nonlinear – not sequential or straightforward; (physics) involving a lack of linearity between two qualities such as input and output; (mathematics) – involving measurement in more than one dimension
One day a few weeks ago, while nowhere near any musical instruments, I found myself thinking about the sound of cymbals—how their infinite variety of pwssshhh sounds are a kind of chaotic white noise that is both interesting and sometimes annoying. Cymbals are metallic percussion instruments, specifically self-sounding idiophones that are related to gongs and bells. Sometimes cymbals have clear pitches to them, but usually they produce indefinite pitches. It’s for this reason that we don’t usually play melodies on cymbals, but instead use them to accentuate or add color to a musical texture. That’s what the drummer is doing when she plays a drum fill around the tom toms and then hits a crash cymbal to mark the beginning of the big chorus. Cymbals are excitement generators! But the reason I was thinking about cymbals is that there’s a lot going on in them sound-wise. Because of the way they’re tuned— hammered by hand or by machine—cymbals are full of overtones that are not even multiples of a fundamental frequency. This is what gives them their “shimmering” pwssshhh sound.
Thinking about the cymbal’s chaotic sound led me to thinking about how the instrument is the perfect representation of the power of nonlinearity in music. Nonlinearity is a term from mathematics and the physical sciences that describes a situation in which the change in a system’s output is not proportional to the change in the input. In other words, nonlinear is how we describe a situation in which small changes can have huge effects. Cymbals are like this in that they don’t have a single sound the way say, a piano does. A cymbal can be played anywhere along its top, bottom, or sides, and every playing location produces a different sound. The briefest of cymbal strikes can trigger an unpredictable sound shape that hovers, lingers, and decays like no other instrument’s sound can.
From the nonlinear qualities of a cymbal’s sound we can move to the implications of nonlinearity for thinking about creativity in music generally. For instance, any good music performance is a nonlinear system in which the smallest details of action can lead to momentarily wonderful or dreadful results. A performance is a complex system of many inputs and outputs whose unfolding depends not just on the performer but on the audience’s willingness to go along—or not—as well as factors having to do with the performance space, sound system, and so on. Improvising and composing are also nonlinear: here, insightful moments almost always seem to happen when one makes an unexpected leap for which there is no adequate explanation except “it felt right” at the time or “my hands just knew.” Like the cymbal crash, the performative, improvisational, or compositional moment is a brief shimmering opening into the dynamics of how creativity works.