List of octave-reduced harmonics: Difference between revisions

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**Imported revision 79309271 - Original comment: added factorization, note names, & some notes (more to come later)**
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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.
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-06-24 16:35:35 UTC</tt>.<br>
: The original revision id was <tt>79309271</tt>.<br>
: The revision comment was: <tt>added factorization, note names, & some notes (more to come later)</tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">A list of many overtones in an octave, arranged by ascending pitch, octave reduced. Prime overtones are highlighted.


|| overtone || cents || factorization || name || notes ||
{| class="wikitable center-1 right-2 sortable"
|| 1 || 0 ||  || unison ||   ||
|-
|| 65 || 26.841 || 5 x 13 ||   || 13-limit ||
! Harmonic
|| 33 || 53.273 || 3 x 11 || undecimal comma || 11-limit / close to quarter-tone (1 degree of [[24edo]]) ||
! Size ([[cents|¢]])<ref>cent values are given for the octave reduced equivalent</ref>
|| 67 || 79.307 || prime ||  || close to 1 degree of [[15edo]] ||
! class="unsortable" | Factorization
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||  || 5-limit ||
! class="unsortable" | Name
|| 17 || 104.955 || prime || overtone half-step ||  ||
! class="unsortable" | Remarks
|| 69 || 130.229 || 3 x 23 ||  || close to 1 degree of [[9edo]] ||
|-
|| 35 || 155.140 || 5 x 7 ||  || 7-limit / close to 3 degrees of [[24edo]] ||
| [[1/1|1]]
|| 71 || 179.697 || prime ||   || close to 3 degrees of [[20edo]] ||
| 0
|| 9 || 203.910 || 3 x 3 || major whole-tone / Pythagorean whole tone || 3-limit ||
| 1
|| 73 || 227.789 || prime ||   || close to 3 degrees of [[16edo]] / 4 degrees of [[21edo]] ||
| unison
|| 147 || 239.607 || 3 x 7 x 7 ||   || 7-limit / close to 1 degree of [[5edo]] ||
| present in all tunings and tonal systems
|| 37 || 251.344 || prime ||   || close to 5 degrees of [[24edo]] ||
|-
|| 75 || 274.582 || 3 x 5 x 5 || augmented second || 5-limit / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]] ||
| [[129/128|129]]
|| 19 || 297.513 || prime || overtone minor third || close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]]) ||
| 13.473
|| 39 || 342.483 || 3 x 13 ||  || 13-limit / close to 2 degrees of [[7edo]] ||
| 3 × 43
|| 79 || 364.537 || prime ||  || close to 7 degrees of [[23edo]] ||
|
|| 5 || 386.314 || prime || 5-limit major third || 5-limit / close to 10 degrees of [[31edo]] ||
|
|| 81 || 407.820 || 9 x 9 || Pythagorean major third || 3-limit ||
|-
|| 41 || 429.062 || prime ||  || close to 5 degrees of [[14edo]] ||
| [[65/64|65]]
|| 21 || 470.781 || 3 x 7 || narrow fourth / septimal fourth || 7-limit / close to 9 degrees of [[23edo]] ||
| 26.841
|| 85 || 491.269 || 5 x 17 ||   || near fourth / close to 9 degrees of [[22edo]] ||
| 5 × 13
|| 43 || 511.518 || prime ||  || close to 3 degrees of [[7edo]] ||
|  
|| 87 || 531.532 || 3 x 29 ||  || close to 4 degrees of [[9edo]] ||
| [[13-limit]]
|| 11 || 551.318 || prime || undecimal semi-augmented fourth / undecimal tritone || 11-limit / close to 11 degrees of [[24edo]] ||
|-
|| 89 || 570.880 || prime ||  || close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] ||
| '''[[131/128|131]]'''
|| 45 || 590.224 || 3 x 3 x 5 || high 5-limit tritone || 5-limit ||
| '''40.108'''
|| 91 || 609.354 || 7 x 13 ||   || 13-limit ||
| '''prime'''
|| 23 || 628.274 || prime ||   || close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] ||
|
|| 93 || 646.991 || 3 x 31 ||  || close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]] ||
| '''close to square root of 67'''
|| 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]] ||
| [[33/32|33]]
|| 95 || 683.827 || 5 x 19 ||  || close to 4 degrees of [[7edo]] ||
| 53.273
|| 3 || 701.955 || prime || just perfect fifth || 3-limit / close to 7 degrees of [[12edo]] ||
| 3 × 11
|| 97 || 719.895 || prime ||   || close to 3 degrees of [[5edo]] ||
| undecimal comma
|| 49 || 737.652 || 7 x 7 ||  || 7-limit / close to 8 degrees of [[13edo]] ||
| [[11-limit]] / close to quarter-tone (1 [[degree]] of [[24edo]]), square root of 17
|| 99 || 755.228 || 3 x 3 x 11 ||   || 11-limit ||
|-
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit ||
| [[133/128|133]]
|| 101 || 789.854 || prime ||   ||   ||
| 66.339
|| 51 || 806.910 || 3 x 17 ||   ||   ||
| 7 × 19
|| 103 || 823.801 || prime ||   ||  ||
|  
|| 13 || 840.528 || prime || overtone sixth || 13-limit ||
| close to 1 degree of [[18edo]] / [[19edo]], square root of 69
|| 105 || 857.095 || 3 x 5 x 7 ||  || 7-limit ||
|-
|| 53 || 873.505 || prime ||  ||  ||
| '''[[67/64|67]]'''
|| 27 || 905.865 || 3 x 3 x 3 || Pythagorean major sixth || 3-limit ||
| '''79.307'''
|| 109 || 921.821 || prime ||  ||  ||
| '''prime'''
|| 55 || 937.632 || 5 x 11 ||  || 11-limit ||
|  
|| 111 || 953.299 || 3 x 37 ||  ||  ||
| '''close to 1 degree of [[15edo]]'''
|| 7 || 968.826 || prime || harmonic seventh / septimal minor seventh || 7-limit ||
|-
|| 113 || 984.215 || prime ||  ||  ||
| [[135/128|135]]
|| 57 || 999.468 || 3 x 19 ||   ||   ||
| 92.179
|| 115 || 1014.588 || 5 x 23 ||   ||   ||
| 3 × 3 × 3 × 5
|| 29 || 1029.577 || prime ||   ||  ||
|  
|| 117 || 1044.438 || 3 x 3 x13 ||   || 13-limit ||
| [[5-limit]], close to 1 degree of [[13edo]] / square root of 71
|| 59 || 1059.172 || prime ||   ||   ||
|-
|| 119 || 1073.781 || 7 x 17 ||  ||  ||
| '''[[17/16|17]]'''
|| 15 || 1088.269 || 3 x 5 || 5-limit major seventh || 5-limit ||
| '''104.955'''
|| 121 || 1102.636 || 11 x 11 ||   || 11-limit ||
| '''prime'''
|| 243 || 1109.775 || 3 x 3 x 3 x 3 x 3 || Pythagorean major seventh ||  ||
| '''harmonic half-step'''
|| 61 || 1116.885 || prime ||   ||   ||
| '''close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]'''
|| 123 || 1131.017 || 3 x 41 ||  ||  ||
|-
|| 31 || 1145.036 || prime ||   ||   ||
| '''[[137/128|137]]'''
|| 125 || 1158.941 || 5 x 5 x 5 ||   || 5-limit ||
| '''117.6385'''
|| 63 || 1172.736 || 3 x 3 x 7 ||   || 7-limit ||
| '''prime'''
|| 127 || 1186.422 || prime ||   ||   ||
| '''harmonic [[secor]]'''
|| 2 || 1200 || prime || octave || 2-limit ||</pre></div>
| '''close to 3 degrees of [[31edo]],''' '''square root of 73'''
<h4>Original HTML content:</h4>
|-
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;ListOfOvertones&lt;/title&gt;&lt;/head&gt;&lt;body&gt;A list of many overtones in an octave, arranged by ascending pitch, octave reduced. Prime overtones are highlighted.&lt;br /&gt;
| [[69/64|69]]
&lt;br /&gt;
| 130.229
| 3 × 23
|  
| close to 1 degree of [[9edo]]
|-
| '''[[139/128|139]]'''
| '''142.729'''
| '''prime'''
|  
| '''close to 2 degrees of [[17edo]]'''
|-
| [[35/32|35]]
| 155.140
| 5 × 7
|  
| [[7-limit]] / close to 3 degrees of [[24edo]]
|-
| [[141/128|141]]
| 167.462
| 3 × 47
|  
|  
|-
| '''[[71/64|71]]'''
| '''179.697'''
| '''prime'''
|  
| '''close to 3 degrees of [[20edo]], square root of 79'''
|-
| [[143/128|143]]
| 191.846
| 11 × 13
| 11-13 meantone
| [[13-limit]] / close to square root of 5 (a.k.a. 5 degrees of [[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]]'''
|-
| [[147/128|147]]
| 239.607
| 3 × 7 × 7
|  
| [[7-limit]] / close to 1 degree of [[5edo]], square root of 21
|-
| '''[[37/32|37]]'''
| '''251.344'''
| '''prime'''
| '''harmonic''' '''hemifourth'''
| '''close to 5 degrees of [[24edo]]'''
|-
| '''[[149/128|149]]'''
| '''263.002'''
| '''prime'''
| '''harmonic subminor third'''
|  
|-
| [[75/64|75]]
| 274.582
| 3 × 5 × 5
| augmented second
| [[5-limit]] / close to 5 degrees of [[22edo]], 3 degrees of [[13edo]], square root of 11
|-
| '''[[151/128|151]]'''
| '''286.086'''
| '''prime'''
| '''harmonic gentle minor third'''
| '''close to 4 degrees of [[17edo]]'''
|-
| '''[[19/16|19]]'''
| '''297.513'''
| '''prime'''
| '''harmonic minor third'''
| '''close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]])'''
|-
| [[153/128|153]]
| 308.865
| 3 × 3 × 17
|  
| close to 8 degrees of [[31edo]]
|-
| [[77/64|77]]
| 320.144
| 7 × 11
|  
| close to 4 degrees of [[15edo]]
|-
| [[155/128|155]]
| 331.349
| 5 × 31
|
|  
|-
| [[39/32|39]]
| 342.483
| 3 × 13
|  
| [[13-limit]] / close to 2 degrees of [[7edo]]
|-
| '''[[157/128|157]]'''
| '''353.545'''
| '''prime'''
| '''harmonic''' '''hemififth'''
| '''close to 5 degrees of [[17edo]]'''
|-
| '''[[79/64|79]]'''
| '''364.537'''
| '''prime'''
|  
| '''close to 7 degrees of [[23edo]]'''
|-
| [[159/128|159]]
| 375.4595
| 3 × 53
|  
| close to 5 degrees of [[16edo]]
|-
| '''[[5/4|5]]'''
| '''386.314'''
| '''prime'''
| '''5-limit major third'''
| '''[[5-limit]] / close to 10 degrees of [[31edo]]'''
|-
| [[161/128|161]]
| 397.100
| 7 × 23
|  
| close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])
|-
| [[81/64|81]]
| 407.820
| 3 × 3 × 3 × 3
| Pythagorean major third
| [[3-limit]]
|-
| '''[[163/128|163]]'''
| '''418.474'''
| '''prime'''
| '''overtone gentle major third'''
| '''close to 8 degrees of [[23edo]] / square root of phi'''
|-
| '''[[41/32|41]]'''
| '''429.062'''
| '''prime'''
|  
| '''close to 5 degrees of [[14edo]]'''
|-
| [[165/128|165]]
| 439.587
| 3 × 5 × 11
|  
|  
|-
| '''[[83/64|83]]'''
| '''450.047'''
| '''prime'''
|  
| '''close to 3 degrees of [[8edo]]'''
|-
| '''[[167/128|167]]'''
| '''460.445'''
| '''prime'''
|  
|  
|-
| [[21/16|21]]
| 470.781
| 3 × 7
| narrow fourth / septimal fourth
| [[7-limit]] / close to 9 degrees of [[23edo]]
|-
| [[169/128|169]]
| 481.055
| 13 × 13
|  
| [[13-limit]] / close to 2 degrees of [[5edo]], square root of 7
|-
| [[85/64|85]]
| 491.269
| 5 × 17
| near fourth
| close to 9 degrees of [[22edo]]
|-
| [[171/128|171]]
| 501.423
| 3 × 3 × 19
|  
| close to 5 degrees of [[12edo]]
|-
| '''[[43/32|43]]'''
| '''511.518'''
| '''prime'''
|  
| '''close to 3 degrees of [[7edo]] / square root of 29'''
|-
| '''[[173/128|173]]'''
| '''521.554'''
| '''prime'''
|  
| '''close to 10 degrees of [[23edo]]'''
|-
| [[87/64|87]]
| 531.532
| 3 × 29
|  
| close to 4 degrees of [[9edo]]
|-
| [[175/128|175]]
| 541.453
| 5 × 5 × 7
|  
| close to 9 degrees of [[20edo]]
|-
| '''[[11/8|11]]'''
| '''551.318'''
| '''prime'''
| '''undecimal semi-augmented fourth / undecimal tritone'''
| '''[[11-limit]] / close to 11 degrees of [[24edo]]'''
|-
| [[177/128|177]]
| 561.127
| 3 × 59
|  
| close to 7 degrees of [[15edo]]
|-
| '''[[89/64|89]]'''
| '''570.880'''
| '''prime'''
|  
| '''close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] / square root of 31'''
|-
| '''[[179/128|179]]'''
| '''580.579'''
| '''prime'''
|  
| '''close to 15 degrees of [[31edo]]'''
|-
| [[45/32|45]]
| 590.224
| 3 × 3 × 5
| high 5-limit tritone
| [[5-limit]] / close to square root of 15
|-
| '''[[181/128|181]]'''
| '''599.815'''
| '''prime'''
|  
| '''close to square root of 2'''
|-
| [[91/64|91]]
| 609.354
| 7 × 13
|  
| [[13-limit]]
|-
| [[183/61|183]]
| 618.840
| 3 × 61
|  
|  
|-
| '''[[23/16|23]]'''
| '''628.274'''
| '''prime'''
|  
| '''close to 11 degrees of [[21edo]] / 10 degrees of [[19edo]] / square root of 33'''
|-
| [[185/128|185]]
| 637.658
| 5 × 37
|  
|  
|-
| [[93/64|93]]
| 646.991
| 3 × 31
|  
| close to 7 degrees of [[13edo]] / 13 degrees of [[24edo]]
|-
| [[187/128|187]]
| 656.273
| 11 × 17
|  
| close to 11 degrees of [[20edo]]
|-
| '''[[47/32|47]]'''
| '''665.507'''
| '''prime'''
|
| '''close to 5 degrees of [[9edo]]'''
|-
| [[189/128|189]]
| 674.691
| 3 × 3 × 3 × 7
|  
| [[7-limit]] / close to 9 degrees of [[16edo]], square root of 35
|-
| [[95/64|95]]
| 683.827
| 5 × 19
|  
| close to 4 degrees of [[7edo]]
|-
| '''[[191/128|191]]'''
| '''692.9155'''
| '''prime'''
|  
| '''close to 11 degrees of [[19edo]]'''
|-
| '''[[3/2|3]]'''
| '''701.955'''
| '''prime'''
| '''just perfect fifth'''
| '''[[3-limit]] / close to 7 degrees of [[12edo]]'''
|-
| '''[[193/128|193]]'''
| '''710.948'''
| '''prime'''
|  
| '''close to 13 degrees of [[22edo]]'''
|-
| '''[[97/64|97]]'''
| '''719.895'''
| '''prime'''
|  
| '''close to 3 degrees of [[5edo]]'''
|-
| [[195/128|195]]
| 728.796
| 3 × 5 × 13
|  
| [[13-limit]] / close to 19 degrees of [[31edo]], square root of 37
|-
| [[49/32|49]]
| 737.652
| 7 × 7
|  
| [[7-limit]] / close to 8 degrees of [[13edo]]
|-
| '''[[197/128|197]]'''
| '''746.462'''
| '''prime'''
|  
|  
|-
| [[99/64|99]]
| 755.228
| 3 × 3 × 11
|  
| [[11-limit]] / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]]
|-
| '''[[199/128|199]]'''
| '''763.9495'''
| '''prime'''
|
| '''close to 7 degrees of [[11edo]]'''
|-
| [[25/16|25]]
| 772.627
| 5 × 5
| augmented fifth
| [[5-limit]] / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39
|-
| [[201/128|201]]
| 781.262
| 3 × 67
| harmonic gentle minor sixth, circular sixth
| close to 19 degrees of [[23edo]] / pi
|-
| '''[[101/64|101]]'''
| '''789.854'''
| '''prime'''
|
|
|-
| [[203/128|203]]
| 798.403
| 7 × 29
|
| close to 8 degrees of [[12edo]] (a.k.a. 2 degrees of [[3edo]])
|-
| [[51/32|51]]
| 806.910
| 3 × 17
|
|
|-
| [[205/128|205]]
| 815.376
| 5 × 41
|
| close to 21 degrees of [[31edo]], square root of 41 ,
|-
| '''[[103/64|103]]'''
| '''823.801'''
| '''prime'''
|
| '''close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]]'''
|-
| [[207/128|207]]
| 832.143
| 3 × 3 × 23
|
| close to 17 degrees of [[22edo]], 10 degrees of [[13edo]]
|-
| '''[[13/8|13]]'''
| '''840.528'''
| '''prime'''
| '''harmonic sixth, golden overtone'''
| '''[[13-limit]] / close to 7 degrees of [[10edo]], golden ratio'''
|-
| [[209/128|209]]
| 848.831
| 11 × 19
| 11-19 hemieleventh
| close to 12 degrees of [[17edo]]
|-
| [[105/64|105]]
| 857.095
| 3 × 5 × 7
|
| [[7-limit]] / close to 5 degrees of [[7edo]], square root of 43
|-
| '''[[211/128|211]]'''
| '''865.319'''
| '''prime'''
|
| '''close to 13 degrees of [[18edo]]'''
|-
| '''[[53/32|53]]'''
| '''873.505'''
| '''prime'''
|
| '''close to 8 degrees of [[11edo]]'''
|-
| [[213/128|213]]
| 881.652
| 3 × 71
|
| close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]]
|-
| '''[[107/64|107]]'''
| ''' 889.760'''
| '''prime'''
|
|
|-
| [[215/128|215]]
| 897.831
| 5 × 43
|
| close to 9 degrees of [[12edo]] (a.k.a. 3 degrees of [[4edo]]), square root of 45
|-
| [[27/16|27]]
| 905.865
| 3 × 3 × 3
| Pythagorean major sixth
| [[3-limit]]
|-
| [[217/128|217]]
| 913.8615
| 7 × 31
| harmonic gentle major third
| close to 13 degrees of [[17edo]]
|-
| '''[[109/64|109]]'''
| '''921.821'''
| '''prime'''
|
| '''close to 10 degrees of [[13edo]]'''
|-
| [[219/128|219]]
| 929.7445
| 3 × 73
|
| close to 24 degrees of [[31edo]], square root of 47
|-
| [[55/32|55]]
| 937.632
| 5 × 11
|
| [[11-limit]] / close to 18 degrees of [[23edo]]
|-
| [[221/128|221]]
| 945.483
| 13 × 17
|
| close to 15 degrees of [[19edo]]
|-
| [[111/64|111]]
| 953.299
| 3 × 37
| harmonic hemitwelfth
| close to 19 degrees of [[24edo]] / square root of 3
|-
| '''[[223/128|223]]'''
| '''961.080'''
| '''prime'''
|
| '''close to 4 degrees of [[5edo]]'''
|-
| '''[[7/4|7]]'''
| '''968.826'''
| '''prime'''
| '''harmonic seventh / septimal minor seventh'''
| '''[[7-limit]] / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]]'''
|-
| [[225/128|225]]
| 976.537
| 3 × 3 × 5 × 5
| 5-limit subminor seventh
| [[5-limit]] / close to 11 degrees of [[16edo]]
|-
| '''[[113/64|113]]'''
| '''984.215'''
| '''prime'''
|
| '''close to 9 degrees of [[11edo]]'''
|-
| '''[[227/128|227]]'''
| '''991.858'''
| '''prime'''
|
|
|-
| [[57/32|57]]
| 999.468
| 3 × 19
|
| close to 10 degrees of [[12edo]] (a.k.a. 5 degrees of [[6edo]]), square root of 51
|-
| '''[[229/128|229]]'''
| '''1007.0445'''
| '''prime'''
|
|
|-
| [[115/64|115]]
| 1014.588
| 5 × 23
|
| close to 11 degrees of [[13edo]]
|-
| [[231/128|231]]
| 1022.099
| 3 × 7 × 11
|
| close to square root of 13
|-
| '''[[29/16|29]]'''
| '''1029.577'''
| '''prime'''
|
| '''close to 6 degrees of [[7edo]]'''
|-
| '''[[233/128|233]]'''
| '''1037.023'''
| '''prime'''
|
| '''close to square root of 53'''
|-
| [[117/64|117]]
| 1044.438
| 3 × 3 × 13
|
| [[13-limit]] / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]]
|-
| [[235/128|235]]
| 1051.820
| 5 × 47
|
| close to 21 degrees of [[24edo]]
|-
| '''[[59/32|59]]'''
| '''1059.172'''
| '''prime'''
|
| '''close to 15 degrees of [[17edo]]'''
|-
| [[237/128|237]]
| 1066.492
| 3 × 79
|
| close to 8 degrees of [[9edo]], square root of 55
|-
| [[119/64|119]]
| 1073.781
| 7 × 17
|
| close to 17 degrees of [[19edo]]
|-
| '''[[239/128|239]]'''
| '''1081.040'''
| '''prime'''
|
| '''close to 3 degrees of [[31edo]]'''
|-
| [[15/8|15]]
| 1088.269
| 3 × 5
| 5-limit major seventh
| [[5-limit]] / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]]
|-
| '''[[241/128|241]]'''
| '''1095.467'''
| '''prime'''
|
|
|-
| [[121/64|121]]
| 1102.636
| 11 × 11
|
| [[11-limit]] / close to 11 degrees of [[12edo]], square root of 57
|-
| [[243/128|243]]
| 1109.775
| 3 × 3 × 3 × 3 × 3
| Pythagorean major seventh
| close to 12 degrees of [[13edo]]
|-
| '''[[61/32|61]]'''
| '''1116.885'''
| '''prime'''
|
| '''close to 13 degrees of [[14edo]]'''
|-
| [[245/128|245]]
| 1123.9655
| 5 × 7 × 7
|
| close to 16 degrees of [[17edo]]
|-
| [[123/64|123]]
| 1131.017
| 3 × 41
|
| close to 17 degrees of [[18edo]], 18 degrees of [[19edo]], square root of 59
|-
| [[247/128|247]]
| 1138.041
| 13 × 19
|
| close to 19 degrees of [[20edo]]
|-
| '''[[31/16|31]]'''
| '''1145.036'''
| '''prime'''
|
| '''close to 21 degrees of [[22edo]]'''
|-
| [[249/128|249]]
| 1152.002
| 3 × 83
|
| close to 24 degrees of [[25edo]]
|-
| [[125/64|125]]
| 1158.941
| 5 × 5 × 5
|
| [[5-limit]], close to square root of 61
|-
| '''[[251/128|251]]'''
| '''1165.852'''
| '''prime'''
|
|
|-
| [[63/32|63]]
| 1172.736
| 3 × 3 × 7
|
| [[7-limit]]
|-
| [[253/128|253]]
| 1179.592
| 11 × 23
|
|
|-
| '''[[127/64|127]]'''
| '''1186.422'''
| '''prime'''
|
| '''close to square root of 63'''
|-
| [[255/128|255]]
| 1193.224
| 3 × 5 × 17
|
|
|-
| '''[[2/1|2]]'''
| '''1200'''
| '''prime'''
| '''octave'''
| '''[[2-limit]]'''
|}
<references />


== See also ==
* [[List of tritave reduced harmonics]]
* [[Pentave Reduced Harmonics]]


&lt;table class="wiki_table"&gt;
[[Category:Octave-reduced harmonics| ]] <!-- main article -->
    &lt;tr&gt;
[[Category:Lists of intervals]]
        &lt;td&gt;overtone&lt;br /&gt;
[[Category:Harmonic]]
&lt;/td&gt;
        &lt;td&gt;cents&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;factorization&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;name&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;notes&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;1&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;0&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;unison&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;65&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;26.841&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;33&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;53.273&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undecimal comma&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-limit / close to quarter-tone (1 degree of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;67&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;79.307&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 1 degree of &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;135&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;92.179&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 3 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;104.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;overtone half-step&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;69&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;130.229&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 1 degree of &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;35&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;155.140&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit / close to 3 degrees of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;71&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;179.697&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 3 degrees of &lt;a class="wiki_link" href="/20edo"&gt;20edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;203.910&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;major whole-tone / Pythagorean whole tone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;73&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;227.789&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 3 degrees of &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; / 4 degrees of &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;147&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;239.607&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 7 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit / close to 1 degree of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;251.344&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 5 degrees of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;75&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;274.582&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 5 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;augmented second&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit / close to 5 degrees of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;, 3 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;297.513&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;overtone minor third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 3 degrees of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; (a.k.a. 1 degree of &lt;a class="wiki_link" href="/4edo"&gt;4edo&lt;/a&gt;)&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;39&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;342.483&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-limit / close to 2 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;79&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;364.537&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 7 degrees of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;386.314&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit / close to 10 degrees of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;81&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;407.820&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;9 x 9&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pythagorean major third&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;429.062&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 5 degrees of &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;21&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;470.781&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;narrow fourth / septimal fourth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit / close to 9 degrees of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;85&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;491.269&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;near fourth / close to 9 degrees of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;43&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;511.518&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 3 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;87&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;531.532&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 4 degrees of &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;551.318&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;undecimal semi-augmented fourth / undecimal tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-limit / close to 11 degrees of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;89&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;570.880&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 10 degrees of &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; / 9 degrees of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;45&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;590.224&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;high 5-limit tritone&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;91&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;609.354&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7 x 13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;628.274&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 11 degrees of &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; / 10 degrees of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;93&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;646.991&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 7 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt; / 13 degrees of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;47&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;665.507&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 5 degrees of &lt;a class="wiki_link" href="/9edo"&gt;9edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;189&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;674.691&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 3 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit / close to 9 degrees of &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;95&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;683.827&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 4 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;701.955&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;just perfect fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-limit / close to 7 degrees of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;97&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;719.895&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;close to 3 degrees of &lt;a class="wiki_link" href="/5edo"&gt;5edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;49&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;737.652&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit / close to 8 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;99&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;755.228&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;772.627&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;augmented fifth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;101&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;789.854&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;51&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;806.910&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;103&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;823.801&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;840.528&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;overtone sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;105&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;857.095&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 5 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;53&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;873.505&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;27&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;905.865&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pythagorean major sixth&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;109&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;921.821&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;55&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;937.632&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;111&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;953.299&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 37&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;968.826&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;harmonic seventh / septimal minor seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;113&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;984.215&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;57&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;999.468&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 19&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;115&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1014.588&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 23&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;29&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1029.577&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;117&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1044.438&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x13&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;13-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;59&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1059.172&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;119&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1073.781&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7 x 17&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;15&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1088.269&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;121&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1102.636&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11 x 11&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;11-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;243&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1109.775&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 3 x 3 x 3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;Pythagorean major seventh&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;61&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1116.885&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;123&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1131.017&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 41&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;31&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1145.036&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;125&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1158.941&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5 x 5 x 5&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;63&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1172.736&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3 x 3 x 7&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;7-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;127&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1186.422&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;1200&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;prime&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;octave&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;2-limit&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>

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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