List of octave-reduced harmonics: Difference between revisions

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Added 83 and 107 harmonics; fixed typo (because 161 and 247 are composite)
 
Line 9: Line 9:
! class="unsortable" | Remarks
! class="unsortable" | Remarks
|-
|-
| 1
| [[1/1|1]]
| 0
| 0
| 1
| 1
Line 15: Line 15:
| present in all tunings and tonal systems
| present in all tunings and tonal systems
|-
|-
| 129
| [[129/128|129]]
| 13.473
| 13.473
| 3 x 43
| 3 × 43
|  
|  
|  
|  
|-
|-
| 65
| [[65/64|65]]
| 26.841
| 26.841
| 5 x 13
| 5 × 13
|  
|  
| [[13-limit]]
| [[13-limit]]
|-
|-
| '''131'''
| '''[[131/128|131]]'''
| '''40.108'''
| '''40.108'''
| '''prime'''
| '''prime'''
Line 33: Line 33:
| '''close to square root of 67'''
| '''close to square root of 67'''
|-
|-
| 33
| [[33/32|33]]
| 53.273
| 53.273
| 3 x 11
| 3 × 11
| undecimal comma
| undecimal comma
| [[11-limit]] / close to quarter-tone (1 [[degree]] of [[24edo]]), square root of 17
| [[11-limit]] / close to quarter-tone (1 [[degree]] of [[24edo]]), square root of 17
|-
|-
| 133
| [[133/128|133]]
| 66.339
| 66.339
| 7 x 19
| 7 × 19
|  
|  
| close to 1 degree of [[18edo]] / [[19edo]], square root of 69
| close to 1 degree of [[18edo]] / [[19edo]], square root of 69
|-
|-
| '''67'''
| '''[[67/64|67]]'''
| '''79.307'''
| '''79.307'''
| '''prime'''
| '''prime'''
Line 51: Line 51:
| '''close to 1 degree of [[15edo]]'''
| '''close to 1 degree of [[15edo]]'''
|-
|-
| 135
| [[135/128|135]]
| 92.179
| 92.179
| 3 x 3 x 3 x 5
| 3 × 3 × 3 × 5
|  
|  
| [[5-limit]], close to 1 degree of [[13edo]] / square root of 71
| [[5-limit]], close to 1 degree of [[13edo]] / square root of 71
|-
|-
| '''17'''
| '''[[17/16|17]]'''
| '''104.955'''
| '''104.955'''
| '''prime'''
| '''prime'''
Line 63: Line 63:
| '''close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]'''
| '''close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]'''
|-
|-
| '''137'''
| '''[[137/128|137]]'''
| '''117.6385'''
| '''117.6385'''
| '''prime'''
| '''prime'''
Line 69: Line 69:
| '''close to 3 degrees of [[31edo]],''' '''square root of 73'''
| '''close to 3 degrees of [[31edo]],''' '''square root of 73'''
|-
|-
| 69
| [[69/64|69]]
| 130.229
| 130.229
| 3 x 23
| 3 × 23
|  
|  
| close to 1 degree of [[9edo]]
| close to 1 degree of [[9edo]]
|-
|-
| '''139'''
| '''[[139/128|139]]'''
| '''142.729'''
| '''142.729'''
| '''prime'''
| '''prime'''
Line 81: Line 81:
| '''close to 2 degrees of [[17edo]]'''
| '''close to 2 degrees of [[17edo]]'''
|-
|-
| 35
| [[35/32|35]]
| 155.140
| 155.140
| 5 x 7
| 5 × 7
|  
|  
| [[7-limit]] / close to 3 degrees of [[24edo]]
| [[7-limit]] / close to 3 degrees of [[24edo]]
|-
|-
| 141
| [[141/128|141]]
| 167.462
| 167.462
| 3 x 47
| 3 × 47
|  
|  
|  
|  
|-
|-
| '''71'''
| '''[[71/64|71]]'''
| '''179.697'''
| '''179.697'''
| '''prime'''
| '''prime'''
Line 99: Line 99:
| '''close to 3 degrees of [[20edo]], square root of 79'''
| '''close to 3 degrees of [[20edo]], square root of 79'''
|-
|-
| 143
| [[143/128|143]]
| 191.846
| 191.846
| 11 x 13
| 11 × 13
| 11-13 meantone
| 11-13 meantone
| [[13-limit]] / close to square root of 5 (a.k.a. 5 degrees of [[31edo]])
| [[13-limit]] / close to square root of 5 (a.k.a. 5 degrees of [[31edo]])
|-
|-
| 9
| [[9/8|9]]
| 203.910
| 203.910
| 3 x 3
| 3 × 3
| major whole-tone / Pythagorean whole tone
| major whole-tone / Pythagorean whole tone
| [[3-limit]]
| [[3-limit]]
|-
|-
| 145
| [[145/128|145]]
| 215.891
| 215.891
| 5 x 29
| 5 × 29
| 5-29 eventone
| 5-29 eventone
| close to 2 degrees of [[11edo]]
| close to 2 degrees of [[11edo]]
|-
|-
| '''73'''
| '''[[73/64|73]]'''
| '''227.789'''
| '''227.789'''
| '''prime'''
| '''prime'''
Line 123: Line 123:
| '''close to 3 degrees of [[16edo]] / 4 degrees of [[21edo]]'''
| '''close to 3 degrees of [[16edo]] / 4 degrees of [[21edo]]'''
|-
|-
| 147
| [[147/128|147]]
| 239.607
| 239.607
| 3 x 7 x 7
| 3 × 7 × 7
|  
|  
| [[7-limit]] / close to 1 degree of [[5edo]], square root of 21
| [[7-limit]] / close to 1 degree of [[5edo]], square root of 21
|-
|-
| '''37'''
| '''[[37/32|37]]'''
| '''251.344'''
| '''251.344'''
| '''prime'''
| '''prime'''
Line 135: Line 135:
| '''close to 5 degrees of [[24edo]]'''
| '''close to 5 degrees of [[24edo]]'''
|-
|-
| '''149'''
| '''[[149/128|149]]'''
| '''263.002'''
| '''263.002'''
| '''prime'''
| '''prime'''
Line 141: Line 141:
|  
|  
|-
|-
| 75
| [[75/64|75]]
| 274.582
| 274.582
| 3 x 5 x 5
| 3 × 5 × 5
| augmented second
| augmented second
| [[5-limit]] / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11
| [[5-limit]] / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11
|-
|-
| '''151'''
| '''[[151/128|151]]'''
| '''286.086'''
| '''286.086'''
| '''prime'''
| '''prime'''
Line 153: Line 153:
| '''close to 4 degrees of [[17edo]]'''
| '''close to 4 degrees of [[17edo]]'''
|-
|-
| '''19'''
| '''[[19/16|19]]'''
| '''297.513'''
| '''297.513'''
| '''prime'''
| '''prime'''
Line 159: Line 159:
| '''close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]])'''
| '''close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]])'''
|-
|-
| 153
| [[153/128|153]]
| 308.865
| 308.865
| 3 x 3 x 17
| 3 × 3 × 17
|  
|  
| close to 8 degrees of [[31edo]]
| close to 8 degrees of [[31edo]]
|-
|-
| 77
| [[77/64|77]]
| 320.144
| 320.144
| 7 x 11
| 7 × 11
|
|  
|  
| close to 4 degrees of [[15edo]]
|-
|-
| 155
| [[155/128|155]]
| 331.349
| 331.349
| 5 x 31
| 5 × 31
|  
|  
|  
|  
|-
|-
| 39
| [[39/32|39]]
| 342.483
| 342.483
| 3 x 13
| 3 × 13
|  
|  
| [[13-limit]] / close to 2 degrees of [[7edo]]
| [[13-limit]] / close to 2 degrees of [[7edo]]
|-
|-
| '''157'''
| '''[[157/128|157]]'''
| '''353.545'''
| '''353.545'''
| '''prime'''
| '''prime'''
Line 189: Line 189:
| '''close to 5 degrees of [[17edo]]'''
| '''close to 5 degrees of [[17edo]]'''
|-
|-
| '''79'''
| '''[[79/64|79]]'''
| '''364.537'''
| '''364.537'''
| '''prime'''
| '''prime'''
Line 195: Line 195:
| '''close to 7 degrees of [[23edo]]'''
| '''close to 7 degrees of [[23edo]]'''
|-
|-
| 159
| [[159/128|159]]
| 375.4595
| 375.4595
| 3 x 53
| 3 × 53
|  
|  
| close to 5 degrees of [[16edo]]
| close to 5 degrees of [[16edo]]
|-
|-
| '''5'''
| '''[[5/4|5]]'''
| '''386.314'''
| '''386.314'''
| '''prime'''
| '''prime'''
Line 207: Line 207:
| '''[[5-limit]] / close to 10 degrees of [[31edo]]'''
| '''[[5-limit]] / close to 10 degrees of [[31edo]]'''
|-
|-
| '''161'''
| [[161/128|161]]
| '''397.100'''
| 397.100
| '''prime'''
| 7 × 23
|  
|  
| '''close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])'''
| close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])
|-
|-
| 81
| [[81/64|81]]
| 407.820
| 407.820
| 3 x 3 × 3 × 3
| 3 × 3 × 3 × 3
| Pythagorean major third
| Pythagorean major third
| [[3-limit]]
| [[3-limit]]
|-
|-
| '''163'''
| '''[[163/128|163]]'''
| '''418.474'''
| '''418.474'''
| '''prime'''
| '''prime'''
Line 225: Line 225:
| '''close to 8 degrees of [[23edo]] / square root of phi'''
| '''close to 8 degrees of [[23edo]] / square root of phi'''
|-
|-
| '''41'''
| '''[[41/32|41]]'''
| '''429.062'''
| '''429.062'''
| '''prime'''
| '''prime'''
Line 231: Line 231:
| '''close to 5 degrees of [[14edo]]'''
| '''close to 5 degrees of [[14edo]]'''
|-
|-
| 165
| [[165/128|165]]
| 439.587
| 439.587
| 3 x 5 x 11
| 3 × 5 × 11
|  
|  
|  
|  
|-
|-
| '''167'''
| '''[[83/64|83]]'''
| '''450.047'''
| '''prime'''
|
| '''close to 3 degrees of [[8edo]]'''
|-
| '''[[167/128|167]]'''
| '''460.445'''
| '''460.445'''
| '''prime'''
| '''prime'''
Line 243: Line 249:
|  
|  
|-
|-
| 21
| [[21/16|21]]
| 470.781
| 470.781
| 3 x 7
| 3 × 7
| narrow fourth / septimal fourth
| narrow fourth / septimal fourth
| [[7-limit]] / close to 9 degrees of [[23edo]]
| [[7-limit]] / close to 9 degrees of [[23edo]]
|-
|-
| 169
| [[169/128|169]]
| 481.055
| 481.055
| 13 x 13
| 13 × 13
|  
|  
| [[13-limit]] / close to 2 degrees of [[5edo]], square root of 7
| [[13-limit]] / close to 2 degrees of [[5edo]], square root of 7
|-
|-
| 85
| [[85/64|85]]
| 491.269
| 491.269
| 5 x 17
| 5 × 17
| near fourth
| near fourth
| close to 9 degrees of [[22edo]]
| close to 9 degrees of [[22edo]]
|-
|-
| 171
| [[171/128|171]]
| 501.423
| 501.423
| 3 x 3 x 19
| 3 × 3 × 19
|  
|  
| close to 5 degrees of [[12edo]]
| close to 5 degrees of [[12edo]]
|-
|-
| '''43'''
| '''[[43/32|43]]'''
| '''511.518'''
| '''511.518'''
| '''prime'''
| '''prime'''
Line 273: Line 279:
| '''close to 3 degrees of [[7edo]] / square root of 29'''
| '''close to 3 degrees of [[7edo]] / square root of 29'''
|-
|-
| '''173'''
| '''[[173/128|173]]'''
| '''521.554'''
| '''521.554'''
| '''prime'''
| '''prime'''
Line 279: Line 285:
| '''close to 10 degrees of [[23edo]]'''
| '''close to 10 degrees of [[23edo]]'''
|-
|-
| 87
| [[87/64|87]]
| 531.532
| 531.532
| 3 x 29
| 3 × 29
|  
|  
| close to 4 degrees of [[9edo]]
| close to 4 degrees of [[9edo]]
|-
|-
| 175
| [[175/128|175]]
| 541.453
| 541.453
| 5 x 5 x 7
| 5 × 5 × 7
|  
|  
| close to 9 degrees of [[20edo]]
| close to 9 degrees of [[20edo]]
|-
|-
| '''11'''
| '''[[11/8|11]]'''
| '''551.318'''
| '''551.318'''
| '''prime'''
| '''prime'''
Line 297: Line 303:
| '''[[11-limit]] / close to 11 degrees of [[24edo]]'''
| '''[[11-limit]] / close to 11 degrees of [[24edo]]'''
|-
|-
| 177
| [[177/128|177]]
| 561.127
| 561.127
| 3 x 59
| 3 × 59
|  
|  
| close to 7 degrees of [[15edo]]
| close to 7 degrees of [[15edo]]
|-
|-
| '''89'''
| '''[[89/64|89]]'''
| '''570.880'''
| '''570.880'''
| '''prime'''
| '''prime'''
Line 309: Line 315:
| '''close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] / square root of 31'''
| '''close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] / square root of 31'''
|-
|-
| '''179'''
| '''[[179/128|179]]'''
| '''580.579'''
| '''580.579'''
| '''prime'''
| '''prime'''
Line 315: Line 321:
| '''close to 15 degrees of [[31edo]]'''
| '''close to 15 degrees of [[31edo]]'''
|-
|-
| 45
| [[45/32|45]]
| 590.224
| 590.224
| 3 x 3 x 5
| 3 × 3 × 5
| high 5-limit tritone
| high 5-limit tritone
| [[5-limit]] / close to square root of 15
| [[5-limit]] / close to square root of 15
|-
|-
| '''181'''
| '''[[181/128|181]]'''
| '''599.815'''
| '''599.815'''
| '''prime'''
| '''prime'''
Line 327: Line 333:
| '''close to square root of 2'''
| '''close to square root of 2'''
|-
|-
| 91
| [[91/64|91]]
| 609.354
| 609.354
| 7 x 13
| 7 × 13
|  
|  
| [[13-limit]]
| [[13-limit]]
|-
|-
| 183
| [[183/61|183]]
| 618.840
| 618.840
| 3 x 61
| 3 × 61
|  
|  
|  
|  
|-
|-
| '''23'''
| '''[[23/16|23]]'''
| '''628.274'''
| '''628.274'''
| '''prime'''
| '''prime'''
Line 345: Line 351:
| '''close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] / square root of 33'''
| '''close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] / square root of 33'''
|-
|-
| 185
| [[185/128|185]]
| 637.658
| 637.658
| 5 x 37
| 5 × 37
|  
|  
|  
|  
|-
|-
| 93
| [[93/64|93]]
| 646.991
| 646.991
| 3 x 31
| 3 × 31
|  
|  
| close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]]
| close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]]
|-
|-
| 187
| [[187/128|187]]
| 656.273
| 656.273
| 11 x 17
| 11 × 17
|  
|  
| close to 11 degrees of [[20edo]]
| close to 11 degrees of [[20edo]]
|-
|-
| '''47'''
| '''[[47/32|47]]'''
| '''665.507'''
| '''665.507'''
| '''prime'''
| '''prime'''
Line 369: Line 375:
| '''close to 5 degrees of [[9edo]]'''
| '''close to 5 degrees of [[9edo]]'''
|-
|-
| 189
| [[189/128|189]]
| 674.691
| 674.691
| 3 x 3 x 3 x 7
| 3 × 3 × 3 × 7
|  
|  
| [[7-limit]] / close to 9 degrees of [[16edo]], square root of 35
| [[7-limit]] / close to 9 degrees of [[16edo]], square root of 35
|-
|-
| 95
| [[95/64|95]]
| 683.827
| 683.827
| 5 x 19
| 5 × 19
|  
|  
| close to 4 degrees of [[7edo]]
| close to 4 degrees of [[7edo]]
|-
|-
| '''191'''
| '''[[191/128|191]]'''
| '''692.9155'''
| '''692.9155'''
| '''prime'''
| '''prime'''
Line 387: Line 393:
| '''close to 11 degrees of [[19edo]]'''
| '''close to 11 degrees of [[19edo]]'''
|-
|-
| '''3'''
| '''[[3/2|3]]'''
| '''701.955'''
| '''701.955'''
| '''prime'''
| '''prime'''
Line 393: Line 399:
| '''[[3-limit]] / close to 7 degrees of [[12edo]]'''
| '''[[3-limit]] / close to 7 degrees of [[12edo]]'''
|-
|-
| '''193'''
| '''[[193/128|193]]'''
| '''710.948'''
| '''710.948'''
| '''prime'''
| '''prime'''
Line 399: Line 405:
| '''close to 13 degrees of [[22edo]]'''
| '''close to 13 degrees of [[22edo]]'''
|-
|-
| '''97'''
| '''[[97/64|97]]'''
| '''719.895'''
| '''719.895'''
| '''prime'''
| '''prime'''
Line 405: Line 411:
| '''close to 3 degrees of [[5edo]]'''
| '''close to 3 degrees of [[5edo]]'''
|-
|-
| 195
| [[195/128|195]]
| 728.796
| 728.796
| 3 x 5 x 13
| 3 × 5 × 13
|  
|  
| [[13-limit]] / close to 19 degrees of [[31edo]], square root of 37
| [[13-limit]] / close to 19 degrees of [[31edo]], square root of 37
|-
|-
| 49
| [[49/32|49]]
| 737.652
| 737.652
| 7 x 7
| 7 × 7
|  
|  
| [[7-limit]] / close to 8 degrees of [[13edo]]
| [[7-limit]] / close to 8 degrees of [[13edo]]
|-
|-
| '''197'''
| '''[[197/128|197]]'''
| '''746.462'''
| '''746.462'''
| '''prime'''
| '''prime'''
Line 423: Line 429:
|  
|  
|-
|-
| 99
| [[99/64|99]]
| 755.228
| 755.228
| 3 x 3 x 11
| 3 × 3 × 11
|  
|  
| [[11-limit]] / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]]
| [[11-limit]] / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]]
|-
|-
| '''199'''
| '''[[199/128|199]]'''
| '''763.9495'''
| '''763.9495'''
| '''prime'''
| '''prime'''
Line 435: Line 441:
| '''close to 7 degrees of [[11edo]]'''
| '''close to 7 degrees of [[11edo]]'''
|-
|-
| 25
| [[25/16|25]]
| 772.627
| 772.627
| 5 x 5
| 5 × 5
| augmented fifth
| augmented fifth
| [[5-limit]] / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39
| [[5-limit]] / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39
|-
|-
| 201
| [[201/128|201]]
| 781.262
| 781.262
| 3 x 67
| 3 × 67
| harmonic gentle minor sixth, circular sixth
| harmonic gentle minor sixth, circular sixth
| close to 19 degrees of [[23edo]] / pi
| close to 19 degrees of [[23edo]] / pi
|-
|-
| '''101'''
| '''[[101/64|101]]'''
| '''789.854'''
| '''789.854'''
| '''prime'''
| '''prime'''
Line 453: Line 459:
|  
|  
|-
|-
| 203
| [[203/128|203]]
| 798.403
| 798.403
| 7 x 29
| 7 × 29
|  
|  
| close to 8 degrees of [[12edo]] (a.k.a. 2 degrees of [[3edo]])
| close to 8 degrees of [[12edo]] (a.k.a. 2 degrees of [[3edo]])
|-
|-
| 51
| [[51/32|51]]
| 806.910
| 806.910
| 3 x 17
| 3 × 17
|  
|  
|  
|  
|-
|-
| 205
| [[205/128|205]]
| 815.376
| 815.376
| 5 x 41
| 5 × 41
|  
|  
| close to 21 degrees of [[31edo]], square root of 41 ,
| close to 21 degrees of [[31edo]], square root of 41 ,
|-
|-
| '''103'''
| '''[[103/64|103]]'''
| '''823.801'''
| '''823.801'''
| '''prime'''
| '''prime'''
Line 477: Line 483:
| '''close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]]'''
| '''close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]]'''
|-
|-
| 207
| [[207/128|207]]
| 832.143
| 832.143
| 3 x 3 x 23
| 3 × 3 × 23
|  
|  
| close to 17 degrees of [[22edo]], 10 degrees of [[13edo]]
| close to 17 degrees of [[22edo]], 10 degrees of [[13edo]]
|-
|-
| '''13'''
| '''[[13/8|13]]'''
| '''840.528'''
| '''840.528'''
| '''prime'''
| '''prime'''
Line 489: Line 495:
| '''[[13-limit]] / close to 7 degrees of [[10edo]], golden ratio'''
| '''[[13-limit]] / close to 7 degrees of [[10edo]], golden ratio'''
|-
|-
| 209
| [[209/128|209]]
| 848.831
| 848.831
| 11 x 19
| 11 × 19
| 11-19 hemieleventh
| 11-19 hemieleventh
| close to 12 degrees of [[17edo]]
| close to 12 degrees of [[17edo]]
|-
|-
| 105
| [[105/64|105]]
| 857.095
| 857.095
| 3 x 5 x 7
| 3 × 5 × 7
|  
|  
| [[7-limit]] / close to 5 degrees of [[7edo]], square root of 43
| [[7-limit]] / close to 5 degrees of [[7edo]], square root of 43
|-
|-
| '''211'''
| '''[[211/128|211]]'''
| '''865.319'''
| '''865.319'''
| '''prime'''
| '''prime'''
Line 507: Line 513:
| '''close to 13 degrees of [[18edo]]'''
| '''close to 13 degrees of [[18edo]]'''
|-
|-
| '''53'''
| '''[[53/32|53]]'''
| '''873.505'''
| '''873.505'''
| '''prime'''
| '''prime'''
Line 513: Line 519:
| '''close to 8 degrees of [[11edo]]'''
| '''close to 8 degrees of [[11edo]]'''
|-
|-
| 213
| [[213/128|213]]
| 881.6515
| 881.652
| 3 x 71
| 3 × 71
|  
|  
| close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]]
| close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]]
|-
|-
| 215
| '''[[107/64|107]]'''
| ''' 889.760'''
| '''prime'''
|
|
|-
| [[215/128|215]]
| 897.831
| 897.831
| 5 x 43
| 5 × 43
|  
|  
| close to 9 degrees of [[12edo]] (a.k.a. 3 degrees of [[4edo]]), square root of 45
| close to 9 degrees of [[12edo]] (a.k.a. 3 degrees of [[4edo]]), square root of 45
|-
|-
| 27
| [[27/16|27]]
| 905.865
| 905.865
| 3 x 3 x 3
| 3 × 3 × 3
| Pythagorean major sixth
| Pythagorean major sixth
| [[3-limit]]
| [[3-limit]]
|-
|-
| 217
| [[217/128|217]]
| 913.8615
| 913.8615
| 7 x 31
| 7 × 31
| harmonic gentle major third
| harmonic gentle major third
| close to 13 degrees of [[17edo]]
| close to 13 degrees of [[17edo]]
|-
|-
| '''109'''
| '''[[109/64|109]]'''
| '''921.821'''
| '''921.821'''
| '''prime'''
| '''prime'''
Line 543: Line 555:
| '''close to 10 degrees of [[13edo]]'''
| '''close to 10 degrees of [[13edo]]'''
|-
|-
| 219
| [[219/128|219]]
| 929.7445
| 929.7445
| 3 x 73
| 3 × 73
|  
|  
| close to 24 degrees of [[31edo]], square root of 47
| close to 24 degrees of [[31edo]], square root of 47
|-
|-
| 55
| [[55/32|55]]
| 937.632
| 937.632
| 5 x 11
| 5 × 11
|  
|  
| [[11-limit]] / close to 18 degrees of [[23edo]]
| [[11-limit]] / close to 18 degrees of [[23edo]]
|-
|-
| 221
| [[221/128|221]]
| 945.483
| 945.483
| 13 x 17
| 13 × 17
|  
|  
| close to 15 degrees of [[19edo]]
| close to 15 degrees of [[19edo]]
|-
|-
| 111
| [[111/64|111]]
| 953.299
| 953.299
| 3 x 37
| 3 × 37
| harmonic hemitwelfth
| harmonic hemitwelfth
| close to 19 degrees of [[24edo]] / square root of 3
| close to 19 degrees of [[24edo]] / square root of 3
|-
|-
| '''223'''
| '''[[223/128|223]]'''
| '''961.080'''
| '''961.080'''
| '''prime'''
| '''prime'''
Line 573: Line 585:
| '''close to 4 degrees of [[5edo]]'''
| '''close to 4 degrees of [[5edo]]'''
|-
|-
| '''7'''
| '''[[7/4|7]]'''
| '''968.826'''
| '''968.826'''
| '''prime'''
| '''prime'''
Line 579: Line 591:
| '''[[7-limit]] / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]]'''
| '''[[7-limit]] / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]]'''
|-
|-
| 225
| [[225/128|225]]
| 976.537
| 976.537
| 3 x 3 x 5 x 5
| 3 × 3 × 5 × 5
| 5-limit subminor seventh
| 5-limit subminor seventh
| [[5-limit]] / close to 11 degrees of [[16edo]]
| [[5-limit]] / close to 11 degrees of [[16edo]]
|-
|-
| '''113'''
| '''[[113/64|113]]'''
| '''984.215'''
| '''984.215'''
| '''prime'''
| '''prime'''
Line 591: Line 603:
| '''close to 9 degrees of [[11edo]]'''
| '''close to 9 degrees of [[11edo]]'''
|-
|-
| '''227'''
| '''[[227/128|227]]'''
| '''991.858'''
| '''991.858'''
| '''prime'''
| '''prime'''
Line 597: Line 609:
|  
|  
|-
|-
| 57
| [[57/32|57]]
| 999.468
| 999.468
| 3 x 19
| 3 × 19
|  
|  
| close to 10 degrees of [[12edo]] (a.k.a. 5 degrees of [[6edo]]), square root of 51
| close to 10 degrees of [[12edo]] (a.k.a. 5 degrees of [[6edo]]), square root of 51
|-
|-
| '''229'''
| '''[[229/128|229]]'''
| '''1007.0445'''
| '''1007.0445'''
| '''prime'''
| '''prime'''
Line 609: Line 621:
|  
|  
|-
|-
| 115
| [[115/64|115]]
| 1014.588
| 1014.588
| 5 x 23
| 5 × 23
|  
|  
| close to 11 degrees of [[13edo]]
| close to 11 degrees of [[13edo]]
|-
|-
| 231
| [[231/128|231]]
| 1022.099
| 1022.099
| 3 x 7 x 11
| 3 × 7 × 11
|  
|  
| close to square root of 13
| close to square root of 13
|-
|-
| '''29'''
| '''[[29/16|29]]'''
| '''1029.577'''
| '''1029.577'''
| '''prime'''
| '''prime'''
Line 627: Line 639:
| '''close to 6 degrees of [[7edo]]'''
| '''close to 6 degrees of [[7edo]]'''
|-
|-
| '''233'''
| '''[[233/128|233]]'''
| '''1037.023'''
| '''1037.023'''
| '''prime'''
| '''prime'''
Line 633: Line 645:
| '''close to square root of 53'''
| '''close to square root of 53'''
|-
|-
| 117
| [[117/64|117]]
| 1044.438
| 1044.438
| 3 x 3 x 13
| 3 × 3 × 13
|  
|  
| [[13-limit]] / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]]
| [[13-limit]] / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]]
|-
|-
| 235
| [[235/128|235]]
| 1051.820
| 1051.820
| 5 x 47
| 5 × 47
|  
|  
| close to 21 degrees of [[24edo]]
| close to 21 degrees of [[24edo]]
|-
|-
| '''59'''
| '''[[59/32|59]]'''
| '''1059.172'''
| '''1059.172'''
| '''prime'''
| '''prime'''
Line 651: Line 663:
| '''close to 15 degrees of [[17edo]]'''
| '''close to 15 degrees of [[17edo]]'''
|-
|-
| 237
| [[237/128|237]]
| 1066.492
| 1066.492
| 3 x 79
| 3 × 79
|  
|  
| close to 8 degrees of [[9edo]], square root of 55
| close to 8 degrees of [[9edo]], square root of 55
|-
|-
| 119
| [[119/64|119]]
| 1073.781
| 1073.781
| 7 x 17
| 7 × 17
|  
|  
| close to 17 degrees of [[19edo]]
| close to 17 degrees of [[19edo]]
|-
|-
| '''239'''
| '''[[239/128|239]]'''
| '''1081.040'''
| '''1081.040'''
| '''prime'''
| '''prime'''
Line 669: Line 681:
| '''close to 3 degrees of [[31edo]]'''
| '''close to 3 degrees of [[31edo]]'''
|-
|-
| 15
| [[15/8|15]]
| 1088.269
| 1088.269
| 3 x 5
| 3 × 5
| 5-limit major seventh
| 5-limit major seventh
| [[5-limit]] / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]]
| [[5-limit]] / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]]
|-
|-
| '''241'''
| '''[[241/128|241]]'''
| '''1095.467'''
| '''1095.467'''
| '''prime'''
| '''prime'''
Line 681: Line 693:
|  
|  
|-
|-
| 121
| [[121/64|121]]
| 1102.636
| 1102.636
| 11 x 11
| 11 × 11
|  
|  
| [[11-limit]] / close to 11 degrees of [[12edo]], square root of 57
| [[11-limit]] / close to 11 degrees of [[12edo]], square root of 57
|-
|-
| 243
| [[243/128|243]]
| 1109.775
| 1109.775
| 3 x 3 x 3 x 3 × 3
| 3 × 3 × 3 × 3 × 3
| Pythagorean major seventh
| Pythagorean major seventh
| close to 12 degrees of [[13edo]]
| close to 12 degrees of [[13edo]]
|-
|-
| '''61'''
| '''[[61/32|61]]'''
| '''1116.885'''
| '''1116.885'''
| '''prime'''
| '''prime'''
Line 699: Line 711:
| '''close to 13 degrees of [[14edo]]'''
| '''close to 13 degrees of [[14edo]]'''
|-
|-
| 245
| [[245/128|245]]
| 1123.9655
| 1123.9655
| 5 x 7 x 7
| 5 × 7 × 7
|  
|  
| close to 16 degrees of [[17edo]]
| close to 16 degrees of [[17edo]]
|-
|-
| 123
| [[123/64|123]]
| 1131.017
| 1131.017
| 3 x 41
| 3 × 41
|  
|  
| close to 17 degrees of [[18edo]], 18 degrees of [[19edo]], square root of 59
| close to 17 degrees of [[18edo]], 18 degrees of [[19edo]], square root of 59
|-
|-
| '''247'''
| [[247/128|247]]
| '''1138.041'''
| 1138.041
| '''prime'''
| 13 × 19
|  
|  
| '''close to 19 degrees of [[20edo]]'''
| close to 19 degrees of [[20edo]]
|-
|-
| '''31'''
| '''[[31/16|31]]'''
| '''1145.036'''
| '''1145.036'''
| '''prime'''
| '''prime'''
Line 723: Line 735:
| '''close to 21 degrees of [[22edo]]'''
| '''close to 21 degrees of [[22edo]]'''
|-
|-
| 249
| [[249/128|249]]
| 1152.002
| 1152.002
| 3 x 83
| 3 × 83
|  
|  
| close to 24 degrees of [[25edo]]
| close to 24 degrees of [[25edo]]
|-
|-
| 125
| [[125/64|125]]
| 1158.941
| 1158.941
| 5 x 5 x 5
| 5 × 5 × 5
|  
|  
| [[5-limit]], close to square root of 61
| [[5-limit]], close to square root of 61
|-
|-
| '''251'''
| '''[[251/128|251]]'''
| '''1165.852'''
| '''1165.852'''
| '''prime'''
| '''prime'''
Line 741: Line 753:
|  
|  
|-
|-
| 63
| [[63/32|63]]
| 1172.736
| 1172.736
| 3 x 3 x 7
| 3 × 3 × 7
|  
|  
| [[7-limit]]
| [[7-limit]]
|-
|-
| 253
| [[253/128|253]]
| 1179.592
| 1179.592
| 11 x 23
| 11 × 23
|  
|  
|  
|  
|-
|-
| '''127'''
| '''[[127/64|127]]'''
| '''1186.422'''
| '''1186.422'''
| '''prime'''
| '''prime'''
Line 759: Line 771:
| '''close to square root of 63'''
| '''close to square root of 63'''
|-
|-
| 255
| [[255/128|255]]
| 1193.224
| 1193.224
| 3 x 5 x 17
| 3 × 5 × 17
|  
|  
|  
|  
|-
|-
| '''2'''
| '''[[2/1|2]]'''
| '''1200'''
| '''1200'''
| '''prime'''
| '''prime'''

Latest revision as of 14:19, 31 May 2025

This is a list of harmonics up to 255, sorted by ascending pitch of their octave-reduced equivalent (except the octave, which is not reduced). Prime harmonics are in bold.

Harmonic Size (¢)[1] Factorization Name Remarks
1 0 1 unison present in all tunings and tonal systems
129 13.473 3 × 43
65 26.841 5 × 13 13-limit
131 40.108 prime close to square root of 67
33 53.273 3 × 11 undecimal comma 11-limit / close to quarter-tone (1 degree of 24edo), square root of 17
133 66.339 7 × 19 close to 1 degree of 18edo / 19edo, square root of 69
67 79.307 prime close to 1 degree of 15edo
135 92.179 3 × 3 × 3 × 5 5-limit, close to 1 degree of 13edo / square root of 71
17 104.955 prime harmonic half-step close to 1 degree of 11edo / 2 degrees of 23edo
137 117.6385 prime harmonic secor close to 3 degrees of 31edo, square root of 73
69 130.229 3 × 23 close to 1 degree of 9edo
139 142.729 prime close to 2 degrees of 17edo
35 155.140 5 × 7 7-limit / close to 3 degrees of 24edo
141 167.462 3 × 47
71 179.697 prime close to 3 degrees of 20edo, square root of 79
143 191.846 11 × 13 11-13 meantone 13-limit / close to square root of 5 (a.k.a. 5 degrees of 31edo)
9 203.910 3 × 3 major whole-tone / Pythagorean whole tone 3-limit
145 215.891 5 × 29 5-29 eventone close to 2 degrees of 11edo
73 227.789 prime close to 3 degrees of 16edo / 4 degrees of 21edo
147 239.607 3 × 7 × 7 7-limit / close to 1 degree of 5edo, square root of 21
37 251.344 prime harmonic hemifourth close to 5 degrees of 24edo
149 263.002 prime harmonic subminor third
75 274.582 3 × 5 × 5 augmented second 5-limit / close to 5 degrees of 22edo, 3 degrees of 13edo, square root of 11
151 286.086 prime harmonic gentle minor third close to 4 degrees of 17edo
19 297.513 prime harmonic minor third close to 3 degrees of 12edo (a.k.a. 1 degree of 4edo)
153 308.865 3 × 3 × 17 close to 8 degrees of 31edo
77 320.144 7 × 11 close to 4 degrees of 15edo
155 331.349 5 × 31
39 342.483 3 × 13 13-limit / close to 2 degrees of 7edo
157 353.545 prime harmonic hemififth close to 5 degrees of 17edo
79 364.537 prime close to 7 degrees of 23edo
159 375.4595 3 × 53 close to 5 degrees of 16edo
5 386.314 prime 5-limit major third 5-limit / close to 10 degrees of 31edo
161 397.100 7 × 23 close to 4 degrees of 12edo (a.k.a. 1 degree of 3edo)
81 407.820 3 × 3 × 3 × 3 Pythagorean major third 3-limit
163 418.474 prime overtone gentle major third close to 8 degrees of 23edo / square root of phi
41 429.062 prime close to 5 degrees of 14edo
165 439.587 3 × 5 × 11
83 450.047 prime close to 3 degrees of 8edo
167 460.445 prime
21 470.781 3 × 7 narrow fourth / septimal fourth 7-limit / close to 9 degrees of 23edo
169 481.055 13 × 13 13-limit / close to 2 degrees of 5edo, square root of 7
85 491.269 5 × 17 near fourth close to 9 degrees of 22edo
171 501.423 3 × 3 × 19 close to 5 degrees of 12edo
43 511.518 prime close to 3 degrees of 7edo / square root of 29
173 521.554 prime close to 10 degrees of 23edo
87 531.532 3 × 29 close to 4 degrees of 9edo
175 541.453 5 × 5 × 7 close to 9 degrees of 20edo
11 551.318 prime undecimal semi-augmented fourth / undecimal tritone 11-limit / close to 11 degrees of 24edo
177 561.127 3 × 59 close to 7 degrees of 15edo
89 570.880 prime close to 10 degrees of 21edo / 9 degrees of 19edo / square root of 31
179 580.579 prime close to 15 degrees of 31edo
45 590.224 3 × 3 × 5 high 5-limit tritone 5-limit / close to square root of 15
181 599.815 prime close to square root of 2
91 609.354 7 × 13 13-limit
183 618.840 3 × 61
23 628.274 prime close to 11 degrees of 21edo / 10 degrees of 19edo / square root of 33
185 637.658 5 × 37
93 646.991 3 × 31 close to 7 degrees of 13edo / 13 degrees of 24edo
187 656.273 11 × 17 close to 11 degrees of 20edo
47 665.507 prime close to 5 degrees of 9edo
189 674.691 3 × 3 × 3 × 7 7-limit / close to 9 degrees of 16edo, square root of 35
95 683.827 5 × 19 close to 4 degrees of 7edo
191 692.9155 prime close to 11 degrees of 19edo
3 701.955 prime just perfect fifth 3-limit / close to 7 degrees of 12edo
193 710.948 prime close to 13 degrees of 22edo
97 719.895 prime close to 3 degrees of 5edo
195 728.796 3 × 5 × 13 13-limit / close to 19 degrees of 31edo, square root of 37
49 737.652 7 × 7 7-limit / close to 8 degrees of 13edo
197 746.462 prime
99 755.228 3 × 3 × 11 11-limit / close to 5 degrees of 8edo / 12 degrees of 19edo
199 763.9495 prime close to 7 degrees of 11edo
25 772.627 5 × 5 augmented fifth 5-limit / close to 9 degrees of 14edo / 11 degrees of 17edo, square root of 39
201 781.262 3 × 67 harmonic gentle minor sixth, circular sixth close to 19 degrees of 23edo / pi
101 789.854 prime
203 798.403 7 × 29 close to 8 degrees of 12edo (a.k.a. 2 degrees of 3edo)
51 806.910 3 × 17
205 815.376 5 × 41 close to 21 degrees of 31edo, square root of 41 ,
103 823.801 prime close to 11 degrees of 16edo / 13 degrees of 19edo
207 832.143 3 × 3 × 23 close to 17 degrees of 22edo, 10 degrees of 13edo
13 840.528 prime harmonic sixth, golden overtone 13-limit / close to 7 degrees of 10edo, golden ratio
209 848.831 11 × 19 11-19 hemieleventh close to 12 degrees of 17edo
105 857.095 3 × 5 × 7 7-limit / close to 5 degrees of 7edo, square root of 43
211 865.319 prime close to 13 degrees of 18edo
53 873.505 prime close to 8 degrees of 11edo
213 881.652 3 × 71 close to 11 degrees of 15edo / close to 14 degrees of 19edo
107 889.760 prime
215 897.831 5 × 43 close to 9 degrees of 12edo (a.k.a. 3 degrees of 4edo), square root of 45
27 905.865 3 × 3 × 3 Pythagorean major sixth 3-limit
217 913.8615 7 × 31 harmonic gentle major third close to 13 degrees of 17edo
109 921.821 prime close to 10 degrees of 13edo
219 929.7445 3 × 73 close to 24 degrees of 31edo, square root of 47
55 937.632 5 × 11 11-limit / close to 18 degrees of 23edo
221 945.483 13 × 17 close to 15 degrees of 19edo
111 953.299 3 × 37 harmonic hemitwelfth close to 19 degrees of 24edo / square root of 3
223 961.080 prime close to 4 degrees of 5edo
7 968.826 prime harmonic seventh / septimal minor seventh 7-limit / close to 17 degrees of 21edo / 25 degrees of 31edo
225 976.537 3 × 3 × 5 × 5 5-limit subminor seventh 5-limit / close to 11 degrees of 16edo
113 984.215 prime close to 9 degrees of 11edo
227 991.858 prime
57 999.468 3 × 19 close to 10 degrees of 12edo (a.k.a. 5 degrees of 6edo), square root of 51
229 1007.0445 prime
115 1014.588 5 × 23 close to 11 degrees of 13edo
231 1022.099 3 × 7 × 11 close to square root of 13
29 1029.577 prime close to 6 degrees of 7edo
233 1037.023 prime close to square root of 53
117 1044.438 3 × 3 × 13 13-limit / close to 13 degrees of 15edo / 20 degrees of 23edo
235 1051.820 5 × 47 close to 21 degrees of 24edo
59 1059.172 prime close to 15 degrees of 17edo
237 1066.492 3 × 79 close to 8 degrees of 9edo, square root of 55
119 1073.781 7 × 17 close to 17 degrees of 19edo
239 1081.040 prime close to 3 degrees of 31edo
15 1088.269 3 × 5 5-limit major seventh 5-limit / close to 19 degrees of 21edo / 10 degrees of 11edo
241 1095.467 prime
121 1102.636 11 × 11 11-limit / close to 11 degrees of 12edo, square root of 57
243 1109.775 3 × 3 × 3 × 3 × 3 Pythagorean major seventh close to 12 degrees of 13edo
61 1116.885 prime close to 13 degrees of 14edo
245 1123.9655 5 × 7 × 7 close to 16 degrees of 17edo
123 1131.017 3 × 41 close to 17 degrees of 18edo, 18 degrees of 19edo, square root of 59
247 1138.041 13 × 19 close to 19 degrees of 20edo
31 1145.036 prime close to 21 degrees of 22edo
249 1152.002 3 × 83 close to 24 degrees of 25edo
125 1158.941 5 × 5 × 5 5-limit, close to square root of 61
251 1165.852 prime
63 1172.736 3 × 3 × 7 7-limit
253 1179.592 11 × 23
127 1186.422 prime close to square root of 63
255 1193.224 3 × 5 × 17
2 1200 prime octave 2-limit
  1. ↑ cent values are given for the octave reduced equivalent

See also

Retrieved from "https://en.xen.wiki/index.php?title=List_of_octave-reduced_harmonics&oldid=198246"