Jimi Hendrix and musical acoustics
Last year, I was attending a reception at a McGill event. I was standing in the back – perhaps too far in the back – and a colleague asked me if I had ever thought about writing a book about the physics of Jimi Hendrix’s guitar sounds. Huh, I said – just before a microphonic feedback howl announced that the reception’s speeches were about to begin.
My colleague said Hendrix’s playing must involve complex nonlinear dynamics (yes, my colleague was drinking the wine offered at the event). The second thing I told my colleague was that, unlike most guitarists these days, Hendrix played so loud that he literally played the room, but, however that might be, room acoustics are linear, not nonlinear. Then I stopped, because my colleague was right, there was something nonlinear going on in Hendrix’s playing. The answer is not enough for a book, but fits a blog entry well.
The physics of how various musical instruments produce sound is a messy mathematical problem, but it is reasonably well understood. Room acoustics are much the same thing: you can imagine a room as if you are inside a large ungainly oblong musical instrument where you start the air vibrating by, say, clapping your hands. In a typical room, a hand clap might set up a reverberation lasting half a second, or 500 ms. This time is that for the exponential decay of sound of the clap by about 60dB of dynamic range. It corresponds to an intrinsic time scale for the build up or decay of that sound, of 1/20th of the reverb time, from the 60dB exponential decay. That is, about 25ms.
This is pretty fast. Most rooms can dump all the energy from a hand clap, or another source of stimulus like a public address system, into the room’s air vibrations very quickly. If one sets up a microphone, an amplifier, and speaker, and talk into the microphone, a resonance in the room’s acoustics is set up. If one sets things up badly, which happens occasionally for speeches at McGill receptions, one gets howling feedback. The feedback builds up exponentially on the same intrinsic time scale of 25ms. Pretty fast.
I say pretty fast, because I am comparing this to the time scales on which our brains work. Our reaction times are in the range of 100ms to 200ms, the same scale of time for a typical quick note in a musical motif. This is clearly not fast enough to catch a squealing microphone: it only takes 25ms to get out of control! The same problem occurs when one uses a microphone to amplify, for example, an acoustic guitar. The acoustic guitar can be thought of as a tiny little room driven by the strings vibrating the teeny tiny room’s walls. The strings couple efficiently to the guitar’s thin body, and so the strings’ energy is quickly dumped into the air.
The solid-body electric guitar is a way around this feedback problem. It makes sound via electromagnetic pickups. The strings work in the same way as an acoustic guitar, but, in usual practice, the thick body does not vibrate to any significant degree. So the strings do not dump energy efficiently into the body. Play an unplugged electric guitar. Although it is not loud, the strings stay ringing at the same loudness for longer than an acoustic guitar, because the energy is not transferred efficiently to the thick solid body. The time scale for the energy to be transferred to the electric guitar’s body is of order 5 or 10 times longer than that of an acoustic guitar. Or, similar to reaction times.
There’s the trick. Jimi Hendrix could manipulate his guitar and control the feedback from the room’s acoustics, because he had a solid-body electric, and was quick-witted enough to react to the room’s acoustics in a musical way. If he had been an amplified French horn player, or an amplified acoustic guitar player, he would have been out of luck.
Finally, the nonlinear part my colleague intuitively knew was present was not in the room’s acoustics, or in the electric guitar’s sounds, but rather in the most prosaic of locations: Hendrix’s brain. Hendrix could use the feedback, reacting and controlling it within musical motifs – which as I said have quick passages of notes on yet again the same time scales as reaction times: no mean feat! He was composing on the fly, right on the edge of what our brains can do.