The most rational minds in history have always yielded to a slight mystic haze when the subject of music has been broached, recognizing the beautiful and utterly satisfying combination of mathematics and magic that music is. Plato and Socrates knew that the study of music is one of the finest disciplines for the adolescent mind, and insisted on it as a sine qua non of education: and just for those reasons of its combined scientific and “spiritual” qualities. Yet when Plato speaks of music—scientific as he is about almost everything else—he wanders into vague generalizations about harmony, love, rhythm, and those deities who could presumably carry a tune. But he knew that there was nothing like piped music to carry soldiers inspired into battle—and everyone else knows it too. And that certain Greek modes were better than others for love or war or wine festivals or crowning an athlete. Just as the Hindus, with their most mathematically complicated scales, rhythms and “ragas,” knew that certain ones had to be for morning hours, or sunset, or Siva festivals, or marching, or windy days. And no amount of mathematics could or can explain that.

We are still, in our own day, faced with this magical block. We try to be scientific about it, in our bumbling way—to employ principles of physics, acoustics, mathematics, and formal logic. We employ philosophical devices like empiricism and teleological method. But what does it accomplish for us? The “magic” questions are still unanswered. For example, we can try to explain the “shape” of a theme from a Beethoven quartet by saying that it follows the formal principle of synthesis: that there is a short statement (thesis), followed by a “questioning answer” (antithesis), followed by a development arising out of the conflict of the two (synthesis). The Germans call this form “Stollen.” Others say “syllogistic.” Words, words, words. Why is the theme beautiful? There’s the rub. We can find a hundred themes shaped in this way, or based on variants of this principle; but only one or two will be beautiful.

When I was at Harvard, Professor Birkhoff had just published a system of aesthetic measure—actually trying to evolve a mathematical system whereby any object of art could be awarded a beauty-rating on a given continuum of aesthetic worth. It was a noble effort; but when all is said and done, it comes to a dead end. The five human senses are capable of measuring objects up to a certain point (the eye can decide that “X” is twice as long as “Y”; the ear can guess that one trombone is playing twice as loud as the other); but can the senses’ own aesthetic responses be measured? How far is the smell of pork from the smell of beans? What beans? Cooked how? Raw? In what climate? If the Eroica earns a grade of 3.2, what mark do you give Tristan? Or a one-page Bach prelude?

We bumble. We imitate scientific method in our attempts to explain magic phenomena by fact, forces, mass, energy. But we simply can’t explain human reaction to these phenomena. Science can “explain” thunderstorms, but can it “explain” the fear with which people react to them? And even if it can, in psychology’s admittedly unsatisfactory terminology, how does science explain the sense of glory we feel in a thunderstorm, break down this sense of glory into its parts? Three parts electrical stimulation, one part aural excitement, one part visual excitement, four parts identification-feelings with the beyond, two parts adoration of almighty forces—an impossible cocktail.

But some people have “explained” the glory of a thunderstorm—now and then, with varying degrees of success—and such people are called poets. Only artists can explain magic; only art can substitute for nature. By the same token, only art can substitute for art. And so the only way one can really say anything about music is to write music.

Leonard Bernstein