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.
A list of many overtones in an octave, arranged by ascending pitch, [[octave reduced]]. Prime overtones are highlighted.


{| class="wikitable"
{| class="wikitable center-1 right-2"
|-
|-
| | overtone
! Overtone
| | cents
! Size ([[cents|¢]])<ref>cent values are given for the ocave reduced equivalent</ref>
| | factorization
! Factorization
| | name
! Name
| | notes
! Remarks
|-
|-
| | 1
| 1
| | 0
| 0
| |
| 1
| | unison
| unison
| | '''present in all tunings and tonal systems'''
| present in all tunings and tonal systems
|-
|-
| | 129
| 129
| | 13.473
| 13.473
| | 3 x 43
| 3 x 43
| |  
|  
| |  
|  
|-
|-
| | 65
| 65
| | 26.841
| 26.841
| | 5 x 13
| 5 x 13
| |  
|  
| | [[13-limit|13-limit]]
| [[13-limit]]
|-
|-
| | '''131'''
| '''131'''
| | '''40.108'''
| '''40.108'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to square root of 67'''
| '''close to square root of 67'''
|-
|-
| | 33
| 33
| | 53.273
| 53.273
| | 3 x 11
| 3 x 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
| | 66.339
| 66.339
| | 7 x 19
| 7 x 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'''
| | '''79.307'''
| '''79.307'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 1 degree of [[15edo|15edo]]'''
| '''close to 1 degree of [[15edo]]'''
|-
|-
| | 135
| 135
| | 92.179
| 92.179
| | 3 x 3 x 3 x 5
| 3 x 3 x 3 x 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'''
| | '''104.955'''
| '''104.955'''
| | '''prime'''
| '''prime'''
| | '''overtone half-step'''
| '''overtone 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'''
| | '''117.6385'''
| '''117.6385'''
| | '''prime'''
| '''prime'''
| | '''overtone secor'''
| '''overtone secor'''
| | '''close to 3 degrees of [[31edo|31edo]],''' '''square root of 73'''
| '''close to 3 degrees of [[31edo]],''' '''square root of 73'''
|-
|-
| | 69
| 69
| | 130.229
| 130.229
| | 3 x 23
| 3 x 23
| |  
|  
| | close to 1 degree of [[9edo|9edo]]
| close to 1 degree of [[9edo]]
|-
|-
| | '''139'''
| '''139'''
| | '''142.729'''
| '''142.729'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 2 degrees of [[17edo|17edo]]'''
| '''close to 2 degrees of [[17edo]]'''
|-
|-
| | 35
| 35
| | 155.140
| 155.140
| | 5 x 7
| 5 x 7
| |  
|  
| | [[7-limit|7-limit]] / close to 3 degrees of [[24edo|24edo]]
| [[7-limit]] / close to 3 degrees of [[24edo]]
|-
|-
| | 141
| 141
| | 167.462
| 167.462
| | 3 x 47
| 3 x 47
| |  
|  
| |  
|  
|-
|-
| | '''71'''
| '''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
| | 191.846
| 191.846
| | 11 x 13
| 11 x 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
| 9
| | 203.910
| 203.910
| | 3 x 3
| 3 x 3
| | major whole-tone / Pythagorean whole tone
| major whole-tone / Pythagorean whole tone
| | 3-limit
| 3-limit
|-
|-
| | 145
| 145
| | 215.891
| 215.891
| | 5 x 29
| 5 x 29
| | 5-29 eventone
| 5-29 eventone
| | close to 2 degrees of [[11edo|11edo]]
| close to 2 degrees of [[11edo]]
|-
|-
| | '''73'''
| '''73'''
| | '''227.789'''
| '''227.789'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[16edo|16edo]] / 4 degrees of [[21edo|21edo]]'''
| '''close to 3 degrees of [[16edo]] / 4 degrees of [[21edo]]'''
|-
|-
| | 147
| 147
| | 239.607
| 239.607
| | 3 x 7 x 7
| 3 x 7 x 7
| |  
|  
| | 7-limit / close to 1 degree of [[5edo|5edo]], square root of 21
| 7-limit / close to 1 degree of [[5edo]], square root of 21
|-
|-
| | '''37'''
| '''37'''
| | '''251.344'''
| '''251.344'''
| | '''prime'''
| '''prime'''
| | '''overtone''' '''hemifourth'''
| '''overtone''' '''hemifourth'''
| | '''close to 5 degrees of [[24edo|24edo]]'''
| '''close to 5 degrees of [[24edo]]'''
|-
|-
| | '''149'''
| '''149'''
| | '''263.002'''
| '''263.002'''
| | '''prime'''
| '''prime'''
| | '''overtone subminor third'''
| '''overtone subminor third'''
| |  
|  
|-
|-
| | 75
| 75
| | 274.582
| 274.582
| | 3 x 5 x 5
| 3 x 5 x 5
| | augmented second
| augmented second
| | 5-limit / close to 5 degrees of [[22edo|22edo]], 3 degrees of [[13edo|13edo]], square root of 11
| 5-limit / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11
|-
|-
| | '''151'''
| '''151'''
| | '''286.086'''
| '''286.086'''
| | '''prime'''
| '''prime'''
| | '''overtone gentle minor third'''
| '''overtone gentle minor third'''
| | '''close to 4 degrees of [[17edo|17edo]]'''
| '''close to 4 degrees of [[17edo]]'''
|-
|-
| | '''19'''
| '''19'''
| | '''297.513'''
| '''297.513'''
| | '''prime'''
| '''prime'''
| | '''overtone minor third'''
| '''overtone minor third'''
| | '''close to 3 degrees of [[12edo|12edo]] (a.k.a. 1 degree of [[4edo|4edo]])'''
| '''close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]])'''
|-
|-
| | 153
| 153
| | 308.865
| 308.865
| | 3 x 3 x 17
| 3 x 3 x 17
| |  
|  
| | close to 8 degrees of [[31edo|31edo]]
| close to 8 degrees of [[31edo]]
|-
|-
| | 155
| 155
| | 331.349
| 331.349
| | 5 x 31
| 5 x 31
| |  
|  
| |  
|  
|-
|-
| | 39
| 39
| | 342.483
| 342.483
| | 3 x 13
| 3 x 13
| |  
|  
| | 13-limit / close to 2 degrees of [[7edo|7edo]]
| 13-limit / close to 2 degrees of [[7edo]]
|-
|-
| | '''157'''
| '''157'''
| | '''353.545'''
| '''353.545'''
| | '''prime'''
| '''prime'''
| | '''overtone''' '''hemififth'''
| '''overtone''' '''hemififth'''
| | '''close to 5 degrees of [[17edo|17edo]]'''
| '''close to 5 degrees of [[17edo]]'''
|-
|-
| | '''79'''
| '''79'''
| | '''364.537'''
| '''364.537'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 7 degrees of [[23edo|23edo]]'''
| '''close to 7 degrees of [[23edo]]'''
|-
|-
| | 159
| 159
| | 375.4595
| 375.4595
| | 3 x 53
| 3 x 53
| |  
|  
| | close to 5 degrees of [[16edo|16edo]]
| close to 5 degrees of [[16edo]]
|-
|-
| | '''5'''
| '''5'''
| | '''386.314'''
| '''386.314'''
| | '''prime'''
| '''prime'''
| | '''5-limit major third'''
| '''5-limit major third'''
| | '''5-limit / close to 10 degrees of [[31edo|31edo]]'''
| '''5-limit / close to 10 degrees of [[31edo]]'''
|-
|-
| | '''161'''
| '''161'''
| | '''397.100'''
| '''397.100'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 4 degrees of [[12edo|12edo]] (a.k.a. 1 degree of [[3edo|3edo]])'''
| '''close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])'''
|-
|-
| | 81
| 81
| | 407.820
| 407.820
| | 9 x 9
| 9 x 9
| | Pythagorean major third
| Pythagorean major third
| | 3-limit
| 3-limit
|-
|-
| | '''163'''
| '''163'''
| | '''418.474'''
| '''418.474'''
| | '''prime'''
| '''prime'''
| | '''overtone gentle major third'''
| '''overtone gentle major third'''
| | '''close to 8 degrees of [[23edo|23edo]] / square root of phi'''
| '''close to 8 degrees of [[23edo]] / square root of phi'''
|-
|-
| | '''41'''
| '''41'''
| | '''429.062'''
| '''429.062'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 5 degrees of [[14edo|14edo]]'''
| '''close to 5 degrees of [[14edo]]'''
|-
|-
| | 165
| 165
| | 439.587
| 439.587
| | 3 x 5 x 11
| 3 x 5 x 11
| |  
|  
| |  
|  
|-
|-
| | '''167'''
| '''167'''
| | '''460.445'''
| '''460.445'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 21
| 21
| | 470.781
| 470.781
| | 3 x 7
| 3 x 7
| | narrow fourth / septimal fourth
| narrow fourth / septimal fourth
| | 7-limit / close to 9 degrees of [[23edo|23edo]]
| 7-limit / close to 9 degrees of [[23edo]]
|-
|-
| | 169
| 169
| | 481.055
| 481.055
| | 13 x 13
| 13 x 13
| |  
|  
| | 13-limit / close to 2 degrees of [[5edo|5edo]], square root of 7
| 13-limit / close to 2 degrees of [[5edo]], square root of 7
|-
|-
| | 85
| 85
| | 491.269
| 491.269
| | 5 x 17
| 5 x 17
| | near fourth
| near fourth
| | close to 9 degrees of [[22edo|22edo]]
| close to 9 degrees of [[22edo]]
|-
|-
| | 171
| 171
| | 501.423
| 501.423
| | 3 x 3 x 19
| 3 x 3 x 19
| |  
|  
| | close to 5 degrees of [[12edo|12edo]]
| close to 5 degrees of [[12edo]]
|-
|-
| | '''43'''
| '''43'''
| | '''511.518'''
| '''511.518'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[7edo|7edo]] / square root of 29'''
| '''close to 3 degrees of [[7edo]] / square root of 29'''
|-
|-
| | '''173'''
| '''173'''
| | '''521.554'''
| '''521.554'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 10 degrees of [[23edo|23edo]]'''
| '''close to 10 degrees of [[23edo]]'''
|-
|-
| | 87
| 87
| | 531.532
| 531.532
| | 3 x 29
| 3 x 29
| |  
|  
| | close to 4 degrees of [[9edo|9edo]]
| close to 4 degrees of [[9edo]]
|-
|-
| | 175
| 175
| | 541.453
| 541.453
| | 5 x 5 x 7
| 5 x 5 x 7
| |  
|  
| | close to 9 degrees of [[20edo|20edo]]
| close to 9 degrees of [[20edo]]
|-
|-
| | '''11'''
| '''11'''
| | '''551.318'''
| '''551.318'''
| | '''prime'''
| '''prime'''
| | '''undecimal semi-augmented fourth / undecimal tritone'''
| '''undecimal semi-augmented fourth / undecimal tritone'''
| | '''11-limit / close to 11 degrees of [[24edo|24edo]]'''
| '''11-limit / close to 11 degrees of [[24edo]]'''
|-
|-
| | 177
| 177
| | 561.127
| 561.127
| | 3 x 59
| 3 x 59
| |  
|  
| | close to 7 degrees of [[15edo|15edo]]
| close to 7 degrees of [[15edo]]
|-
|-
| | '''89'''
| '''89'''
| | '''570.880'''
| '''570.880'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 10 degrees of [[21edo|21edo]] / 9 degrees of [[19edo|19edo]] /'''
| '''close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] / square root of 31'''
 
'''square root of 31'''
|-
|-
| | '''179'''
| '''179'''
| | '''580.579'''
| '''580.579'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 15 degrees of [[31edo|31edo]]'''
| '''close to 15 degrees of [[31edo]]'''
|-
|-
| | 45
| 45
| | 590.224
| 590.224
| | 3 x 3 x 5
| 3 x 3 x 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'''
| | '''599.815'''
| '''599.815'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to square root of 2'''
| '''close to square root of 2'''
|-
|-
| | 91
| 91
| | 609.354
| 609.354
| | 7 x 13
| 7 x 13
| |  
|  
| | 13-limit
| 13-limit
|-
|-
| | 183
| 183
| | 618.840
| 618.840
| | 3 x 61
| 3 x 61
| |  
|  
| |  
|  
|-
|-
| | '''23'''
| '''23'''
| | '''628.274'''
| '''628.274'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 11 degrees of [[21edo|21edo]] / 10 degrees of [[19edo|19edo]] / square root of 33'''
| '''close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] / square root of 33'''
|-
|-
| | 185
| 185
| | 637.658
| 637.658
| | 5 x 37
| 5 x 37
| |  
|  
| |  
|  
|-
|-
| | 93
| 93
| | 646.991
| 646.991
| | 3 x 31
| 3 x 31
| |  
|  
| | close to 7 degrees of [[13edo|13edo]] / 13 degrees of [[24edo|24edo]]
| close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]]
|-
|-
| | 187
| 187
| | 656.273
| 656.273
| | 11 x 17
| 11 x 17
| |  
|  
| | close to 11 degrees of [[20edo|20edo]]
| close to 11 degrees of [[20edo]]
|-
|-
| | '''47'''
| '''47'''
| | '''665.507'''
| '''665.507'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 5 degrees of [[9edo|9edo]]'''
| '''close to 5 degrees of [[9edo]]'''
|-
|-
| | 189
| 189
| | 674.691
| 674.691
| | 3 x 3 x 3 x 7
| 3 x 3 x 3 x 7
| |  
|  
| | 7-limit / close to 9 degrees of [[16edo|16edo]], square root of 35
| 7-limit / close to 9 degrees of [[16edo]], square root of 35
|-
|-
| | 95
| 95
| | 683.827
| 683.827
| | 5 x 19
| 5 x 19
| |  
|  
| | close to 4 degrees of [[7edo|7edo]]
| close to 4 degrees of [[7edo]]
|-
|-
| | '''191'''
| '''191'''
| | '''692.9155'''
| '''692.9155'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 11 degrees of [[19edo|19edo]]'''
| '''close to 11 degrees of [[19edo]]'''
|-
|-
| | '''3'''
| '''3'''
| | '''701.955'''
| '''701.955'''
| | '''prime'''
| '''prime'''
| | '''just perfect fifth'''
| '''just perfect fifth'''
| | '''3-limit / close to 7 degrees of [[12edo|12edo]]'''
| '''3-limit / close to 7 degrees of [[12edo]]'''
|-
|-
| | '''193'''
| '''193'''
| | '''710.948'''
| '''710.948'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[22edo|22edo]]'''
| '''close to 13 degrees of [[22edo]]'''
|-
|-
| | '''97'''
| '''97'''
| | '''719.895'''
| '''719.895'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[5edo|5edo]]'''
| '''close to 3 degrees of [[5edo]]'''
|-
|-
| | 195
| 195
| | 728.796
| 728.796
| | 3 x 5 x 13
| 3 x 5 x 13
| |  
|  
| | 13-limit / close to 19 degrees of [[31edo|31edo]], square root of 37
| 13-limit / close to 19 degrees of [[31edo]], square root of 37
|-
|-
| | 49
| 49
| | 737.652
| 737.652
| | 7 x 7
| 7 x 7
| |  
|  
| | 7-limit / close to 8 degrees of [[13edo|13edo]]
| 7-limit / close to 8 degrees of [[13edo]]
|-
|-
| | '''197'''
| '''197'''
| | '''746.462'''
| '''746.462'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 99
| 99
| | 755.228
| 755.228
| | 3 x 3 x 11
| 3 x 3 x 11
| |  
|  
| | 11-limit / close to 5 degrees of [[8edo|8edo]] / 12 degrees of [[19edo|19edo]]
| 11-limit / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]]
|-
|-
| | '''199'''
| '''199'''
| | '''763.9495'''
| '''763.9495'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 7 degrees of [[11edo|11edo]]'''
| '''close to 7 degrees of [[11edo]]'''
|-
|-
| | 25
| 25
| | 772.627
| 772.627
| | 5 x 5
| 5 x 5
| | augmented fifth
| augmented fifth
| | 5-limit / close to 9 degrees of [[14edo|14edo]] / 11 degrees of [[17edo|17edo]], square root of 39
| 5-limit / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39
|-
|-
| | 201
| 201
| | 781.262
| 781.262
| | 3 x 67
| 3 x 67
| | overtone gentle minor sixth, circular sixth
| overtone gentle minor sixth, circular sixth
| | close to 19 degrees of [[23edo|23edo]] / pi
| close to 19 degrees of [[23edo]] / pi
|-
|-
| | '''101'''
| '''101'''
| | '''789.854'''
| '''789.854'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 203
| 203
| | 798.403
| 798.403
| | 7 x 29
| 7 x 29
| |  
|  
| | close to 8 degrees of [[12edo|12edo]] (a.k.a. 2 degrees of [[3edo|3edo]])
| close to 8 degrees of [[12edo]] (a.k.a. 2 degrees of [[3edo]])
|-
|-
| | 51
| 51
| | 806.910
| 806.910
| | 3 x 17
| 3 x 17
| |  
|  
| |  
|  
|-
|-
| | 205
| 205
| | 815.376
| 815.376
| | 5 x 41
| 5 x 41
| |  
|  
| | close to 21 degrees of [[31edo|31edo]], square root of 41 ,
| close to 21 degrees of [[31edo]], square root of 41 ,
|-
|-
| | '''103'''
| '''103'''
| | '''823.801'''
| '''823.801'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 11 degrees of [[16edo|16edo]] / 13 degrees of [[19edo|19edo]]'''
| '''close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]]'''
|-
|-
| | 207
| 207
| | 832.143
| 832.143
| | 3 x 3 x 23
| 3 x 3 x 23
| |  
|  
| | close to 17 degrees of [[22edo|22edo]], 10 degrees of [[13edo|13edo]]
| close to 17 degrees of [[22edo]], 10 degrees of [[13edo]]
|-
|-
| | '''13'''
| '''13'''
| | '''840.528'''
| '''840.528'''
| | '''prime'''
| '''prime'''
| | '''overtone sixth, golden overtone'''
| '''overtone sixth, golden overtone'''
| | '''13-limit / close to 7 degrees of [[10edo|10edo]], golden ratio'''
| '''13-limit / close to 7 degrees of [[10edo]], golden ratio'''
|-
|-
| | 209
| 209
| | 848.831
| 848.831
| | 11 x 19
| 11 x 19
| | 11-19 hemieleventh
| 11-19 hemieleventh
| | close to 12 degrees of [[17edo|17edo]]
| close to 12 degrees of [[17edo]]
|-
|-
| | 105
| 105
| | 857.095
| 857.095
| | 3 x 5 x 7
| 3 x 5 x 7
| |  
|  
| | 7-limit / close to 5 degrees of [[7edo|7edo]], square root of 43
| 7-limit / close to 5 degrees of [[7edo]], square root of 43
|-
|-
| | '''211'''
| '''211'''
| | '''865.319'''
| '''865.319'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[18edo|18edo]]'''
| '''close to 13 degrees of [[18edo]]'''
|-
|-
| | '''53'''
| '''53'''
| | '''873.505'''
| '''873.505'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 8 degrees of [[11edo|11edo]]'''
| '''close to 8 degrees of [[11edo]]'''
|-
|-
| | 213
| 213
| | 881.6515
| 881.6515
| | 3 x 71
| 3 x 71
| |  
|  
| | close to 11 degrees of [[15edo|15edo]] / close to 14 degrees of [[19edo|19edo]]
| close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]]
|-
|-
| | 215
| 215
| | 897.831
| 897.831
| | 5 x 43
| 5 x 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
| | 905.865
| 905.865
| | 3 x 3 x 3
| 3 x 3 x 3
| | Pythagorean major sixth
| Pythagorean major sixth
| | 3-limit
| 3-limit
|-
|-
| | 217
| 217
| | 913.8615
| 913.8615
| | 7 x 31
| 7 x 31
| | overtone gentle major third
| overtone gentle major third
| | close to 13 degrees of [[17edo|17edo]]
| close to 13 degrees of [[17edo]]
|-
|-
| | '''109'''
| '''109'''
| | '''921.821'''
| '''921.821'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 10 degrees of [[13edo|13edo]]'''
| '''close to 10 degrees of [[13edo]]'''
|-
|-
| | 219
| 219
| | 929.7445
| 929.7445
| | 3 x 73
| 3 x 73
| |  
|  
| | close to 24 degrees of [[31edo|31edo]], square root of 47
| close to 24 degrees of [[31edo]], square root of 47
|-
|-
| | 55
| 55
| | 937.632
| 937.632
| | 5 x 11
| 5 x 11
| |  
|  
| | 11-limit / close to 18 degrees of [[23edo|23edo]]
| 11-limit / close to 18 degrees of [[23edo]]
|-
|-
| | 221
| 221
| | 945.483
| 945.483
| | 13 x 17
| 13 x 17
| |  
|  
| | close to 15 degrees of [[19edo|19edo]]
| close to 15 degrees of [[19edo]]
|-
|-
| | 111
| 111
| | 953.299
| 953.299
| | 3 x 37
| 3 x 37
| | overtone hemitwelfth
| overtone hemitwelfth
| | close to 19 degrees of [[24edo|24edo]] / square root of 3
| close to 19 degrees of [[24edo]] / square root of 3
|-
|-
| | '''223'''
| '''223'''
| | '''961.080'''
| '''961.080'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 4 degrees of [[5edo|5edo]]'''
| '''close to 4 degrees of [[5edo]]'''
|-
|-
| | '''7'''
| '''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
| | 976.537
| 976.537
| | 3 x 3 x 5 x 5
| 3 x 3 x 5 x 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'''
| | '''984.215'''
| '''984.215'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 9 degrees of [[11edo|11edo]]'''
| '''close to 9 degrees of [[11edo]]'''
|-
|-
| | '''227'''
| '''227'''
| | '''991.858'''
| '''991.858'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 57
| 57
| | 999.468
| 999.468
| | 3 x 19
| 3 x 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'''
| | '''1007.0445'''
| '''1007.0445'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 115
| 115
| | 1014.588
| 1014.588
| | 5 x 23
| 5 x 23
| |  
|  
| | close to 11 degrees of [[13edo|13edo]]
| close to 11 degrees of [[13edo]]
|-
|-
| | 231
| 231
| | 1022.099
| 1022.099
| | 3 x 7 x 11
| 3 x 7 x 11
| |  
|  
| | close to square root of 13
| close to square root of 13
|-
|-
| | '''29'''
| '''29'''
| | '''1029.577'''
| '''1029.577'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 6 degrees of [[7edo|7edo]]'''
| '''close to 6 degrees of [[7edo]]'''
|-
|-
| | '''233'''
| '''233'''
| | '''1037.023'''
| '''1037.023'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to square root of 53'''
| '''close to square root of 53'''
|-
|-
| | 117
| 117
| | 1044.438
| 1044.438
| | 3 x 3 x 13
| 3 x 3 x 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
| | 1051.820
| 1051.820
| | 5 x 47
| 5 x 47
| |  
|  
| | close to 21 degrees of [[24edo|24edo]]
| close to 21 degrees of [[24edo]]
|-
|-
| | '''59'''
| '''59'''
| | '''1059.172'''
| '''1059.172'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 15 degrees of [[17edo|17edo]]'''
| '''close to 15 degrees of [[17edo]]'''
|-
|-
| | 237
| 237
| | 1066.492
| 1066.492
| | 3 x 79
| 3 x 79
| |  
|  
| | close to 8 degrees of [[9edo|9edo]], square root of 55
| close to 8 degrees of [[9edo]], square root of 55
|-
|-
| | 119
| 119
| | 1073.781
| 1073.781
| | 7 x 17
| 7 x 17
| |  
|  
| | close to 17 degrees of [[19edo|19edo]]
| close to 17 degrees of [[19edo]]
|-
|-
| | '''239'''
| '''239'''
| | '''1081.040'''
| '''1081.040'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 3 degrees of [[31edo|31edo]]'''
| '''close to 3 degrees of [[31edo]]'''
|-
|-
| | 15
| 15
| | 1088.269
| 1088.269
| | 3 x 5
| 3 x 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'''
| | '''1095.467'''
| '''1095.467'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 121
| 121
| | 1102.636
| 1102.636
| | 11 x 11
| 11 x 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
| | 1109.775
| 1109.775
| | 3 x 3 x 3 x 9
| 3 x 3 x 3 x 9
| | Pythagorean major seventh
| Pythagorean major seventh
| | close to 12 degrees of [[13edo|13edo]]
| close to 12 degrees of [[13edo]]
|-
|-
| | '''61'''
| '''61'''
| | '''1116.885'''
| '''1116.885'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 13 degrees of [[14edo|14edo]]'''
| '''close to 13 degrees of [[14edo]]'''
|-
|-
| | 245
| 245
| | 1123.9655
| 1123.9655
| | 5 x 7 x 7
| 5 x 7 x 7
| |  
|  
| | close to 16 degrees of [[17edo|17edo]]
| close to 16 degrees of [[17edo]]
|-
|-
| | 123
| 123
| | 1131.017
| 1131.017
| | 3 x 41
| 3 x 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'''
| | '''1138.041'''
| '''1138.041'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 19 degrees of [[20edo|20edo]]'''
| '''close to 19 degrees of [[20edo]]'''
|-
|-
| | '''31'''
| '''31'''
| | '''1145.036'''
| '''1145.036'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to 21 degrees of [[22edo|22edo]]'''
| '''close to 21 degrees of [[22edo]]'''
|-
|-
| | 249
| 249
| | 1152.002
| 1152.002
| | 3 x 83
| 3 x 83
| |  
|  
| | close to 24 degrees of [[25edo|25edo]]
| close to 24 degrees of [[25edo]]
|-
|-
| | 125
| 125
| | 1158.941
| 1158.941
| | 5 x 5 x 5
| 5 x 5 x 5
| |  
|  
| | 5-limit, close to square root of 61
| 5-limit, close to square root of 61
|-
|-
| | '''251'''
| '''251'''
| | '''1165.852'''
| '''1165.852'''
| | '''prime'''
| '''prime'''
| |  
|  
| |  
|  
|-
|-
| | 63
| 63
| | 1172.736
| 1172.736
| | 3 x 3 x 7
| 3 x 3 x 7
| |  
|  
| | 7-limit
| 7-limit
|-
|-
| | 253
| 253
| | 1179.592
| 1179.592
| | 11 x 23
| 11 x 23
| |  
|  
| |  
|  
|-
|-
| | '''127'''
| '''127'''
| | '''1186.422'''
| '''1186.422'''
| | '''prime'''
| '''prime'''
| |  
|  
| | '''close to square root of 63'''
| '''close to square root of 63'''
|-
|-
| | 255
| 255
| | 1193.224
| 1193.224
| | 3 x 5 x 17
| 3 x 5 x 17
| |  
|  
| |  
|  
|-
|-
| | '''2'''
| '''2'''
| | '''1200'''
| '''1200'''
| | '''prime'''
| '''prime'''
| | '''octave'''
| '''octave'''
| | '''[[2-limit|2-limit]]'''
| '''[[2-limit]]'''
|}
|}
<references/>


[[Category:Theory]]
[[Category:Theory]]

Revision as of 07:17, 22 June 2020

A list of many overtones in an octave, arranged by ascending pitch, octave reduced. Prime overtones are highlighted.

Overtone Size (¢)[1] Factorization Name Remarks
1 0 1 unison present in all tunings and tonal systems
129 13.473 3 x 43
65 26.841 5 x 13 13-limit
131 40.108 prime close to square root of 67
33 53.273 3 x 11 undecimal comma 11-limit / close to quarter-tone (1 degree of 24edo), square root of 17
133 66.339 7 x 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 x 3 x 3 x 5 5-limit, close to 1 degree of 13edo / square root of 71
17 104.955 prime overtone half-step close to 1 degree of 11edo / 2 degrees of 23edo
137 117.6385 prime overtone secor close to 3 degrees of 31edo, square root of 73
69 130.229 3 x 23 close to 1 degree of 9edo
139 142.729 prime close to 2 degrees of 17edo
35 155.140 5 x 7 7-limit / close to 3 degrees of 24edo
141 167.462 3 x 47
71 179.697 prime close to 3 degrees of 20edo, square root of 79
143 191.846 11 x 13 11-13 meantone 13-limit / close to square root of 5 (a.k.a. 5 degrees of 31edo)
9 203.910 3 x 3 major whole-tone / Pythagorean whole tone 3-limit
145 215.891 5 x 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 x 7 x 7 7-limit / close to 1 degree of 5edo, square root of 21
37 251.344 prime overtone hemifourth close to 5 degrees of 24edo
149 263.002 prime overtone subminor third
75 274.582 3 x 5 x 5 augmented second 5-limit / close to 5 degrees of 22edo, 3 degrees of 13edo, square root of 11
151 286.086 prime overtone gentle minor third close to 4 degrees of 17edo
19 297.513 prime overtone minor third close to 3 degrees of 12edo (a.k.a. 1 degree of 4edo)
153 308.865 3 x 3 x 17 close to 8 degrees of 31edo
155 331.349 5 x 31
39 342.483 3 x 13 13-limit / close to 2 degrees of 7edo
157 353.545 prime overtone hemififth close to 5 degrees of 17edo
79 364.537 prime close to 7 degrees of 23edo
159 375.4595 3 x 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 prime close to 4 degrees of 12edo (a.k.a. 1 degree of 3edo)
81 407.820 9 x 9 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 x 5 x 11
167 460.445 prime
21 470.781 3 x 7 narrow fourth / septimal fourth 7-limit / close to 9 degrees of 23edo
169 481.055 13 x 13 13-limit / close to 2 degrees of 5edo, square root of 7
85 491.269 5 x 17 near fourth close to 9 degrees of 22edo
171 501.423 3 x 3 x 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 x 29 close to 4 degrees of 9edo
175 541.453 5 x 5 x 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 x 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 x 3 x 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 x 13 13-limit
183 618.840 3 x 61
23 628.274 prime close to 11 degrees of 21edo / 10 degrees of 19edo / square root of 33
185 637.658 5 x 37
93 646.991 3 x 31 close to 7 degrees of 13edo / 13 degrees of 24edo
187 656.273 11 x 17 close to 11 degrees of 20edo
47 665.507 prime close to 5 degrees of 9edo
189 674.691 3 x 3 x 3 x 7 7-limit / close to 9 degrees of 16edo, square root of 35
95 683.827 5 x 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 x 5 x 13 13-limit / close to 19 degrees of 31edo, square root of 37
49 737.652 7 x 7 7-limit / close to 8 degrees of 13edo
197 746.462 prime
99 755.228 3 x 3 x 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 x 5 augmented fifth 5-limit / close to 9 degrees of 14edo / 11 degrees of 17edo, square root of 39
201 781.262 3 x 67 overtone gentle minor sixth, circular sixth close to 19 degrees of 23edo / pi
101 789.854 prime
203 798.403 7 x 29 close to 8 degrees of 12edo (a.k.a. 2 degrees of 3edo)
51 806.910 3 x 17
205 815.376 5 x 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 x 3 x 23 close to 17 degrees of 22edo, 10 degrees of 13edo
13 840.528 prime overtone sixth, golden overtone 13-limit / close to 7 degrees of 10edo, golden ratio
209 848.831 11 x 19 11-19 hemieleventh close to 12 degrees of 17edo
105 857.095 3 x 5 x 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
213 881.6515 3 x 71 close to 11 degrees of 15edo / close to 14 degrees of 19edo
215 897.831 5 x 43 close to 9 degrees of 12edo (a.k.a. 3 degrees of 4edo), square root of 45
27 905.865 3 x 3 x 3 Pythagorean major sixth 3-limit
217 913.8615 7 x 31 overtone gentle major third close to 13 degrees of 17edo
109 921.821 prime close to 10 degrees of 13edo
219 929.7445 3 x 73 close to 24 degrees of 31edo, square root of 47
55 937.632 5 x 11 11-limit / close to 18 degrees of 23edo
221 945.483 13 x 17 close to 15 degrees of 19edo
111 953.299 3 x 37 overtone 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 x 3 x 5 x 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 x 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 x 23 close to 11 degrees of 13edo
231 1022.099 3 x 7 x 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 x 3 x 13 13-limit / close to 13 degrees of 15edo / 20 degrees of 23edo
235 1051.820 5 x 47 close to 21 degrees of 24edo
59 1059.172 prime close to 15 degrees of 17edo
237 1066.492 3 x 79 close to 8 degrees of 9edo, square root of 55
119 1073.781 7 x 17 close to 17 degrees of 19edo
239 1081.040 prime close to 3 degrees of 31edo
15 1088.269 3 x 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 x 11 11-limit / close to 11 degrees of 12edo, square root of 57
243 1109.775 3 x 3 x 3 x 9 Pythagorean major seventh close to 12 degrees of 13edo
61 1116.885 prime close to 13 degrees of 14edo
245 1123.9655 5 x 7 x 7 close to 16 degrees of 17edo
123 1131.017 3 x 41 close to 17 degrees of 18edo, 18 degrees of 19edo, square root of 59
247 1138.041 prime close to 19 degrees of 20edo
31 1145.036 prime close to 21 degrees of 22edo
249 1152.002 3 x 83 close to 24 degrees of 25edo
125 1158.941 5 x 5 x 5 5-limit, close to square root of 61
251 1165.852 prime
63 1172.736 3 x 3 x 7 7-limit
253 1179.592 11 x 23
127 1186.422 prime close to square root of 63
255 1193.224 3 x 5 x 17
2 1200 prime octave 2-limit
  1. ↑ cent values are given for the ocave reduced equivalent
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