List of octave-reduced harmonics: Difference between revisions

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A list of many overtones in an octave, arranged by ascending pitch, [[octave_reduced|octave reduced]]. Prime overtones are highlighted.
This is a list of [[harmonic]]s up to 255, sorted by ascending pitch of their [[Octave reduction|octave-reduced]] equivalent (except the octave, which is not reduced). Prime harmonics are in bold.


{| class="wikitable"
{| class="wikitable center-1 right-2 sortable"
|-
|-
| | overtone
! Harmonic
| | cents
! Size ([[cents|¢]])<ref>cent values are given for the octave reduced equivalent</ref>
| | factorization
! class="unsortable" | Factorization
| | name
! class="unsortable" | Name
| | notes
! class="unsortable" | Remarks
|-
|-
| | 1
| [[1/1|1]]
| | 0
| 0
| |
| 1
| | unison
| unison
| | '''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]]
| [[13-limit]]
|-
|-
| | '''131'''
| '''[[131/128|131]]'''
| | '''40.108'''
| '''40.108'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''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|11-limit]] / close to quarter-tone (1 [[Degree|degree]] of [[24edo|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|18edo]] / [[19edo|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'''
| |  
|  
| | '''close to 1 degree of [[15edo|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|5-limit]], close to 1 degree of [[13edo|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'''
| | '''overtone half-step'''
| '''harmonic half-step'''
| | '''close to 1 degree of [[11edo|11edo]] / 2 degrees of [[23edo|23edo]]'''
| '''close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]'''
|-
|-
| | '''137'''
| '''[[137/128|137]]'''
| | '''117.6385'''
| '''117.6385'''
| | '''prime'''
| '''prime'''
| | '''overtone secor'''
| '''harmonic [[secor]]'''
| | '''close to 3 degrees of [[31edo|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|9edo]]
| close to 1 degree of [[9edo]]
|-
|-
| | '''139'''
| '''[[139/128|139]]'''
| | '''142.729'''
| '''142.729'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 2 degrees of [[17edo|17edo]]'''
| '''close to 2 degrees of [[17edo]]'''
|-
|-
| | 35
| [[35/32|35]]
| | 155.140
| 155.140
| | 5 x 7
| 5 × 7
| |  
|  
| | [[7-limit|7-limit]] / close to 3 degrees of [[24edo|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'''
| |  
|  
| | '''close to 3 degrees of [[20edo|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|13-limit]] / close to square root of 5 (a.k.a.
| [[13-limit]] / close to square root of 5 (a.k.a. 5 degrees of [[31edo]])
 
|-
5 degrees of [[31edo|31edo]])
| [[9/8|9]]
| 203.910
| 3 × 3
| major whole-tone / Pythagorean whole tone
| [[3-limit]]
|-
| [[145/128|145]]
| 215.891
| 5 × 29
| 5-29 eventone
| close to 2 degrees of [[11edo]]
|-
| '''[[73/64|73]]'''
| '''227.789'''
| '''prime'''
|
| '''close to 3 degrees of [[16edo]] / 4 degrees of [[21edo]]'''
|-
|-
| | 9
| [[147/128|147]]
| | 203.910
| 239.607
| | 3 x 3
| 3 × 7 × 7
| | major whole-tone / Pythagorean whole tone
|  
| | 3-limit
| [[7-limit]] / close to 1 degree of [[5edo]], square root of 21
|-
|-
| | 145
| '''[[37/32|37]]'''
| | 215.891
| '''251.344'''
| | 5 x 29
| '''prime'''
| | 5-29 eventone
| '''harmonic''' '''hemifourth'''
| | close to 2 degrees of [[11edo|11edo]]
| '''close to 5 degrees of [[24edo]]'''
|-
|-
| | '''73'''
| '''[[149/128|149]]'''
| | '''227.789'''
| '''263.002'''
| | '''prime'''
| '''prime'''
| |
| '''harmonic subminor third'''
| | '''close to 3 degrees of [[16edo|16edo]] / 4 degrees of [[21edo|21edo]]'''
|
|-
|-
| | 147
| [[75/64|75]]
| | 239.607
| 274.582
| | 3 x 7 x 7
| 3 × 5 × 5
| |
| augmented second
| | 7-limit / close to 1 degree of [[5edo|5edo]], square root of 21
| [[5-limit]] / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11
|-
|-
| | '''37'''
| '''[[151/128|151]]'''
| | '''251.344'''
| '''286.086'''
| | '''prime'''
| '''prime'''
| | '''overtone''' '''hemifourth'''
| '''harmonic gentle minor third'''
| | '''close to 5 degrees of [[24edo|24edo]]'''
| '''close to 4 degrees of [[17edo]]'''
|-
|-
| | '''149'''
| '''[[19/16|19]]'''
| | '''263.002'''
| '''297.513'''
| | '''prime'''
| '''prime'''
| | '''overtone subminor third'''
| '''harmonic minor third'''
| |
| '''close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]])'''
|-
|-
| | 75
| [[153/128|153]]
| | 274.582
| 308.865
| | 3 x 5 x 5
| 3 × 3 × 17
| | augmented second
|  
| | 5-limit / close to 5 degrees of [[22edo|22edo]], 3 degrees of [[13edo|13edo]], square root of 11
| close to 8 degrees of [[31edo]]
|-
|-
| | '''151'''
| [[77/64|77]]
| | '''286.086'''
| 320.144
| | '''prime'''
| 7 × 11
| | '''overtone gentle minor third'''
|  
| | '''close to 4 degrees of [[17edo|17edo]]'''
| close to 4 degrees of [[15edo]]
|-
|-
| | '''19'''
| [[155/128|155]]
| | '''297.513'''
| 331.349
| | '''prime'''
| 5 × 31
| | '''overtone minor third'''
|  
| | '''close to 3 degrees of [[12edo|12edo]] (a.k.a. 1 degree of [[4edo|4edo]])'''
|  
|-
|-
| | 153
| [[39/32|39]]
| | 308.865
| 342.483
| | 3 x 3 x 17
| 3 × 13
| |  
|  
| | close to 8 degrees of [[31edo|31edo]]
| [[13-limit]] / close to 2 degrees of [[7edo]]
|-
|-
| | 155
| '''[[157/128|157]]'''
| | 331.349
| '''353.545'''
| | 5 x 31
| '''prime'''
| |
| '''harmonic''' '''hemififth'''
| |
| '''close to 5 degrees of [[17edo]]'''
|-
|-
| | 39
| '''[[79/64|79]]'''
| | 342.483
| '''364.537'''
| | 3 x 13
| '''prime'''
| |  
|  
| | 13-limit / close to 2 degrees of [[7edo|7edo]]
| '''close to 7 degrees of [[23edo]]'''
|-
|-
| | '''157'''
| [[159/128|159]]
| | '''353.545'''
| 375.4595
| | '''prime'''
| 3 × 53
| | '''overtone''' '''hemififth'''
|  
| | '''close to 5 degrees of [[17edo|17edo]]'''
| close to 5 degrees of [[16edo]]
|-
|-
| | '''79'''
| '''[[5/4|5]]'''
| | '''364.537'''
| '''386.314'''
| | '''prime'''
| '''prime'''
| |
| '''5-limit major third'''
| | '''close to 7 degrees of [[23edo|23edo]]'''
| '''[[5-limit]] / close to 10 degrees of [[31edo]]'''
|-
|-
| | 159
| [[161/128|161]]
| | 375.4595
| 397.100
| | 3 x 53
| 7 × 23
| |  
|  
| | close to 5 degrees of [[16edo|16edo]]
| close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])
|-
|-
| | '''5'''
| [[81/64|81]]
| | '''386.314'''
| 407.820
| | '''prime'''
| 3 × 3 × 3 × 3
| | '''5-limit major third'''
| Pythagorean major third
| | '''5-limit / close to 10 degrees of [[31edo|31edo]]'''
| [[3-limit]]
|-
|-
| | '''161'''
| '''[[163/128|163]]'''
| | '''397.100'''
| '''418.474'''
| | '''prime'''
| '''prime'''
| |
| '''overtone gentle major third'''
| | '''close to 4 degrees of [[12edo|12edo]] (a.k.a. 1 degree of [[3edo|3edo]])'''
| '''close to 8 degrees of [[23edo]] / square root of phi'''
|-
|-
| | 81
| '''[[41/32|41]]'''
| | 407.820
| '''429.062'''
| | 9 x 9
| '''prime'''
| | Pythagorean major third
|  
| | 3-limit
| '''close to 5 degrees of [[14edo]]'''
|-
|-
| | '''163'''
| [[165/128|165]]
| | '''418.474'''
| 439.587
| | '''prime'''
| 3 × 5 × 11
| | '''overtone gentle major third'''
|  
| | '''close to 8 degrees of [[23edo|23edo]] / square root of phi'''
|  
|-
|-
| | '''41'''
| '''[[83/64|83]]'''
| | '''429.062'''
| '''450.047'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 5 degrees of [[14edo|14edo]]'''
| '''close to 3 degrees of [[8edo]]'''
|-
|-
| | 165
| '''[[167/128|167]]'''
| | 439.587
| '''460.445'''
| | 3 x 5 x 11
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | '''167'''
| [[21/16|21]]
| | '''460.445'''
| 470.781
| | '''prime'''
| 3 × 7
| |
| narrow fourth / septimal fourth
| |
| [[7-limit]] / close to 9 degrees of [[23edo]]
|-
|-
| | 21
| [[169/128|169]]
| | 470.781
| 481.055
| | 3 x 7
| 13 × 13
| | narrow fourth / septimal fourth
|  
| | 7-limit / close to 9 degrees of [[23edo|23edo]]
| [[13-limit]] / close to 2 degrees of [[5edo]], square root of 7
|-
|-
| | 169
| [[85/64|85]]
| | 481.055
| 491.269
| | 13 x 13
| 5 × 17
| |
| near fourth
| | 13-limit / close to 2 degrees of [[5edo|5edo]], square root of 7
| close to 9 degrees of [[22edo]]
|-
|-
| | 85
| [[171/128|171]]
| | 491.269
| 501.423
| | 5 x 17
| 3 × 3 × 19
| | near fourth
|  
| | close to 9 degrees of [[22edo|22edo]]
| close to 5 degrees of [[12edo]]
|-
|-
| | 171
| '''[[43/32|43]]'''
| | 501.423
| '''511.518'''
| | 3 x 3 x 19
| '''prime'''
| |  
|  
| | close to 5 degrees of [[12edo|12edo]]
| '''close to 3 degrees of [[7edo]] / square root of 29'''
|-
|-
| | '''43'''
| '''[[173/128|173]]'''
| | '''511.518'''
| '''521.554'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[7edo|7edo]] / square root of 29'''
| '''close to 10 degrees of [[23edo]]'''
|-
|-
| | '''173'''
| [[87/64|87]]
| | '''521.554'''
| 531.532
| | '''prime'''
| 3 × 29
| |  
|  
| | '''close to 10 degrees of [[23edo|23edo]]'''
| close to 4 degrees of [[9edo]]
|-
|-
| | 87
| [[175/128|175]]
| | 531.532
| 541.453
| | 3 x 29
| 5 × 5 × 7
| |  
|  
| | close to 4 degrees of [[9edo|9edo]]
| close to 9 degrees of [[20edo]]
|-
|-
| | 175
| '''[[11/8|11]]'''
| | 541.453
| '''551.318'''
| | 5 x 5 x 7
| '''prime'''
| |
| '''undecimal semi-augmented fourth / undecimal tritone'''
| | close to 9 degrees of [[20edo|20edo]]
| '''[[11-limit]] / close to 11 degrees of [[24edo]]'''
|-
|-
| | '''11'''
| [[177/128|177]]
| | '''551.318'''
| 561.127
| | '''prime'''
| 3 × 59
| | '''undecimal semi-augmented fourth / undecimal tritone'''
|  
| | '''11-limit / close to 11 degrees of [[24edo|24edo]]'''
| close to 7 degrees of [[15edo]]
|-
|-
| | 177
| '''[[89/64|89]]'''
| | 561.127
| '''570.880'''
| | 3 x 59
| '''prime'''
| |  
|  
| | close to 7 degrees of [[15edo|15edo]]
| '''close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] / square root of 31'''
|-
|-
| | '''89'''
| '''[[179/128|179]]'''
| | '''570.880'''
| '''580.579'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 10 degrees of [[21edo|21edo]] / 9 degrees of [[19edo|19edo]] /'''
| '''close to 15 degrees of [[31edo]]'''
 
'''square root of 31'''
|-
|-
| | '''179'''
| [[45/32|45]]
| | '''580.579'''
| 590.224
| | '''prime'''
| 3 × 3 × 5
| |
| high 5-limit tritone
| | '''close to 15 degrees of [[31edo|31edo]]'''
| [[5-limit]] / close to square root of 15
|-
|-
| | 45
| '''[[181/128|181]]'''
| | 590.224
| '''599.815'''
| | 3 x 3 x 5
| '''prime'''
| | high 5-limit tritone
|  
| | 5-limit / close to square root of 15
| '''close to square root of 2'''
|-
|-
| | '''181'''
| [[91/64|91]]
| | '''599.815'''
| 609.354
| | '''prime'''
| 7 × 13
| |  
|  
| | '''close to square root of 2'''
| [[13-limit]]
|-
|-
| | 91
| [[183/61|183]]
| | 609.354
| 618.840
| | 7 x 13
| 3 × 61
| |  
|  
| | 13-limit
|  
|-
|-
| | 183
| '''[[23/16|23]]'''
| | 618.840
| '''628.274'''
| | 3 x 61
| '''prime'''
| |  
|  
| |
| '''close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] / square root of 33'''
|-
|-
| | '''23'''
| [[185/128|185]]
| | '''628.274'''
| 637.658
| | '''prime'''
| 5 × 37
| |  
|  
| | '''close to 11 degrees of [[21edo|21edo]] / 10 degrees of [[19edo|19edo]] / square root of 33'''
|  
|-
|-
| | 185
| [[93/64|93]]
| | 637.658
| 646.991
| | 5 x 37
| 3 × 31
| |  
|  
| |
| close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]]
|-
|-
| | 93
| [[187/128|187]]
| | 646.991
| 656.273
| | 3 x 31
| 11 × 17
| |  
|  
| | close to 7 degrees of [[13edo|13edo]] / 13 degrees of [[24edo|24edo]]
| close to 11 degrees of [[20edo]]
|-
|-
| | 187
| '''[[47/32|47]]'''
| | 656.273
| '''665.507'''
| | 11 x 17
| '''prime'''
| |  
|  
| | close to 11 degrees of [[20edo|20edo]]
| '''close to 5 degrees of [[9edo]]'''
|-
|-
| | '''47'''
| [[189/128|189]]
| | '''665.507'''
| 674.691
| | '''prime'''
| 3 × 3 × 3 × 7
| |  
|  
| | '''close to 5 degrees of [[9edo|9edo]]'''
| [[7-limit]] / close to 9 degrees of [[16edo]], square root of 35
|-
|-
| | 189
| [[95/64|95]]
| | 674.691
| 683.827
| | 3 x 3 x 3 x 7
| 5 × 19
| |  
|  
| | 7-limit / close to 9 degrees of [[16edo|16edo]], square root of 35
| close to 4 degrees of [[7edo]]
|-
|-
| | 95
| '''[[191/128|191]]'''
| | 683.827
| '''692.9155'''
| | 5 x 19
| '''prime'''
| |  
|  
| | close to 4 degrees of [[7edo|7edo]]
| '''close to 11 degrees of [[19edo]]'''
|-
|-
| | '''191'''
| '''[[3/2|3]]'''
| | '''692.9155'''
| '''701.955'''
| | '''prime'''
| '''prime'''
| |
| '''just perfect fifth'''
| | '''close to 11 degrees of [[19edo|19edo]]'''
| '''[[3-limit]] / close to 7 degrees of [[12edo]]'''
|-
|-
| | '''3'''
| '''[[193/128|193]]'''
| | '''701.955'''
| '''710.948'''
| | '''prime'''
| '''prime'''
| | '''just perfect fifth'''
|  
| | '''3-limit / close to 7 degrees of [[12edo|12edo]]'''
| '''close to 13 degrees of [[22edo]]'''
|-
|-
| | '''193'''
| '''[[97/64|97]]'''
| | '''710.948'''
| '''719.895'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[22edo|22edo]]'''
| '''close to 3 degrees of [[5edo]]'''
|-
|-
| | '''97'''
| [[195/128|195]]
| | '''719.895'''
| 728.796
| | '''prime'''
| 3 × 5 × 13
| |  
|  
| | '''close to 3 degrees of [[5edo|5edo]]'''
| [[13-limit]] / close to 19 degrees of [[31edo]], square root of 37
|-
|-
| | 195
| [[49/32|49]]
| | 728.796
| 737.652
| | 3 x 5 x 13
| 7 × 7
| |  
|  
| | 13-limit / close to 19 degrees of [[31edo|31edo]], square root of 37
| [[7-limit]] / close to 8 degrees of [[13edo]]
|-
|-
| | 49
| '''[[197/128|197]]'''
| | 737.652
| '''746.462'''
| | 7 x 7
| '''prime'''
| |  
|  
| | 7-limit / close to 8 degrees of [[13edo|13edo]]
|  
|-
|-
| | '''197'''
| [[99/64|99]]
| | '''746.462'''
| 755.228
| | '''prime'''
| 3 × 3 × 11
| |  
|  
| |
| [[11-limit]] / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]]
|-
|-
| | 99
| '''[[199/128|199]]'''
| | 755.228
| '''763.9495'''
| | 3 x 3 x 11
| '''prime'''
| |  
|  
| | 11-limit / close to 5 degrees of [[8edo|8edo]] / 12 degrees of [[19edo|19edo]]
| '''close to 7 degrees of [[11edo]]'''
|-
|-
| | '''199'''
| [[25/16|25]]
| | '''763.9495'''
| 772.627
| | '''prime'''
| 5 × 5
| |
| augmented fifth
| | '''close to 7 degrees of [[11edo|11edo]]'''
| [[5-limit]] / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39
|-
|-
| | 25
| [[201/128|201]]
| | 772.627
| 781.262
| | 5 x 5
| 3 × 67
| | augmented fifth
| harmonic gentle minor sixth, circular sixth
| | 5-limit / close to 9 degrees of [[14edo|14edo]] / 11 degrees of [[17edo|17edo]], square root of 39
| close to 19 degrees of [[23edo]] / pi
|-
|-
| | 201
| '''[[101/64|101]]'''
| | 781.262
| '''789.854'''
| | 3 x 67
| '''prime'''
| | overtone gentle minor sixth, circular sixth
|  
| | close to 19 degrees of [[23edo|23edo]] / pi
|  
|-
|-
| | '''101'''
| [[203/128|203]]
| | '''789.854'''
| 798.403
| | '''prime'''
| 7 × 29
| |  
|  
| |
| close to 8 degrees of [[12edo]] (a.k.a. 2 degrees of [[3edo]])
|-
|-
| | 203
| [[51/32|51]]
| | 798.403
| 806.910
| | 7 x 29
| 3 × 17
| |  
|  
| | close to 8 degrees of [[12edo|12edo]] (a.k.a. 2 degrees of [[3edo|3edo]])
|  
|-
|-
| | 51
| [[205/128|205]]
| | 806.910
| 815.376
| | 3 x 17
| 5 × 41
| |  
|  
| |
| close to 21 degrees of [[31edo]], square root of 41 ,
|-
|-
| | 205
| '''[[103/64|103]]'''
| | 815.376
| '''823.801'''
| | 5 x 41
| '''prime'''
| |  
|  
| | close to 21 degrees of [[31edo|31edo]], square root of 41 ,
| '''close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]]'''
|-
|-
| | '''103'''
| [[207/128|207]]
| | '''823.801'''
| 832.143
| | '''prime'''
| 3 × 3 × 23
| |  
|  
| | '''close to 11 degrees of [[16edo|16edo]] / 13 degrees of [[19edo|19edo]]'''
| close to 17 degrees of [[22edo]], 10 degrees of [[13edo]]
|-
|-
| | 207
| '''[[13/8|13]]'''
| | 832.143
| '''840.528'''
| | 3 x 3 x 23
| '''prime'''
| |
| '''harmonic sixth, golden overtone'''
| | close to 17 degrees of [[22edo|22edo]], 10 degrees of [[13edo|13edo]]
| '''[[13-limit]] / close to 7 degrees of [[10edo]], golden ratio'''
|-
|-
| | '''13'''
| [[209/128|209]]
| | '''840.528'''
| 848.831
| | '''prime'''
| 11 × 19
| | '''overtone sixth, golden overtone'''
| 11-19 hemieleventh
| | '''13-limit / close to 7 degrees of [[10edo|10edo]], golden ratio'''
| close to 12 degrees of [[17edo]]
|-
|-
| | 209
| [[105/64|105]]
| | 848.831
| 857.095
| | 11 x 19
| 3 × 5 × 7
| | 11-19 hemieleventh
|  
| | close to 12 degrees of [[17edo|17edo]]
| [[7-limit]] / close to 5 degrees of [[7edo]], square root of 43
|-
|-
| | 105
| '''[[211/128|211]]'''
| | 857.095
| '''865.319'''
| | 3 x 5 x 7
| '''prime'''
| |  
|  
| | 7-limit / close to 5 degrees of [[7edo|7edo]], square root of 43
| '''close to 13 degrees of [[18edo]]'''
|-
|-
| | '''211'''
| '''[[53/32|53]]'''
| | '''865.319'''
| '''873.505'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[18edo|18edo]]'''
| '''close to 8 degrees of [[11edo]]'''
|-
|-
| | '''53'''
| [[213/128|213]]
| | '''873.505'''
| 881.652
| | '''prime'''
| 3 × 71
| |  
|  
| | '''close to 8 degrees of [[11edo|11edo]]'''
| close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]]
|-
|-
| | 213
| '''[[107/64|107]]'''
| | 881.6515
| ''' 889.760'''
| | 3 x 71
| '''prime'''
| |  
|  
| | close to 11 degrees of [[15edo|15edo]] / close to 14 degrees of [[19edo|19edo]]
|  
|-
|-
| | 215
| [[215/128|215]]
| | 897.831
| 897.831
| | 5 x 43
| 5 × 43
| |  
|  
| | close to 9 degrees of [[12edo|12edo]] (a.k.a. 3 degrees of [[4edo|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
| | overtone gentle major third
| harmonic gentle major third
| | close to 13 degrees of [[17edo|17edo]]
| close to 13 degrees of [[17edo]]
|-
|-
| | '''109'''
| '''[[109/64|109]]'''
| | '''921.821'''
| '''921.821'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 10 degrees of [[13edo|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|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|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|19edo]]
| close to 15 degrees of [[19edo]]
|-
|-
| | 111
| [[111/64|111]]
| | 953.299
| 953.299
| | 3 x 37
| 3 × 37
| | overtone hemitwelfth
| harmonic hemitwelfth
| | close to 19 degrees of [[24edo|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'''
| |  
|  
| | '''close to 4 degrees of [[5edo|5edo]]'''
| '''close to 4 degrees of [[5edo]]'''
|-
|-
| | '''7'''
| '''[[7/4|7]]'''
| | '''968.826'''
| '''968.826'''
| | '''prime'''
| '''prime'''
| | '''harmonic seventh / septimal minor seventh'''
| '''harmonic seventh / septimal minor seventh'''
| | '''7-limit / close to 17 degrees of [[21edo|21edo]] / 25 degrees of [[31edo|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|16edo]]
| [[5-limit]] / close to 11 degrees of [[16edo]]
|-
|-
| | '''113'''
| '''[[113/64|113]]'''
| | '''984.215'''
| '''984.215'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 9 degrees of [[11edo|11edo]]'''
| '''close to 9 degrees of [[11edo]]'''
|-
|-
| | '''227'''
| '''[[227/128|227]]'''
| | '''991.858'''
| '''991.858'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 57
| [[57/32|57]]
| | 999.468
| 999.468
| | 3 x 19
| 3 × 19
| |  
|  
| | close to 10 degrees of [[12edo|12edo]] (a.k.a. 5 degrees of [[6edo|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'''
| |  
|  
| |  
|  
|-
|-
| | 115
| [[115/64|115]]
| | 1014.588
| 1014.588
| | 5 x 23
| 5 × 23
| |  
|  
| | close to 11 degrees of [[13edo|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'''
| |  
|  
| | '''close to 6 degrees of [[7edo|7edo]]'''
| '''close to 6 degrees of [[7edo]]'''
|-
|-
| | '''233'''
| '''[[233/128|233]]'''
| | '''1037.023'''
| '''1037.023'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''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|15edo]] / 20 degrees of [[23edo|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|24edo]]
| close to 21 degrees of [[24edo]]
|-
|-
| | '''59'''
| '''[[59/32|59]]'''
| | '''1059.172'''
| '''1059.172'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 15 degrees of [[17edo|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|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|19edo]]
| close to 17 degrees of [[19edo]]
|-
|-
| | '''239'''
| '''[[239/128|239]]'''
| | '''1081.040'''
| '''1081.040'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[31edo|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|21edo]] / 10 degrees of [[11edo|11edo]]
| [[5-limit]] / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]]
|-
|-
| | '''241'''
| '''[[241/128|241]]'''
| | '''1095.467'''
| '''1095.467'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 121
| [[121/64|121]]
| | 1102.636
| 1102.636
| | 11 x 11
| 11 × 11
| |  
|  
| | 11-limit / close to 11 degrees of [[12edo|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 9
| 3 × 3 × 3 × 3 × 3
| | Pythagorean major seventh
| Pythagorean major seventh
| | close to 12 degrees of [[13edo|13edo]]
| close to 12 degrees of [[13edo]]
|-
|-
| | '''61'''
| '''[[61/32|61]]'''
| | '''1116.885'''
| '''1116.885'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[14edo|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|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|18edo]], 18 degrees of [[19edo|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|20edo]]'''
| close to 19 degrees of [[20edo]]
|-
|-
| | '''31'''
| '''[[31/16|31]]'''
| | '''1145.036'''
| '''1145.036'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 21 degrees of [[22edo|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|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'''
| |  
|  
| |  
|  
|-
|-
| | 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'''
| |  
|  
| | '''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'''
| | '''octave'''
| '''octave'''
| | '''[[2-limit|2-limit]]'''
| '''[[2-limit]]'''
|}
|}
<references />
== See also ==
* [[List of tritave reduced harmonics]]
* [[Pentave Reduced Harmonics]]


[[Category:Theory]]
[[Category:Octave-reduced harmonics| ]] <!-- main article -->
[[Category:Interval collection]]
[[Category:Lists of intervals]]
[[Category:Just]]
[[Category:Harmonic]]
[[Category:Overtone]]
[[Category:Partial tone]]

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

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