# rhythm and pitch in music

rhythm and pitch synchronisation

## rhythm and pitch synchronisation

For every piece of music, there is a correct rate or rhythm for maximum harmony: this is the rate at which the basic rhythmic pulse is synchronised with the musical keynote. This page explains why and presents a means of calculating proper rhythmic rate from keynote.

Rhythm and pitch in sonic form are essentially one and the same thing - repeated pulses - the latter being a version of the former directly detectable as audio frequency within the range of hearing.
This is true of even complex, random rhythms, which have a 'pitch' equal to the rate of the fundamental pulse (the decorations - provided they are mutually in time with the pulse on repeated cycles merely causing an overall shift in phase). Normal, slower, overtly sounded rhythms - typical of percussion in music - are at subsonic frequency and are heard and felt as discrete repeating sounds.

Accordingly, since both pitch and rhythm are frequency based, it is possible to 'tune' subsonic pulse, or rhythm, which can be detected aurally but not heard as 'frequency', with musical pitch: in other words:

### there is a 'correct' rhythmic rate or rates - for a piece of music in any given musical key, a rate equal to a subsonic octave of that key

This true rate, in beats per minute, can be calculated by taking the key frequency of the music, repeatedly dividing by two (successively reducing octave) until a value typically between something like one, and two and a half cycles per second is reached (the commonly acceptable rhythmic rates for music), and then multiplying by sixty.

Example for key of A (440Hz): 440/(2 x 2 x 2 x 2 x 2 x 2 x 2 x 2) = 1.71875. 1.71875 x 60 = 103.125 bpm: the 'correct' rhythmic rate for music in the key of A, the rate at which the fundamental sunbsonic pulse will resonate with the keynote, is 103.125 bpm (or 51.5625 at another octave down).
The table below works this in reverse, showing the nearest keys for basic frequencies from 1 to 2.6 Hz (60 to 156 bpm): equal temperament tuning is assumed (i.e. piano tuning at a ratio of 1.059463 {=1+ twelfth root of 2} between adjacent notes).

Beats per Second........1...1.2...1.4...1.6...1.8....2.0....2.2....2.4...2.6
Beats per Minute........60...72...84.....96...108...120...132...144...156
Nearest Corresp Key..C....Eb....F.....Ab....Bb.....C.......D......Eb....E

Actual 'True' Frequency for these keys (bpm to 2 dp) is:
C.......Eb.......F......Ab.....Bb.......C.........D.........Eb........E
61.32 72.92 81.85 97.34 109.26 122.64 137.66 145.84 154.51

Purists/experimental percussionists will note that the foregoing all refers to keynotes - assuming the 'key' to be the continuous essential sonic 'rhythm' of the music: it is of course possible to extend the principle to individual scalar notes within a given key...
Similarly, the use of irregular rhythms (e.g. the recurring motif patterns that often occur in any decent musica) creates timbral effects when speeded up...

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