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| Line 1: |
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| <h2>IMPORTED REVISION FROM WIKISPACES</h2>
| | This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones. |
| 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>2015-11-11 15:11:03 UTC</tt>.<br>
| |
| : The original revision id was <tt>566086773</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, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
| |
| || || || Cents ||
| |
| || 0/1 || || 0 ||
| |
| || 1/17 || || 70.588 ||
| |
| || || 4/67 || 71.641 ||
| |
| || || 3/50 || 72 ||
| |
| || || 2/33 || 72.727 ||
| |
| || || 3/49 || 73.469 ||
| |
| || || 4/65 || 73.846 ||
| |
| || || 5/81 || 74.074 ||
| |
| || 1/16 || || 75 ||
| |
| || || 3/47 || 76.596 ||
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| || || 2/31 || 77.419 ||
| |
| || || 3/46 || 78.261 ||
| |
| || || 4/61 || 78.6885 ||
| |
| || || 5/76 || 78.947 ||
| |
| || || 6/91 || 79.121 ||
| |
| || || || 1200/(12+pi) ||
| |
| || 1/15 || || 80 ||
| |
| || || || 1200/(12+e) ||
| |
| || || 3/44 || 81.818 ||
| |
| || || || 1200/(13+phi) ||
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| || || 2/29 || 82.759 ||
| |
| || || 3/43 || 83.721 ||
| |
| || || 4/57 || 84.2105 ||
| |
| || 1/14 || || 85.714 ||
| |
| || || 4/55 || 86.364 ||
| |
| || || || 1200/(12+sqrt(3)) ||
| |
| || || 3/41 || 87.805 ||
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| || || || 1200/(12+phi) ||
| |
| || || 5/68 || 88.235 ||
| |
| || || || 1200/(12+pi/2) ||
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| || 2/27 || || 88.889 ||
| |
| || || 5/67 || 89.552 ||
| |
| || 3/40 || || 90 ||
| |
| || 4/53 || || 90.556 ||
| |
| || 1/13 || || 92.308 ||</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 12s</title></head><body>This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.<br />
| |
|
| |
|
| | | {| class="wikitable" |
| <table class="wiki_table">
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | Cents |
| <td><br />
| | |- |
| </td>
| | | | 0/1 |
| <td>Cents<br />
| | | | |
| </td>
| | | | 0 |
| </tr>
| | |- |
| <tr>
| | | | 1/17 |
| <td>0/1<br />
| | | | |
| </td>
| | | | 70.588 |
| <td><br />
| | |- |
| </td>
| | | | |
| <td>0<br />
| | | | 4/67 |
| </td>
| | | | 71.641 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td>1/17<br />
| | | | 3/50 |
| </td>
| | | | 72 |
| <td><br />
| | |- |
| </td>
| | | | |
| <td>70.588<br />
| | | | 2/33 |
| </td>
| | | | 72.727 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 3/49 |
| </td>
| | | | 73.469 |
| <td>4/67<br />
| | |- |
| </td>
| | | | |
| <td>71.641<br />
| | | | 4/65 |
| </td>
| | | | 73.846 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 5/81 |
| </td>
| | | | 74.074 |
| <td>3/50<br />
| | |- |
| </td>
| | | | 1/16 |
| <td>72<br />
| | | | |
| </td>
| | | | 75 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 3/47 |
| </td>
| | | | 76.596 |
| <td>2/33<br />
| | |- |
| </td>
| | | | |
| <td>72.727<br />
| | | | 2/31 |
| </td>
| | | | 77.419 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 3/46 |
| </td>
| | | | 78.261 |
| <td>3/49<br />
| | |- |
| </td>
| | | | |
| <td>73.469<br />
| | | | 4/61 |
| </td>
| | | | 78.6885 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 5/76 |
| </td>
| | | | 78.947 |
| <td>4/65<br />
| | |- |
| </td>
| | | | |
| <td>73.846<br />
| | | | 6/91 |
| </td>
| | | | 79.121 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(12+pi) |
| <td>5/81<br />
| | |- |
| </td>
| | | | 1/15 |
| <td>74.074<br />
| | | | |
| </td>
| | | | 80 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td>1/16<br />
| | | | |
| </td>
| | | | 1200/(12+e) |
| <td><br />
| | |- |
| </td>
| | | | |
| <td>75<br />
| | | | 3/44 |
| </td>
| | | | 81.818 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(13+phi) |
| <td>3/47<br />
| | |- |
| </td>
| | | | |
| <td>76.596<br />
| | | | 2/29 |
| </td>
| | | | 82.759 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 3/43 |
| </td>
| | | | 83.721 |
| <td>2/31<br />
| | |- |
| </td>
| | | | |
| <td>77.419<br />
| | | | 4/57 |
| </td>
| | | | 84.2105 |
| </tr>
| | |- |
| <tr>
| | | | 1/14 |
| <td><br />
| | | | |
| </td>
| | | | 85.714 |
| <td>3/46<br />
| | |- |
| </td>
| | | | |
| <td>78.261<br />
| | | | 4/55 |
| </td>
| | | | 86.364 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(12+sqrt(3)) |
| <td>4/61<br />
| | |- |
| </td>
| | | | |
| <td>78.6885<br />
| | | | 3/41 |
| </td>
| | | | 87.805 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(12+phi) |
| <td>5/76<br />
| | |- |
| </td>
| | | | |
| <td>78.947<br />
| | | | 5/68 |
| </td>
| | | | 88.235 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | |
| </td>
| | | | 1200/(12+pi/2) |
| <td>6/91<br />
| | |- |
| </td>
| | | | 2/27 |
| <td>79.121<br />
| | | | |
| </td>
| | | | 88.889 |
| </tr>
| | |- |
| <tr>
| | | | |
| <td><br />
| | | | 5/67 |
| </td>
| | | | 89.552 |
| <td><br />
| | |- |
| </td>
| | | | 3/40 |
| <td>1200/(12+pi)<br />
| | | | |
| </td>
| | | | 90 |
| </tr>
| | |- |
| <tr>
| | | | 4/53 |
| <td>1/15<br />
| | | | |
| </td>
| | | | 90.556 |
| <td><br />
| | |- |
| </td>
| | | | 1/13 |
| <td>80<br />
| | | | |
| </td>
| | | | 92.308 |
| </tr>
| | |} |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(12+e)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3/44<br />
| |
| </td>
| |
| <td>81.818<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(13+phi)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>2/29<br />
| |
| </td>
| |
| <td>82.759<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3/43<br />
| |
| </td>
| |
| <td>83.721<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>4/57<br />
| |
| </td>
| |
| <td>84.2105<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1/14<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>85.714<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>4/55<br />
| |
| </td>
| |
| <td>86.364<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(12+sqrt(3))<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>3/41<br />
| |
| </td>
| |
| <td>87.805<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(12+phi)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5/68<br />
| |
| </td>
| |
| <td>88.235<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>1200/(12+pi/2)<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>2/27<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>88.889<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td><br />
| |
| </td>
| |
| <td>5/67<br />
| |
| </td>
| |
| <td>89.552<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>3/40<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>90<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>4/53<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>90.556<br />
| |
| </td>
| |
| </tr>
| |
| <tr>
| |
| <td>1/13<br />
| |
| </td>
| |
| <td><br />
| |
| </td>
| |
| <td>92.308<br />
| |
| </td>
| |
| </tr>
| |
| </table>
| |
| | |
| </body></html></pre></div>
| |
This MOS, the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.
|
|
|
Cents
|
| 0/1
|
|
0
|
| 1/17
|
|
70.588
|
|
|
4/67
|
71.641
|
|
|
3/50
|
72
|
|
|
2/33
|
72.727
|
|
|
3/49
|
73.469
|
|
|
4/65
|
73.846
|
|
|
5/81
|
74.074
|
| 1/16
|
|
75
|
|
|
3/47
|
76.596
|
|
|
2/31
|
77.419
|
|
|
3/46
|
78.261
|
|
|
4/61
|
78.6885
|
|
|
5/76
|
78.947
|
|
|
6/91
|
79.121
|
|
|
|
1200/(12+pi)
|
| 1/15
|
|
80
|
|
|
|
1200/(12+e)
|
|
|
3/44
|
81.818
|
|
|
|
1200/(13+phi)
|
|
|
2/29
|
82.759
|
|
|
3/43
|
83.721
|
|
|
4/57
|
84.2105
|
| 1/14
|
|
85.714
|
|
|
4/55
|
86.364
|
|
|
|
1200/(12+sqrt(3))
|
|
|
3/41
|
87.805
|
|
|
|
1200/(12+phi)
|
|
|
5/68
|
88.235
|
|
|
|
1200/(12+pi/2)
|
| 2/27
|
|
88.889
|
|
|
5/67
|
89.552
|
| 3/40
|
|
90
|
| 4/53
|
|
90.556
|
| 1/13
|
|
92.308
|