@@ Line 465: / Line 465: @@
 === Emulatory Series ===
 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 traditional musical 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 this variation the "emulatory a-edharmonic series", because it is emulating the harmonic series.
+{| class="wikitable"
+|+
+! rowspan="2" |pitch #
+! colspan="4" |harmonic series
+! colspan="5" |edharmonic series
+|-
+|'''frequency multiplier (decimal)'''
+|'''pitch (¢)'''
+|'''pitch Δ (¢)'''
+|'''octave reduced pitch (¢)'''
+|'''frequency multiplier (definition)'''
+|'''frequency multiplier (decimal)'''
+|'''pitch (¢)'''
+|'''pitch Δ (¢)'''
+|'''octave reduced pitch (¢)'''
+|-
+|1
+|1.000000
+|0
+| -
+|0
+|2<sup>H(0)</sup> = 2<sup>0</sup>
+|1.000000000
+|0
+| -
+|0
+|-
+|2
+|2.000000
+|1200
+|1200
+|0
+|2<sup>H(1)</sup> = 2<sup>1</sup>
+|2.000000000
+|1200.00
+|1200.00
+|0.00
+|-
+|3
+|3.000000
+|1901.955001
+|701.955001
+|701.955001
+|2<sup>H(2)</sup> = 2<sup>3/2</sup>
+|2.828427125
+|1800.00
+|600.00
+|600.00
+|-
+|4
+|4.000000
+|2400
+|498.044999
+|0
+|2<sup>H(3)</sup> = 2<sup>11/6</sup>
+|3.563594873
+|2200.00
+|400.00
+|1000.00
+|-
+|5
+|5.000000
+|2786.313714
+|386.313714
+|386.313714
+|2<sup>H(4)</sup> = 2<sup>25/12</sup>
+|4.237852377
+|2500.00
+|300.00
+|100.00
+|-
+|6
+|6.000000
+|3101.955001
+|315.6412870
+|701.955001
+|2<sup>H(5)</sup> = 2<sup>137/60</sup>
+|4.868014055
+|2740.00
+|240.00
+|340.00
+|-
+|7
+|7.000000
+|3368.825906
+|266.8709056
+|968.825906
+|2<sup>H(6)</sup> = 2<sup>49/20</sup>
+|5.464161027
+|2940.00
+|200.00
+|540.00
+|-
+|8
+|8.000000
+|3600
+|231.1740935
+|0
+|2<sup>H(7)</sup> = 2<sup>363/140</sup>
+|6.032922891
+|3111.43
+|171.43
+|711.43
+|-
+|9
+|9.000000
+|3803.910002
+|203.9100017
+|203.910002
+|2<sup>H(8)</sup> = 2<sup>761/280</sup>
+|6.578949063
+|3261.43
+|150.00
+|861.43
+|-
+|10
+|10.000000
+|3986.313714
+|182.4037121
+|386.313714
+|2<sup>H(9)</sup> = 2<sup>7129/2520</sup>
+|7.105658007
+|3394.76
+|133.33
+|994.76
+|-
+|11
+|11.000000
+|4151.317942
+|165.0042285
+|551.317942
+|2<sup>H(10)</sup>
+|7.615655686
+|3514.76
+|120.00
+|1114.76
+|-
+|12
+|12.000000
+|4301.955001
+|150.6370585
+|701.955001
+|2<sup>H(11)</sup>
+|8.110986229
+|3623.85
+|109.09
+|23.85
+|-
+|13
+|13.000000
+|4440.527662
+|138.5726609
+|840.527662
+|2<sup>H(12)</sup>
+|8.593290568
+|3723.85
+|100.00
+|123.85
+|-
+|14
+|14.000000
+|4568.825906
+|128.2982447
+|968.825906
+|2<sup>H(13)</sup>
+|9.063911377
+|3816.16
+|92.31
+|216.16
+|-
+|15
+|15.000000
+|4688.268715
+|119.4428083
+|1088.268715
+|2<sup>H(14)</sup>
+|9.523965051
+|3901.87
+|85.71
+|301.87
+|-
+|16
+|16.000000
+|4800
+|111.7312853
+|0
+|2<sup>H(15)</sup>
+|9.974392624
+|3981.87
+|80.00
+|381.87
+|}
 == See also ==
 [[Logharmonic series|Logharmonic series]]

Powharmonic series: Difference between revisions