What the Sonorous Number Is

A Previous Definition and Its Deficiency

We must know then that some, wishing to give an account of this number, have said that the Sonorous Number is nothing other than the number of the parts of a sonorous body — such as would be a string, which taking the account of discrete quantity, gives us certainty of the quantity of the sound produced by it. Which definition, although it might seem good to some, nonetheless, in my judgment, appears truncated and imperfect — for Voices, which are principally considered by the Musician and are not remote from Sonorous Number, having proportion among themselves, would not fall under this definition: since they have their origin from animate and human bodies, that is from man. And it is reasonable that all things considered in a science — even though they may not be considered by themselves but only in relation to the Subject — should be reduced to that Subject; just as it is also reasonable that a definition should agree with the thing defined.

And although man is a body, this is not sufficient: for it is further required that he be sonorous. Whence he must have three conditions — first that he be smooth, then that he be hard, and finally that he be broad — conditions which I do not know how all can be found in him. But let us grant that man has all these conditions: even so one could not obtain knowledge of the quantity of Voices by way of man, because the parts where they arise are not subjected to the senses in such a way that one can obtain from them any determinate measure. And whoever should say that Voices are applied to the sounds that arise from strings, and that by this means one comes to have the account of their proportions, and that by this same means they come to be reduced under the said definition — such a person would speak improperly: for sounds are applied to voices so that one may have true and determinate account of them, and not the contrary.

The Correct Definition

It seems to me therefore that it would be better to say that the Sonorous Number is Relative Number related to voices and to sounds — which is found artificially in a sonorous body, as in some string, which receiving the account of some number in its parts gives us certainty of the quantity of the sound produced from it, and of the quantity of voices, by referring or applying those sounds to those voices.

And this I say when such a number is considered universally in every interval. But when it is considered particularly in those intervals only which are consonant, one could say that it is the account of the proportions which are the forms of the consonances — considered first in Music — such as are those shown above, contained among the parts of the Senary number, which are found with art in the parts of a sonorous body, and related in the manner described above.

The String as Instrument of Measurement

And because the differences found between voices and between grave and acute sounds are not known except through the medium of sonorous bodies, musicians therefore, considering this, chose a string made of metal or other material that would produce sound — one that should be uniform in every way throughout, as that from which (being less mutable and less variable in every part than any other sonorous body) they could have certainty of all that they sought.

They being of the opinion that the quantity of the sound of the string was as great as the number of the parts considered in it — knowing its length according to the number of its measured parts, they were immediately able to judge the distances found between grave and acute sounds, and vice versa, and to know the proportion of every interval.

And this they did not do without purpose, as we can see from experience: for if we stretch a string of whatever length over a plane surface and divide it by ratio into two equal parts, making the comparison of its whole to one part, we shall clearly know that the sounds produced from these — having struck them together — are distant from each other by a Diapason, in Duple proportion; as we shall see in the Second Part. Whence dividing it in this way also into more parts, and comparing the whole to two, three, four, or more of them, we shall always be able to know varied distances and hear varied sounds arising from them according to the diversity of the parts in relation to their whole; and we shall together know that the whole is the cause of the Grave, and that the parts, the smaller they are, are the cause of acute sounds.

Conclusion: Number and Sound as Form and Matter

By this means therefore, and by this path — as the more secure one, according to the counsel of Ptolemy, with reason joined to sense — musicians go first investigating the reasons for consonances and then for every other interval and every difference found between grave and acute sounds, having recourse to Voices and Sounds (which are the matter of every musical interval) and to Numbers and Proportions (which, as I have said at other times, are their form).

Joining these two things together, I say therefore that the Sonorous Number is the true Subject of Music, and not the Sonorous Body — for although all bodies are apt for the production of sounds, they are not apt for the generation of consonances except when they are proportioned and contained under some determined form, that is, under the account of harmonic numbers.