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In his exuberant and inspiring book The Physics of Jazz, physicist and musician Stephon Alexander narrates how he came to understand the parallels between quantum particle theory and jazz composition:
About a decade ago, I sat alone in a dim café on the main drag of Amherst, Massachusetts, preparing for a physics faculty job presentation when an urge hit me. I found a pay phone with a local phone book and mustered up the courage to call Yusef Lateef, a legendary jazz musician, who had recently retired from the music department of the University of Massachusetts, Amherst. I had something I had to tell him.
Like an addict after a fix, my fingers raced through the pages anxiously seeking the number. I found it. The brisk wind of a New England autumn hit my face as I called him. At the risk of rudely imposing, I let the phone ring for quite a while.
“Hello?” a male voice finally answered.
“Hi, is Professor Lateef available?” I asked.
“Professor Lateef is not here,” said the voice, flatly.
“Could I leave him a message about the diagram that John Coltrane gave him as a birthday gift in ’61? I think I figured out what it means.”
There was a long pause. “Professor Lateef is here.”
We spoke for nearly two hours about the diagram that appeared in his acclaimed book Repository of Scales and Melodic Patterns, which is a compilation of a myriad of scales from Europe, Asia, Africa, and all over the world. I expressed how I thought the diagram was related to another and seemingly unrelated field of study — quantum gravity — a grand theory intended to unify quantum mechanics with Einstein’s theory of general relativity. What I had realized, I told Lateef, was that the same geometric principle that motivated Einstein’s theory was reflected in Coltrane’s diagram.
One of the most memorable and influential moments in my physics research occurred one morning when I walked into Brian Eno’s studio. Normally, Brian was working on the details of a new tune — getting his bass sorted out just right for a track, getting a line just slightly behind the beat. He was a pioneer of ambient music and a prolific installation artist.
Eno described his work in the liner notes for his record, Ambient 1: Music for Airports: “Ambient music must be able to accommodate many levels of listening attention without enforcing one in particular; it must be as ignorable as it is interesting.” What he sought was a music of tone and atmosphere, rather than music that demanded active listening. But creating an easy listening track is anything but easy, so he often had his head immersed in meticulous sound analysis.
That particular morning, Brian was manipulating waveforms on his computer with an intimacy that made it feel as if he were speaking Wavalian, some native tongue of sound waves. What struck me was that Brian was playing with, arguably, the most fundamental concept in the universe — the physics of vibration. To quantum physicists, particles are described by the physics of vibration. And to quantum cosmologists, vibrations of fundamental entities such as strings could possibly be the key to the physics of the entire universe. The quantum scales those strings play are, unfortunately, terribly intangible, both mentally and physically, but there it was in front of me — sound — a tangible manifestation of vibration.
Sound is a vibration that pushes a medium, such as air or something solid, to create traveling waves of pressure. Different sounds create different vibrations, which in turn create different pressure waves. We can draw pictures of these waves, called waveforms. A key point in the physics of vibrations is that every wave has a measurable wavelength and height. With respect to sound, the wavelength dictates the pitch, high or low, and the height, or amplitude, describes the volume.
If something is measurable, such as the length and height of waves, then you can give it a number. If you can put a number to something, then you can add more than one of them together, just by adding numbers together. And that’s what Brian was doing — adding up waveforms to get new ones. He was mixing simpler waveforms to make intricate sounds.
To physicists, this notion of adding up waves is known as the Fourier transform. It’s an intuitive idea, clearly demonstrated by dropping stones in a pond. If you drop a stone in a pond, a circular wave of a definite frequency radiates from the point of contact. If you drop another stone nearby, a second circular wave radiates outward, and the waves from the two stones start to interfere with each other, creating a more complicated wave pattern. What is incredible about the Fourier idea is that any waveform can be constructed by adding waves of the simplest form together. These simple “pure waves” are ones that regularly repeat themselves.
Note: Quotations by Stephon Alexander are drawn from BrainPickings by Maria Popova.