List of octave-reduced harmonics: Difference between revisions

Wikispaces>Andrew_Heathwaite
**Imported revision 79309271 - Original comment: added factorization, note names, & some notes (more to come later)**
Wikispaces>Andrew_Heathwaite
**Imported revision 79340329 - Original comment: **
Line 1: Line 1:
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
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>
: This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-06-24 21:53:14 UTC</tt>.<br>
: The original revision id was <tt>79309271</tt>.<br>
: The original revision id was <tt>79340329</tt>.<br>
: The revision comment was: <tt>added factorization, note names, & some notes (more to come later)</tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<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>
<h4>Original Wikitext content:</h4>
Line 14: Line 14:
|| 67 || 79.307 || prime ||  || close to 1 degree of [[15edo]] ||
|| 67 || 79.307 || prime ||  || close to 1 degree of [[15edo]] ||
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||  || 5-limit ||
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||  || 5-limit ||
|| 17 || 104.955 || prime || overtone half-step ||   ||
|| 17 || 104.955 || prime || overtone half-step || close to 1 degree of [[11edo]] / 2 degrees of [[23edo]] ||
|| 69 || 130.229 || 3 x 23 ||  || close to 1 degree of [[9edo]] ||
|| 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]] ||
|| 35 || 155.140 || 5 x 7 ||  || 7-limit / close to 3 degrees of [[24edo]] ||
Line 45: Line 45:
|| 97 || 719.895 || prime ||  || close to 3 degrees of [[5edo]] ||
|| 97 || 719.895 || prime ||  || close to 3 degrees of [[5edo]] ||
|| 49 || 737.652 || 7 x 7 ||  || 7-limit / close to 8 degrees of [[13edo]] ||
|| 49 || 737.652 || 7 x 7 ||  || 7-limit / close to 8 degrees of [[13edo]] ||
|| 99 || 755.228 || 3 x 3 x 11 ||  || 11-limit ||
|| 99 || 755.228 || 3 x 3 x 11 ||  || 11-limit / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]] ||
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit ||
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]] ||
|| 101 || 789.854 || prime ||  ||  ||
|| 101 || 789.854 || prime ||  ||  ||
|| 51 || 806.910 || 3 x 17 ||  ||  ||
|| 51 || 806.910 || 3 x 17 ||  ||  ||
|| 103 || 823.801 || prime ||  ||   ||
|| 103 || 823.801 || prime ||  || close to 11 degrees of [[16edo]] / 13 degrees of [[19edo]] ||
|| 13 || 840.528 || prime || overtone sixth || 13-limit ||
|| 13 || 840.528 || prime || overtone sixth || 13-limit / close to 7 degrees of [[10edo]] ||
|| 105 || 857.095 || 3 x 5 x 7 ||  || 7-limit ||
|| 105 || 857.095 || 3 x 5 x 7 ||  || 7-limit / close to 5 degrees of [[7edo]] ||
|| 53 || 873.505 || prime ||  ||   ||
|| 53 || 873.505 || prime ||  || close to 8 degrees of [[11edo]] ||
|| 27 || 905.865 || 3 x 3 x 3 || Pythagorean major sixth || 3-limit ||
|| 27 || 905.865 || 3 x 3 x 3 || Pythagorean major sixth || 3-limit ||
|| 109 || 921.821 || prime ||  ||   ||
|| 109 || 921.821 || prime ||  || close to 10 degrees of [[13edo]] ||
|| 55 || 937.632 || 5 x 11 ||  || 11-limit ||
|| 55 || 937.632 || 5 x 11 ||  || 11-limit / close to 18 degrees of [[23edo]] ||
|| 111 || 953.299 || 3 x 37 ||  ||   ||
|| 111 || 953.299 || 3 x 37 ||  || close to 19 degrees of [[24edo]] ||
|| 7 || 968.826 || prime || harmonic seventh / septimal minor seventh || 7-limit ||
|| 7 || 968.826 || prime || harmonic seventh / septimal minor seventh || 7-limit / close to 17 degrees of [[21edo]] / 25 degrees of [[31edo]] ||
|| 113 || 984.215 || prime ||  ||   ||
|| 113 || 984.215 || prime ||  || close to 9 degrees of [[11edo]] ||
|| 57 || 999.468 || 3 x 19 ||  ||   ||
|| 57 || 999.468 || 3 x 19 ||  || close to 10 degrees of [[12edo]] (a.k.a. 5 degrees of [[6edo]] ||
|| 115 || 1014.588 || 5 x 23 ||  ||   ||
|| 115 || 1014.588 || 5 x 23 ||  || close to 11 degrees of [[13edo]] ||
|| 29 || 1029.577 || prime ||  ||   ||
|| 29 || 1029.577 || prime ||  || close to 6 degrees of [[7edo]] ||
|| 117 || 1044.438 || 3 x 3 x13 ||  || 13-limit ||
|| 117 || 1044.438 || 3 x 3 x13 ||  || 13-limit / close to 13 degrees of [[15edo]] / 20 degrees of [[23edo]] ||
|| 59 || 1059.172 || prime ||  ||   ||
|| 59 || 1059.172 || prime ||  || close to 15 degrees of [[17edo]] ||
|| 119 || 1073.781 || 7 x 17 ||  ||   ||
|| 119 || 1073.781 || 7 x 17 ||  || close to 17 degrees of [[19edo]] ||
|| 15 || 1088.269 || 3 x 5 || 5-limit major seventh || 5-limit ||
|| 15 || 1088.269 || 3 x 5 || 5-limit major seventh || 5-limit / close to 19 degrees of [[21edo]] / 10 degrees of [[11edo]] ||
|| 121 || 1102.636 || 11 x 11 ||  || 11-limit ||
|| 121 || 1102.636 || 11 x 11 ||  || 11-limit / close to 11 degrees of [[12edo]] ||
|| 243 || 1109.775 || 3 x 3 x 3 x 3 x 3 || Pythagorean major seventh ||   ||
|| 243 || 1109.775 || 3 x 3 x 3 x 3 x 3 || Pythagorean major seventh || close to 12 degrees of [[13edo]] ||
|| 61 || 1116.885 || prime ||  ||   ||
|| 61 || 1116.885 || prime ||  || close to 13 degrees of [[14edo]] ||
|| 123 || 1131.017 || 3 x 41 ||  ||   ||
|| 123 || 1131.017 || 3 x 41 ||  || close to 17 degrees of [[18edo]] ||
|| 31 || 1145.036 || prime ||  ||   ||
|| 31 || 1145.036 || prime ||  || close to 21 degrees of [[22edo]] ||
|| 125 || 1158.941 || 5 x 5 x 5 ||  || 5-limit ||
|| 125 || 1158.941 || 5 x 5 x 5 ||  || 5-limit ||
|| 63 || 1172.736 || 3 x 3 x 7 ||  || 7-limit ||
|| 63 || 1172.736 || 3 x 3 x 7 ||  || 7-limit ||
Line 162: Line 162:
         &lt;td&gt;overtone half-step&lt;br /&gt;
         &lt;td&gt;overtone half-step&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 1 degree of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt; / 2 degrees of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 534: Line 534:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11-limit&lt;br /&gt;
         &lt;td&gt;11-limit / close to 5 degrees of &lt;a class="wiki_link" href="/8edo"&gt;8edo&lt;/a&gt; / 12 degrees of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 546: Line 546:
         &lt;td&gt;augmented fifth&lt;br /&gt;
         &lt;td&gt;augmented fifth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5-limit&lt;br /&gt;
         &lt;td&gt;5-limit / close to 9 degrees of &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt; / 11 degrees of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 582: Line 582:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 11 degrees of &lt;a class="wiki_link" href="/16edo"&gt;16edo&lt;/a&gt; / 13 degrees of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 594: Line 594:
         &lt;td&gt;overtone sixth&lt;br /&gt;
         &lt;td&gt;overtone sixth&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13-limit&lt;br /&gt;
         &lt;td&gt;13-limit / close to 7 degrees of &lt;a class="wiki_link" href="/10edo"&gt;10edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 606: Line 606:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7-limit&lt;br /&gt;
         &lt;td&gt;7-limit / close to 5 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 618: Line 618:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 8 degrees of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 642: Line 642:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 10 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 654: Line 654:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11-limit&lt;br /&gt;
         &lt;td&gt;11-limit / close to 18 degrees of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 666: Line 666:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 19 degrees of &lt;a class="wiki_link" href="/24edo"&gt;24edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 678: Line 678:
         &lt;td&gt;harmonic seventh / septimal minor seventh&lt;br /&gt;
         &lt;td&gt;harmonic seventh / septimal minor seventh&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7-limit&lt;br /&gt;
         &lt;td&gt;7-limit / close to 17 degrees of &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; / 25 degrees of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 690: Line 690:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 9 degrees of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 702: Line 702:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 10 degrees of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt; (a.k.a. 5 degrees of &lt;a class="wiki_link" href="/6edo"&gt;6edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 714: Line 714:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 11 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 726: Line 726:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 6 degrees of &lt;a class="wiki_link" href="/7edo"&gt;7edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 738: Line 738:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;13-limit&lt;br /&gt;
         &lt;td&gt;13-limit / close to 13 degrees of &lt;a class="wiki_link" href="/15edo"&gt;15edo&lt;/a&gt; / 20 degrees of &lt;a class="wiki_link" href="/23edo"&gt;23edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 750: Line 750:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 15 degrees of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 762: Line 762:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 17 degrees of &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 774: Line 774:
         &lt;td&gt;5-limit major seventh&lt;br /&gt;
         &lt;td&gt;5-limit major seventh&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;5-limit&lt;br /&gt;
         &lt;td&gt;5-limit / close to 19 degrees of &lt;a class="wiki_link" href="/21edo"&gt;21edo&lt;/a&gt; / 10 degrees of &lt;a class="wiki_link" href="/11edo"&gt;11edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 786: Line 786:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;11-limit&lt;br /&gt;
         &lt;td&gt;11-limit / close to 11 degrees of &lt;a class="wiki_link" href="/12edo"&gt;12edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 798: Line 798:
         &lt;td&gt;Pythagorean major seventh&lt;br /&gt;
         &lt;td&gt;Pythagorean major seventh&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 12 degrees of &lt;a class="wiki_link" href="/13edo"&gt;13edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 810: Line 810:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 13 degrees of &lt;a class="wiki_link" href="/14edo"&gt;14edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 822: Line 822:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 17 degrees of &lt;a class="wiki_link" href="/18edo"&gt;18edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 834: Line 834:
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;close to 21 degrees of &lt;a class="wiki_link" href="/22edo"&gt;22edo&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;