I just noticed that New Scientist had an interview with Benoit Mandelbrot last week. Not since Einstein and relativity, perhaps, has an obscure mathematical concept like fractals become a popular byword. Maybe that's because it's the first engaging piece of math to come out in decades that you can visualize: Einstein had the enduring look, but Mandelbrot has the unforgettable graphics.
Interview, theory, and practice. And, of course, the book.
It was a big shift in my music listening when I went from symphonies to solos. I was, for the longest, a deeply-entrenched Tchaikovsky listener (everyone should be once), with a good measure of Beethoven thrown in. Mozart's great 40th symphony was in the mix, gaining a foothold since it was on the flip side of Beethoven's Fifth.
This was a matter of chance, not choice, since I had inherited an old console record player from an aunt, along with exactly one record. Eugene Ormandy: symphony on one side, symphony on the other. To my mind, I had ascended the ladder of musical hierarchy in a single bound, skipping over all the lesser forms of quartet, octet, and chamber orchestra to arrive at the summit of musical expression. Any symphony composer would agree.
In reality, though, an orchestra is really one instrument with many colors, and not the fifty at once that it appears to be. It plays as one (what "symphony" means, after all), and is heard the same way. Sometimes one instrument is allowed to step to the fore, like the cello in the William Tell overture, the woodwind in Beethoven's Fifth, or the flute in "Afternoon of a Faun". But those exceptions are themselves just a single instrument, playing instead of, not alongside, the orchestra.
So the progression to solo instrumentals was, in a way, natural. Hearing solo guitar for the first time was a revelation because it gave me, oddly enough, more of what I was already listening to: many sounds combining into one. But now those sounds were not entire instruments: for the first time I was hearing the individual notes of music themselves. It was like musical X-ray vision, or the discovery of atoms. You could not only hear music being made, but how.
Even though the guitar can summon a wealth of notes at once, and a piano a whole army of them, there's still a limit to the music one instrument can convey. So, after a few years, I was listening to a lot more duos: violin and piano, lute and harpsichord, guitar and voice. This revived the whole experience of hearing music happen. A piece could be heard as a whole, and at the same time as a conversation of two voices: three things to listen to at once, really, and to marvel at.
I went to a piano trio performance recently, and that same experience of the whole coexisting with its parts was intensified. At any time could be seen and heard a solo instrument standing out, a dialog between any two of the three on stage, or the united efforts of all three: a combinatorics many times richer than the duo, and yet never overwhelming the ear or the mind. Anyone can toss two balls repeatedly into the air, but juggling only happens when you reach three. It's that sensation with a trio, that there are just enough colors on the palette to paint everything, but no more.
Strangely enough, there's not another such leap from three instruments to the quartet. Four instrumentalists are fascinating to watch, but almost impossible to hear separately at will. In part, that's because they're often not playing as four, but either as three (a string quartet has two violins, usually supporting each other), or as one: the quartet starts to become a miniature symphony that subsumes its parts. There are many exceptions, and great joys when a quartet continually shifts before the ear from its single voice to its unique parts. But it's clear that the pleasure of listening with two minds starts to break down after the number three.
So there's something about three that manages to balance both complexity and clarity, and gives it a special place in the repertoire of perception. If music were motion, it is like the dramatic shift from the two-body problem to the three: two objects orbiting one another can find a mutual center, and thus order their wanderings. But the possibility of a static pattern vanishes when a third object is added to the system. Mathematically, it is unsolvable; physically, it is unstable. There is coherence — a middle ground between collapse and dispersion — but not predictability. When three moving bodies interact under gravity, there is an inextinguishable risk that chaos will take over, and the marvel of such systems as the sun and planets is that they stave this off as they make their grand patterns. There is this same psychological awareness listening to three musicians, I think: a sense of the defiance of probability at work, of treading between simplicity and confusion and making it matter to the ear.
Three musicians and three bodies