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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators). |
| This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
| |
| : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-11-09 11:49:39 UTC</tt>.<br>
| |
| : The original revision id was <tt>565733327</tt>.<br>
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| : The revision comment was: <tt></tt><br>
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| 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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| <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">This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
| |
| || 0/1 || || || || || 0 ||
| |
| || || || || || 1/15 || 80 ||
| |
| || || || || 1/14 || || 85.714 ||
| |
| || || || || || 2/27 || 88.889 ||
| |
| || || || || || || 1200/(10+pi) ||
| |
| || || || 1/13 || || || 92.308 ||
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| || || || || || || 1200/(10+e) ||
| |
| || || || || || 3/38 || 94.737 ||
| |
| || || || || || || 1200/(11+phi) ||
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| || || || || 2/25 || || 96 ||
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| || || || || || 3/37 || 97.297 ||
| |
| || || 1/12 || || || || 100 ||
| |
| || || || || || || 1200/(10+sqrt(3)) ||
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| || || || || || 4/47 || 102.128 ||
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| || || || || 3/35 || || 102.857 ||
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| || || || || || || 1200/(10+phi) ||
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| || || || || || 5/58 || 103.448 ||
| |
| || || || || || || 1200/(10+pi/2) ||
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| || || || 2/23 || || || 104.348 ||
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| || || || || || 5/57 || 105.263 ||
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| || || || || 3/34 || || 105.882 ||
| |
| || || || || || 4/45 || 106.667 ||
| |
| || 1/11 || || || || || 109.091 ||</pre></div>
| |
| <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>1L 10s</title></head><body>This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).<br />
| |
|
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|
| | | {| class="wikitable" |
| <table class="wiki_table">
| | |- |
| <tr>
| | | | 0/1 |
| <td>0/1<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 0 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>0<br />
| | | | 1/15 |
| </td>
| | | | 80 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1/14 |
| </td>
| | | | |
| <td><br />
| | | | 85.714 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>1/15<br />
| | | | |
| </td>
| | | | |
| <td>80<br />
| | | | 2/27 |
| </td>
| | | | 88.889 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1200/(10+pi) |
| </td>
| | |- |
| <td>1/14<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1/13 |
| </td>
| | | | |
| <td>85.714<br />
| | | | |
| </td>
| | | | 92.308 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1200/(10+e) |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>2/27<br />
| | | | |
| </td>
| | | | |
| <td>88.889<br />
| | | | 3/38 |
| </td>
| | | | 94.737 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1200/(11+phi) |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 2/25 |
| <td>1200/(10+pi)<br />
| | | | |
| </td>
| | | | 96 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 3/37 |
| <td>1/13<br />
| | | | 97.297 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | 1/12 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>92.308<br />
| | | | |
| </td>
| | | | 100 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 1200/(10+sqrt(3)) |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>1200/(10+e)<br />
| | | | 4/47 |
| </td>
| | | | 102.128 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 3/35 |
| </td>
| | | | |
| <td><br />
| | | | 102.857 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>3/38<br />
| | | | |
| </td>
| | | | |
| <td>94.737<br />
| | | | |
| </td>
| | | | 1200/(10+phi) |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 5/58 |
| <td><br />
| | | | 103.448 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>1200/(11+phi)<br />
| | | | |
| </td>
| | | | 1200/(10+pi/2) |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 2/23 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 104.348 |
| </td>
| | |- |
| <td>2/25<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>96<br />
| | | | 5/57 |
| </td>
| | | | 105.263 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 3/34 |
| </td>
| | | | |
| <td><br />
| | | | 105.882 |
| </td>
| | |- |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>3/37<br />
| | | | |
| </td>
| | | | |
| <td>97.297<br />
| | | | 4/45 |
| </td>
| | | | 106.667 |
| </tr>
| | |- |
| <tr>
| | | | 1/11 |
| <td><br />
| | | | |
| </td>
| | | | |
| <td>1/12<br />
| | | | |
| </td>
| | | | |
| <td><br />
| | | | 109.091 |
| </td>
| | |} |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>100<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(10+sqrt(3))<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/47<br />
| |
| </td>
| |
| <td>102.128<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/35<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>102.857<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(10+phi)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/58<br />
| |
| </td>
| |
| <td>103.448<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(10+pi/2)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>2/23<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>104.348<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>5/57<br />
| |
| </td>
| |
| <td>105.263<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>3/34<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>105.882<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>4/45<br />
| |
| </td>
| |
| <td>106.667<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1/11<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>109.091<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
This MOS, generated by any interval up to a diatonic semitone of 1/11edo (109.091 cents), achieves its simplest harmonic entropy minimum where two generators equal 9/8. The temperament which occupies this harmonic entropy minimum is called Ripple, but there are several lower (and more complex) harmonic entropy minima of note including (in descending order of generator height): Passion (6/5=+3 generators), Octacot (3/2=+8 generators), Nautilus (3/2=-6 generators) and Valentine (7/4=-3 generators).
| 0/1
|
|
|
|
|
0
|
|
|
|
|
|
1/15
|
80
|
|
|
|
|
1/14
|
|
85.714
|
|
|
|
|
|
2/27
|
88.889
|
|
|
|
|
|
|
1200/(10+pi)
|
|
|
|
1/13
|
|
|
92.308
|
|
|
|
|
|
|
1200/(10+e)
|
|
|
|
|
|
3/38
|
94.737
|
|
|
|
|
|
|
1200/(11+phi)
|
|
|
|
|
2/25
|
|
96
|
|
|
|
|
|
3/37
|
97.297
|
|
|
1/12
|
|
|
|
100
|
|
|
|
|
|
|
1200/(10+sqrt(3))
|
|
|
|
|
|
4/47
|
102.128
|
|
|
|
|
3/35
|
|
102.857
|
|
|
|
|
|
|
1200/(10+phi)
|
|
|
|
|
|
5/58
|
103.448
|
|
|
|
|
|
|
1200/(10+pi/2)
|
|
|
|
2/23
|
|
|
104.348
|
|
|
|
|
|
5/57
|
105.263
|
|
|
|
|
3/34
|
|
105.882
|
|
|
|
|
|
4/45
|
106.667
|
| 1/11
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|
|
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|
109.091
|