7L 2s: Difference between revisions
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Wikispaces>JosephRuhf **Imported revision 529863140 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 540661612 - 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:JosephRuhf|JosephRuhf]] and made on <tt> | : This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2015-02-11 16:15:09 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>540661612</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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Optional types of 'JI [[Blown Fifth]]' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169. | Optional types of 'JI [[Blown Fifth]]' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169. | ||
||||||~ Generator ||~ <span style="text-align: center;">**Generator size (cents)**</span> ||~ Pentachord steps ||~ Comments || | |||
||< 4\[[7edo|7]] | ||< 4\[[7edo|7]] ||< ||< ||< 685.714 ||< 1 1 1 0 ||< || | ||
||< 21\37 | ||< 21\37 ||< ||< ||< 681.081 ||< 5 5 5 1 ||< || | ||
||< 17\30 | ||< 17\30 ||< ||< ||< 680 ||< 4 4 4 1 ||< L/s = 4 || | ||
||< ||< 30\53 ||< ||< 679.245 ||< 7 7 7 2 ||< || | |||
|| 43\76 | || || 43\76 || || 678.947 || 10 10 10 3 || || | ||
|| || 56\99 | || || 56\99 || || 678.788 || 13 13 13 4 || || | ||
|| || 69\122 || || 678.6885 || 16 16 16 5 || || | |||
|| || 82\145 || || 678.621 || 19 19 19 6 || || | |||
|| || 95\168 || || 678.571 || 22 22 22 7 || || | |||
|| || 108\191 || || 678.534 || 25 25 25 8 || || | |||
||< ||< 121\214 ||< ||< 678.505 ||< 28 28 28 9 ||< 28;9 Superdiatonic 1/28-tone | |||
<span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span> || | |||
||< 13\23 | ||< ||< 134\237 ||< ||< 678.481 ||< 31 31 31 10 ||< HORNBOSTEL TEMPERAMENT | ||
L/s = 3 | <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> || | ||
||< ||< | ||< 13\23 ||< ||< ||< 678.261 ||< 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT | ||
L/s = 3 | |||
<span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> || | |||
||< ||< 126\223 ||< ||< 678.027 ||< 29 29 29 10 ||< HORNBOSTEL TEMPERAMENT | |||
<span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span> || | |||
||< ||< 113\200 ||< ||< 678 ||< 26 26 26 9 ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT | |||
<span style="font-size: 12.8000001907349px;">(Armodue 1/26-tone;</span> | |||
<span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')</span> || | <span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')</span> || | ||
||< ||< | ||< ||< 100\177 ||< ||< 677.966 ||< 23 23 23 8 ||< || | ||
||< ||< | ||< ||< 87\154 ||< ||< 677.922 ||< 20 20 20 7 ||< || | ||
||< | ||< ||< 74\131 ||< ||< 677.863 ||< 17 17 17 6 ||< Armodue-Hornbostel 1/17-tone | ||
<span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span> || | |||
||< ||< | ||< ||< 61\108 ||< ||< 677.778 ||< 14 14 14 5 ||< Armodue-Hornbostel 1/14-tone || | ||
||< ||< ||< 109\193 ||< 677.720 ||< 25 25 25 9 ||< Armodue-Hornbostel 1/25-tone || | |||
||< | ||< ||< 48\85 ||< ||< 677.647 ||< 11 11 11 4 ||< Armodue-<span style="font-size: 13px; line-height: 1.5;">Hornbostel 1/11-tone</span> | ||
<span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">(Optimum accuracy of Phi interval, the note '7')</span> || | |||
||< ||< | ||< ||< 35\62 ||< ||< 677.419 ||< 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || | ||
||< ||< 92\163 ||< ||< 677.301 ||< 21 21 21 8 ||< 21;8 Superdiatonic 1/21-tone || | |||
||< ||< | ||< ||< ||< ||< 677.2804 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span> ||< Split φ superdiatonic relation | ||
||< | (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..) || | ||
||< ||< | ||< ||< 57\101 ||< ||< 677.228 ||< 13 13 13 5 ||< 13;5 Superdiatonic 1/13-tone || | ||
||< ||< | ||< 22\39 ||< ||< ||< 676.923 ||< 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone | ||
<span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> || | |||
||< ||< | ||< ||< 75\133 ||< ||< 676.692 ||< 17 17 17 7 ||< 17;7 Superdiatonic 1/17-tone | ||
||< | <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span> || | ||
||< ||< ||< ||< | ||< ||< 53\94 ||< ||< 676.596 ||< 12 12 12 5 ||< || | ||
||< | ||< ||< 31\55 ||< ||< 676.364 ||< 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || | ||
||< ||< | ||< ||< 40\71 ||< ||< 676.056 ||< 9 9 9 4 ||< 9;4 Superdiatonic 1/9-tone || | ||
||< ||< | ||< ||< 49\87 ||< ||< 675.862 ||< 11 11 11 5 ||< 11;5 Superdiatonic 1/11-tone || | ||
||< ||< | ||< ||< 58\103 ||< ||< 675.728 ||< 13 13 13 6 ||< 13;6 Superdiatonic 1/13-tone || | ||
||< 9\16 ||< ||< ||< 675 ||< 2 2 2 1 ||< <span style="display: block; text-align: left;">**[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]**</span>ARMODUE ESADECAFONIA (or Goldsmith Temperament) || | |||
||< ||< 59\105 ||< ||< 674.286 ||< 13 13 13 7 ||< Armodue-Mávila 1/13-tone || | |||
||< ||< 50\89 ||< ||< 674.157 ||< 11 11 11 6 ||< Armodue-Mávila 1/11-tone || | |||
||< ||< 41\73 ||< ||< 673.973 ||< 9 9 9 5 ||< Armodue-Mávila 1/9-tone | |||
<span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span> || | |||
||< ||< 32\57 ||< ||< 673.684 ||< 7 7 7 4 ||< Armodue-Mávila 1/7-tone | |||
<span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the </span><span style="font-size: 12.8000001907349px;">[[xenharmonic/7_4|7/4]]</span><span style="font-size: 12.8000001907349px;"> interval, the note '8')</span> || | |||
||< ||< 55\98 ||< ||< 673.469 ||< 12 12 12 7 ||< || | |||
||< ||< 78\139 ||< ||< 673.381 ||< 17 17 17 10 ||< Armodue-Mávila 1/17-tone || | |||
||< ||< 101\180 ||< ||< 673.333 ||< 22 22 22 13 ||< || | |||
||< 23\41 ||< ||< ||< 673.171 ||< 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || | |||
||< ||< 60\107 ||< ||< 672.897 ||< 13 13 13 8 ||< 13;8 Golden Mávila 1/13-tone || | |||
||< ||< ||< ||< 672.8503 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span> ||< GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span> || | |||
||< ||< ||< 97\173 ||< 672.832 ||< 21 21 21 13 ||< 21;13 Golden Mávila 1/21-tone | |||
<span style="font-size: 12.8000001907349px;">(ratio between large and small steps is Phi, and Phi is the step 120\173)</span> || | |||
||< ||< 37\66 ||< ||< 672.727 ||< 8 8 8 5 ||< 8;5 Golden Mávila 1/8-tone || | |||
||< ||< | ||< ||< 51\91 ||< ||< 672.527 ||< 11 11 11 7 ||< 11;7 Superdiatonic 1/11-tone || | ||
||< 14\25 | ||< ||< ||< 116\207 ||< 672.464 ||< 25 25 25 16 ||< 25;16 Superdiatonic 1/25-tone || | ||
||< ||< 65\116 ||< ||< 672.414 ||< 14 14 14 9 ||< 14;9 Superdiatonic 1/14-tone || | |||
||< ||< 79\141 ||< ||< 672.340 ||< 17 17 17 11 ||< 17;11 Superdiatonic 1/17-tone || | |||
||< ||< 93\166 ||< ||< 672.289 ||< 20 20 20 13 ||< || | |||
||< ||< 107\191 ||< ||< 672.251 ||< 23 23 23 15 ||< || | |||
||< ||< 121\216 ||< ||< 672.222 ||< 26 26 26 17 ||< 26;17 Superdiatonic 1/26-tone || | |||
||< ||< 135\241 ||< ||< 672.199 ||< 29 29 29 19 ||< 29;19 Superdiatonic 1/29-tone || | |||
||< ||< 61\109 | ||< 14\25 ||< ||< ||< 672 ||< 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || | ||
||< 47\84 | ||< ||< 145\259 ||< ||< 671.815 ||< 31 31 31 21 ||< 31;21 Superdiatonic 1/31-tone || | ||
||< 33\59 | ||< ||< 131\234 ||< ||< 671.795 ||< 28 28 28 19 ||< 28;19 Superdiatonic 1/28-tone || | ||
||< 19\34 | ||< ||< 117\209 ||< ||< 671.770 ||< 25 25 25 17 ||< || | ||
||< 24\43 | ||< ||< 103\184 ||< ||< 671.739 ||< 22 22 22 15 ||< || | ||
||< 5\[[9edo|9]] | ||< ||< 89\159 ||< ||< 671.698 ||< 19 19 19 13 ||< || | ||
||< ||< 75\134 ||< ||< 671.642 ||< 16 16 16 11 ||< || | |||
||< ||< 61\109 ||< ||< 671.560 ||< 13 13 13 9 ||< || | |||
||< 47\84 ||< ||< ||< 671.429 ||< 10 10 10 7 ||< || | |||
||< 33\59 ||< ||< ||< 671.186 ||< 7 7 7 5 ||< || | |||
||< 19\34 ||< ||< ||< 670.588 ||< 4 4 4 3 ||< || | |||
||< 24\43 ||< ||< ||< 669.767 ||< 5 5 5 4 ||< || | |||
||< 5\[[9edo|9]] ||< ||< ||< 666.667 ||< 1 1 1 1 ||< ||</pre></div> | |||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>7L 2s</title></head><body>This page is about of a <a class="wiki_link" href="/MOSScales">MOSScale</a> with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).<br /> | <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>7L 2s</title></head><body>This page is about of a <a class="wiki_link" href="/MOSScales">MOSScale</a> with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).<br /> | ||
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<table class="wiki_table"> | <table class="wiki_table"> | ||
<tr> | <tr> | ||
<th><br /> | <th colspan="3">Generator<br /> | ||
</th> | </th> | ||
<th>< | <th><span style="text-align: center;"><strong>Generator size (cents)</strong></span><br /> | ||
</ | |||
</th> | </th> | ||
<th>Pentachord steps<br /> | <th>Pentachord steps<br /> | ||
</th> | </th> | ||
<th>Comments<br /> | <th>Comments<br /> | ||
</th> | </th> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">4\<a class="wiki_link" href="/7edo">7</a><br /> | <td style="text-align: left;">4\<a class="wiki_link" href="/7edo">7</a><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">21\37<br /> | <td style="text-align: left;">21\37<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">17\30<br /> | <td style="text-align: left;">17\30<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;">L/s = 4<br /> | <td style="text-align: left;">L/s = 4<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"> | <td style="text-align: left;">30\53<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td> | <td>43\76<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>10 10 10 3<br /> | <td>10 10 10 3<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>56\99<br /> | <td>56\99<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>13 13 13 4<br /> | <td>13 13 13 4<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>69\122<br /> | <td>69\122<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>16 16 16 5<br /> | <td>16 16 16 5<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>82\145<br /> | <td>82\145<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>19 19 19 6<br /> | <td>19 19 19 6<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>95\168<br /> | <td>95\168<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>22 22 22 7<br /> | <td>22 22 22 7<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td><br /> | <td><br /> | ||
</td> | </td> | ||
<td>108\191<br /> | <td>108\191<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</td> | </td> | ||
<td>25 25 25 8<br /> | <td>25 25 25 8<br /> | ||
</td> | </td> | ||
<td><br /> | <td><br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">121\214<br /> | <td style="text-align: left;">121\214<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;">28;9 Superdiatonic 1/28-tone<br /> | <td style="text-align: left;">28;9 Superdiatonic 1/28-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
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</td> | </td> | ||
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> | <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> | ||
<span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">13\23<br /> | <td style="text-align: left;">13\23<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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<td style="text-align: left;">3 3 3 1<br /> | <td style="text-align: left;">3 3 3 1<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT <br /> | <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> | ||
L/s = 3<br /> | L/s = 3<br /> | ||
<span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
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<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;">126\223<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">678.027<br /> | <td style="text-align: left;">678.027<br /> | ||
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</td> | </td> | ||
<td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> | <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> | ||
<span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
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</td> | </td> | ||
<td style="text-align: left;">HORNBOSTEL (&amp; <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT<br /> | <td style="text-align: left;">HORNBOSTEL (&amp; <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT<br /> | ||
<span style="font-size: 12.8000001907349px;">(Armodue 1/26-tone;</span><br /> | |||
<span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' &amp; '8')</span><br /> | <span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' &amp; '8')</span><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">100\177<br /> | <td style="text-align: left;">100\177<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">87\154<br /> | <td style="text-align: left;">87\154<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">74\131<br /> | <td style="text-align: left;">74\131<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 610: | Line 371: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/17-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/17-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">61\108<br /> | <td style="text-align: left;">61\108<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 638: | Line 386: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 652: | Line 394: | ||
</td> | </td> | ||
<td style="text-align: left;">109\193<br /> | <td style="text-align: left;">109\193<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">677.720<br /> | <td style="text-align: left;">677.720<br /> | ||
Line 666: | Line 400: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">48\85<br /> | <td style="text-align: left;">48\85<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 693: | Line 413: | ||
<td style="text-align: left;">11 11 11 4<br /> | <td style="text-align: left;">11 11 11 4<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-<span style="font-size: 13px; line-height: 1.5;">Hornbostel 1/11-tone </span><br /> | <td style="text-align: left;">Armodue-<span style="font-size: 13px; line-height: 1.5;">Hornbostel 1/11-tone</span><br /> | ||
<span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">(Optimum accuracy of Phi interval, the note '7')</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Line 702: | Line 421: | ||
</td> | </td> | ||
<td style="text-align: left;">35\62<br /> | <td style="text-align: left;">35\62<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 722: | Line 429: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/8-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/8-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">92\163<br /> | <td style="text-align: left;">92\163<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 750: | Line 443: | ||
</td> | </td> | ||
<td style="text-align: left;">21;8 Superdiatonic 1/21-tone<br /> | <td style="text-align: left;">21;8 Superdiatonic 1/21-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 779: | Line 458: | ||
<td style="text-align: left;">Split φ superdiatonic relation<br /> | <td style="text-align: left;">Split φ superdiatonic relation<br /> | ||
(34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)<br /> | (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">57\101<br /> | <td style="text-align: left;">57\101<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 807: | Line 472: | ||
</td> | </td> | ||
<td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br /> | <td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">22\39<br /> | <td style="text-align: left;">22\39<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 835: | Line 486: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Hornbostel 1/5-tone<br /> | <td style="text-align: left;">Armodue-Hornbostel 1/5-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">75\133<br /> | <td style="text-align: left;">75\133<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 863: | Line 501: | ||
</td> | </td> | ||
<td style="text-align: left;">17;7 Superdiatonic 1/17-tone<br /> | <td style="text-align: left;">17;7 Superdiatonic 1/17-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">53\94<br /> | <td style="text-align: left;">53\94<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 891: | Line 516: | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 899: | Line 522: | ||
</td> | </td> | ||
<td style="text-align: left;">31\55<br /> | <td style="text-align: left;">31\55<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 919: | Line 530: | ||
</td> | </td> | ||
<td style="text-align: left;">7;3 Superdiatonic 1/7-tone<br /> | <td style="text-align: left;">7;3 Superdiatonic 1/7-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">40\71<br /> | <td style="text-align: left;">40\71<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 947: | Line 544: | ||
</td> | </td> | ||
<td style="text-align: left;">9;4 Superdiatonic 1/9-tone<br /> | <td style="text-align: left;">9;4 Superdiatonic 1/9-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">49\87<br /> | <td style="text-align: left;">49\87<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 975: | Line 558: | ||
</td> | </td> | ||
<td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br /> | <td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">58\103<br /> | <td style="text-align: left;">58\103<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,003: | Line 572: | ||
</td> | </td> | ||
<td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br /> | <td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">9\16<br /> | <td style="text-align: left;">9\16<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,031: | Line 586: | ||
</td> | </td> | ||
<td style="text-align: left;"><span style="display: block; text-align: left;"><strong>[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]</strong></span>ARMODUE ESADECAFONIA (or Goldsmith Temperament)<br /> | <td style="text-align: left;"><span style="display: block; text-align: left;"><strong>[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]</strong></span>ARMODUE ESADECAFONIA (or Goldsmith Temperament)<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">59\105<br /> | <td style="text-align: left;">59\105<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,059: | Line 600: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/13-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/13-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">50\89<br /> | <td style="text-align: left;">50\89<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,087: | Line 614: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/11-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/11-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">41\73<br /> | <td style="text-align: left;">41\73<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,115: | Line 628: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/9-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/9-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Line 1,123: | Line 635: | ||
</td> | </td> | ||
<td style="text-align: left;">32\57<br /> | <td style="text-align: left;">32\57<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,143: | Line 643: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/7-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/7-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the </span><span style="font-size: 12.8000001907349px;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a></span><span style="font-size: 12.8000001907349px;"> interval, the note '8')</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">55\98<br /> | <td style="text-align: left;">55\98<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,171: | Line 658: | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">78\139<br /> | <td style="text-align: left;">78\139<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,199: | Line 672: | ||
</td> | </td> | ||
<td style="text-align: left;">Armodue-Mávila 1/17-tone<br /> | <td style="text-align: left;">Armodue-Mávila 1/17-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">101\180<br /> | <td style="text-align: left;">101\180<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,227: | Line 686: | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">23\41<br /> | <td style="text-align: left;">23\41<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,255: | Line 700: | ||
</td> | </td> | ||
<td style="text-align: left;">5;3 Golden Armodue-Mávila 1/5-tone<br /> | <td style="text-align: left;">5;3 Golden Armodue-Mávila 1/5-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">60\107<br /> | <td style="text-align: left;">60\107<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,283: | Line 714: | ||
</td> | </td> | ||
<td style="text-align: left;">13;8 Golden Mávila 1/13-tone<br /> | <td style="text-align: left;">13;8 Golden Mávila 1/13-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 1,314: | Line 731: | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 1,321: | Line 736: | ||
</td> | </td> | ||
<td style="text-align: left;">97\173<br /> | <td style="text-align: left;">97\173<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">672.832<br /> | <td style="text-align: left;">672.832<br /> | ||
Line 1,337: | Line 742: | ||
</td> | </td> | ||
<td style="text-align: left;">21;13 Golden Mávila 1/21-tone<br /> | <td style="text-align: left;">21;13 Golden Mávila 1/21-tone<br /> | ||
<span style="font-size: 12.8000001907349px;">(ratio between large and small steps is Phi, and Phi is the step 120\173)</span><br /> | |||
</td> | </td> | ||
</tr> | </tr> | ||
Line 1,345: | Line 749: | ||
</td> | </td> | ||
<td style="text-align: left;">37\66<br /> | <td style="text-align: left;">37\66<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,365: | Line 757: | ||
</td> | </td> | ||
<td style="text-align: left;">8;5 Golden Mávila 1/8-tone<br /> | <td style="text-align: left;">8;5 Golden Mávila 1/8-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">51\91<br /> | <td style="text-align: left;">51\91<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,393: | Line 771: | ||
</td> | </td> | ||
<td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br /> | <td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 1,407: | Line 779: | ||
</td> | </td> | ||
<td style="text-align: left;">116\207<br /> | <td style="text-align: left;">116\207<br /> | ||
</td> | </td> | ||
<td style="text-align: left;">672.464<br /> | <td style="text-align: left;">672.464<br /> | ||
Line 1,421: | Line 785: | ||
</td> | </td> | ||
<td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br /> | <td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">65\116<br /> | <td style="text-align: left;">65\116<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,449: | Line 799: | ||
</td> | </td> | ||
<td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br /> | <td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">79\141<br /> | <td style="text-align: left;">79\141<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,477: | Line 813: | ||
</td> | </td> | ||
<td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br /> | <td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">93\166<br /> | <td style="text-align: left;">93\166<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,505: | Line 827: | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">107\191<br /> | <td style="text-align: left;">107\191<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
Line 1,533: | Line 841: | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
Line 1,561: | Line 855: | ||
</td> | </td> | ||
<td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br /> | <td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
Line 1,568: | Line 860: | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;"> | <td style="text-align: left;">135\241<br /> | ||
</td> | </td> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">672.199<br /> | <td style="text-align: left;">672.199<br /> | ||
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</td> | </td> | ||
<td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br /> | <td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;">14\25<br /> | <td style="text-align: left;">14\25<br /> | ||
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<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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<td style="text-align: left;">3;2 Golden Armodue-Mávila 1/3-tone<br /> | <td style="text-align: left;">3;2 Golden Armodue-Mávila 1/3-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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</td> | </td> | ||
<td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br /> | <td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">131\234<br /> | <td style="text-align: left;">131\234<br /> | ||
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<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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<td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br /> | <td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br /> | ||
</td> | </td> | ||
</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
</td> | </td> | ||
<td style="text-align: left;">117\209<br /> | <td style="text-align: left;">117\209<br /> | ||
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<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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<td style="text-align: left;"><br /> | <td style="text-align: left;"><br /> | ||
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<td style="text-align: left;">103\184<br /> | <td style="text-align: left;">103\184<br /> | ||
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<td style="text-align: left;">89\159<br /> | <td style="text-align: left;">89\159<br /> | ||
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<td style="text-align: left;">75\134<br /> | <td style="text-align: left;">75\134<br /> | ||
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<td style="text-align: left;">61\109<br /> | <td style="text-align: left;">61\109<br /> | ||
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<td style="text-align: left;">47\84<br /> | <td style="text-align: left;">47\84<br /> | ||
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<td style="text-align: left;">33\59<br /> | <td style="text-align: left;">33\59<br /> | ||
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<td style="text-align: left;">19\34<br /> | <td style="text-align: left;">19\34<br /> | ||
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<td style="text-align: left;">24\43<br /> | <td style="text-align: left;">24\43<br /> | ||
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<td style="text-align: left;">5\<a class="wiki_link" href="/9edo">9</a><br /> | <td style="text-align: left;">5\<a class="wiki_link" href="/9edo">9</a><br /> | ||
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Revision as of 16:15, 11 February 2015
IMPORTED REVISION FROM WIKISPACES
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This page is about of a [[MOSScales|MOSScale]] with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL). If you're looking for highly accurate scales (that is, ones that approximate JI closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, if 678 cents is an acceptable '3/2' to you), then [[Pelogic family|mávila]] is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'. These scales are strongly associated with the [[Armodue]] project/system applied too on Septimal-mávila and Hornbostel temperaments. Optional types of 'JI [[Blown Fifth]]' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169. ||||||~ Generator ||~ <span style="text-align: center;">**Generator size (cents)**</span> ||~ Pentachord steps ||~ Comments || ||< 4\[[7edo|7]] ||< ||< ||< 685.714 ||< 1 1 1 0 ||< || ||< 21\37 ||< ||< ||< 681.081 ||< 5 5 5 1 ||< || ||< 17\30 ||< ||< ||< 680 ||< 4 4 4 1 ||< L/s = 4 || ||< ||< 30\53 ||< ||< 679.245 ||< 7 7 7 2 ||< || || || 43\76 || || 678.947 || 10 10 10 3 || || || || 56\99 || || 678.788 || 13 13 13 4 || || || || 69\122 || || 678.6885 || 16 16 16 5 || || || || 82\145 || || 678.621 || 19 19 19 6 || || || || 95\168 || || 678.571 || 22 22 22 7 || || || || 108\191 || || 678.534 || 25 25 25 8 || || ||< ||< 121\214 ||< ||< 678.505 ||< 28 28 28 9 ||< 28;9 Superdiatonic 1/28-tone <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span> || ||< ||< 134\237 ||< ||< 678.481 ||< 31 31 31 10 ||< HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span> || ||< 13\23 ||< ||< ||< 678.261 ||< 3 3 3 1 ||< HORNBOSTEL TEMPERAMENT L/s = 3 <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span> || ||< ||< 126\223 ||< ||< 678.027 ||< 29 29 29 10 ||< HORNBOSTEL TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span> || ||< ||< 113\200 ||< ||< 678 ||< 26 26 26 9 ||< HORNBOSTEL (& [[Alexei Stepanovich Ogolevets|OGOLEVETS]]) TEMPERAMENT <span style="font-size: 12.8000001907349px;">(Armodue 1/26-tone;</span> <span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')</span> || ||< ||< 100\177 ||< ||< 677.966 ||< 23 23 23 8 ||< || ||< ||< 87\154 ||< ||< 677.922 ||< 20 20 20 7 ||< || ||< ||< 74\131 ||< ||< 677.863 ||< 17 17 17 6 ||< Armodue-Hornbostel 1/17-tone <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span> || ||< ||< 61\108 ||< ||< 677.778 ||< 14 14 14 5 ||< Armodue-Hornbostel 1/14-tone || ||< ||< ||< 109\193 ||< 677.720 ||< 25 25 25 9 ||< Armodue-Hornbostel 1/25-tone || ||< ||< 48\85 ||< ||< 677.647 ||< 11 11 11 4 ||< Armodue-<span style="font-size: 13px; line-height: 1.5;">Hornbostel 1/11-tone</span> <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">(Optimum accuracy of Phi interval, the note '7')</span> || ||< ||< 35\62 ||< ||< 677.419 ||< 8 8 8 3 ||< Armodue-Hornbostel 1/8-tone || ||< ||< 92\163 ||< ||< 677.301 ||< 21 21 21 8 ||< 21;8 Superdiatonic 1/21-tone || ||< ||< ||< ||< 677.2804 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span> ||< Split φ superdiatonic relation (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..) || ||< ||< 57\101 ||< ||< 677.228 ||< 13 13 13 5 ||< 13;5 Superdiatonic 1/13-tone || ||< 22\39 ||< ||< ||< 676.923 ||< 5 5 5 2 ||< Armodue-Hornbostel 1/5-tone <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span> || ||< ||< 75\133 ||< ||< 676.692 ||< 17 17 17 7 ||< 17;7 Superdiatonic 1/17-tone <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span> || ||< ||< 53\94 ||< ||< 676.596 ||< 12 12 12 5 ||< || ||< ||< 31\55 ||< ||< 676.364 ||< 7 7 7 3 ||< 7;3 Superdiatonic 1/7-tone || ||< ||< 40\71 ||< ||< 676.056 ||< 9 9 9 4 ||< 9;4 Superdiatonic 1/9-tone || ||< ||< 49\87 ||< ||< 675.862 ||< 11 11 11 5 ||< 11;5 Superdiatonic 1/11-tone || ||< ||< 58\103 ||< ||< 675.728 ||< 13 13 13 6 ||< 13;6 Superdiatonic 1/13-tone || ||< 9\16 ||< ||< ||< 675 ||< 2 2 2 1 ||< <span style="display: block; text-align: left;">**[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]**</span>ARMODUE ESADECAFONIA (or Goldsmith Temperament) || ||< ||< 59\105 ||< ||< 674.286 ||< 13 13 13 7 ||< Armodue-Mávila 1/13-tone || ||< ||< 50\89 ||< ||< 674.157 ||< 11 11 11 6 ||< Armodue-Mávila 1/11-tone || ||< ||< 41\73 ||< ||< 673.973 ||< 9 9 9 5 ||< Armodue-Mávila 1/9-tone <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span> || ||< ||< 32\57 ||< ||< 673.684 ||< 7 7 7 4 ||< Armodue-Mávila 1/7-tone <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the </span><span style="font-size: 12.8000001907349px;">[[xenharmonic/7_4|7/4]]</span><span style="font-size: 12.8000001907349px;"> interval, the note '8')</span> || ||< ||< 55\98 ||< ||< 673.469 ||< 12 12 12 7 ||< || ||< ||< 78\139 ||< ||< 673.381 ||< 17 17 17 10 ||< Armodue-Mávila 1/17-tone || ||< ||< 101\180 ||< ||< 673.333 ||< 22 22 22 13 ||< || ||< 23\41 ||< ||< ||< 673.171 ||< 5 5 5 3 ||< 5;3 Golden Armodue-Mávila 1/5-tone || ||< ||< 60\107 ||< ||< 672.897 ||< 13 13 13 8 ||< 13;8 Golden Mávila 1/13-tone || ||< ||< ||< ||< 672.8503 ||< <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span> ||< GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span> || ||< ||< ||< 97\173 ||< 672.832 ||< 21 21 21 13 ||< 21;13 Golden Mávila 1/21-tone <span style="font-size: 12.8000001907349px;">(ratio between large and small steps is Phi, and Phi is the step 120\173)</span> || ||< ||< 37\66 ||< ||< 672.727 ||< 8 8 8 5 ||< 8;5 Golden Mávila 1/8-tone || ||< ||< 51\91 ||< ||< 672.527 ||< 11 11 11 7 ||< 11;7 Superdiatonic 1/11-tone || ||< ||< ||< 116\207 ||< 672.464 ||< 25 25 25 16 ||< 25;16 Superdiatonic 1/25-tone || ||< ||< 65\116 ||< ||< 672.414 ||< 14 14 14 9 ||< 14;9 Superdiatonic 1/14-tone || ||< ||< 79\141 ||< ||< 672.340 ||< 17 17 17 11 ||< 17;11 Superdiatonic 1/17-tone || ||< ||< 93\166 ||< ||< 672.289 ||< 20 20 20 13 ||< || ||< ||< 107\191 ||< ||< 672.251 ||< 23 23 23 15 ||< || ||< ||< 121\216 ||< ||< 672.222 ||< 26 26 26 17 ||< 26;17 Superdiatonic 1/26-tone || ||< ||< 135\241 ||< ||< 672.199 ||< 29 29 29 19 ||< 29;19 Superdiatonic 1/29-tone || ||< 14\25 ||< ||< ||< 672 ||< 3 3 3 2 ||< 3;2 Golden Armodue-Mávila 1/3-tone || ||< ||< 145\259 ||< ||< 671.815 ||< 31 31 31 21 ||< 31;21 Superdiatonic 1/31-tone || ||< ||< 131\234 ||< ||< 671.795 ||< 28 28 28 19 ||< 28;19 Superdiatonic 1/28-tone || ||< ||< 117\209 ||< ||< 671.770 ||< 25 25 25 17 ||< || ||< ||< 103\184 ||< ||< 671.739 ||< 22 22 22 15 ||< || ||< ||< 89\159 ||< ||< 671.698 ||< 19 19 19 13 ||< || ||< ||< 75\134 ||< ||< 671.642 ||< 16 16 16 11 ||< || ||< ||< 61\109 ||< ||< 671.560 ||< 13 13 13 9 ||< || ||< 47\84 ||< ||< ||< 671.429 ||< 10 10 10 7 ||< || ||< 33\59 ||< ||< ||< 671.186 ||< 7 7 7 5 ||< || ||< 19\34 ||< ||< ||< 670.588 ||< 4 4 4 3 ||< || ||< 24\43 ||< ||< ||< 669.767 ||< 5 5 5 4 ||< || ||< 5\[[9edo|9]] ||< ||< ||< 666.667 ||< 1 1 1 1 ||< ||
Original HTML content:
<html><head><title>7L 2s</title></head><body>This page is about of a <a class="wiki_link" href="/MOSScales">MOSScale</a> with 7 large steps and 2 small steps arranged LLLsLLLLs (or any rotation of that, such as LLsLLLsLL).<br /> <br /> If you're looking for highly accurate scales (that is, ones that approximate JI closely), there are much better scale patterns to look at. However, if your harmonic entropy is coarse enough (that is, if 678 cents is an acceptable '3/2' to you), then <a class="wiki_link" href="/Pelogic%20family">mávila</a> is an important harmonic entropy minimum here. So a general name for this MOS pattern could be "Mávila Superdiatonic" or simply 'Superdiatonic'.<br /> These scales are strongly associated with the <a class="wiki_link" href="/Armodue">Armodue</a> project/system applied too on Septimal-mávila and Hornbostel temperaments.<br /> <br /> Optional types of 'JI <a class="wiki_link" href="/Blown%20Fifth">Blown Fifth</a>' Generators: 31/21, 34/23, 65/44, 71/48, 99/67, 105/71, 108/73, 133/90, 145/98, 176/119 & 250/169.<br /> <table class="wiki_table"> <tr> <th colspan="3">Generator<br /> </th> <th><span style="text-align: center;"><strong>Generator size (cents)</strong></span><br /> </th> <th>Pentachord steps<br /> </th> <th>Comments<br /> </th> </tr> <tr> <td style="text-align: left;">4\<a class="wiki_link" href="/7edo">7</a><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">685.714<br /> </td> <td style="text-align: left;">1 1 1 0<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">21\37<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">681.081<br /> </td> <td style="text-align: left;">5 5 5 1<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">17\30<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">680<br /> </td> <td style="text-align: left;">4 4 4 1<br /> </td> <td style="text-align: left;">L/s = 4<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">30\53<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">679.245<br /> </td> <td style="text-align: left;">7 7 7 2<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td><br /> </td> <td>43\76<br /> </td> <td><br /> </td> <td>678.947<br /> </td> <td>10 10 10 3<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>56\99<br /> </td> <td><br /> </td> <td>678.788<br /> </td> <td>13 13 13 4<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>69\122<br /> </td> <td><br /> </td> <td>678.6885<br /> </td> <td>16 16 16 5<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>82\145<br /> </td> <td><br /> </td> <td>678.621<br /> </td> <td>19 19 19 6<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>95\168<br /> </td> <td><br /> </td> <td>678.571<br /> </td> <td>22 22 22 7<br /> </td> <td><br /> </td> </tr> <tr> <td><br /> </td> <td>108\191<br /> </td> <td><br /> </td> <td>678.534<br /> </td> <td>25 25 25 8<br /> </td> <td><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">121\214<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">678.505<br /> </td> <td style="text-align: left;">28 28 28 9<br /> </td> <td style="text-align: left;">28;9 Superdiatonic 1/28-tone<br /> <span style="font-size: 12.8000001907349px;">(a slight exceeded representation of the ratio 262144/177147, the Pythagorean wolf Fifth)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">134\237<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">678.481<br /> </td> <td style="text-align: left;">31 31 31 10<br /> </td> <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> <span style="font-size: 12.8000001907349px;">(1/31-tone; Optimum high size of Hornbostel '6th')</span><br /> </td> </tr> <tr> <td style="text-align: left;">13\23<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">678.261<br /> </td> <td style="text-align: left;">3 3 3 1<br /> </td> <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> L/s = 3<br /> <span style="font-size: 12.8000001907349px;">(Armodue 1/3-tone)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">126\223<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">678.027<br /> </td> <td style="text-align: left;">29 29 29 10<br /> </td> <td style="text-align: left;">HORNBOSTEL TEMPERAMENT<br /> <span style="font-size: 12.8000001907349px;">(Armodue 1/29-tone)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">113\200<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">678<br /> </td> <td style="text-align: left;">26 26 26 9<br /> </td> <td style="text-align: left;">HORNBOSTEL (& <a class="wiki_link" href="/Alexei%20Stepanovich%20Ogolevets">OGOLEVETS</a>) TEMPERAMENT<br /> <span style="font-size: 12.8000001907349px;">(Armodue 1/26-tone;</span><br /> <span style="font-size: 12.8000001907349px;">Best equillibrium between 6/5, Phi (833.1 Cent) and Square root of Pi (990.9 Cent), the notes '3', '7' & '8')</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">100\177<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.966<br /> </td> <td style="text-align: left;">23 23 23 8<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">87\154<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.922<br /> </td> <td style="text-align: left;">20 20 20 7<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">74\131<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.863<br /> </td> <td style="text-align: left;">17 17 17 6<br /> </td> <td style="text-align: left;">Armodue-Hornbostel 1/17-tone<br /> <span style="font-size: 12.8000001907349px;">(the Golden Tone System of Thorvald Kornerup and a temperament of the Alexei Ogolevets's list of temperaments)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">61\108<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.778<br /> </td> <td style="text-align: left;">14 14 14 5<br /> </td> <td style="text-align: left;">Armodue-Hornbostel 1/14-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">109\193<br /> </td> <td style="text-align: left;">677.720<br /> </td> <td style="text-align: left;">25 25 25 9<br /> </td> <td style="text-align: left;">Armodue-Hornbostel 1/25-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">48\85<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.647<br /> </td> <td style="text-align: left;">11 11 11 4<br /> </td> <td style="text-align: left;">Armodue-<span style="font-size: 13px; line-height: 1.5;">Hornbostel 1/11-tone</span><br /> <span style="font-size: 12.8000001907349px; line-height: 15.3600006103516px;">(Optimum accuracy of Phi interval, the note '7')</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">35\62<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.419<br /> </td> <td style="text-align: left;">8 8 8 3<br /> </td> <td style="text-align: left;">Armodue-Hornbostel 1/8-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">92\163<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.301<br /> </td> <td style="text-align: left;">21 21 21 8<br /> </td> <td style="text-align: left;">21;8 Superdiatonic 1/21-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.2804<br /> </td> <td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ+1 φ+1 φ+1 1</span><br /> </td> <td style="text-align: left;">Split φ superdiatonic relation<br /> (34;13 - 55;21 - 89;34 - 144;55 - 233;89 - 377;144 - 610;233..)<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">57\101<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">677.228<br /> </td> <td style="text-align: left;">13 13 13 5<br /> </td> <td style="text-align: left;">13;5 Superdiatonic 1/13-tone<br /> </td> </tr> <tr> <td style="text-align: left;">22\39<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">676.923<br /> </td> <td style="text-align: left;">5 5 5 2<br /> </td> <td style="text-align: left;">Armodue-Hornbostel 1/5-tone<br /> <span style="font-size: 12.8000001907349px;">(Optimum low size of Hornbostel '6th')</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">75\133<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">676.692<br /> </td> <td style="text-align: left;">17 17 17 7<br /> </td> <td style="text-align: left;">17;7 Superdiatonic 1/17-tone<br /> <span style="font-size: 12.8000001907349px;">(Note the very accuracy of the step 75 with the ratio 34/23 with an error of +0.011 Cents)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">53\94<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">676.596<br /> </td> <td style="text-align: left;">12 12 12 5<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">31\55<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">676.364<br /> </td> <td style="text-align: left;">7 7 7 3<br /> </td> <td style="text-align: left;">7;3 Superdiatonic 1/7-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">40\71<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">676.056<br /> </td> <td style="text-align: left;">9 9 9 4<br /> </td> <td style="text-align: left;">9;4 Superdiatonic 1/9-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">49\87<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">675.862<br /> </td> <td style="text-align: left;">11 11 11 5<br /> </td> <td style="text-align: left;">11;5 Superdiatonic 1/11-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">58\103<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">675.728<br /> </td> <td style="text-align: left;">13 13 13 6<br /> </td> <td style="text-align: left;">13;6 Superdiatonic 1/13-tone<br /> </td> </tr> <tr> <td style="text-align: left;">9\16<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">675<br /> </td> <td style="text-align: left;">2 2 2 1<br /> </td> <td style="text-align: left;"><span style="display: block; text-align: left;"><strong>[BOUNDARY OF PROPRIETY: smaller generators are strictly proper]</strong></span>ARMODUE ESADECAFONIA (or Goldsmith Temperament)<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">59\105<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">674.286<br /> </td> <td style="text-align: left;">13 13 13 7<br /> </td> <td style="text-align: left;">Armodue-Mávila 1/13-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">50\89<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">674.157<br /> </td> <td style="text-align: left;">11 11 11 6<br /> </td> <td style="text-align: left;">Armodue-Mávila 1/11-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">41\73<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.973<br /> </td> <td style="text-align: left;">9 9 9 5<br /> </td> <td style="text-align: left;">Armodue-Mávila 1/9-tone<br /> <span style="font-size: 12.8000001907349px;">(with an approximation of the Perfect Fifth + 1/5 Pyth.Comma [706.65 Cents]: 43\73 is 706.85 Cents)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">32\57<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.684<br /> </td> <td style="text-align: left;">7 7 7 4<br /> </td> <td style="text-align: left;">Armodue-Mávila 1/7-tone<br /> <span style="font-size: 12.8000001907349px;">(the 'Commatic' version of Armodue, because its high accuracy of the </span><span style="font-size: 12.8000001907349px;"><a class="wiki_link" href="http://xenharmonic.wikispaces.com/7_4">7/4</a></span><span style="font-size: 12.8000001907349px;"> interval, the note '8')</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">55\98<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.469<br /> </td> <td style="text-align: left;">12 12 12 7<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">78\139<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.381<br /> </td> <td style="text-align: left;">17 17 17 10<br /> </td> <td style="text-align: left;">Armodue-Mávila 1/17-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">101\180<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.333<br /> </td> <td style="text-align: left;">22 22 22 13<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">23\41<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">673.171<br /> </td> <td style="text-align: left;">5 5 5 3<br /> </td> <td style="text-align: left;">5;3 Golden Armodue-Mávila 1/5-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">60\107<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.897<br /> </td> <td style="text-align: left;">13 13 13 8<br /> </td> <td style="text-align: left;">13;8 Golden Mávila 1/13-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.8503<br /> </td> <td style="text-align: left;"><span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ φ φ 1</span><br /> </td> <td style="text-align: left;">GOLDEN MÁVILA (L/s = <span style="background-color: #ffffff; color: #222222; font-family: arial,sans-serif; font-size: small;">φ)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">97\173<br /> </td> <td style="text-align: left;">672.832<br /> </td> <td style="text-align: left;">21 21 21 13<br /> </td> <td style="text-align: left;">21;13 Golden Mávila 1/21-tone<br /> <span style="font-size: 12.8000001907349px;">(ratio between large and small steps is Phi, and Phi is the step 120\173)</span><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">37\66<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.727<br /> </td> <td style="text-align: left;">8 8 8 5<br /> </td> <td style="text-align: left;">8;5 Golden Mávila 1/8-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">51\91<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.527<br /> </td> <td style="text-align: left;">11 11 11 7<br /> </td> <td style="text-align: left;">11;7 Superdiatonic 1/11-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">116\207<br /> </td> <td style="text-align: left;">672.464<br /> </td> <td style="text-align: left;">25 25 25 16<br /> </td> <td style="text-align: left;">25;16 Superdiatonic 1/25-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">65\116<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.414<br /> </td> <td style="text-align: left;">14 14 14 9<br /> </td> <td style="text-align: left;">14;9 Superdiatonic 1/14-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">79\141<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.340<br /> </td> <td style="text-align: left;">17 17 17 11<br /> </td> <td style="text-align: left;">17;11 Superdiatonic 1/17-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">93\166<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.289<br /> </td> <td style="text-align: left;">20 20 20 13<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">107\191<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.251<br /> </td> <td style="text-align: left;">23 23 23 15<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">121\216<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.222<br /> </td> <td style="text-align: left;">26 26 26 17<br /> </td> <td style="text-align: left;">26;17 Superdiatonic 1/26-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">135\241<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672.199<br /> </td> <td style="text-align: left;">29 29 29 19<br /> </td> <td style="text-align: left;">29;19 Superdiatonic 1/29-tone<br /> </td> </tr> <tr> <td style="text-align: left;">14\25<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">672<br /> </td> <td style="text-align: left;">3 3 3 2<br /> </td> <td style="text-align: left;">3;2 Golden Armodue-Mávila 1/3-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">145\259<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.815<br /> </td> <td style="text-align: left;">31 31 31 21<br /> </td> <td style="text-align: left;">31;21 Superdiatonic 1/31-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">131\234<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.795<br /> </td> <td style="text-align: left;">28 28 28 19<br /> </td> <td style="text-align: left;">28;19 Superdiatonic 1/28-tone<br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">117\209<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.770<br /> </td> <td style="text-align: left;">25 25 25 17<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">103\184<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.739<br /> </td> <td style="text-align: left;">22 22 22 15<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">89\159<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.698<br /> </td> <td style="text-align: left;">19 19 19 13<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">75\134<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.642<br /> </td> <td style="text-align: left;">16 16 16 11<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">61\109<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.560<br /> </td> <td style="text-align: left;">13 13 13 9<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">47\84<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.429<br /> </td> <td style="text-align: left;">10 10 10 7<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">33\59<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">671.186<br /> </td> <td style="text-align: left;">7 7 7 5<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">19\34<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">670.588<br /> </td> <td style="text-align: left;">4 4 4 3<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">24\43<br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">669.767<br /> </td> <td style="text-align: left;">5 5 5 4<br /> </td> <td style="text-align: left;"><br /> </td> </tr> <tr> <td style="text-align: left;">5\<a class="wiki_link" href="/9edo">9</a><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;"><br /> </td> <td style="text-align: left;">666.667<br /> </td> <td style="text-align: left;">1 1 1 1<br /> </td> <td style="text-align: left;"><br /> </td> </tr> </table> </body></html>