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For example, the 0.69314718056-powharmonic series gives the series of pitches:
For example, the 0.69314718056-powharmonic series gives the series of pitches:
 
{| class="wikitable"
frequency multiplier pitch ¢ octave reduced ¢ Δ ¢
|+
1 0.00 0.00 831.78
!pitch #
1.616806672 831.78 831.78 486.56
|'''frequency multiplier definition'''
2.141486064 1318.33 118.33 345.22
|'''frequency multiplier (decimal)'''
2.614063815 1663.55 463.55 267.77
|'''pitch (¢)'''
3.05132936 1931.33 731.33 218.79
|'''pitch Δ (¢)'''
3.462368957 2150.11 950.11 184.98
|'''octave reduced pitch (¢)'''
3.852807616 2335.09 1135.09 160.24
|-
4.226435818 2495.33 95.33 141.34
|1
4.585962562 2636.67 236.67 126.43
|1<sup>0.69314718056</sup>
4.933409668 2763.10 363.10 114.37
|1
5.270337212 2877.47 477.47 104.41
|0.00
5.597981231 2981.89 581.89 96.05
| -
5.917342318 3077.94 677.94 88.93
|0.00
6.22924506 3166.87 766.87 82.79
|-
6.5343793 3249.66 849.66 77.45
|2
6.833329631 3327.11 927.11 72.75
|2<sup>0.69314718056</sup>
7.126597 3399.86 999.86 68.59
|1.616806672
7.414614869 3468.45 1068.45 64.88
|831.78
7.697761534 3533.33 1133.33 61.55
|831.78
7.976369668 3594.88 1194.88 58.55
|831.78
8.250733817 3653.43 53.43 55.82
|-
 
|3
|3<sup>0.69314718056</sup>
|2.141486064
|1318.33
|486.56
|118.33
|-
|4
|4<sup>0.69314718056</sup>
|2.614063815
|1663.55
|345.22
|463.55
|-
|5
|5<sup>0.69314718056</sup>
|3.05132936
|1931.33
|267.77
|731.33
|-
|6
|6<sup>0.69314718056</sup>
|3.462368957
|2150.11
|218.79
|950.11
|-
|7
|7<sup>0.69314718056</sup>
|3.852807616
|2335.09
|184.98
|1135.09
|-
|8
|8<sup>0.69314718056</sup>
|4.226435818
|2495.33
|160.24
|95.33
|-
|9
|9<sup>0.69314718056</sup>
|4.585962562
|2636.67
|141.34
|236.67
|-
|10
|10<sup>0.69314718056</sup>
|4.933409668
|2763.10
|126.43
|363.10
|-
|11
|11<sup>0.69314718056</sup>
|5.270337212
|2877.47
|114.37
|477.47
|-
|12
|12<sup>0.69314718056</sup>
|5.597981231
|2981.89
|104.41
|581.89
|-
|13
|13<sup>0.69314718056</sup>
|5.917342318
|3077.94
|96.05
|677.94
|-
|14
|14<sup>0.69314718056</sup>
|6.22924506
|3166.87
|88.93
|766.87
|-
|15
|15<sup>0.69314718056</sup>
|6.5343793
|3249.66
|82.79
|849.66
|-
|16
|16<sup>0.69314718056</sup>
|6.833329631
|3327.11
|77.45
|927.11
|}
The harmonic series is technically a powharmonic series: the 1-powharmonic series.
The harmonic series is technically a powharmonic series: the 1-powharmonic series.


== log-base-b-of-a-powharmonic series ==
== log-base-b-of-a-powharmonic series ==


When we choose a <span><math>p</math></span> of the form <span><math>\log_{b}a</math></span>, the resulting scale will include every integer power of <span><math>a</math></span>, and the count of steps between each power of <span><math>a</math></span> will be equal to the next integer power of <span><math>b</math></span>.  
When we choose a <span><math>p</math></span> of the form <span><math>\log_{b}a</math></span>, the resulting scale will include every integer power of <span><math>a</math></span>, and the count of steps between each power of <span><math>a</math></span> will be equal to the next integer power of <span><math>b</math></span>.


By extension of the naming scheme ''p-powharmonic series'', we call this a ''log-base-b-of-a-powharmonic series''.
By extension of the naming scheme ''p-powharmonic series'', we call this a ''log-base-b-of-a-powharmonic series''.
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