List of distinct EDO scales: Difference between revisions
Wikispaces>Sarzadoce **Imported revision 553456136 - Original comment: ** |
Wikispaces>Sarzadoce **Imported revision 553509376 - 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:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-09 | : This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-06-09 14:29:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>553509376</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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(if someone could format this table a little better, it would be greatly appreciated) | (if someone could format this table a little better, it would be greatly appreciated) | ||
* EDO (Variety = 1) | |||
** Multi-MOS (Max Variety = 2) | |||
†† Strict MOS (Variety = 2) | |||
==1-EDO Scales== | |||
1 * | |||
==2-EDO Scales== | ==2-EDO Scales== | ||
11 | 11 * | ||
==3-EDO Scales== | ==3-EDO Scales== | ||
21 | 21 †† | ||
111 | 111 * | ||
==4-EDO Scales== | ==4-EDO Scales== | ||
31 | 31 †† | ||
211 | 211 †† | ||
1111 | 1111 * | ||
==5-EDO Scales== | ==5-EDO Scales== | ||
32 | 32 †† | ||
41 | 41 †† | ||
221 | 221 †† | ||
311 | 311 †† | ||
2111 | 2111 †† | ||
11111 | 11111 * | ||
==6-EDO Scales== | ==6-EDO Scales== | ||
51 | 51 †† | ||
312 | 312 | ||
321 | 321 | ||
411 | 411 †† | ||
2121 | 2121 ** | ||
2211 | 2211 | ||
3111 | 3111 †† | ||
21111 | 21111 †† | ||
111111 | 111111 * | ||
==7-EDO Scales== | ==7-EDO Scales== | ||
43 | 43 †† | ||
52 | 52 †† | ||
61 | 61 †† | ||
322 | 322 †† | ||
331 | 331 †† | ||
412 | 412 | ||
421 | 421 | ||
511 | 511 †† | ||
2221 | 2221 †† | ||
3112 | 3112 | ||
3121 | 3121 | ||
3211 | 3211 | ||
4111 | 4111 †† | ||
21211 | 21211 †† | ||
22111 | 22111 | ||
31111 | 31111 †† | ||
211111 | 211111 †† | ||
1111111 | 1111111 * | ||
==8-EDO Scales== | ==8-EDO Scales== | ||
53 | 53 †† | ||
71 | 71 †† | ||
332 | 332 †† | ||
413 | 413 | ||
431 | 431 | ||
512 | 512 | ||
521 | 521 | ||
611 | 611 †† | ||
3122 | 3122 | ||
3131 | 3131 ** | ||
3212 | 3212 | ||
3221 | 3221 | ||
| Line 109: | Line 118: | ||
4121 | 4121 | ||
4211 | 4211 | ||
5111 | 5111 †† | ||
22121 | 22121 †† | ||
22211 | 22211 | ||
31112 | 31112 | ||
| Line 116: | Line 125: | ||
31211 | 31211 | ||
32111 | 32111 | ||
41111 | 41111 †† | ||
211211 | 211211 ** | ||
212111 | 212111 | ||
221111 | 221111 | ||
311111 | 311111 †† | ||
2111111 | 2111111 †† | ||
11111111 | 11111111 * | ||
==9-EDO Scales== | ==9-EDO Scales== | ||
54 | 54 †† | ||
72 | 72 †† | ||
81 | 81 †† | ||
423 | 423 | ||
432 | 432 | ||
441 | 441 †† | ||
513 | 513 | ||
522 | 522 †† | ||
531 | 531 | ||
612 | 612 | ||
621 | 621 | ||
711 | 711 †† | ||
3222 | 3222 †† | ||
3231 | 3231 | ||
3312 | 3312 | ||
| Line 151: | Line 160: | ||
5121 | 5121 | ||
5211 | 5211 | ||
6111 | 6111 †† | ||
22221 | 22221 †† | ||
31122 | 31122 | ||
31212 | 31212 | ||
31221 | 31221 | ||
31311 | 31311 †† | ||
32112 | 32112 | ||
32121 | 32121 | ||
| Line 165: | Line 174: | ||
41211 | 41211 | ||
42111 | 42111 | ||
51111 | 51111 †† | ||
212121 | 212121 ** | ||
221121 | 221121 | ||
221211 | 221211 | ||
| Line 175: | Line 184: | ||
312111 | 312111 | ||
321111 | 321111 | ||
411111 | 411111 †† | ||
2112111 | 2112111 †† | ||
2121111 | 2121111 | ||
2211111 | 2211111 | ||
3111111 | 3111111 †† | ||
21111111 | 21111111 †† | ||
111111111 | 111111111 * | ||
==10-EDO Scales== | ==10-EDO Scales== | ||
73 | 73 †† | ||
91 | 91 †† | ||
433 | 433 †† | ||
514 | 514 | ||
523 | 523 | ||
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712 | 712 | ||
721 | 721 | ||
811 | 811 †† | ||
3232 | 3232 ** | ||
3322 | 3322 | ||
3331 | 3331 †† | ||
4123 | 4123 | ||
4132 | 4132 | ||
4141 | 4141 ** | ||
4213 | 4213 | ||
4231 | 4231 | ||
| Line 217: | Line 226: | ||
6121 | 6121 | ||
6211 | 6211 | ||
7111 | 7111 †† | ||
31222 | 31222 | ||
31312 | 31312 | ||
| Line 242: | Line 251: | ||
51211 | 51211 | ||
52111 | 52111 | ||
61111 | 61111 †† | ||
221221 | 221221 ** | ||
222121 | 222121 | ||
222211 | 222211 | ||
| Line 249: | Line 258: | ||
311212 | 311212 | ||
311221 | 311221 | ||
311311 | 311311 ** | ||
312112 | 312112 | ||
312121 | 312121 | ||
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412111 | 412111 | ||
421111 | 421111 | ||
511111 | 511111 †† | ||
2121211 | 2121211 †† | ||
2211121 | 2211121 | ||
2211211 | 2211211 | ||
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3121111 | 3121111 | ||
3211111 | 3211111 | ||
4111111 | 4111111 †† | ||
21112111 | 21112111 ** | ||
21121111 | 21121111 | ||
21211111 | 21211111 | ||
22111111 | 22111111 | ||
31111111 | 31111111 †† | ||
211111111 | 211111111 †† | ||
1111111111</pre></div> | 1111111111 *</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>Distinct EDO Scales</title></head><body>Each <a class="wiki_link" href="/Equal%20division%20of%20the%20octave">EDO</a> has a finite number of distinct scales, assuming that the scales are equivalent up to cyclical permutation and that they are also irreducible. By irreducible is meant a scale that is not supported by a smaller EDO (e.g. 4424442, the diatonic scale in 24-EDO, is reducible because it is also contained in 12-EDO).<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>Distinct EDO Scales</title></head><body>Each <a class="wiki_link" href="/Equal%20division%20of%20the%20octave">EDO</a> has a finite number of distinct scales, assuming that the scales are equivalent up to cyclical permutation and that they are also irreducible. By irreducible is meant a scale that is not supported by a smaller EDO (e.g. 4424442, the diatonic scale in 24-EDO, is reducible because it is also contained in 12-EDO).<br /> | ||
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<br /> | <br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-2-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule: | <br /> | ||
<ul><li>EDO (Variety = 1)<ul><li>Multi-MOS (Max Variety = 2)</li></ul></li></ul>†† Strict MOS (Variety = 2)<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-1-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:0 -->1-EDO Scales</h2> | |||
<br /> | |||
1 *<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-2-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:2 -->2-EDO Scales</h2> | |||
<br /> | <br /> | ||
11<br /> | 11 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-3-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->3-EDO Scales</h2> | ||
<br /> | <br /> | ||
21<br /> | 21 ††<br /> | ||
111<br /> | 111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-4-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->4-EDO Scales</h2> | ||
<br /> | <br /> | ||
31<br /> | 31 ††<br /> | ||
211<br /> | 211 ††<br /> | ||
1111<br /> | 1111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-5-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->5-EDO Scales</h2> | ||
<br /> | <br /> | ||
32<br /> | 32 ††<br /> | ||
41<br /> | 41 ††<br /> | ||
221<br /> | 221 ††<br /> | ||
311<br /> | 311 ††<br /> | ||
2111<br /> | 2111 ††<br /> | ||
11111<br /> | 11111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-6-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->6-EDO Scales</h2> | ||
<br /> | <br /> | ||
51<br /> | 51 ††<br /> | ||
312<br /> | 312<br /> | ||
321<br /> | 321<br /> | ||
411<br /> | 411 ††<br /> | ||
2121<br /> | 2121 **<br /> | ||
2211<br /> | 2211<br /> | ||
3111<br /> | 3111 ††<br /> | ||
21111<br /> | 21111 ††<br /> | ||
111111<br /> | 111111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-7-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->7-EDO Scales</h2> | ||
<br /> | <br /> | ||
43<br /> | 43 ††<br /> | ||
52<br /> | 52 ††<br /> | ||
61<br /> | 61 ††<br /> | ||
322<br /> | 322 ††<br /> | ||
331<br /> | 331 ††<br /> | ||
412<br /> | 412<br /> | ||
421<br /> | 421<br /> | ||
511<br /> | 511 ††<br /> | ||
2221<br /> | 2221 ††<br /> | ||
3112<br /> | 3112<br /> | ||
3121<br /> | 3121<br /> | ||
3211<br /> | 3211<br /> | ||
4111<br /> | 4111 ††<br /> | ||
21211<br /> | 21211 ††<br /> | ||
22111<br /> | 22111<br /> | ||
31111<br /> | 31111 ††<br /> | ||
211111<br /> | 211111 ††<br /> | ||
1111111<br /> | 1111111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-8-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:14 -->8-EDO Scales</h2> | ||
<br /> | <br /> | ||
53<br /> | 53 ††<br /> | ||
71<br /> | 71 ††<br /> | ||
332<br /> | 332 ††<br /> | ||
413<br /> | 413<br /> | ||
431<br /> | 431<br /> | ||
512<br /> | 512<br /> | ||
521<br /> | 521<br /> | ||
611<br /> | 611 ††<br /> | ||
3122<br /> | 3122<br /> | ||
3131<br /> | 3131 <strong><br /> | ||
3212<br /> | 3212<br /> | ||
3221<br /> | 3221<br /> | ||
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4121<br /> | 4121<br /> | ||
4211<br /> | 4211<br /> | ||
5111<br /> | 5111 ††<br /> | ||
22121<br /> | 22121 ††<br /> | ||
22211<br /> | 22211<br /> | ||
31112<br /> | 31112<br /> | ||
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31211<br /> | 31211<br /> | ||
32111<br /> | 32111<br /> | ||
41111<br /> | 41111 ††<br /> | ||
211211<br /> | 211211 </strong><br /> | ||
212111<br /> | 212111<br /> | ||
221111<br /> | 221111<br /> | ||
311111<br /> | 311111 ††<br /> | ||
2111111<br /> | 2111111 ††<br /> | ||
11111111<br /> | 11111111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-9-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:16 -->9-EDO Scales</h2> | ||
<br /> | <br /> | ||
54<br /> | 54 ††<br /> | ||
72<br /> | 72 ††<br /> | ||
81<br /> | 81 ††<br /> | ||
423<br /> | 423<br /> | ||
432<br /> | 432<br /> | ||
441<br /> | 441 ††<br /> | ||
513<br /> | 513<br /> | ||
522<br /> | 522 ††<br /> | ||
531<br /> | 531<br /> | ||
612<br /> | 612<br /> | ||
621<br /> | 621<br /> | ||
711<br /> | 711 ††<br /> | ||
3222<br /> | 3222 ††<br /> | ||
3231<br /> | 3231<br /> | ||
3312<br /> | 3312<br /> | ||
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5121<br /> | 5121<br /> | ||
5211<br /> | 5211<br /> | ||
6111<br /> | 6111 ††<br /> | ||
22221<br /> | 22221 ††<br /> | ||
31122<br /> | 31122<br /> | ||
31212<br /> | 31212<br /> | ||
31221<br /> | 31221<br /> | ||
31311<br /> | 31311 ††<br /> | ||
32112<br /> | 32112<br /> | ||
32121<br /> | 32121<br /> | ||
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41211<br /> | 41211<br /> | ||
42111<br /> | 42111<br /> | ||
51111<br /> | 51111 ††<br /> | ||
212121<br /> | 212121 **<br /> | ||
221121<br /> | 221121<br /> | ||
221211<br /> | 221211<br /> | ||
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312111<br /> | 312111<br /> | ||
321111<br /> | 321111<br /> | ||
411111<br /> | 411111 ††<br /> | ||
2112111<br /> | 2112111 ††<br /> | ||
2121111<br /> | 2121111<br /> | ||
2211111<br /> | 2211111<br /> | ||
3111111<br /> | 3111111 ††<br /> | ||
21111111<br /> | 21111111 ††<br /> | ||
111111111<br /> | 111111111 *<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-10-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:18 -->10-EDO Scales</h2> | ||
<br /> | <br /> | ||
73<br /> | 73 ††<br /> | ||
91<br /> | 91 ††<br /> | ||
433<br /> | 433 ††<br /> | ||
514<br /> | 514<br /> | ||
523<br /> | 523<br /> | ||
| Line 1,220: | Line 1,236: | ||
712<br /> | 712<br /> | ||
721<br /> | 721<br /> | ||
811<br /> | 811 ††<br /> | ||
3232<br /> | 3232 <strong><br /> | ||
3322<br /> | 3322<br /> | ||
3331<br /> | 3331 ††<br /> | ||
4123<br /> | 4123<br /> | ||
4132<br /> | 4132<br /> | ||
4141<br /> | 4141 </strong><br /> | ||
4213<br /> | 4213<br /> | ||
4231<br /> | 4231<br /> | ||
| Line 1,241: | Line 1,257: | ||
6121<br /> | 6121<br /> | ||
6211<br /> | 6211<br /> | ||
7111<br /> | 7111 ††<br /> | ||
31222<br /> | 31222<br /> | ||
31312<br /> | 31312<br /> | ||
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51211<br /> | 51211<br /> | ||
52111<br /> | 52111<br /> | ||
61111<br /> | 61111 ††<br /> | ||
221221<br /> | 221221 <strong><br /> | ||
222121<br /> | 222121<br /> | ||
222211<br /> | 222211<br /> | ||
| Line 1,273: | Line 1,289: | ||
311212<br /> | 311212<br /> | ||
311221<br /> | 311221<br /> | ||
311311<br /> | 311311 </strong><br /> | ||
312112<br /> | 312112<br /> | ||
312121<br /> | 312121<br /> | ||
| Line 1,288: | Line 1,304: | ||
412111<br /> | 412111<br /> | ||
421111<br /> | 421111<br /> | ||
511111<br /> | 511111 ††<br /> | ||
2121211<br /> | 2121211 ††<br /> | ||
2211121<br /> | 2211121<br /> | ||
2211211<br /> | 2211211<br /> | ||
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3121111<br /> | 3121111<br /> | ||
3211111<br /> | 3211111<br /> | ||
4111111<br /> | 4111111 ††<br /> | ||
21112111<br /> | 21112111 **<br /> | ||
21121111<br /> | 21121111<br /> | ||
21211111<br /> | 21211111<br /> | ||
22111111<br /> | 22111111<br /> | ||
31111111<br /> | 31111111 ††<br /> | ||
211111111<br /> | 211111111 ††<br /> | ||
1111111111</body></html></pre></div> | 1111111111 *</body></html></pre></div> | ||