MUSIC OF THE SPHERES

(The Pythagorean series continues in this entry. As I probably ought to reiterate, I have been giving a lot of attention to Pythagoras throughout my book, but it is largely scattered over several sections, and there is no chance, and probably little need, to collect them all in one place, as this is not the basic principle on which my book is built.)

In the previous entry, I was rather untowardly dismissive toward the members of the Pythagorean order. It was unfair on my part, I admit. After all, they appear to have been decent people, living communistically, professing and practicing equality of men and women, being kind to animals, working hard in science and mathematics, and on top of that intensely preoccupied with mysticism. I happen to share many proclivities and cultivated interests with them, too, particularly, our love for music. But it is not incidentally that music becomes the central theme of this entry.

My interest in music was fourfold. I loved to listen to good music, to play good music, to compose… what I believed then and still believe was good music, and to analyze music, too (as evidenced by my University thesis at one time, titled The Semiotics of Music, which I mentioned in one or two earlier sections). Now, I am aware that the Pythagoreans, exhibited all four of these predilections, as music was an essential part of their lifestyle. According to the philosopher Iamblichus of Chalcis, the Pythagoreans followed a structured life of religious teaching, common meals, exercise, reading, and philosophical study. Music featured as an essential organizing factor of this life: the disciples sang hymns to Apollo together regularly, they used the lyre to cure illnesses of the soul and body, and regular poetry recitations took place before and after sleep to aid the memory.

But it is the fourth of my musical interests, namely, the scientific analysis of music, which interests me the most here. And, rather than paraphrase other writings on the subject, I shall now quote that selfsame W. T. Jones, whom I strongly criticized before, but who deserves some credit for writing at some length about the Pythagorean exploration of the physics of music:

The Pythagoreans made some interesting applications of mathematics to natural phenomena. Of these the most striking is their study of harmonics. They observed that the relationships between the lengths of the strings of a tuned lyre were capable of mathematical treatment: that they were indeed simple proportions. The lyre of Pythagoras’ day was a seven-stringed instrument, where four strings, the first, fourth, fifth and seventh, were harmonically basic. In tuning the lyre, the first and seventh (the octave) were attuned, then these and the fourth and fifth were brought into attunement. This was done by tightening, or relaxing, the tension of the strings. Hence Pythagoras could not simply look at the strings of the tuned lyre and observe the mathematical relationships which obtained. He had to perform an experiment in the modern sense of the term. This of course was not difficult to do. But the point is that since it could not be done by a direct observation, he had first to have an idea, a hypothesis, and then check it. When it was done, measurement showed that the section of the string sounding an octave above the low was half as long as the latter. The fourth string gave the ratio 3:4 with the first, and the fifth 2:3. From these simple ratios arose the concept of the arithmetic and the harmonic mean.

And now follows the big jump from the mathematics of music to the mathematics of everything else:

The idea of the mean gave Pythagoras a completely new slant on the conflict of the opposites, which could not be resolved by the Milesians. Far from being irreconcilable, the opposites could be harmonized just as high and low notes are. And if the mean that harmonized them were similarly capable of being expressed mathematically, it followed that all relations between opposites were thoroughly intelligible. This notion was also applied to medicine. Health was conceived as an attunement and harmony of the opposites. The body is healthy when it is neither too cold nor too hot, etc. This doctrine was easily transferable to moral theory, defining the good generally as the mean. Thus the old notion of sophrosyne, moderation, received a precise and formal statement.

This concept of mathematically expressible harmony was further applied to the movement of the celestial bodies, called the music of the spheres. Here is the famous passage from Aristotle’s Metaphysics, dealing with this issue:

Some think it necessary that noise should arise when so great bodies are in motion, since sound does arise from bodies among us, which are not so large and do not move so swiftly; and from the sun and moon and from the stars in such great number, and of such great size, moving so swiftly, there must necessarily arise a sound inconceivably great. Assuming this, and that the swiftness has the principle of harmony by reason of the intervals, they say that the sound of the stars moving in a circle becomes musical. And since it seems unreasonable that we also do not hear this sound, they say that the reason for this is that the noise exists in the very nature of things, so as not to be distinguishable from the opposite silence; because the distinction of sound and silence lies in their contrast to each other, so that, as blacksmiths think that there is no difference between them, because they are accustomed to the sound, so the same thing happens to men. (ii.9; 290 b15.)

This is, of course, the origin of the concept of the harmony and music of the spheres. This discussion ought to be of particular interest in the mystical sense, but, unfortunately, we have it from the mouth of Aristotle, who, it seems to me, is not much interested in mysticism. (If he is, that side of him eludes me completely!) …But that is a totally different matter, and it has nothing to do with Pythagoras himself, who was of course the epitome of the consummate mystic.