List of distinct EDO scales: Difference between revisions
Wikispaces>Sarzadoce **Imported revision 553510530 - Original comment: ** |
Wikispaces>Sarzadoce **Imported revision 555135841 - 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- | : This revision was by author [[User:Sarzadoce|Sarzadoce]] and made on <tt>2015-07-09 21:48:30 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>555135841</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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Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by OEIS entries [[http://oeis.org/A059966|A059966]] and [[http://oeis.org/A001037|A001037]]. | Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by OEIS entries [[http://oeis.org/A059966|A059966]] and [[http://oeis.org/A001037|A001037]]. | ||
==Breakdown of Scales by EDO and Number of Notes== | |||
|| || || || || || || || || || || EDO || || || || || || || || | || || || || || || || || || || || EDO || || || || || || || || | ||
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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) | ||
==Breakdown of Scales by EDO Only== | |||
|| n-EDO || Number of Scales | |||
in n-EDO || Number of Scales | |||
//up to// n-EDO || | |||
|| n || f(n) || g(n) || | |||
|| 1 || 1 || 1 || | |||
|| 2 || 1 || 2 || | |||
|| 3 || 2 || 4 || | |||
|| 4 || 3 || 7 || | |||
|| 5 || 6 || 13 || | |||
|| 6 || 9 || 22 || | |||
|| 7 || 18 || 40 || | |||
|| 8 || 30 || 70 || | |||
|| 9 || 56 || 126 || | |||
|| 10 || 99 || 225 || | |||
|| 11 || 186 || 411 || | |||
|| 12 || 335 || 746 || | |||
|| 13 || 630 || 1376 || | |||
|| 14 || 1161 || 2537 || | |||
|| 15 || 2182 || 4719 || | |||
|| 16 || 4080 || 8799 || | |||
|| 17 || 7710 || 16509 || | |||
|| 18 || 14532 || 31041 || | |||
|| 19 || 27594 || 58635 || | |||
|| 20 || 52377 || 111012 || | |||
<span style="line-height: 1.5;"> ∆ EDO (Variety = 1)</span> | <span style="line-height: 1.5;"> ∆ EDO (Variety = 1)</span> | ||
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Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by OEIS entries <a class="wiki_link_ext" href="http://oeis.org/A059966" rel="nofollow">A059966</a> and <a class="wiki_link_ext" href="http://oeis.org/A001037" rel="nofollow">A001037</a>.<br /> | Below is a table which counts every possible scale for a given EDO (columns) and number of steps/notes (rows). Note that the total number of scales for each EDO is given by OEIS entries <a class="wiki_link_ext" href="http://oeis.org/A059966" rel="nofollow">A059966</a> and <a class="wiki_link_ext" href="http://oeis.org/A001037" rel="nofollow">A001037</a>.<br /> | ||
<br /> | <br /> | ||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-Breakdown of Scales by EDO and Number of Notes"></a><!-- ws:end:WikiTextHeadingRule:0 -->Breakdown of Scales by EDO and Number of Notes</h2> | |||
<br /> | |||
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<br /> | <br /> | ||
(if someone could format this table a little better, it would be greatly appreciated)<br /> | (if someone could format this table a little better, it would be greatly appreciated)<br /> | ||
<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="x-Breakdown of Scales by EDO Only"></a><!-- ws:end:WikiTextHeadingRule:2 -->Breakdown of Scales by EDO Only</h2> | |||
<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<td>n-EDO<br /> | |||
</td> | |||
<td>Number of Scales<br /> | |||
in n-EDO<br /> | |||
</td> | |||
<td>Number of Scales<br /> | |||
<em>up to</em> n-EDO<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>n<br /> | |||
</td> | |||
<td>f(n)<br /> | |||
</td> | |||
<td>g(n)<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>2<br /> | |||
</td> | |||
<td>1<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>3<br /> | |||
</td> | |||
<td>2<br /> | |||
</td> | |||
<td>4<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>4<br /> | |||
</td> | |||
<td>3<br /> | |||
</td> | |||
<td>7<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>5<br /> | |||
</td> | |||
<td>6<br /> | |||
</td> | |||
<td>13<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>6<br /> | |||
</td> | |||
<td>9<br /> | |||
</td> | |||
<td>22<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>7<br /> | |||
</td> | |||
<td>18<br /> | |||
</td> | |||
<td>40<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>8<br /> | |||
</td> | |||
<td>30<br /> | |||
</td> | |||
<td>70<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>9<br /> | |||
</td> | |||
<td>56<br /> | |||
</td> | |||
<td>126<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>10<br /> | |||
</td> | |||
<td>99<br /> | |||
</td> | |||
<td>225<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>11<br /> | |||
</td> | |||
<td>186<br /> | |||
</td> | |||
<td>411<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>12<br /> | |||
</td> | |||
<td>335<br /> | |||
</td> | |||
<td>746<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>13<br /> | |||
</td> | |||
<td>630<br /> | |||
</td> | |||
<td>1376<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>14<br /> | |||
</td> | |||
<td>1161<br /> | |||
</td> | |||
<td>2537<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>15<br /> | |||
</td> | |||
<td>2182<br /> | |||
</td> | |||
<td>4719<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>16<br /> | |||
</td> | |||
<td>4080<br /> | |||
</td> | |||
<td>8799<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>17<br /> | |||
</td> | |||
<td>7710<br /> | |||
</td> | |||
<td>16509<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>18<br /> | |||
</td> | |||
<td>14532<br /> | |||
</td> | |||
<td>31041<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>19<br /> | |||
</td> | |||
<td>27594<br /> | |||
</td> | |||
<td>58635<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<td>20<br /> | |||
</td> | |||
<td>52377<br /> | |||
</td> | |||
<td>111012<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | |||
<br /> | |||
<br /> | |||
<br /> | |||
<br /> | <br /> | ||
<span style="line-height: 1.5;"> ∆ EDO (Variety = 1)</span><br /> | <span style="line-height: 1.5;"> ∆ EDO (Variety = 1)</span><br /> | ||
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†† Strict MOS (Variety = 2)<br /> | †† Strict MOS (Variety = 2)<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x-1-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->1-EDO Scales</h2> | ||
<br /> | <br /> | ||
1 ∆<br /> | 1 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x-2-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->2-EDO Scales</h2> | ||
<br /> | <br /> | ||
11 ∆<br /> | 11 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x-3-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->3-EDO Scales</h2> | ||
<br /> | <br /> | ||
21 ††<br /> | 21 ††<br /> | ||
111 ∆<br /> | 111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x-4-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->4-EDO Scales</h2> | ||
<br /> | <br /> | ||
31 ††<br /> | 31 ††<br /> | ||
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1111 ∆<br /> | 1111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="x-5-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->5-EDO Scales</h2> | ||
<br /> | <br /> | ||
32 ††<br /> | 32 ††<br /> | ||
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11111 ∆<br /> | 11111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="x-6-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:14 -->6-EDO Scales</h2> | ||
<br /> | <br /> | ||
51 ††<br /> | 51 ††<br /> | ||
| Line 1,108: | Line 1,337: | ||
111111 ∆<br /> | 111111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x-7-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:16 -->7-EDO Scales</h2> | ||
<br /> | <br /> | ||
43 ††<br /> | 43 ††<br /> | ||
| Line 1,129: | Line 1,358: | ||
1111111 ∆<br /> | 1111111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x-8-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:18 -->8-EDO Scales</h2> | ||
<br /> | <br /> | ||
53 ††<br /> | 53 ††<br /> | ||
| Line 1,162: | Line 1,391: | ||
11111111 ∆<br /> | 11111111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="x-9-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:20 -->9-EDO Scales</h2> | ||
<br /> | <br /> | ||
54 ††<br /> | 54 ††<br /> | ||
| Line 1,221: | Line 1,450: | ||
111111111 ∆<br /> | 111111111 ∆<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="x-10-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:22 -->10-EDO Scales</h2> | ||
<br /> | <br /> | ||
73 ††<br /> | 73 ††<br /> | ||