Xenharmonic Wiki

List of octave-reduced harmonics: Difference between revisions

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Wikispaces>xenwolf
**Imported revision 561306519 - Original comment: added a link for a small page that describes octave reduction**
Wikispaces>JosephRuhf
**Imported revision 598348160 - 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:xenwolf|xenwolf]] and made on <tt>2015-10-05 03:43:16 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-11-04 07:59:51 UTC</tt>.<br>
: The original revision id was <tt>561306519</tt>.<br>
: The original revision id was <tt>598348160</tt>.<br>
: The revision comment was: <tt>added a link for a small page that describes octave reduction</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 18: Line 18:
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||  || [[5-limit]], close to 1 degree of [[13edo]] / square root of 71 ||
|| 135 || 92.179 || 3 x 3 x 3 x 5 ||  || [[5-limit]], close to 1 degree of [[13edo]] / square root of 71 ||
|| **17** || **104.955** || **prime** || **overtone half-step** || **close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]** ||
|| **17** || **104.955** || **prime** || **overtone half-step** || **close to 1 degree of [[11edo]] / 2 degrees of [[23edo]]** ||
|| **137** || **117.6385** || **prime** || **overtone seco** || **close to 3 degrees of [[31edo]],** **square root of 73** ||
|| **137** || **[[tel:117.6385|117.6385]]** || **prime** || **overtone secor** || **close to 3 degrees of [[31edo]],** **square root of 73** ||
|| 69 || 130.229 || 3 x 23 ||  || close to 1 degree of [[9edo]] ||
|| 69 || 130.229 || 3 x 23 ||  || close to 1 degree of [[9edo]] ||
|| **139** || **142.729** || **prime** ||  || **close to 4 degrees of [[17edo]]** ||
|| **139** || **142.729** || **prime** ||  || **close to 2 degrees of [[17edo]]** ||
|| 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]] ||
|| 141 || 167.462 || 3 x 47 ||  ||  ||
|| 141 || 167.462 || 3 x 47 ||  ||  ||
Line 40: Line 40:
|| **157** || **353.545** || **prime** || **overtone** **hemififth** || **close to 5 degrees of [[17edo]]** ||
|| **157** || **353.545** || **prime** || **overtone** **hemififth** || **close to 5 degrees of [[17edo]]** ||
|| **79** || **364.537** || **prime** ||  || **close to 7 degrees of [[23edo]]** ||
|| **79** || **364.537** || **prime** ||  || **close to 7 degrees of [[23edo]]** ||
|| 159 || 375.4595 || 3 x 53 ||  || close to 5 degrees of [[16edo]] ||
|| 159 || [[tel:375.4595|375.4595]] || 3 x 53 ||  || close to 5 degrees of [[16edo]] ||
|| **5** || **386.314** || **prime** || **5-limit major third** || **5-limit / close to 10 degrees of [[31edo]]** ||
|| **5** || **386.314** || **prime** || **5-limit major third** || **5-limit / close to 10 degrees of [[31edo]]** ||
|| **161** || **397.100** || **prime** ||  || **close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])** ||
|| **161** || **397.100** || **prime** ||  || **close to 4 degrees of [[12edo]] (a.k.a. 1 degree of [[3edo]])** ||
Line 58: Line 58:
|| **11** || **551.318** || **prime** || **undecimal semi-augmented fourth / undecimal tritone** || **11-limit / close to 11 degrees of [[24edo]]** ||
|| **11** || **551.318** || **prime** || **undecimal semi-augmented fourth / undecimal tritone** || **11-limit / close to 11 degrees of [[24edo]]** ||
|| 177 || 561.127 || 3 x 59 ||  || close to 7 degrees of [[15edo]] ||
|| 177 || 561.127 || 3 x 59 ||  || close to 7 degrees of [[15edo]] ||
|| **89** || **570.880** || **prime** ||  || **close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] /**  
|| **89** || **570.880** || **prime** ||  || **close to 10 degrees of [[21edo]] / 9 degrees of [[19edo]] /**
**square root of 31** ||
**square root of 31** ||
|| **179** || **580.579** || **prime** ||  || **close to 15 degrees of [[31edo]]** ||
|| **179** || **580.579** || **prime** ||  || **close to 15 degrees of [[31edo]]** ||
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|| 189 || 674.691 || 3 x 3 x 3 x 7 ||  || 7-limit / close to 9 degrees of [[16edo]], square root of 35 ||
|| 189 || 674.691 || 3 x 3 x 3 x 7 ||  || 7-limit / close to 9 degrees of [[16edo]], square root of 35 ||
|| 95 || 683.827 || 5 x 19 ||  || close to 4 degrees of [[7edo]] ||
|| 95 || 683.827 || 5 x 19 ||  || close to 4 degrees of [[7edo]] ||
|| **191** || **692.9155** || **prime** ||  || **close to 11 degrees of [[19edo]]** ||
|| **191** || **[[tel:692.9155|692.9155]]** || **prime** ||  || **close to 11 degrees of [[19edo]]** ||
|| **3** || **701.955** || **prime** || **just perfect fifth** || **3-limit / close to 7 degrees of [[12edo]]** ||
|| **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]]** ||
|| **193** || **710.948** || **prime** ||  || **close to 13 degrees of [[22edo]]** ||
Line 80: Line 80:
|| **197** || **746.462** || **prime** ||  ||  ||
|| **197** || **746.462** || **prime** ||  ||  ||
|| 99 || 755.228 || 3 x 3 x 11 ||  || 11-limit / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]] ||
|| 99 || 755.228 || 3 x 3 x 11 ||  || 11-limit / close to 5 degrees of [[8edo]] / 12 degrees of [[19edo]] ||
|| **199** || **763.9495** || **prime** ||  || **close to 7 degrees of [[11edo]]** ||
|| **199** || **[[tel:763.9495|763.9495]]** || **prime** ||  || **close to 7 degrees of [[11edo]]** ||
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39 ||
|| 25 || 772.627 || 5 x 5 || augmented fifth || 5-limit / close to 9 degrees of [[14edo]] / 11 degrees of [[17edo]], square root of 39 ||
|| 201 || 781.262 || 3 x 67 || overtone gentle minor sixth, circular sixth || close to 19 degrees of [[23edo]] / pi ||
|| 201 || 781.262 || 3 x 67 || overtone gentle minor sixth, circular sixth || close to 19 degrees of [[23edo]] / pi ||
Line 94: Line 94:
|| **211** || **865.319** || **prime** ||  || **close to 13 degrees of [[18edo]]** ||
|| **211** || **865.319** || **prime** ||  || **close to 13 degrees of [[18edo]]** ||
|| **53** || **873.505** || **prime** ||  || **close to 8 degrees of [[11edo]]** ||
|| **53** || **873.505** || **prime** ||  || **close to 8 degrees of [[11edo]]** ||
|| 213 || 881.6515 || 3 x 71 ||  || close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]] ||
|| 213 || [[tel:881.6515|881.6515]] || 3 x 71 ||  || close to 11 degrees of [[15edo]] / close to 14 degrees of [[19edo]] ||
|| 215 || 897.831 || 5 x 43 ||  || close to 9 degrees of [[12edo]] (a.k.a. 3 degrees of [[4edo]]), square root of 45 ||
|| 215 || 897.831 || 5 x 43 ||  || close to 9 degrees of [[12edo]] (a.k.a. 3 degrees of [[4edo]]), square root of 45 ||
|| 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 ||
|| 217 || 913.8615 || 7 x 31 || overtone gentle major third || close to 13 degrees of [[17edo]] ||
|| 217 || [[tel:913.8615|913.8615]] || 7 x 31 || overtone gentle major third || close to 13 degrees of [[17edo]] ||
|| **109** || **921.821** || **prime** ||  || **close to 10 degrees of [[13edo]]** ||
|| **109** || **921.821** || **prime** ||  || **close to 10 degrees of [[13edo]]** ||
|| 219 || 929.7445 || 3 x 73 ||  || close to 24 degrees of [[31edo]], square root of 47 ||
|| 219 || [[tel:929.7445|929.7445]] || 3 x 73 ||  || close to 24 degrees of [[31edo]], square root of 47 ||
|| 55 || 937.632 || 5 x 11 ||  || 11-limit / close to 18 degrees of [[23edo]] ||
|| 55 || 937.632 || 5 x 11 ||  || 11-limit / close to 18 degrees of [[23edo]] ||
|| 221 || 945.483 || 13 x 17 ||  || close to 15 degrees of [[19edo]] ||
|| 221 || 945.483 || 13 x 17 ||  || close to 15 degrees of [[19edo]] ||
Line 266: Line 266:
         &lt;td&gt;&lt;strong&gt;137&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;137&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;117.6385&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/117.6385"&gt;117.6385&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;overtone seco&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;overtone secor&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;close to 3 degrees of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;,&lt;/strong&gt; &lt;strong&gt;square root of 73&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;close to 3 degrees of &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;,&lt;/strong&gt; &lt;strong&gt;square root of 73&lt;/strong&gt;&lt;br /&gt;
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         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;close to 4 degrees of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;close to 2 degrees of &lt;a class="wiki_link" href="/17edo"&gt;17edo&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
Line 519: Line 519:
         &lt;td&gt;159&lt;br /&gt;
         &lt;td&gt;159&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;375.4595&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/375.4595"&gt;375.4595&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3 x 53&lt;br /&gt;
         &lt;td&gt;3 x 53&lt;br /&gt;
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         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&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;/strong&gt; &lt;br /&gt;
         &lt;td&gt;&lt;strong&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;/strong&gt;&lt;br /&gt;
&lt;strong&gt;square root of 31&lt;/strong&gt;&lt;br /&gt;
&lt;strong&gt;square root of 31&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
Line 892: Line 892:
         &lt;td&gt;&lt;strong&gt;191&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;191&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;692.9155&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/692.9155"&gt;692.9155&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
Line 988: Line 988:
         &lt;td&gt;&lt;strong&gt;199&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;199&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;763.9495&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/763.9495"&gt;763.9495&lt;/a&gt;&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;prime&lt;/strong&gt;&lt;br /&gt;
Line 1,156: Line 1,156:
         &lt;td&gt;213&lt;br /&gt;
         &lt;td&gt;213&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;881.6515&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/881.6515"&gt;881.6515&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3 x 71&lt;br /&gt;
         &lt;td&gt;3 x 71&lt;br /&gt;
Line 1,192: Line 1,192:
         &lt;td&gt;217&lt;br /&gt;
         &lt;td&gt;217&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;913.8615&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/913.8615"&gt;913.8615&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;7 x 31&lt;br /&gt;
         &lt;td&gt;7 x 31&lt;br /&gt;
Line 1,216: Line 1,216:
         &lt;td&gt;219&lt;br /&gt;
         &lt;td&gt;219&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;929.7445&lt;br /&gt;
         &lt;td&gt;&lt;a class="wiki_link" href="http://tel.wikispaces.com/929.7445"&gt;929.7445&lt;/a&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3 x 73&lt;br /&gt;
         &lt;td&gt;3 x 73&lt;br /&gt;
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