Powharmonic series: Difference between revisions
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Multiplying the exponent of a powharmonic series by some constant c is equivalent to multiplying each of its pitches' cents by that constant c. For example, the 1.5-powharmonic series would be like stretching each octave of the harmonic series from 1200¢ to 1800¢. If you were to instead manipulate a harmonic series by adding or subtracting frequency, rather than exponentiating it, you instead get an [[AFS|AFS (arithmetic frequency sequence)]]. | Multiplying the exponent of a powharmonic series by some constant c is equivalent to multiplying each of its pitches' cents by that constant c. For example, the 1.5-powharmonic series would be like stretching each octave of the harmonic series from 1200¢ to 1800¢. If you were to instead manipulate a harmonic series by adding or subtracting frequency, rather than exponentiating it, you instead get an [[AFS|AFS (arithmetic frequency sequence)]]. | ||
Using a negative power for the exponent gives a similar, but inverted effect. <span><math>f(n) = n^{-1}</math></span> is simply the subharmonic series. Other negative powers give you the subharmonic equivalent of their (super) powharmonic counterpart. You could call these subpowharmonic series. | |||
== log-base-b-of-a-powharmonic series == | == log-base-b-of-a-powharmonic series == | ||