Hoc in volumine haec opera continentur

[continues from previous page] than others [are] unmodulated; some are more [so]. Therefore, in which of them there is more communication, they are more modulable; in which there is less, they are more lacking in modulation. Since it is necessary for every mutation to have something common, either a note or an interval or a system, communication is grasped through the similarity of notes. For when they fall into mutations between one another, similar notes become modulable through the participation of density; but when they are dissimilar, the mutation is lacking in modulation through the melopoeia composition of melody, when the mutation is made from a diastatic manner into a systaltic or hesychastic or into one of the others. The diastatic manner of melopoeia is that by which magnificence and the exaltation of a manly soul and heroic deeds and affections accommodated to these are signified. Tragedy uses these primarily, and the others which are assigned to this figure. The systaltic [manner is that] by which the soul is gathered, devolved into humility and an affection that is not at all manly. This kind of constitution is suitable for amorous affections and groanings and lamentations and others of that kind. The hesychastic manner is the melopoeia to which happens the peaceful constitution of the soul and the liberal and peaceful [state], to which hymns, paeans, proclamations, counsels, and other things of this kind are congruent.

¶ Concerning Melopoeia

A decorative initial 'M' is depicted. Melopoeia is the use of the aforementioned parts of harmony and those which have power; there are four [modes] by which melopoeia is constructed: Agoge succession of notes, Ploce weaving of intervals, Pettia selection of notes, Tone tenor of the voice. Agoge, therefore, is the melody from consecutive notes. Ploce is the mutual position of intervals [in a] parallel [manner]; Pettia is the percussion which is often made from one tone; Tone is that which dwells longer in one note, containing the powers of the modulators in a plain figure described by the voice.

¶ Concerning Power,

A decorative initial 'P' is depicted. Power is the order of a note in a system by which any note is known. Melopoeia is the use of the things subject to harmonic treatment for that which is its own [nature], [for] any hypothesis [of] this is the limit of the action which is according to the modulation.

¶ Concerning notes.

A decorative initial 'S' is depicted. If there is rest and immobility, there will certainly be silence; but with silence existing and the motion of nothing being made, nothing will be heard; if, therefore, anything is to be heard, it is necessary that a strike and motion be first. For since all notes are made from some strike being made, but a strike cannot be made at all unless a prior motion has preceded it. Of motions, some are denser, others rarer; the denser ones indeed render higher notes; but the rarer ones [render] lower [notes]. It is necessary for them to be [as they are] because they consist of denser and more numerous motions; but the lower ones [consist of] rarer and fewer motions; so that the higher ones are more relaxed, so that they might be [as] they are; [they] should be lower [through] the removal of motion, [or] that they be extended [to be] higher [through] the addition of motion that is required; therefore, it must be said that notes consist of portions, since they are [matters of] cognizance by addition and removal. But all things consisting of particles are said to be conjectured among themselves by the ratio of numbers. It is necessary that they be said [to be related] among themselves in the ratio of numbers; but some numbers are said to be in a multiple ratio, others in a superparticular, others in a superpartient; and likewise, it is necessary that notes be said [to be related] to each other in ratios of this kind; of these, indeed, some are called multiple and superparticular by one name among themselves. We also recognize that some notes are consonant, while others are dissonant; and consonant ones indeed make one mixture out of both; but dissonant ones do not. Since these things are so, it is fair that consonant notes (since they make one mixture out of both voices) should be called by one name among themselves of numbers, whether they be multiple or superparticular. If the interval b c is multiple, [and] b of c is such that c is to b as d is to d, I also claim it to be a multiple of c; for since b is a multiple of c, c therefore measures b; and it was also as c is to b, [so] b is to d; and likewise c also measures d; therefore d is a multiple of c. If an interval twice composed makes a whole multiple, it itself will also be a multiple; let the interval be b c, and let it be such that c is to b as d is to d, and let d be a multiple of c. I also claim b to be a multiple of c; for since d is a multiple of c, c therefore measures d; but we have learned that if there are as many proportional numbers as you like, [and] this measures the last, it will also measure those interjected in the middle; therefore c measures b; therefore b is a multiple of c. Neither one nor many proportional numbers will fall into a superparticular interval; for let there be a superparticular interval b of c, and let the minima in the same ratio of them be b, c, d, f, h. These, therefore, are measured by unity alone as a common measure; take away a part equal to h, which let be K; F, the remaining unit. Therefore, the superparticular d, f of h, the excess d K, the common measure of d, f, and h is unity; therefore d K [is not measured by it]; therefore no mean will fall into d, f, h; for the one falling into it will be smaller than d, f and larger than h, and likewise unity is divided, which can in no way happen; therefore no one will fall into d, f, h; but truly, in the minima, no mean will fall. But none will fall into d, f, h, nor will it fall into b, c. If an interval that is not multiple is twice composed, the whole will neither be multiple nor superparticular; for let the interval be not multiple b, c; let it be such that c is to b as b is to d. I claim d of c to be neither multiple nor superparticular. For let it first be a multiple of d of c; therefore we learned that if an interval twice composed makes a whole multiple, it itself is also a multiple.