Attempt at a New Theory of Music

through which grace and charm are won for the sounds themselves:
one of these is based on the distinction between the gravity original: "gravitatem"; referring to low-pitched or "heavy" sounds and the sharpness original: "acumen"; referring to high-pitched or "acute" sounds of sounds,
while the other truly consists in the duration of sounds. Modern music, indeed, is usually seasoned with both types of sweetness; nevertheless, even now one may see examples in which only one of the two types evokes grace. In this treatise, however, we have decided to develop primarily that sweetness which is born from the distinction of sounds by reason of gravity and sharpness; for the other type is less difficult to treat, and may be easily completed once the first has been explained. For just as in the distinction of gravity and sharpness, no other proportions find a place as of yet except those constituted by the numbers 2, 3, and 5, so too in the distinction of duration, musicians have not even reached this point, but have derived all sweetness of this kind from the numbers 2 and 3 alone.