Galilei, Dialogo, 136, 2; text: 24. 12. 26. 8. 9. 6.] line 51: [Bottrigari, Marginalia ad Galilei, Dialogo, 136, 3; text: 18. 12. 9. 6. 3.] line 60: [Bottrigari, Marginalia ad Galialeum, 136, 4; text: [[12. 3. 6.]] 24. 12. 6. 144. [[16.]]] line 62: diuisore. Venghiamo [diuisore uenghiamo ante corr.] [-137-] line 3: [Bottrigari, Marginalia ad Galilei, Dialogo, 137, 1; text: 144. 24. 12. 6. 144.] [line 8: 12 x 12 = 144 add. m. rec.] [line 9: 26 x 6 = 144 add. m. rec.] line 12: [Bottrigari, Marginalia ad Galilei, Dialogo, 137, 2; text: arithmetic, 4. 3. 2. Harmonic, 6. 4. 3.] line 15: [Bottrigari, Marginalia ad Galilei, Dialogo, 137, 3; text: Divisor Harmonically smaller 6. 12. 8. 6. 18. 36. 2.] line 26: D. line 26: [[D.]] line 28: Zarlino, Supplementi page 301. line 32: Pythagorean Hammers et cetera, page 130. line 33: namely, 24. line 35: Zarlino page 30j. [300. ante corr.] line 37: E. line 38: observed, line 38: that, line 40: books, line 42: Zarlino page 302. line 49. [Bottrigari, Marginalia ad Galilei, Dialogo, 137, 4; text: 12. 9. 8. 6.] line 60: F. line 62: Zarlino, page 302. infra line 62: [Bottrigari, Marginalia ad Galilei, Dialogo, 137, 5; text; in the ancient Diatone. 24. 12. 9. 8. 6.] [-138-] line 2: Zarlino page 302. line 3: G. lin 4: [Bottrigari, Marginalia ad Galilei, Dialogo, 138; text: 6. 5. 4. 3.] line 11: [signum] [-139-] line 10: [signum] line 10: one could say that he meant Zarlino, and perhaps himself. line 27: [signum] line 27: Fronimo Dialogue by the same Author [-140-] line 31: [signum] [-142-] line 12: page prima [28. 29. add. supra line] 38. 64. 83. 127. 146. line 13: [signum] line 17: [signum] [-143-] line 48: Distribution and way to tune the double Harps. [-144-] line 1: [Bottrigari, Marginalia ad Galilei, Dialogo, 144; text: double, DISTRIBUTION OF THE STRINGS OF THE DOUBLE HARP.] line 10. page 40. 41. line 12: [signum] line 31: Harpsichord line 34: [signum] line 37: See also Il Desiderio, Dialogue page 40. m. line 41: all [tuttta ante corr.] [-145-] line 22: [signum] line 22: Aristotle, Problema number 49, which is also number 30. line 45: [signum] line 45: There is no error in the text, if it is taken as a Proposition. One must be very doubtful abut the resolutions, because of the scant understanding that one can derive from them. [-146-] line 16: or line 16: Theocritus, Idyll, I have a Pan flute made of seven pipes stuck together. line 19: [Bottrigari, Marginalia ad Galilei, Dialogo, 146; text: Syrinx.] line 56: Lute. line 58: page, 1, [28. 29. add. supra line] 38. 64. 83. 127. 142. [-147-] line 5: Guido in his Micrologus admits that the Gammaut was in use in his times. line 9: 2. line 10: 1. line 18: Lute. line 44: page 48. line 51: page 100. [-148-] line 3: [signum] line 25: Sersillabi line 56: [signum] [-I-] line 44: 145. line 45: He wrote many books on Mathematics and was a student of Aristotle’ s 53. [-III-] line 57: [[proportions]] Harmony [-IIII-] line 27. Giouanni de Muris 37 line 31: , et essere lo istesso della Siringa infra line 59. carte 6. 8. 13. 17. 29. 32. 28. 48. 54. 55. 59. 60. 61. 63. 65. 68. 71. 72. 74. 76. 77. 80. 81. 82. 83. 84. 88. 90. 94. 96. 98. 100. 103. 104. 105. 107. 112. 117. 118. 120. 1212. 122. 129. 142. 144. 146. [-V-] line 6: Lute. 146. line 22: -137. line 32: Lute. 146. [-VI-] line 1: [Pietro Strozzi add. supra line] line 49: Arithmetic Progression which is also called proportionality. 136 is its divisior, Geometric proportionality, Progressione aritmetica; che anco proportionalità si dice. 136. Et suo diuisore. Proportionalità geometrica, et suo diuisore 136. Proportionalità Harmonica, e suo diuisore 137. add. supra line [-VIII-] line 10: [Don Teseo Ambrosio 99. add. supra line] [-VIIII-] line 21: Z line 22: Zarlino 6. 8. 13. 17. 29. 32. 28. 58. 54. 55. 59. 60. 63. 65. 66. 68. 71. 72. 74. 76. 77. 80. 81. 82. 83. 84. 88. 90. 94. 96. 98. 100. 103. 104. 107. 112. 117. 118. 120. 121. 122. 123. 132. 144. 146.