31edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 160901431 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 160909315 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-09-07 14: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2010-09-07 14:43:37 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>160909315</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> | ||
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====MOS Scales generated by 6\31:==== | ====MOS Scales generated by 6\31:==== | ||
||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
|| | || pentatonic (quasi-equal) || [[1L 4s]] || 6 || || || || || || 6 || || || || || || 6 || || || || || || 6 || || || || || || 7 || || || || || || || | ||
|| | || hexatonic || [[5L 1s]] || 6 || || || || || || 6 || || || || || || 6 || || || || || || 6 || || || || || || 6 || || || || || || 1 || | ||
|| | || 11-tone || [[5L 6s]] || 5 || || || || || 1 || 5 || || || || || 1 || 5 || || || || || 1 || 5 || || || || || 1 || 5 || || || || || 1 || 1 || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || 16-tone || [[5L 11s]] || 4 || || || || 1 || 1 || 4 || || || || 1 || 1 || 4 || || || || 1 || 1 || 4 || || || || 1 || 1 || 4 || || || || 1 || 1 || 1 || | ||
|| 21-tone || [[5L 16s]] || 3 || || || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || | |||
|| 26-tone || [[5L 21s]] || 2 || || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || | |||
===7\31 octave - approx. 270.97¢ - Subminor Third=== | ===7\31 octave - approx. 270.97¢ - Subminor Third=== | ||
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====MOS Scales generated by 7\31:==== | ====MOS Scales generated by 7\31:==== | ||
||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
|| | || pentatonic || [[4L 1s]] || 7 || || || || || || || 7 || || || || || || || 7 || || || || || || || 7 || || || || || || || 3 || || || | ||
|| | || nonatonic (quasi-equal; Orwell[9]) || [[4L 5s]] || 4 || || || || 3 || || || 4 || || || || 3 || || || 4 || || || || 3 || || || 4 || || || || 3 || || || 3 || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || | || 13-tone (Orwell[13]) || [[9L 4s]] || 1 || 3 || || || 3 || || || 1 || 3 || || || 3 || || || 1 || 3 || || || 3 || || || 1 || 3 || || || 3 || || || 3 || || || | ||
|| 22-tone (Orwell[22]) || [[9L 13s]] || 1 || 1 || 2 || || 1 || 2 || || 1 || 1 || 2 || || 1 || 2 || || 1 || 1 || 2 || || 1 || 2 || || 1 || 1 || 2 || || 1 || 2 || || 1 || 2 || || | |||
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====MOS Scales generated by 8\31:==== | ====MOS Scales generated by 8\31:==== | ||
||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || tetratonic (quasi-equal) || [[3L 1s]] || 8 || || || || || || || || 8 || || || || || || || || 8 || || || || || || || || 7 || || || || || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || heptatonic || [[4L 3s]] || 1 || 7 || || || || || || || 1 || 7 || || || || || || || 1 || 7 || || || || || || || 7 || || || || || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || 11-tone || [[4L 7s]] || 1 || 1 || 6 || || || || || || 1 || 1 || 6 || || || || || || 1 || 1 || 6 || || || || || || 1 || 6 || || || || || || | ||
|| 15-tone || [[4L 11s]] || 1 || 1 || 1 || 5 || || || || || 1 || 1 || 1 || 5 || || || || || 1 || 1 || 1 || 5 || || || || || 1 || 1 || 5 || || || || || | |||
|| 19-tone || [[4L 15s]] || 1 || 1 || 1 || 1 || 4 || || || || 1 || 1 || 1 || 1 || 4 || || || || 1 || 1 || 1 || 1 || 4 || || || || 1 || 1 || 1 || 4 || || || || | |||
|| 23-tone || [[4L 19s]] || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 3 || || || | |||
|| 27-tone || [[4L 23s]] || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 2 || || | |||
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====MOS Scales generated by 9\31:==== | ====MOS Scales generated by 9\31:==== | ||
||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
|| | || tetratonic || [[3L 1s]] || 9 || || || || || || || || || 9 || || || || || || || || || 9 || || || || || || || || || 4 || || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || heptatonic (quasi-equal) || [[3L 4s]] || 5 || || || || || 4 || || || || 5 || || || || || 4 || || || || 5 || || || || || 4 || || || || 4 || || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || 10-tone || [[7L 3s]] || 1 || 4 || || || || 4 || || || || 1 || 4 || || || || 4 || || || || 1 || 4 || || || || 4 || || || || 4 || || || || | ||
|| 17-tone || [[7L 10s]] || 1 || 1 || 3 || || || 1 || 3 || || || 1 || 1 || 3 || || || 1 || 3 || || || 1 || 1 || 3 || || || 1 || 3 || || || 1 || 3 || || || | |||
|| 24-tone || [[7L 17s]] || 1 || 1 || 1 || 2 || || 1 || 1 || 2 || || 1 || 1 || 1 || 2 || || 1 || 1 || 2 || || 1 || 1 || 1 || 2 || || 1 || 1 || 2 || || 1 || 1 || 2 || || | |||
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====MOS Scales generated by 10\31:==== | ====MOS Scales generated by 10\31:==== | ||
||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||~ # of tones ||~ MOS class ||~ 0 ||~ 1 ||~ 2 ||~ 3 ||~ 4 ||~ 5 ||~ 6 ||~ 7 ||~ 8 ||~ 9 ||~ 10 ||~ 11 ||~ 12 ||~ 13 ||~ 14 ||~ 15 ||~ 16 ||~ 17 ||~ 18 ||~ 19 ||~ 20 ||~ 21 ||~ 22 ||~ 23 ||~ 24 ||~ 25 ||~ 26 ||~ 27 ||~ 28 ||~ 29 ||~ 30 || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || tritonic (quasi-equal) || [[1L 2s]] || 10 || || || || || || || || || || 10 || || || || || || || || || || 11 || || || || || || || || || || || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || tetratonic || [[3L 1s]] || 10 || || || || || || || || || || 10 || || || || || || || || || || 10 || || || || || || || || || || 1 || | ||
|| || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || || | || heptatonic || [[3L 4s]] || 9 || || || || || || || || || 1 || 9 || || || || || || || || || 1 || 9 || || || || || || || || || 1 || 1 || | ||
|| 10-tone || [[3L 7s]] || 8 || || || || || || || || 1 || 1 || 8 || || || || || || || || 1 || 1 || 8 || || || || || || || || 1 || 1 || 1 || | |||
|| 13-tone || [[3L 10s]] || 7 || || || || || || || 1 || 1 || 1 || 7 || || || || || || || 1 || 1 || 1 || 7 || || || || || || || 1 || 1 || 1 || 1 || | |||
|| 16-tone || [[3L 13s]] || 6 || || || || || || 1 || 1 || 1 || 1 || 6 || || || || || || 1 || 1 || 1 || 1 || 6 || || || || || || 1 || 1 || 1 || 1 || 1 || | |||
|| 19-tone || [[3L 16s]] || 5 || || || || || 1 || 1 || 1 || 1 || 1 || 5 || || || || || 1 || 1 || 1 || 1 || 1 || 5 || || || || || 1 || 1 || 1 || 1 || 1 || 1 || | |||
|| 22-tone || [[3L 19s]] || 4 || || || || 1 || 1 || 1 || 1 || 1 || 1 || 4 || || || || 1 || 1 || 1 || 1 || 1 || 1 || 4 || || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || | |||
|| 25-tone || [[3L 22s]] || 3 || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 3 || || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || | |||
|| 28-tone || [[3L 25s]] || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 2 || || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || 1 || | |||
===11\31 octave - approx. 425.806¢ - Supermajor Third=== | ===11\31 octave - approx. 425.806¢ - Supermajor Third=== | ||
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<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>31edo</title></head><body><!-- ws:start:WikiTextTocRule:92:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Music in 31-edo">Music in 31-edo</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> | <a href="#Practical Theory / Books">Practical Theory / Books</a><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Other Articles">Other Articles</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | <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>31edo</title></head><body><!-- ws:start:WikiTextTocRule:92:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:92 --><!-- ws:start:WikiTextTocRule:93: --><a href="#Intervals">Intervals</a><!-- ws:end:WikiTextTocRule:93 --><!-- ws:start:WikiTextTocRule:94: --><!-- ws:end:WikiTextTocRule:94 --><!-- ws:start:WikiTextTocRule:95: --><!-- ws:end:WikiTextTocRule:95 --><!-- ws:start:WikiTextTocRule:96: --><!-- ws:end:WikiTextTocRule:96 --><!-- ws:start:WikiTextTocRule:97: --><!-- ws:end:WikiTextTocRule:97 --><!-- ws:start:WikiTextTocRule:98: --><!-- ws:end:WikiTextTocRule:98 --><!-- ws:start:WikiTextTocRule:99: --><!-- ws:end:WikiTextTocRule:99 --><!-- ws:start:WikiTextTocRule:100: --><!-- ws:end:WikiTextTocRule:100 --><!-- ws:start:WikiTextTocRule:101: --><!-- ws:end:WikiTextTocRule:101 --><!-- ws:start:WikiTextTocRule:102: --><!-- ws:end:WikiTextTocRule:102 --><!-- ws:start:WikiTextTocRule:103: --><!-- ws:end:WikiTextTocRule:103 --><!-- ws:start:WikiTextTocRule:104: --><!-- ws:end:WikiTextTocRule:104 --><!-- ws:start:WikiTextTocRule:105: --><!-- ws:end:WikiTextTocRule:105 --><!-- ws:start:WikiTextTocRule:106: --><!-- ws:end:WikiTextTocRule:106 --><!-- ws:start:WikiTextTocRule:107: --><!-- ws:end:WikiTextTocRule:107 --><!-- ws:start:WikiTextTocRule:108: --><!-- ws:end:WikiTextTocRule:108 --><!-- ws:start:WikiTextTocRule:109: --><!-- ws:end:WikiTextTocRule:109 --><!-- ws:start:WikiTextTocRule:110: --><!-- ws:end:WikiTextTocRule:110 --><!-- ws:start:WikiTextTocRule:111: --><!-- ws:end:WikiTextTocRule:111 --><!-- ws:start:WikiTextTocRule:112: --><!-- ws:end:WikiTextTocRule:112 --><!-- ws:start:WikiTextTocRule:113: --><!-- ws:end:WikiTextTocRule:113 --><!-- ws:start:WikiTextTocRule:114: --><!-- ws:end:WikiTextTocRule:114 --><!-- ws:start:WikiTextTocRule:115: --><!-- ws:end:WikiTextTocRule:115 --><!-- ws:start:WikiTextTocRule:116: --><!-- ws:end:WikiTextTocRule:116 --><!-- ws:start:WikiTextTocRule:117: --><!-- ws:end:WikiTextTocRule:117 --><!-- ws:start:WikiTextTocRule:118: --><!-- ws:end:WikiTextTocRule:118 --><!-- ws:start:WikiTextTocRule:119: --><!-- ws:end:WikiTextTocRule:119 --><!-- ws:start:WikiTextTocRule:120: --><!-- ws:end:WikiTextTocRule:120 --><!-- ws:start:WikiTextTocRule:121: --><!-- ws:end:WikiTextTocRule:121 --><!-- ws:start:WikiTextTocRule:122: --><!-- ws:end:WikiTextTocRule:122 --><!-- ws:start:WikiTextTocRule:123: --><!-- ws:end:WikiTextTocRule:123 --><!-- ws:start:WikiTextTocRule:124: --><!-- ws:end:WikiTextTocRule:124 --><!-- ws:start:WikiTextTocRule:125: --><!-- ws:end:WikiTextTocRule:125 --><!-- ws:start:WikiTextTocRule:126: --><!-- ws:end:WikiTextTocRule:126 --><!-- ws:start:WikiTextTocRule:127: --><!-- ws:end:WikiTextTocRule:127 --><!-- ws:start:WikiTextTocRule:128: --><!-- ws:end:WikiTextTocRule:128 --><!-- ws:start:WikiTextTocRule:129: --><!-- ws:end:WikiTextTocRule:129 --><!-- ws:start:WikiTextTocRule:130: --><!-- ws:end:WikiTextTocRule:130 --><!-- ws:start:WikiTextTocRule:131: --><!-- ws:end:WikiTextTocRule:131 --><!-- ws:start:WikiTextTocRule:132: --><!-- ws:end:WikiTextTocRule:132 --><!-- ws:start:WikiTextTocRule:133: --> | <a href="#Modes">Modes</a><!-- ws:end:WikiTextTocRule:133 --><!-- ws:start:WikiTextTocRule:134: --><!-- ws:end:WikiTextTocRule:134 --><!-- ws:start:WikiTextTocRule:135: --> | <a href="#Music in 31-edo">Music in 31-edo</a><!-- ws:end:WikiTextTocRule:135 --><!-- ws:start:WikiTextTocRule:136: --><!-- ws:end:WikiTextTocRule:136 --><!-- ws:start:WikiTextTocRule:137: --> | <a href="#Practical Theory / Books">Practical Theory / Books</a><!-- ws:end:WikiTextTocRule:137 --><!-- ws:start:WikiTextTocRule:138: --> | <a href="#Other Articles">Other Articles</a><!-- ws:end:WikiTextTocRule:138 --><!-- ws:start:WikiTextTocRule:139: --> | ||
<!-- ws:end:WikiTextTocRule:139 --><hr /> | <!-- ws:end:WikiTextTocRule:139 --><hr /> | ||
<em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by <a class="wiki_link" href="/Adriaan%20Fokker">Adriaan Fokker</a>. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. 31's perfect fifth is flat of the just interval 3:2 (over five cents), as befits a tuning supporting meantone, but the major third is less than a cent sharp (of just 5:4). 31's approximation of 7:4, a cent flat, is also very close to just. Because of these near-just values 31-et is relatively quite accurate and is in fact the sixth Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule: | <em>Thirty-one tone equal temperament</em>, also called <em>31-tET</em>, <em>31-EDO</em>, <em>31-et</em>, or <em>tricesimoprimal meantone temperament</em>, is the scale derived by dividing the octave into 31 <a class="wiki_link" href="/equal">equally</a> large steps. The term 'Tricesimoprimal' was first used by <a class="wiki_link" href="/Adriaan%20Fokker">Adriaan Fokker</a>. Each step is equivalent to a frequency ratio of the 31st root of 2, or 38.71 <a class="wiki_link" href="/cents">cents</a>. 31's perfect fifth is flat of the just interval 3:2 (over five cents), as befits a tuning supporting meantone, but the major third is less than a cent sharp (of just 5:4). 31's approximation of 7:4, a cent flat, is also very close to just. Because of these near-just values 31-et is relatively quite accurate and is in fact the sixth Zeta function integral tuning, <!-- ws:start:WikiTextUrlRule:8457:http://www.research.att.com/~njas/sequences/A117538 --><a class="wiki_link_ext" href="http://www.research.att.com/~njas/sequences/A117538" rel="nofollow">http://www.research.att.com/~njas/sequences/A117538</a><!-- ws:end:WikiTextUrlRule:8457 -->. Many 7-limit JI scales are well-approximated in 31 (with tempering, of course). For JI that uses primes 3 and 7, but no 5, try <a class="wiki_link" href="/36edo">36edo</a>.<br /> | ||
<br /> | <br /> | ||
For more encyclopedic info, see <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/31_equal_temperament" rel="nofollow">Wikipedia's article</a>.<br /> | For more encyclopedic info, see <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/31_equal_temperament" rel="nofollow">Wikipedia's article</a>.<br /> | ||
| Line 1,487: | Line 1,503: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>pentatonic (quasi-equal)<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/1L%204s">1L 4s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,503: | Line 1,519: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,515: | Line 1,531: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,527: | Line 1,543: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,539: | Line 1,555: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,555: | Line 1,571: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>hexatonic<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/5L%201s">5L 1s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,571: | Line 1,587: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,583: | Line 1,599: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,595: | Line 1,611: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,607: | Line 1,623: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,619: | Line 1,635: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>11-tone<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/5L%206s">5L 6s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,637: | Line 1,653: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,661: | Line 1,677: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,673: | Line 1,689: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,685: | Line 1,701: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>16-tone<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/5L%2011s">5L 11s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,703: | Line 1,719: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,715: | Line 1,731: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,727: | Line 1,743: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,739: | Line 1,755: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | |||
<td>4<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,748: | Line 1,766: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>21-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/5L%2016s">5L 16s</a><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,757: | Line 1,797: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
< | <td>1<br /> | ||
</td> | |||
</ | <td>1<br /> | ||
< | </td> | ||
</ | <td>1<br /> | ||
< | </td> | ||
</ | <td>3<br /> | ||
< | </td> | ||
<td><br /> | |||
</td> | |||
</ | <td><br /> | ||
< | </td> | ||
</ | <td>1<br /> | ||
< | </td> | ||
</ | <td>1<br /> | ||
< | </td> | ||
</ | <td>1<br /> | ||
< | </td> | ||
</ | <td>3<br /> | ||
< | </td> | ||
</ | <td><br /> | ||
< | </td> | ||
</ | <td><br /> | ||
< | </td> | ||
</ | <td>1<br /> | ||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td>26-tone<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/5L%2021s">5L 21s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>1<br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
< | </tr> | ||
</ | </table> | ||
< | |||
</ | <br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Intervals--7\31 octave - approx. 270.97¢ - Subminor Third"></a><!-- ws:end:WikiTextHeadingRule:24 -->7\31 octave - approx. 270.97¢ - Subminor Third</h3> | ||
</ | Exactly one half of a superfourth (11:8 approximation). In 7-limit tonal music, 7\31 stands in for 7:6 (266.87¢). A generator for Orwell temperament (but not as good as 12\53 or 19/84). Generates <a class="wiki_link" href="/Semicomma%20family">orwell temperament</a>.<br /> | ||
< | <!-- ws:start:WikiTextHeadingRule:26:&lt;h4&gt; --><h4 id="toc13"><!-- ws:end:WikiTextHeadingRule:26 --> </h4> | ||
</ | <!-- ws:start:WikiTextHeadingRule:28:&lt;h4&gt; --><h4 id="toc14"><a name="Intervals--7\31 octave - approx. 270.97¢ - Subminor Third-MOS Scales generated by 7\31:"></a><!-- ws:end:WikiTextHeadingRule:28 -->MOS Scales generated by 7\31:</h4> | ||
< | |||
</ | |||
< | <table class="wiki_table"> | ||
</ | <tr> | ||
< | <th><ol><li>of tones</li></ol></th> | ||
</ | <th>MOS class<br /> | ||
< | </th> | ||
</ | <th>0<br /> | ||
< | </th> | ||
</ | <th>1<br /> | ||
< | </th> | ||
</ | <th>2<br /> | ||
< | </th> | ||
</ | <th>3<br /> | ||
< | </th> | ||
</ | <th>4<br /> | ||
< | </th> | ||
</ | <th>5<br /> | ||
< | </th> | ||
</ | <th>6<br /> | ||
< | </th> | ||
</ | <th>7<br /> | ||
< | </th> | ||
</ | <th>8<br /> | ||
< | </th> | ||
</ | <th>9<br /> | ||
< | </th> | ||
</ | <th>10<br /> | ||
< | </th> | ||
</ | <th>11<br /> | ||
<td><br /> | </th> | ||
<th>12<br /> | |||
</th> | |||
<th>13<br /> | |||
</th> | |||
<th>14<br /> | |||
</th> | |||
<th>15<br /> | |||
</th> | |||
<th>16<br /> | |||
</th> | |||
<th>17<br /> | |||
</th> | |||
<th>18<br /> | |||
</th> | |||
<th>19<br /> | |||
</th> | |||
<th>20<br /> | |||
</th> | |||
<th>21<br /> | |||
</th> | |||
<th>22<br /> | |||
</th> | |||
<th>23<br /> | |||
</th> | |||
<th>24<br /> | |||
</th> | |||
<th>25<br /> | |||
</th> | |||
<th>26<br /> | |||
</th> | |||
<th>27<br /> | |||
</th> | |||
<th>28<br /> | |||
</th> | |||
<th>29<br /> | |||
</th> | |||
<th>30<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>pentatonic<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/4L%201s">4L 1s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,968: | Line 2,006: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 1,984: | Line 2,020: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>7<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 1,993: | Line 2,029: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,005: | Line 2,047: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td>nonatonic (quasi-equal; Orwell[9])<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/4L%205s">4L 5s</a><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,015: | Line 2,067: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>4<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,025: | Line 2,081: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>4<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,039: | Line 2,123: | ||
</td> | </td> | ||
</tr> | </tr> | ||
< | <tr> | ||
<td>13-tone (Orwell[13])<br /> | |||
< | </td> | ||
<br /> | <td><a class="wiki_link" href="/9L%204s">9L 4s</a><br /> | ||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
< | <td>3<br /> | ||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</ | </td> | ||
< | <td>1<br /> | ||
</td> | |||
<td>3<br /> | |||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>3<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,128: | Line 2,184: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>3<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,134: | Line 2,190: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td>22-tone (Orwell[22])<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/9L%2013s">9L 13s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td>2<br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Intervals--8\31 octave - approx. 309.68¢ - Minor Third"></a><!-- ws:end:WikiTextHeadingRule:30 -->8\31 octave - approx. 309.68¢ - Minor Third</h3> | |||
A minor third, closer to the just 6:5 (315.64¢) than 12-edo. Exactly twice a neutral second, four times a minor semitone, and half of a large tritone. Generates <a class="wiki_link" href="/Starling%20temperaments">myna temperament</a>.<br /> | |||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h4&gt; --><h4 id="toc16"><!-- ws:end:WikiTextHeadingRule:32 --> </h4> | |||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h4&gt; --><h4 id="toc17"><a name="Intervals--8\31 octave - approx. 309.68¢ - Minor Third-MOS Scales generated by 8\31:"></a><!-- ws:end:WikiTextHeadingRule:34 -->MOS Scales generated by 8\31:</h4> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th><ol><li>of tones</li></ol></th> | |||
<th>MOS class<br /> | |||
</th> | |||
<th>0<br /> | |||
</th> | |||
<th>1<br /> | |||
</th> | |||
<th>2<br /> | |||
</th> | |||
<th>3<br /> | |||
</th> | |||
<th>4<br /> | |||
</th> | |||
<th>5<br /> | |||
</th> | |||
<th>6<br /> | |||
</th> | |||
<th>7<br /> | |||
</th> | |||
<th>8<br /> | |||
</th> | |||
<th>9<br /> | |||
</th> | |||
<th>10<br /> | |||
</th> | |||
<th>11<br /> | |||
</th> | |||
<th>12<br /> | |||
</th> | |||
<th>13<br /> | |||
</th> | |||
<th>14<br /> | |||
</th> | |||
<th>15<br /> | |||
</th> | |||
<th>16<br /> | |||
</th> | |||
<th>17<br /> | |||
</th> | |||
<th>18<br /> | |||
</th> | |||
<th>19<br /> | |||
</th> | |||
<th>20<br /> | |||
</th> | |||
<th>21<br /> | |||
</th> | |||
<th>22<br /> | |||
</th> | |||
<th>23<br /> | |||
</th> | |||
<th>24<br /> | |||
</th> | |||
<th>25<br /> | |||
</th> | |||
<th>26<br /> | |||
</th> | |||
<th>27<br /> | |||
</th> | |||
<th>28<br /> | |||
</th> | |||
<th>29<br /> | |||
</th> | |||
<th>30<br /> | |||
</th> | |||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td>tetratonic (quasi-equal)<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%201s">3L 1s</a><br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 2,267: | Line 2,357: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>8<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,281: | Line 2,373: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>8<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,295: | Line 2,389: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>7<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,307: | Line 2,403: | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
</tr> | |||
<tr> | |||
<td>heptatonic<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/4L%203s">4L 3s</a><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,320: | Line 2,426: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
< | </td> | ||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>7<br /> | |||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>7<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | </tr> | ||
</ | <tr> | ||
< | <td>11-tone<br /> | ||
</ | </td> | ||
< | <td><a class="wiki_link" href="/4L%207s">4L 7s</a><br /> | ||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
< | |||
</ | |||
< | |||
</ | |||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,418: | Line 2,494: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,434: | Line 2,510: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,450: | Line 2,526: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td> | <td>6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,468: | Line 2,542: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>15-tone<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/4L%2011s">4L 11s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,488: | Line 2,562: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,504: | Line 2,578: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,520: | Line 2,594: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,536: | Line 2,610: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td>19-tone<br /> | ||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/4L%2015s">4L 15s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,556: | Line 2,630: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,572: | Line 2,646: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,588: | Line 2,662: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,603: | Line 2,677: | ||
</td> | </td> | ||
</tr> | </tr> | ||
< | <tr> | ||
<td>23-tone<br /> | |||
< | </td> | ||
<br /> | <td><a class="wiki_link" href="/4L%2019s">4L 19s</a><br /> | ||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
< | </td> | ||
<td>1<br /> | |||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | </td> | ||
< | <td>3<br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td><br /> | ||
</ | </td> | ||
< | <td>1<br /> | ||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
< | |||
</ | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>3<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,696: | Line 2,744: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td>27-tone<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/4L%2023s">4L 23s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>1<br /> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>1<br /> | ||
</td> | </td> | ||
<td><br /> | <td>2<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
< | </tr> | ||
</ | </table> | ||
< | |||
</ | <br /> | ||
< | <br /> | ||
</ | <!-- ws:start:WikiTextHeadingRule:36:&lt;h3&gt; --><h3 id="toc18"><a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third"></a><!-- ws:end:WikiTextHeadingRule:36 -->9\31 octave - approx. 348.39¢ - Neutral Third</h3> | ||
< | A neutral 3rd, practically equivalent to 11:9 (347.41¢). Exactly half a perfect fifth (making it a suitable generator for neutral third scales such as <a class="wiki_link" href="/3L%204s">3L 4s</a>). Is also thrice a major semitone. Generates <a class="wiki_link" href="/Meantone%20family">mohajira temperament</a>.<br /> | ||
</ | <!-- ws:start:WikiTextHeadingRule:38:&lt;h4&gt; --><h4 id="toc19"><!-- ws:end:WikiTextHeadingRule:38 --> </h4> | ||
< | <!-- ws:start:WikiTextHeadingRule:40:&lt;h4&gt; --><h4 id="toc20"><a name="Intervals--9\31 octave - approx. 348.39¢ - Neutral Third-MOS Scales generated by 9\31:"></a><!-- ws:end:WikiTextHeadingRule:40 -->MOS Scales generated by 9\31:</h4> | ||
</ | |||
< | |||
</ | <table class="wiki_table"> | ||
< | <tr> | ||
</ | <th><ol><li>of tones</li></ol></th> | ||
< | <th>MOS class<br /> | ||
</ | </th> | ||
< | <th>0<br /> | ||
</ | </th> | ||
< | <th>1<br /> | ||
</ | </th> | ||
< | <th>2<br /> | ||
</ | </th> | ||
< | <th>3<br /> | ||
</ | </th> | ||
< | <th>4<br /> | ||
</ | </th> | ||
< | <th>5<br /> | ||
</ | </th> | ||
< | <th>6<br /> | ||
</ | </th> | ||
< | <th>7<br /> | ||
</ | </th> | ||
< | <th>8<br /> | ||
</ | </th> | ||
< | <th>9<br /> | ||
</ | </th> | ||
< | <th>10<br /> | ||
</ | </th> | ||
< | <th>11<br /> | ||
</ | </th> | ||
< | <th>12<br /> | ||
</ | </th> | ||
< | <th>13<br /> | ||
</ | </th> | ||
<td><br /> | <th>14<br /> | ||
</th> | |||
<th>15<br /> | |||
</th> | |||
<th>16<br /> | |||
</th> | |||
<th>17<br /> | |||
</th> | |||
<th>18<br /> | |||
</th> | |||
<th>19<br /> | |||
</th> | |||
<th>20<br /> | |||
</th> | |||
<th>21<br /> | |||
</th> | |||
<th>22<br /> | |||
</th> | |||
<th>23<br /> | |||
</th> | |||
<th>24<br /> | |||
</th> | |||
<th>25<br /> | |||
</th> | |||
<th>26<br /> | |||
</th> | |||
<th>27<br /> | |||
</th> | |||
<th>28<br /> | |||
</th> | |||
<th>29<br /> | |||
</th> | |||
<th>30<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>tetratonic<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/3L%201s">3L 1s</a><br /> | ||
</td> | </td> | ||
<td><br /> | <td>9<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
| Line 2,832: | Line 2,914: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>9<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,850: | Line 2,932: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>9<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,868: | Line 2,950: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td>4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
| Line 2,876: | Line 2,958: | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | </tr> | ||
<tr> | |||
<td>heptatonic (quasi-equal)<br /> | |||
</td> | </td> | ||
<td><br /> | <td><a class="wiki_link" href="/3L%204s">3L 4s</a><br /> | ||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/7L%203s">7L 3s</a><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/7L%2010s">7L 10s</a><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>24-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/7L%2017s">7L 17s</a><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:42:&lt;h3&gt; --><h3 id="toc21"><a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third"></a><!-- ws:end:WikiTextHeadingRule:42 -->10\31 octave - approx. 387.10¢ - Major Third</h3> | |||
A near-just major 3rd (compare with 5:4 = 386.31¢). Has led to the characterization of 31-edo as &quot;smooth&quot;. Generates <a class="wiki_link" href="/Wuerschmidt%20family">wurshmidt/worshmidt temperaments</a>.<br /> | |||
<!-- ws:start:WikiTextHeadingRule:44:&lt;h4&gt; --><h4 id="toc22"><!-- ws:end:WikiTextHeadingRule:44 --> </h4> | |||
<!-- ws:start:WikiTextHeadingRule:46:&lt;h4&gt; --><h4 id="toc23"><a name="Intervals--10\31 octave - approx. 387.10¢ - Major Third-MOS Scales generated by 10\31:"></a><!-- ws:end:WikiTextHeadingRule:46 -->MOS Scales generated by 10\31:</h4> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th><ol><li>of tones</li></ol></th> | |||
<th>MOS class<br /> | |||
</th> | |||
<th>0<br /> | |||
</th> | |||
<th>1<br /> | |||
</th> | |||
<th>2<br /> | |||
</th> | |||
<th>3<br /> | |||
</th> | |||
<th>4<br /> | |||
</th> | |||
<th>5<br /> | |||
</th> | |||
<th>6<br /> | |||
</th> | |||
<th>7<br /> | |||
</th> | |||
<th>8<br /> | |||
</th> | |||
<th>9<br /> | |||
</th> | |||
<th>10<br /> | |||
</th> | |||
<th>11<br /> | |||
</th> | |||
<th>12<br /> | |||
</th> | |||
<th>13<br /> | |||
</th> | |||
<th>14<br /> | |||
</th> | |||
<th>15<br /> | |||
</th> | |||
<th>16<br /> | |||
</th> | |||
<th>17<br /> | |||
</th> | |||
<th>18<br /> | |||
</th> | |||
<th>19<br /> | |||
</th> | |||
<th>20<br /> | |||
</th> | |||
<th>21<br /> | |||
</th> | |||
<th>22<br /> | |||
</th> | |||
<th>23<br /> | |||
</th> | |||
<th>24<br /> | |||
</th> | |||
<th>25<br /> | |||
</th> | |||
<th>26<br /> | |||
</th> | |||
<th>27<br /> | |||
</th> | |||
<th>28<br /> | |||
</th> | |||
<th>29<br /> | |||
</th> | |||
<th>30<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<td>tritonic (quasi-equal)<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/1L%202s">1L 2s</a><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>11<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>tetratonic<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%201s">3L 1s</a><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>10<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>heptatonic<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%204s">3L 4s</a><br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%207s">3L 7s</a><br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>8<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2010s">3L 10s</a><br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2013s">3L 13s</a><br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2016s">3L 16s</a><br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>5<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>22-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2019s">3L 19s</a><br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>25-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2022s">3L 22s</a><br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>28-tone<br /> | |||
</td> | |||
<td><a class="wiki_link" href="/3L%2025s">3L 25s</a><br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
| Line 4,834: | Line 5,938: | ||
<!-- ws:start:WikiTextHeadingRule:88:&lt;h1&gt; --><h1 id="toc44"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:88 -->Practical Theory / Books</h1> | <!-- ws:start:WikiTextHeadingRule:88:&lt;h1&gt; --><h1 id="toc44"><a name="Practical Theory / Books"></a><!-- ws:end:WikiTextHeadingRule:88 -->Practical Theory / Books</h1> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextRemoteImageRule: | <!-- ws:start:WikiTextRemoteImageRule:5724:&lt;a href=&quot;http://www.ronsword.com/books.html&quot; target=&quot;_blank&quot; rel=&quot;nofollow&quot;&gt;&lt;img src=&quot;http://ronsword.com/images/TSG_sm.jpg&quot; alt=&quot;&quot; title=&quot;&quot; style=&quot;height: 116px; width: 87px;&quot; /&gt;&lt;/a&gt; --><a href="http://www.ronsword.com/books.html" target="_blank" rel="nofollow"><img src="http://ronsword.com/images/TSG_sm.jpg" alt="external image TSG_sm.jpg" title="external image TSG_sm.jpg" style="height: 116px; width: 87px;" /></a><!-- ws:end:WikiTextRemoteImageRule:5724 --><a class="wiki_link_ext" href="http://www.ronsword.com/books.html" rel="nofollow" target="_blank">Sword, Ronald. &quot;Tricesimoprimal Scales for Guitar.&quot; IAAA Press, UK-USA. First Ed: March 2009.</a> - A comprehensive approach to 31-EDO and all the families associated for Guitar. Features over 300 scale charts / scale examples.<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:90:&lt;h1&gt; --><h1 id="toc45"><a name="Other Articles"></a><!-- ws:end:WikiTextHeadingRule:90 -->Other Articles</h1> | <!-- ws:start:WikiTextHeadingRule:90:&lt;h1&gt; --><h1 id="toc45"><a name="Other Articles"></a><!-- ws:end:WikiTextHeadingRule:90 -->Other Articles</h1> | ||
<ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/english/index.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span></li></ul></body></html></pre></div> | <ul><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/english/index.html" rel="nofollow">de Beer, Anton, ''The Development of 31-tone Music</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/fokkerorg.html" rel="nofollow">Fokker, Adriaan Daniël, ''Equal Temperament and the Thirty-one-keyed organ</a></span></li><li>Fokker, A.D., &quot;New Music with 31 Notes&quot; translated by Leigh Gerdine</li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/rap31.html" rel="nofollow">Rapoport, Paul, ''About 31-tone Equal Temperament</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/terp31.html" rel="nofollow">Terpstra, Siemen, ''Toward a Theory of Meantone (and 31-et) Harmony''</a></span></li><li><span class="wiki_link_ext"><a class="wiki_link_ext" href="http://tonalsoft.com/enc/number/31edo.aspx" rel="nofollow">Tonalsoft Encyclopedia article</a></span></li></ul></body></html></pre></div> | ||