Powharmonic series: Difference between revisions
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== Introduction == | == Introduction == | ||
A powerharmonic series, like the [[wikipedia:Harmonic_series_(music)|harmonic series]], is an infinitely ascending set of pitches from which scales can be drawn. | A powerharmonic series, like the [[wikipedia:Harmonic_series_(music)|harmonic series]], is an infinitely ascending set of pitches from which scales can be drawn. | ||
== p- | == ''p''-Powharmonic series == | ||
A powharmonic series can be built on any number <span><math>p</math></span>, whether it is rational or irrational, positive or negative. The formula for a ''p-powharmonic series'' is simply: | A powharmonic series can be built on any number <span><math>p</math></span>, whether it is rational or irrational, positive or negative. The formula for a ''p-powharmonic series'' is simply: | ||
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For example, the 0.69314718056-powharmonic series looks like this: | For example, the 0.69314718056-powharmonic series looks like this: | ||
{{powharmonic series|12|expo=0.69314718056}} | |||
{ | |||
|12 | |||
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The harmonic series is technically a powharmonic series: the 1-powharmonic series. <span><math>p</math><span> closer to 1 give powharmonic series closer to the harmonic series, in case a series is desired which is close enough to the harmonic series to evoke it but has some finely alternately tuned characteristics. | The harmonic series is technically a powharmonic series: the 1-powharmonic series. <span><math>p</math><span> closer to 1 give powharmonic series closer to the harmonic series, in case a series is desired which is close enough to the harmonic series to evoke it but has some finely alternately tuned characteristics. | ||