7. Tonus is a high utterance of voice. For it is a difference and measure of harmony which depends on the stress and pitch of the voice. Musicians have divided its kinds into fifteen parts, of which the hyperlydian is the last and highest, the hypodorian the lowest of all.
8. Song is the modulation of the voice, for sound is unmodulated, and sound precedes song.
Chapter 21. On the second division, which is called organica.
1. The second division, organica, has to do with those [instruments] that, filled with currents of breath, are animated so as to sound like the voice, as for example, trumpets, reeds, Pan’s pipes, organs, the pandura, and instruments like these.[261]
Chapter 22. On the third division, which is called rhythmica.
1. The third division is rhythmica, having to do with strings and instruments that are beaten, to which are assigned the different species of cithara, the drum, and the cymbal, the sistrum, acitabula of bronze and silver, and others of metallic stiffness that when struck return a pleasant tinkling sound, and the rest of this sort.[262]
2. The form of the cithara in the beginning is said to have been like the human breast, because as the voice was uttered from the breast so was music from the cithara, and it was so-called for the same reason. For pectus is in the Doric language called κίθαρα.
Chapter 23. On the numbers of music.
1. You inquire into the numbers according to music as follows: setting down the extremes, as for example, VI and XII, you see by how many units VI is surpassed by XII, and it is by VI units; you square it; six times six make XXXVI. You add those first-mentioned extremes, VI and XII; together they make XVIII; you divide XXXVI by XVIII; two is the result. This you add to the smaller amount, VI namely; the result will be VIII and it will be the mean between VI and XII. Because VIII surpasses VI by two units, that is by a third of six, and VIII is surpassed by XII by four units, a third part [of twelve]. By what part, then, the mean surpasses, by the same is it surpassed.
2. Just as this proportion exists in the universe, being constituted by the revolving circles, so also in the microcosm—not to speak of the voice—it has such great power that man does not exist without harmony.[263]