List of octave-reduced harmonics
IMPORTED REVISION FROM WIKISPACES
This is an imported revision from Wikispaces. The revision metadata is included below for reference:
- 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>