List of octave-reduced harmonics

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Revision as of 16:35, 24 June 2009 by Wikispaces>Andrew_Heathwaite (**Imported revision 79309271 - Original comment: added factorization, note names, & some notes (more to come later)**)
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This revision was by author Andrew_Heathwaite and made on 2009-06-24 16:35:35 UTC.
The original revision id was 79309271.
The revision comment was: added factorization, note names, & some notes (more to come later)

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

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

|| overtone || cents || factorization || name || notes ||
|| 1 || 0 ||   || unison ||   ||
|| 65 || 26.841 || 5 x 13 ||   || 13-limit ||
|| 33 || 53.273 || 3 x 11 || undecimal comma || 11-limit / close to quarter-tone (1 degree of [[24edo]]) ||
|| 67 || 79.307 || prime ||   || close to 1 degree of [[15edo]] ||
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||   || 5-limit ||
|| 17 || 104.955 || prime || overtone half-step ||   ||
|| 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]] ||
|| 71 || 179.697 || prime ||   || close to 3 degrees of [[20edo]] ||
|| 9 || 203.910 || 3 x 3 || major whole-tone / Pythagorean whole tone || 3-limit ||
|| 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]] ||
|| 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]] ||
|| 19 || 297.513 || prime || overtone minor third || close to 3 degrees of [[12edo]] (a.k.a. 1 degree of [[4edo]]) ||
|| 39 || 342.483 || 3 x 13 ||   || 13-limit / close to 2 degrees of [[7edo]] ||
|| 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]] ||
|| 21 || 470.781 || 3 x 7 || narrow fourth / septimal fourth || 7-limit / close to 9 degrees of [[23edo]] ||
|| 85 || 491.269 || 5 x 17 ||   || near fourth / close to 9 degrees of [[22edo]] ||
|| 43 || 511.518 || prime ||   || close to 3 degrees of [[7edo]] ||
|| 87 || 531.532 || 3 x 29 ||   || close to 4 degrees of [[9edo]] ||
|| 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]] ||
|| 45 || 590.224 || 3 x 3 x 5 || high 5-limit tritone || 5-limit ||
|| 91 || 609.354 || 7 x 13 ||   || 13-limit ||
|| 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]] ||
|| 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]] ||
|| 95 || 683.827 || 5 x 19 ||   || close to 4 degrees of [[7edo]] ||
|| 3 || 701.955 || prime || just perfect fifth || 3-limit / close to 7 degrees of [[12edo]] ||
|| 97 || 719.895 || prime ||   || close to 3 degrees of [[5edo]] ||
|| 49 || 737.652 || 7 x 7 ||   || 7-limit / close to 8 degrees of [[13edo]] ||
|| 99 || 755.228 || 3 x 3 x 11 ||   || 11-limit ||
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit ||
|| 101 || 789.854 || prime ||   ||   ||
|| 51 || 806.910 || 3 x 17 ||   ||   ||
|| 103 || 823.801 || prime ||   ||   ||
|| 13 || 840.528 || prime || overtone sixth || 13-limit ||
|| 105 || 857.095 || 3 x 5 x 7 ||   || 7-limit ||
|| 53 || 873.505 || prime ||   ||   ||
|| 27 || 905.865 || 3 x 3 x 3 || Pythagorean major sixth || 3-limit ||
|| 109 || 921.821 || prime ||   ||   ||
|| 55 || 937.632 || 5 x 11 ||   || 11-limit ||
|| 111 || 953.299 || 3 x 37 ||   ||   ||
|| 7 || 968.826 || prime || harmonic seventh / septimal minor seventh || 7-limit ||
|| 113 || 984.215 || prime ||   ||   ||
|| 57 || 999.468 || 3 x 19 ||   ||   ||
|| 115 || 1014.588 || 5 x 23 ||   ||   ||
|| 29 || 1029.577 || prime ||   ||   ||
|| 117 || 1044.438 || 3 x 3 x13 ||   || 13-limit ||
|| 59 || 1059.172 || prime ||   ||   ||
|| 119 || 1073.781 || 7 x 17 ||   ||   ||
|| 15 || 1088.269 || 3 x 5 || 5-limit major seventh || 5-limit ||
|| 121 || 1102.636 || 11 x 11 ||   || 11-limit ||
|| 243 || 1109.775 || 3 x 3 x 3 x 3 x 3 || Pythagorean major seventh ||   ||
|| 61 || 1116.885 || prime ||   ||   ||
|| 123 || 1131.017 || 3 x 41 ||   ||   ||
|| 31 || 1145.036 || prime ||   ||   ||
|| 125 || 1158.941 || 5 x 5 x 5 ||   || 5-limit ||
|| 63 || 1172.736 || 3 x 3 x 7 ||   || 7-limit ||
|| 127 || 1186.422 || prime ||   ||   ||
|| 2 || 1200 || prime || octave || 2-limit ||

Original HTML content:

<html><head><title>ListOfOvertones</title></head><body>A list of many overtones in an octave, arranged by ascending pitch, octave reduced. Prime overtones are highlighted.<br />
<br />


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

</body></html>