62edo: Difference between revisions
Wikispaces>Osmiorisbendi **Imported revision 368789204 - Original comment: ** |
Wikispaces>Osmiorisbendi **Imported revision 429137470 - Original comment: ** |
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<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:Osmiorisbendi|Osmiorisbendi]] and made on <tt> | : This revision was by author [[User:Osmiorisbendi|Osmiorisbendi]] and made on <tt>2013-05-06 05:18:24 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>429137470</tt>.<br> | ||
: The revision comment was: <tt></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> | ||
<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">=<span style="color: # | <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">=<span style="color: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span>= | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for [[31 comma temperaments#Gallium|gallium]], [[Starling temperaments#Valentine%20temperament-Semivalentine|semivalentine]] and [[Meantone family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone|hemimeantone]] temperaments. | ||
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* **⌐** = Thin (1/8-tone down) || | * **⌐** = Thin (1/8-tone down) || | ||
|| Degrees || Cents size || Armodue notation || || | || Degrees || Cents size || Armodue notation || || | ||
|| 0 || 0 || 1 || | || 0 || 0 || 1 || : || | ||
|| 1 || 19.35484 || 1Ɨ || || | || 1 || 19.35484 || 1Ɨ || || | ||
|| 2 || 38.70968 || 1‡ (9#) || || | || 2 || 38.70968 || 1‡ (9#) || || | ||
| Line 34: | Line 34: | ||
|| 9 || 174.19355 || 2Ɨ || || | || 9 || 174.19355 || 2Ɨ || || | ||
|| 10 || 193.54839 || 2‡ || || | || 10 || 193.54839 || 2‡ || || | ||
|| 11 || 212.90323 || 3b || | || 11 || 212.90323 || 3b || · || | ||
|| 12 || 232.25806 || 2◊3 || || | || 12 || 232.25806 || 2◊3 || || | ||
|| 13 || 251.6129 || 2# || || | || 13 || 251.6129 || 2# || || | ||
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|| 17 || 329.03226 || 3Ɨ || || | || 17 || 329.03226 || 3Ɨ || || | ||
|| 18 || 348.3871 || 3‡ || || | || 18 || 348.3871 || 3‡ || || | ||
|| 19 || 367.74194 || 4b || | || 19 || 367.74194 || 4b || · || | ||
|| 20 || 387.09677 || 3◊4 || || | || 20 || 387.09677 || 3◊4 || || | ||
|| 21 || 406.45161 || 3# || || | || 21 || 406.45161 || 3# || || | ||
| Line 50: | Line 50: | ||
|| 25 || 483.87097 || 4Ɨ (5v) || || | || 25 || 483.87097 || 4Ɨ (5v) || || | ||
|| 26 || 503.22581 || 5⌐ (4‡) || || | || 26 || 503.22581 || 5⌐ (4‡) || || | ||
|| 27 || 522.58065 || 5 || | || 27 || 522.58065 || 5 || · || | ||
|| 28 || 541.93548 || 5Ɨ || || | || 28 || 541.93548 || 5Ɨ || || | ||
|| 29 || 561.29032 || 5‡ (4#) || || | || 29 || 561.29032 || 5‡ (4#) || || | ||
| Line 58: | Line 58: | ||
|| 33 || 638.70968 || 6v || || | || 33 || 638.70968 || 6v || || | ||
|| 34 || 658.06452 || 6⌐ || || | || 34 || 658.06452 || 6⌐ || || | ||
|| 35 || 677.41935 || 6 || | || 35 || 677.41935 || 6 || · || | ||
|| 36 || 696.77419 || 6Ɨ || || | || 36 || 696.77419 || 6Ɨ || || | ||
|| 37 || 716.12903 || 6‡ || || | || 37 || 716.12903 || 6‡ || || | ||
| Line 66: | Line 66: | ||
|| 41 || 793.54839 || 7v || || | || 41 || 793.54839 || 7v || || | ||
|| 42 || 812.90323 || 7⌐ || || | || 42 || 812.90323 || 7⌐ || || | ||
|| 43 || 832.25806 || 7 || | || 43 || 832.25806 || 7 || · || | ||
|| 44 || 851.6129 || 7Ɨ || || | || 44 || 851.6129 || 7Ɨ || || | ||
|| 45 || 870.96774 || 7‡ || || | || 45 || 870.96774 || 7‡ || || | ||
| Line 74: | Line 74: | ||
|| 49 || 948.3871 || 8v || || | || 49 || 948.3871 || 8v || || | ||
|| 50 || 967.74194 || 8⌐ || || | || 50 || 967.74194 || 8⌐ || || | ||
|| 51 || 987.09677 || 8 || | || 51 || 987.09677 || 8 || · || | ||
|| 52 || 1006.45161 || 8Ɨ || || | || 52 || 1006.45161 || 8Ɨ || || | ||
|| 53 || 1025.80645 || 8‡ || || | || 53 || 1025.80645 || 8‡ || || | ||
| Line 86: | Line 86: | ||
|| 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | || 61 || 1180.64516 || 1⌐ (9‡) || ||</pre></div> | ||
<h4>Original HTML content:</h4> | <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"><html><head><title>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: # | <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"><html><head><title>62edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x62 tone equal temperament"></a><!-- ws:end:WikiTextHeadingRule:0 --><span style="color: #edd637; font-family: 'Times New Roman',Times,serif; font-size: 113%;">62 tone equal temperament</span></h1> | ||
<br /> | <br /> | ||
62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | 62edo divides the octave into 62 equal parts of 19.35484 cents each. 62 = 2 * 31 and the patent val is a contorted 31edo through the 11-limit; in the 13-limit it tempers out 169/168, 1188/1183, 847/845 and 676/675. It provides the optimal patent val for <a class="wiki_link" href="/31%20comma%20temperaments#Gallium">gallium</a>, <a class="wiki_link" href="/Starling%20temperaments#Valentine%20temperament-Semivalentine">semivalentine</a> and <a class="wiki_link" href="/Meantone%20family#Septimal%20meantone-Unidecimal%20meantone%20aka%20Huygens-Hemimeantone">hemimeantone</a> temperaments.<br /> | ||
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