Harmonics & Temperament

Harmonics are just as present in rhythm as in harmony: speed up any series of beats, and a tone will eventually be audible. Conversely, a tone can be slowed down to the point where it sounds like a series of beats.

In harmony, the harmonic series is an infinite series of sine wave tones (partials) that are multiples of a fundamental frequency. The harmonic series can be replicated percussively by using equally spaced pulses. Different pulse frequencies (tempos) will create different harmonics. Tempering these harmonics involves phrasing them to be unequal in spacing.

The harmonic series follows a specific pattern, where each harmonic vibrates at integer multiples of the fundamental frequency (partials). A 120 bpm straight pulse's second harmonic (2/1) would be double the tempo, its third harmonic (3/1) triple the tempo, etc... At the tenth harmonic (10/1), the pulse is now at 1200 bpm (20 Hz). By this point, it often ceases to sound like percussion and instead as an audible tone. However, the listener's perception and the sound's timbre can alter this threshold slightly.

Meters are often tempered purely out of preference or for a specific genre. Swing, MOS rhythm, and microrhythmic phrasing are all examples of tempering harmonic (straight) meters. However, as explained by musician and theorist Malcolm Braff, meters can also be tempered to increase synchronization (proximity) between beats:

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(image source: https://general-theory-of-rhythm.org)