List of distinct EDO scales
IMPORTED REVISION FROM WIKISPACES
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Original Wikitext content:
Each [[Equal division of the octave|EDO]] 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). 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 || || || || || || || || || || || 1 || 2 || 3 || 4 || 5 || 6 || 7 || 8 || 9 || 10 || 11 || 12 || 13 || 14 || 15 || 16 || || || 1 || 1 || || || || || || || || || || || || || || || || || || 2 || || 1 || 1 || 1 || 2 || 1 || 3 || 2 || 3 || 2 || 5 || 2 || 6 || 3 || 4 || 4 || || || 3 || || || 1 || 1 || 2 || 3 || 5 || 6 || 9 || 10 || 15 || 14 || 22 || 21 || 28 || 28 || || || 4 || || || || 1 || 1 || 3 || 5 || 9 || 14 || 21 || 30 || 39 || 55 || 68 || 90 || 106 || || || 5 || || || || || 1 || 1 || 3 || 7 || 14 || 25 || 42 || 65 || 99 || 140 || 200 || 266 || || || 6 || || || || || || 1 || 1 || 4 || 10 || 22 || 42 || 79 || 132 || 216 || 335 || 500 || || || 7 || || || || || || || 1 || 1 || 4 || 12 || 30 || 66 || 132 || 245 || 429 || 714 || || N || 8 || || || || || || || || 1 || 1 || 5 || 15 || 43 || 99 || 217 || 429 || 809 || || || 9 || || || || || || || || || 1 || 1 || 5 || 19 || 55 || 143 || 335 || 715 || || || 10 || || || || || || || || || || 1 || 1 || 6 || 22 || 73 || 201 || 504 || || || 11 || || || || || || || || || || || 1 || 1 || 6 || 26 || 91 || 273 || || || 12 || || || || || || || || || || || || 1 || 1 || 7 || 31 || 116 || || || 13 || || || || || || || || || || || || || 1 || 1 || 7 || 35 || || || 14 || || || || || || || || || || || || || || 1 || 1 || 8 || || || 15 || || || || || || || || || || || || || || || 1 || 1 || || || 16 || || || || || || || || || || || || || || || || 1 || || || || || || || || || || || || || || || || || || || || || || Total || 1 || 1 || 2 || 3 || 6 || 9 || 18 || 30 || 56 || 99 || 186 || 335 || 630 || 1161 || 2182 || 4080 || (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;"> ◊◊ Multi-MOS (Max Variety = 2)</span> †† Strict MOS (Variety = 2) ==1-EDO Scales== 1 ∆ ==2-EDO Scales== 11 ∆ ==3-EDO Scales== 21 †† 111 ∆ ==4-EDO Scales== 31 †† 211 †† 1111 ∆ ==5-EDO Scales== 32 †† 41 †† 221 †† 311 †† 2111 †† 11111 ∆ ==6-EDO Scales== 51 †† 312 321 411 †† 2121 ◊◊ 2211 3111 †† 21111 †† 111111 ∆ ==7-EDO Scales== 43 †† 52 †† 61 †† 322 †† 331 †† 412 421 511 †† 2221 †† 3112 3121 3211 4111 †† 21211 †† 22111 31111 †† 211111 †† 1111111 ∆ ==8-EDO Scales== 53 †† 71 †† 332 †† 413 431 512 521 611 †† 3122 3131 ◊◊ 3212 3221 3311 4112 4121 4211 5111 †† 22121 †† 22211 31112 31121 31211 32111 41111 †† 211211 ◊◊ 212111 221111 311111 †† 2111111 †† 11111111 ∆ ==9-EDO Scales== 54 †† 72 †† 81 †† 423 432 441 †† 513 522 †† 531 612 621 711 †† 3222 †† 3231 3312 3321 4113 4122 4131 4212 4221 4311 5112 5121 5211 6111 †† 22221 †† 31122 31212 31221 31311 †† 32112 32121 32211 33111 41112 41121 41211 42111 51111 †† 212121 ◊◊ 221121 221211 222111 311112 311121 311211 312111 321111 411111 †† 2112111 †† 2121111 2211111 3111111 †† 21111111 †† 111111111 ∆ ==10-EDO Scales== 73 †† 91 †† 433 †† 514 523 532 541 613 631 712 721 811 †† 3232 ◊◊ 3322 3331 †† 4123 4132 4141 ◊◊ 4213 4231 4312 4321 4411 5113 5122 5131 5212 5221 5311 6112 6121 6211 7111 †† 31222 31312 32122 32131 32212 32221 32311 33112 33121 33211 41113 41122 41131 41212 41221 41311 42112 42121 42211 43111 51112 51121 51211 52111 61111 †† 221221 ◊◊ 222121 222211 311122 311212 311221 311311 ◊◊ 312112 312121 312211 313111 321112 321121 321211 322111 331111 411112 411121 411211 412111 421111 511111 †† 2121211 †† 2211121 2211211 2212111 2221111 3111112 3111121 3111211 3112111 3121111 3211111 4111111 †† 21112111 ◊◊ 21121111 21211111 22111111 31111111 †† 211111111 †† 1111111111 ∆
Original HTML content:
<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 />
<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 />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><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 />
<table class="wiki_table">
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>EDO<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>2<br />
</td>
<td>3<br />
</td>
<td>4<br />
</td>
<td>5<br />
</td>
<td>6<br />
</td>
<td>7<br />
</td>
<td>8<br />
</td>
<td>9<br />
</td>
<td>10<br />
</td>
<td>11<br />
</td>
<td>12<br />
</td>
<td>13<br />
</td>
<td>14<br />
</td>
<td>15<br />
</td>
<td>16<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>2<br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>2<br />
</td>
<td>1<br />
</td>
<td>3<br />
</td>
<td>2<br />
</td>
<td>3<br />
</td>
<td>2<br />
</td>
<td>5<br />
</td>
<td>2<br />
</td>
<td>6<br />
</td>
<td>3<br />
</td>
<td>4<br />
</td>
<td>4<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>3<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>2<br />
</td>
<td>3<br />
</td>
<td>5<br />
</td>
<td>6<br />
</td>
<td>9<br />
</td>
<td>10<br />
</td>
<td>15<br />
</td>
<td>14<br />
</td>
<td>22<br />
</td>
<td>21<br />
</td>
<td>28<br />
</td>
<td>28<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>4<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>3<br />
</td>
<td>5<br />
</td>
<td>9<br />
</td>
<td>14<br />
</td>
<td>21<br />
</td>
<td>30<br />
</td>
<td>39<br />
</td>
<td>55<br />
</td>
<td>68<br />
</td>
<td>90<br />
</td>
<td>106<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>5<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>3<br />
</td>
<td>7<br />
</td>
<td>14<br />
</td>
<td>25<br />
</td>
<td>42<br />
</td>
<td>65<br />
</td>
<td>99<br />
</td>
<td>140<br />
</td>
<td>200<br />
</td>
<td>266<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>6<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>4<br />
</td>
<td>10<br />
</td>
<td>22<br />
</td>
<td>42<br />
</td>
<td>79<br />
</td>
<td>132<br />
</td>
<td>216<br />
</td>
<td>335<br />
</td>
<td>500<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>7<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>4<br />
</td>
<td>12<br />
</td>
<td>30<br />
</td>
<td>66<br />
</td>
<td>132<br />
</td>
<td>245<br />
</td>
<td>429<br />
</td>
<td>714<br />
</td>
</tr>
<tr>
<td>N<br />
</td>
<td>8<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>5<br />
</td>
<td>15<br />
</td>
<td>43<br />
</td>
<td>99<br />
</td>
<td>217<br />
</td>
<td>429<br />
</td>
<td>809<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>9<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>5<br />
</td>
<td>19<br />
</td>
<td>55<br />
</td>
<td>143<br />
</td>
<td>335<br />
</td>
<td>715<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>10<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>6<br />
</td>
<td>22<br />
</td>
<td>73<br />
</td>
<td>201<br />
</td>
<td>504<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>11<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>6<br />
</td>
<td>26<br />
</td>
<td>91<br />
</td>
<td>273<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>12<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>7<br />
</td>
<td>31<br />
</td>
<td>116<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>13<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>7<br />
</td>
<td>35<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>14<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>8<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>15<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>16<br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td>1<br />
</td>
</tr>
<tr>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
<td><br />
</td>
</tr>
<tr>
<td><br />
</td>
<td>Total<br />
</td>
<td>1<br />
</td>
<td>1<br />
</td>
<td>2<br />
</td>
<td>3<br />
</td>
<td>6<br />
</td>
<td>9<br />
</td>
<td>18<br />
</td>
<td>30<br />
</td>
<td>56<br />
</td>
<td>99<br />
</td>
<td>186<br />
</td>
<td>335<br />
</td>
<td>630<br />
</td>
<td>1161<br />
</td>
<td>2182<br />
</td>
<td>4080<br />
</td>
</tr>
</table>
<br />
(if someone could format this table a little better, it would be greatly appreciated)<br />
<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><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 />
<span style="line-height: 1.5;"> ∆ EDO (Variety = 1)</span><br />
<span style="line-height: 1.5;"> ◊◊ Multi-MOS (Max Variety = 2)</span><br />
†† Strict MOS (Variety = 2)<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="x-1-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:4 -->1-EDO Scales</h2>
<br />
1 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h2> --><h2 id="toc3"><a name="x-2-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->2-EDO Scales</h2>
<br />
11 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="x-3-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:8 -->3-EDO Scales</h2>
<br />
21 ††<br />
111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><h2 id="toc5"><a name="x-4-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:10 -->4-EDO Scales</h2>
<br />
31 ††<br />
211 ††<br />
1111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="x-5-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:12 -->5-EDO Scales</h2>
<br />
32 ††<br />
41 ††<br />
221 ††<br />
311 ††<br />
2111 ††<br />
11111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="x-6-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:14 -->6-EDO Scales</h2>
<br />
51 ††<br />
312<br />
321<br />
411 ††<br />
2121 ◊◊<br />
2211<br />
3111 ††<br />
21111 ††<br />
111111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="x-7-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:16 -->7-EDO Scales</h2>
<br />
43 ††<br />
52 ††<br />
61 ††<br />
322 ††<br />
331 ††<br />
412<br />
421<br />
511 ††<br />
2221 ††<br />
3112<br />
3121<br />
3211<br />
4111 ††<br />
21211 ††<br />
22111<br />
31111 ††<br />
211111 ††<br />
1111111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="x-8-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:18 -->8-EDO Scales</h2>
<br />
53 ††<br />
71 ††<br />
332 ††<br />
413<br />
431<br />
512<br />
521<br />
611 ††<br />
3122<br />
3131 ◊◊<br />
3212<br />
3221<br />
3311<br />
4112<br />
4121<br />
4211<br />
5111 ††<br />
22121 ††<br />
22211<br />
31112<br />
31121<br />
31211<br />
32111<br />
41111 ††<br />
211211 ◊◊<br />
212111<br />
221111<br />
311111 ††<br />
2111111 ††<br />
11111111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="x-9-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:20 -->9-EDO Scales</h2>
<br />
54 ††<br />
72 ††<br />
81 ††<br />
423<br />
432<br />
441 ††<br />
513<br />
522 ††<br />
531<br />
612<br />
621<br />
711 ††<br />
3222 ††<br />
3231<br />
3312<br />
3321<br />
4113<br />
4122<br />
4131<br />
4212<br />
4221<br />
4311<br />
5112<br />
5121<br />
5211<br />
6111 ††<br />
22221 ††<br />
31122<br />
31212<br />
31221<br />
31311 ††<br />
32112<br />
32121<br />
32211<br />
33111<br />
41112<br />
41121<br />
41211<br />
42111<br />
51111 ††<br />
212121 ◊◊<br />
221121<br />
221211<br />
222111<br />
311112<br />
311121<br />
311211<br />
312111<br />
321111<br />
411111 ††<br />
2112111 ††<br />
2121111<br />
2211111<br />
3111111 ††<br />
21111111 ††<br />
111111111 ∆<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="x-10-EDO Scales"></a><!-- ws:end:WikiTextHeadingRule:22 -->10-EDO Scales</h2>
<br />
73 ††<br />
91 ††<br />
433 ††<br />
514<br />
523<br />
532<br />
541<br />
613<br />
631<br />
712<br />
721<br />
811 ††<br />
3232 ◊◊<br />
3322<br />
3331 ††<br />
4123<br />
4132<br />
4141 ◊◊<br />
4213<br />
4231<br />
4312<br />
4321<br />
4411<br />
5113<br />
5122<br />
5131<br />
5212<br />
5221<br />
5311<br />
6112<br />
6121<br />
6211<br />
7111 ††<br />
31222<br />
31312<br />
32122<br />
32131<br />
32212<br />
32221<br />
32311<br />
33112<br />
33121<br />
33211<br />
41113<br />
41122<br />
41131<br />
41212<br />
41221<br />
41311<br />
42112<br />
42121<br />
42211<br />
43111<br />
51112<br />
51121<br />
51211<br />
52111<br />
61111 ††<br />
221221 ◊◊<br />
222121<br />
222211<br />
311122<br />
311212<br />
311221<br />
311311 ◊◊<br />
312112<br />
312121<br />
312211<br />
313111<br />
321112<br />
321121<br />
321211<br />
322111<br />
331111<br />
411112<br />
411121<br />
411211<br />
412111<br />
421111<br />
511111 ††<br />
2121211 ††<br />
2211121<br />
2211211<br />
2212111<br />
2221111<br />
3111112<br />
3111121<br />
3111211<br />
3112111<br />
3121111<br />
3211111<br />
4111111 ††<br />
21112111 ◊◊<br />
21121111<br />
21211111<br />
22111111<br />
31111111 ††<br />
211111111 ††<br />
1111111111 ∆</body></html>