Of the Subject of Music

Simple and Relative Number

Since in Discrete quantity — called Multitude — some things exist by themselves, such as the numbers 1, 2, 3, 4, and others, and some are spoken of by relation, such as the Duple, the Triple, the Quadruple, and others like them: therefore every number which stands by itself and does not in its being require another added to it is called Simple, and Arithmetic has consideration of it. That which cannot exist by itself, because in its being it requires another, is called Relative Number — and the Musician makes use of such number in his speculations.

The Four Sciences and Their Subjects

So likewise in Continuous quantity — called Magnitude — some things are of perpetual rest: as the Earth, the Line, the Surface, the Triangle, the Square, and every mathematical body; and others are in continual movement, as the celestial bodies. Of the former, Geometry treats; of the latter, which are always in revolution, Chironomia makes profession. So that from the diversity of things differently considered arises the variety of sciences and the diversity of subjects — for just as the Arithmetician considers principally Number, so Number is the Subject of his science.

The Subject of Music: Sonorous Number

And because musicians, in wishing to find the reasons for every musical interval, make use of sonorous bodies and of Relative Number in order to know the distances found between sound and sound, and between voice and voice, and to know how much the one differs from the other in the grave and the acute — bringing together these two parts, that is Number and Sound, making a composite of them, they say that the Subject of Music is the Sonorous Number.

And although Avicenna says that its subject is Tones and Times, nonetheless considering the thing in itself, we shall find it all to be one — that is, that Times refer to Number, and Tones to Sound.