Powharmonic series: Difference between revisions

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The 0th harmonic number is not defined, however, if it were, it seems reasonable to assume it would be defined as 0; in other words, the first step of the harmonic series would be to add <math>\frac11</math> to 0.

In accordance with this observation, it further seems reasonable that any a-edharmonic series could be prefixed with the frequency multiplier 1, rather than beginning straight away with the frequency multiplier <math>a</math>. In the case of the 2-edharmonic series, doing so brings it closer in similarity to the (musical) harmonic series; the first step is exactly an octave, the second step a fifth (701.96¢ vs 600.00¢), the third step a fourth (498.04¢ vs 400.00¢), the fourth step a third, (386.31¢ vs 300¢), etc. We therefore propose referring to ~~this variation the~~ "emulatory a-edharmonic series", because ~~it is~~ emulating the harmonic series.

In accordance with this observation, it further seems reasonable that any a-edharmonic series could be prefixed with the frequency multiplier 1, rather than beginning straight away with the frequency multiplier <math>a</math>. In the case of the 2-edharmonic series, doing so brings it closer in similarity to the (musical) harmonic series; the first step is exactly an octave, the second step a fifth (701.96¢ vs 600.00¢), the third step a fourth (498.04¢ vs 400.00¢), the fourth step a third, (386.31¢ vs 300¢), etc. We therefore propose referring to these variations as "emulatory a-edharmonic series", because they are emulating the harmonic series.

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@@ Line 467: / Line 467: @@
 The 0<sup>th</sup> harmonic number is not defined, however, if it were, it seems reasonable to assume it would be defined as 0; in other words, the first step of the harmonic series would be to add <span><math>\frac11</math></span> to 0.
-In accordance with this observation, it further seems reasonable that any a-edharmonic series could be prefixed with the frequency multiplier 1, rather than beginning straight away with the frequency multiplier <span><math>a</math></span>. In the case of the 2-edharmonic series, doing so brings it closer in similarity to the (musical) harmonic series; the first step is exactly an octave, the second step a fifth (701.96¢ vs 600.00¢), the third step a fourth (498.04¢ vs 400.00¢), the fourth step a third, (386.31¢ vs 300¢), etc. We therefore propose referring to this variation the "emulatory a-edharmonic series", because it is emulating the harmonic series.
+In accordance with this observation, it further seems reasonable that any a-edharmonic series could be prefixed with the frequency multiplier 1, rather than beginning straight away with the frequency multiplier <span><math>a</math></span>. In the case of the 2-edharmonic series, doing so brings it closer in similarity to the (musical) harmonic series; the first step is exactly an octave, the second step a fifth (701.96¢ vs 600.00¢), the third step a fourth (498.04¢ vs 400.00¢), the fourth step a third, (386.31¢ vs 300¢), etc. We therefore propose referring to these variations as "emulatory a-edharmonic series", because they are emulating the harmonic series.
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