Of the Origin and Certainty of Music

Introduction

Although God, the Supreme and Greatest, in His infinite goodness has conceded to man existence in common with the stones, growth in common with the trees, and sensation in common with the other animals — yet wishing, as it were, that from the excellence of the creature the omnipotence of its maker should be known, He endowed it with the gift of intellect, so that it falls but little short of the Angels. And so that man might know his own beginning and end, He created him with his face turned toward the sky, where the seat of God is, and this so that he should not fix his love upon base and earthly things, but raise his intellect to contemplate the superior and celestial, and penetrate the hidden and divine things by means of the things that are, and are comprehended through the five senses.

On the Senses and Hearing

And although, as regards existence, two senses alone would suffice, nonetheless for well-being He added three more: for through touch we know things hard and rough from things tender and polished; and through taste we distinguish between things sweet and bitter and other flavors; and through these two we perceive the differences of cold and hot, of hard and soft, of heavy and light — things that would suffice for our mere existence. Yet it remains that for well-being, seeing, hearing, and smelling are no less necessary; through which man comes to reject what is bad and to choose what is good. Whoever wishes to examine well the virtue of these senses will find, without doubt, that sight, considered in itself, is of greater utility to bodies and is consequently more necessary than the others. Yet one will come to know that hearing is far more necessary and excellent when considered in relation to the things belonging to the intellect: for although through the sense of sight we know more differences of things, since it extends further than hearing, nonetheless hearing extends further in the acquisition of sciences and of intellectual judgment, and brings far greater benefit. Hence it follows that hearing is truly more necessary and more excellent than the other senses — even though all five are called instruments of the intellect, since everything we see, hear, touch, taste, and smell is offered to it by means of the senses and common sense; nor can we have knowledge of anything except through one of these five, it being true that all our knowledge takes its origin from them.

The Origin of Music

From hearing, therefore, as the most necessary of the other senses, the science of Music has had its origin — a science whose nobility can easily be demonstrated from its antiquity. For (as Moses, Josephus, and Berosus the Chaldean say) before the universal flood, Music was discovered at the sound of hammers by Jubal of the line of Cain. Lost afterward through the subsequent flood, it was rediscovered by Mercury: for (as Diodorus holds) he was the first to observe the course of the stars, the harmony of singing, and the proportions of numbers; and he is also said to have been the inventor of the lyre with three strings — an opinion shared by Lucian, though Lactantius, in his book on the False Religion, attributes the invention of the lyre to Apollo, while Pliny wishes the inventor of Music to have been Amphion.

Pythagoras and the Discovery of Musical Proportions

But however that may be, Boethius, siding with the opinion of Macrobius and departing from Diodorus, holds that Pythagoras was the one who discovered the rational basis of musical proportions from the sound of hammers: for, passing by a smiths’ workshop where men were beating a heated iron upon the anvil with different hammers, there came to his ears a certain order of sounds that moved his hearing with delight; and stopping awhile, he began to investigate whence such an effect proceeded. It seeming to him at first that it might arise from the unequal strength of the men, he had those who were striking exchange hammers; but hearing no sound different from the first, he judged (as was indeed the truth) that the diversity of the weights of the hammers was the cause. Wherefore, having had each weighed separately, he found among the numbers of the weights the ratios of the consonances and harmonies, which he afterward industriously extended in this way: having made strings of sheepgut of equal thickness and attaching to them those same weights as the hammers, he found the same consonances — all the more sonorous in that strings by their nature render to the ear a more pleasant sound.

Music as a Mathematical Science

This harmony continued for some time, and afterward his successors — who knew well that its foundations were placed in certain and determinate numbers — making trial of it more subtly, little by little refined it to the point of giving it the name of a perfect and certain science. And removing the false and demonstrating the true concords with the most evident and infallible reasons of number, they set down in writing the clearest rules — as we clearly see has come to pass in all other sciences, where the first inventors (as Aristotle plainly shows) never had perfect knowledge of them; rather, with that little light there were mixed many shadows of error, which being removed by those who recognized them, truth came in their place. Just as Aristotle himself did with the principles of natural philosophy — adducing the various opinions of the ancient philosophers, he approved the good and true, rejected the false, clarified the obscure and poorly understood, and adding his own opinion and authority, demonstrated and taught the true science of natural philosophy. So likewise the later masters of our science of Music, showing the errors of the past and adding their own authority, made it so clear and certain that they numbered it among, and made it a part of, the mathematical sciences — and this for no other reason than its certainty, for this science together with the others surpasses in certainty all other sciences and holds the first degree of truth, as is known from its very name. For mathematica is derived from the Greek word mathesis, which in Latin signifies disciplina and in our Italian tongue means scienza or sapienza — which (as Boethius says) is nothing other than an understanding, or more clearly, a capacity for the truth of things that exist and by their nature cannot change; of which truth the mathematical sciences make particular profession, since they consider things that by their nature possess true being. And they differ so greatly from certain other sciences in that those latter, being founded upon the opinions of diverse men, have no firmness in themselves; whereas these, having sensation for their proof, come to have every certainty. For mathematicians in essential matters are of one and the same opinion and consent only to that which can be grasped by the senses. So great is the certainty of these sciences that by means of numbers one may infallibly determine the revolution of the heavens, the conjunctions of the planets, the phases of the Moon, its eclipse and that of the Sun, and infinitely many other beautiful secrets, without any discord among themselves.

It follows, then, that Music is both noble and most certain, being a part of the mathematical sciences.