Powharmonic series: Difference between revisions
Cmloegcmluin (talk | contribs) |
Cmloegcmluin (talk | contribs) |
||
| Line 181: | Line 181: | ||
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 == | ||