Powharmonic series: Difference between revisions
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== edharmonic series == | == edharmonic series == | ||
=== prerequisite: ln-of-a-powharmonic series === | |||
[[File:Ln-of-2-powharmonic series.png|thumb| | |||
ln-of-2-powharmonic series | |||
]] | |||
Irrational values can be used as <span><math>a</math></span> or <span><math>b</math></span>. | |||
In particular it may be of interest to use [[wikipedia:E_(mathematical_constant)|<span><math>e</math></span>]] as <span><math>b</math></span> — in other words, to use a [[wikipedia:Natural_logarithm|natural logarithm]]. | |||
For example, the ''ln-of-2-powharmonic series'' fits <span><math>e</math></span> times as many many more pitches into each next octave as the previous octave. Because <span><math>e</math></span> is irrational, however, no integer multiples of the octave will ever be reached. | |||
In fact, this series is equivalent to the example given in the introduction, because <span><math>ln(2) ≈ 0.69314718056</math></span>. | |||
=== description === | === description === | ||