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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]]
Retrieved from "https://en.xen.wiki/w/List_of_octave-reduced_harmonics"