Music and Mathematics

According to the preface of "The Music of the Spheres: Music, Science, and the Natural Order of the Universe" (Grove Press; $20.95), the prime agenda of the ensuing 241 pages is a discussion of how music and science relate to each other. In fact, James devotes his attention mostly to an account of the connections between music and science as perceived by thinkers up to the time, more or less, of Isaac Newton. He indeed offers chapters on the 19th and 20th centuries, and his envoi is provocatively titled "Into the Future." But he has little to say on the modern state of affairs, except to observe with undisguised cynicism that things just aren't what they used to be. About the way things were, however, James is both lucid and thorough.

The subject matter, readers should note, is a massive load of data that graduate students in musicology typically grapple with in a killer course on the history of music theory. Yet the presentation is remarkably engaging, and it never strays far from what James calls "the great theme" or "the great tradition." If James were as good at argument as he is at expository writing, "The Music of the Spheres" might easily have turned into a polemic on behalf of New Age philosophy. But perhaps because he knows his weaknesses as well as his strengths, the author - a journalist by training - keeps his beliefs largely to himself. For the most part this is a factual book, not a preachy book; simply for the information it contains, it should be of interest to anyone who takes music seriously.

Central to the book is the concept of music as fundamental to the human condition. Like language, music exists wherever there are people. And as different as music might be from culture to culture, all of it at least seems to derive from the same handful of components. This is not to say, as Longfellow so quotably did, that "music is the universal language of mankind." While anyone can listen to music from a remote land, to hear that music - to understand it - requires a modicum of familiarity with it. To the average Westerner, the subtleties of an Indian raga are no more graspable than the nuances of a poem written in Sanskrit; to an Australian aborigine who has never left the outback, boogie-woogie is as incomprehensibly foreign as a didjeridoo song is to a city-dweller. What is universal is not the "language" of a particular music but, rather, the patently simple mathematical relationships that seem to link the most basic intervals in music worldwide.

The ratio 2:1, for example, represents the interval that in the West is called an octave (if the pitch A vibrates at 440 times per second, the pitch eight scale-tones higher - another A - will vibrate at precisely 880 times per second). Similarly, the ratio 3:2 represents the interval we call a fifth (the fifth note of a do-re-mi scale starting on A is E, which clocks in at 660 vibrations per second). The ratio 4:3 represents the interval of a fourth (the distance between A and the D above), 5:4 represents the so-called major third (the distance from A to C-sharp), and so on. In practice, the math is seldom so pure. But if music is colored or spiced in the actual sounding, its basic ingredients are the intervals just described.

Most basic - presumably because the ratios are the simplest - are the octave, the fifth and the fourth. They are as prominent in bluegrass fiddle tunes as in the chanting of Tibetan monks, as clearly audible in Bulgarian folk song as in the "power chords" of heavy metal rock, as obvious in the music of Japanese kabuki theater as in Gregorian chant. They occur, too, in various non-musical phenomena: in the chirping of certain birds, in the clatter of heels on the floor of a cavernous room, in the whir of a well-maintained automobile engine. These intervals, in other words, are so ubiquitous that they can be considered natural. When astronomers long ago observed that the distances between planets corresponded more or less to the same ratios that describe the musical intervals, they couldn't help but make the connection; so long as they did not calculate too carefully, it seemed that there was an order to the universe.

One of the illustrations in James' book comes from "The History of the Macrocosm" by the 17th-century English philosopher Robert Fludd. As James tactfully points out, Fludd was notoriously behind the times in matters scientific, and he was wrong in just about everything he believed regarding astronomy, physics and chemistry. But at least conceptually, James says, Fludd was not far off the mark with his metaphoric drawing; his "Divine Monochord" depicts the planets, the elements and the notes of the musical scale, all of them harmoniously "resonating" from a single musical instrument that is tuned by the hand of God.

The gist of James' amply documented book is that this image would have made sense to any educated person living in Europe during the previous two millennia. Once upon a time, James reminds us, to be a musician was to be a scientist, and vice-versa. For the last 200 years, however, music and science have blindly gone their separate ways, and in both fields the results have grown increasingly sterile.