Powharmonic series: Difference between revisions

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The harmonic series features counts of pitches of increasing powers of 2 in each next octave, but it also contains counts of pitches of increasing powers of 3 in each next tritave, and counts of pitches in increasing powers of 5 in each next 5/1 interval, and so forth. This is because the harmonic series is equivalent to the log-base-2-of-2-powharmonic series, the log-base-3-of-3-powharmonic series, the log-base-5-of-5-powharmonic series, and so forth (the log-base-b-of-b-powharmonic series). This because any <span><math>\log_{b}b = 1</math></span>.
The harmonic series features counts of pitches of increasing powers of 2 in each next octave, but it also contains counts of pitches of increasing powers of 3 in each next tritave, and counts of pitches in increasing powers of 5 in each next 5/1 interval, and so forth. This is because the harmonic series is equivalent to the log-base-2-of-2-powharmonic series, the log-base-3-of-3-powharmonic series, the log-base-5-of-5-powharmonic series, and so forth (the log-base-b-of-b-powharmonic series). This because any <span><math>\log_{b}b = 1</math></span>.


Any powharmonic series has infinite equivalent ways of being expressed.
Any powharmonic series has infinite equivalent ways of being expressed. We can visualize the equivalences with the following coloration of powharmonic space:
 
[[File:Powharmonic space.png|378x378px]]


== a-edharmonic series ==
== a-edharmonic series ==