11L 3s: Difference between revisions
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The '''11L 3s''' [[MOS scale]] was named the "Ketradektriatoh scale" by [[Osmiorisbendi]] | The '''11L 3s''' [[MOS scale]] was named the "Ketradektriatoh scale" by [[Osmiorisbendi]] | ||
This is a type of scale which denotes the use of a scale placed between [[11edo]] and [[14edo]], employing a ratio generator between 41/32 ~ 9/7 ([[25edo]] being the middle size of the Ketradektriatoh spectrum, in the 2:1 relation), resulting in a variant of tetradecatonic scale which conforms by this scheme: LLLLsLLLLsLLLs. | This is a type of scale which denotes the use of a scale placed between [[11edo]] and [[14edo]], employing a ratio generator between 41/32 ~ 9/7 ([[25edo]] being the middle size of the Ketradektriatoh spectrum, in the 2:1 relation), resulting in a variant of tetradecatonic scale which conforms by this scheme: LLLLsLLLLsLLLs. | ||
== Scale tree == | == Scale tree == | ||
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| style="text-align:center;" | | | style="text-align:center;" | | ||
|} | |} | ||
== Edos that contains this scale == | |||
'''2 2 2 1 2 2 2 2 1 2 2 2 2 1: [[25edo|25]] (Middle range)''' | |||
'''3 3 3 1 3 3 3 3 1 3 3 3 3 1: [[36edo|36]] (Lufsur range)''' | |||
'''3 3 3 2 3 3 3 3 2 3 3 3 3 2: [[39edo|39]] (Fuslur range)''' | |||
4 4 4 1 4 4 4 4 1 4 4 4 4 1: [[47edo|47]] | |||
4 4 4 2 4 4 4 4 2 4 4 4 4 2: [[50edo|50]] | |||
4 4 4 3 4 4 4 4 3 4 4 4 4 3: [[53edo|53]] | |||
5 5 5 1 5 5 5 5 1 5 5 5 5 1: [[58edo|58]] | |||
'''5 5 5 2 5 5 5 5 2 5 5 5 5 2: [[61edo|61]] Split-φ''' | |||
'''5 5 5 3 5 5 5 5 3 5 5 5 5 3: [[64edo|64]]''' '''φ''' | |||
5 5 5 4 5 5 5 5 4 5 5 5 5 4: [[67edo|67]] | |||
6 6 6 1 6 6 6 6 1 6 6 6 6 1: [[69edo|69]] | |||
6 6 6 5 6 6 6 6 5 6 6 6 6 5: [[81edo|81]] | |||
7 7 7 1 7 7 7 7 1 7 7 7 7 1: [[80edo|80]] | |||
7 7 7 2 7 7 7 7 2 7 7 7 7 2: [[83edo|83]] | |||
7 7 7 3 7 7 7 7 3 7 7 7 7 3: [[86edo|86]] | |||
7 7 7 4 7 7 7 7 4 7 7 7 7 4: [[89edo|89]] | |||
7 7 7 5 7 7 7 7 5 7 7 7 7 5: [[92edo|92]] | |||
7 7 7 6 7 7 7 7 6 7 7 7 7 6: [[95edo|95]] | |||
8 8 8 1 8 8 8 8 1 8 8 8 8 1: [[91edo|91]] | |||
'''8 8 8 3 8 8 8 8 3 8 8 8 8 3: [[97edo|97]] Split-φ''' | |||
'''8 8 8 5 8 8 8 8 5 8 8 8 8 5: [[103edo|103]]''' '''φ''' | |||
8 8 8 7 8 8 8 8 7 8 8 8 8 7: [[109edo|109]] | |||
9 9 9 1 9 9 9 9 1 9 9 9 9 1: [[102edo|102]] | |||
9 9 9 2 9 9 9 9 2 9 9 9 9 2: [[105edo|105]] | |||
9 9 9 4 9 9 9 9 4 9 9 9 9 4: [[111edo|111]] | |||
9 9 9 5 9 9 9 9 5 9 9 9 9 5: [[114edo|114]] | |||
9 9 9 7 9 9 9 9 7 9 9 9 9 7: [[120edo|120]] | |||
9 9 9 8 9 9 9 9 8 9 9 9 9 8: [[123edo|123]] | |||
10 10 10 1 10 10 10 10 1 10 10 10 10 1:[[113edo|113]] | |||
10 10 10 3 10 10 10 10 3 10 10 10 10 3: [[119edo|119]] | |||
10 10 10 7 10 10 10 10 7 10 10 10 10 7: [[131edo|131]] | |||
10 10 10 9 10 10 10 10 9 10 10 10 10 9: [[137edo|137]] | |||
11 11 11 '''<span style="color: #006209;">1</span>''' 11 11 11 11 '''<span style="color: #006209;">1</span>''' 11 11 11 11 '''<span style="color: #006209;">1</span>''': [[124edo|124]] | |||
11 11 11 2 11 11 11 11 2 11 11 11 11 2: [[127edo|127]] | |||
11 11 11 3 11 11 11 11 3 11 11 11 11 3: [[130edo|130]] | |||
11 11 11 4 11 11 11 11 4 11 11 11 11 4: [[133edo|133]] | |||
11 11 11 5 11 11 11 11 5 11 11 11 11 5: [[136edo|136]] | |||
11 11 11 6 11 11 11 11 6 11 11 11 11 6: [[139edo|139]] | |||
11 11 11 7 11 11 11 11 7 11 11 11 11 7: [[142edo|142]] | |||
11 11 11 8 11 11 11 11 8 11 11 11 11 8: [[145edo|145]] | |||
11 11 11 9 11 11 11 11 9 11 11 11 11 9 :[[148edo|148]] | |||
11 11 11 10 11 11 11 11 10 11 11 11 11 10: [[151edo|151]] | |||
12 12 12 1 12 12 12 12 1 12 12 12 12 1: [[135edo|135]] | |||
12 12 12 5 12 12 12 12 5 12 12 12 12 5: [[147edo|147]] | |||
12 12 12 7 12 12 12 12 7 12 12 12 12 7: [[153edo|153]] | |||
12 12 12 11 12 12 12 12 11 12 12 12 12 11: [[165edo|165]] | |||
13 13 13 1 13 13 13 13 1 13 13 13 13 1: [[146edo|146]] | |||
13 13 13 2 13 13 13 13 2 13 13 13 13 2: [[149edo|149]] | |||
13 13 13 3 13 13 13 13 3 13 13 13 13 3: [[152edo|152]] | |||
13 13 13 4 13 13 13 13 4 13 13 13 13 4: [[155edo|155]] | |||
'''13 13 13 5 13 13 13 13 5 13 13 13 13 5: [[158edo|158]] Split-φ''' | |||
13 13 13 6 13 13 13 13 6 13 13 13 13 6: [[161edo|161]] | |||
13 13 13 7 13 13 13 13 7 13 13 13 13 7: [[164edo|164]] | |||
'''13 13 13 8 13 13 13 13 8 13 13 13 13 8: [[167edo|167]]''' '''φ''' | |||
13 13 13 9 13 13 13 13 9 13 13 13 13 9: [[170edo|170]] | |||
13 13 13 10 13 13 13 13 10 13 13 13 13 10: [[173edo|173]] | |||
13 13 13 11 13 13 13 13 11 13 13 13 13 11: [[176edo|176]] | |||
13 13 13 12 13 13 13 13 12 13 13 13 13 12: [[179edo|179]] | |||
14 14 14 1 14 14 14 14 1 14 14 14 14 1: [[157edo|157]] | |||
14 14 14 3 14 14 14 14 3 14 14 14 14 3: [[163edo|163]] | |||
14 14 14 5 14 14 14 14 5 14 14 14 14 5: [[169edo|169]] | |||
14 14 14 9 14 14 14 14 9 14 14 14 14 9: [[181edo|181]] | |||
14 14 14 11 14 14 14 14 11 14 14 14 14 11: [[187edo|187]] | |||
14 14 14 13 14 14 14 14 13 14 14 14 14 13: [[193edo|193]] | |||
15 15 15 1 15 15 15 15 1 15 15 15 15 1: [[168edo|168]] | |||
15 15 15 2 15 15 15 15 2 15 15 15 15 2: [[171edo|171]] | |||
15 15 15 4 15 15 15 15 4 15 15 15 15 4: [[177edo|177]] | |||
15 15 15 7 15 15 15 15 7 15 15 15 15 7: [[186edo|186]] | |||
15 15 15 8 15 15 15 15 8 15 15 15 15 8: [[189edo|189]] | |||
15 15 15 11 15 15 15 15 11 15 15 15 15 11: [[198edo|198]] | |||
15 15 15 13 15 15 15 15 13 15 15 15 15 13: [[204edo|204]] | |||
15 15 15 14 15 15 15 15 14 15 15 15 15 14: [[207edo|207]] | |||
16 16 16 1 16 16 16 16 1 16 16 16 16 1: [[179edo|179]] | |||
16 16 16 3 16 16 16 16 3 16 16 16 16 3: [[185edo|185]] | |||
16 16 16 5 16 16 16 16 5 16 16 16 16 5: [[191edo|191]] | |||
16 16 16 7 16 16 16 16 7 16 16 16 16 7: [[197edo|197]] | |||
16 16 16 9 16 16 16 16 9 16 16 16 16 9: [[203edo|203]] | |||
16 16 16 11 16 16 16 16 11 16 16 16 16 11: [[209edo|209]] | |||
16 16 16 13 16 16 16 16 13 16 16 16 16 13: [[215edo|215]] | |||
16 16 16 15 16 16 16 16 15 16 16 16 16 15: [[221edo|221]] | |||
17 17 17 1 17 17 17 17 1 17 17 17 17 1: [[190edo|190]] | |||
17 17 17 2 17 17 17 17 2 17 17 17 17 2: [[193edo|193]] | |||
17 17 17 3 17 17 17 17 3 17 17 17 17 3: [[196edo|196]] | |||
17 17 17 4 17 17 17 17 4 17 17 17 17 4: [[199edo|199]] | |||
'''17 17 17 5 17 17 17 17 5 17 17 17 17 5: [[202edo|202]] (Top limit for Lufsur range)''' | |||
'''17 17 17 6 17 17 17 17 6 17 17 17 17 6: [[205edo|205]]''' | |||
'''17 17 17 7 17 17 17 17 7 17 17 17 17 7: [[208edo|208]]''' | |||
'''17 17 17 8 17 17 17 17 8 17 17 17 17 8: [[211edo|211]]''' | |||
'''17 17 17 9 17 17 17 17 9 17 17 17 17 9: [[214edo|214]]''' | |||
'''17 17 17 10 17 17 17 17 10 17 17 17 17 10: [[217edo|217]]''' | |||
'''17 17 17 11 17 17 17 17 11 17 17 17 17 11: [[220edo|220]]''' | |||
'''17 17 17 12 17 17 17 17 12 17 17 17 17 12: [[223edo|223]] (Top limit for Fuslur range)''' | |||
17 17 17 13 17 17 17 17 13 17 17 17 17 13: [[226edo|226]] | |||
17 17 17 14 17 17 17 17 14 17 17 17 17 14: [[229edo|229]] | |||
17 17 17 15 17 17 17 17 15 17 17 17 17 15: [[232edo|232]] | |||
17 17 17 16 17 17 17 17 16 17 17 17 17 16: [[235edo|235]] | |||
{{todo|cleanup}} | {{todo|cleanup}} | ||
[[Category:14-tone scales]] | [[Category:14-tone scales]] |
Revision as of 07:50, 26 April 2023
↖ 10L 2s | ↑ 11L 2s | 12L 2s ↗ |
← 10L 3s | 11L 3s | 12L 3s → |
↙ 10L 4s | ↓ 11L 4s | 12L 4s ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║║│║║║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLLsLLLL
The 11L 3s MOS scale was named the "Ketradektriatoh scale" by Osmiorisbendi
This is a type of scale which denotes the use of a scale placed between 11edo and 14edo, employing a ratio generator between 41/32 ~ 9/7 (25edo being the middle size of the Ketradektriatoh spectrum, in the 2:1 relation), resulting in a variant of tetradecatonic scale which conforms by this scheme: LLLLsLLLLsLLLs.
Scale tree
The next table below shows an extension of edos which supports the Ketradektriatoh scale, with respect to the principal generator and their results for each L/s sizes:
4\11 | 436.364 | 109.091 | 0 | |||||||
29\80 | 435 | 105 | 15 | |||||||
25\69 | 434.783 | 104.348 | 17.391 | |||||||
21\58 | 434.483 | 103.448 | 20.69 | |||||||
17\47 | 434.043 | 102.128 | 25.532 | |||||||
30\83 | 433.735 | 101.208 | 28.916 | |||||||
73\202 | 433.663 | 100.990 | 29.703 | Since here are the optimal range Lufsur mode (?) | ||||||
43\119 | 433.613 | 100.840 | 30.252 | |||||||
433.459 | 100.377 | 31.95 | ||||||||
13\36 | 433.333 | 100 | 33.333 | |||||||
433.048 | 99.144 | 36.473 | ||||||||
35\97 | 432.99 | 98.969 | 37.113 | |||||||
432.933 | 98.799 | 37.738 | ||||||||
22\61 | 432.787 | 98.361 | 39.344 | |||||||
9\25 | 432 | 96 | 48 | Boundary of propriety;
generators smaller than this are proper | ||||||
431.417 | 94.25 | 54.4155 | ||||||||
23\64 | 431.25 | 93.75 | 56.25 | |||||||
431.1185 | 93.355 | 57.697 | ||||||||
37\103 | 431.068 | 93.204 | 58.25 | |||||||
430.984 | 92.952 | 58.175 | ||||||||
14\39 | 430.769 | 92.308 | 61.538 | |||||||
47\131 | 430.534 | 91.603 | 64.122 | |||||||
80\223 | 430.493 | 91.480 | 64.575 | Until here are the optimal range Fuslur mode (?) | ||||||
33\92 | 430.435 | 91.304 | 65.217 | |||||||
19\53 | 430.189 | 90.566 | 67.925 | |||||||
24\67 | 429.851 | 89.552 | 71.642 | |||||||
29\81 | 429.63 | 88.889 | 74.074 | |||||||
34\95 | 429.474 | 88.421 | 75.7895 | |||||||
5\14 | 428.571 | 85.714 | 85.714 |
Edos that contains this scale
2 2 2 1 2 2 2 2 1 2 2 2 2 1: 25 (Middle range)
3 3 3 1 3 3 3 3 1 3 3 3 3 1: 36 (Lufsur range)
3 3 3 2 3 3 3 3 2 3 3 3 3 2: 39 (Fuslur range)
4 4 4 1 4 4 4 4 1 4 4 4 4 1: 47
4 4 4 2 4 4 4 4 2 4 4 4 4 2: 50
4 4 4 3 4 4 4 4 3 4 4 4 4 3: 53
5 5 5 1 5 5 5 5 1 5 5 5 5 1: 58
5 5 5 2 5 5 5 5 2 5 5 5 5 2: 61 Split-φ
5 5 5 3 5 5 5 5 3 5 5 5 5 3: 64 φ
5 5 5 4 5 5 5 5 4 5 5 5 5 4: 67
6 6 6 1 6 6 6 6 1 6 6 6 6 1: 69
6 6 6 5 6 6 6 6 5 6 6 6 6 5: 81
7 7 7 1 7 7 7 7 1 7 7 7 7 1: 80
7 7 7 2 7 7 7 7 2 7 7 7 7 2: 83
7 7 7 3 7 7 7 7 3 7 7 7 7 3: 86
7 7 7 4 7 7 7 7 4 7 7 7 7 4: 89
7 7 7 5 7 7 7 7 5 7 7 7 7 5: 92
7 7 7 6 7 7 7 7 6 7 7 7 7 6: 95
8 8 8 1 8 8 8 8 1 8 8 8 8 1: 91
8 8 8 3 8 8 8 8 3 8 8 8 8 3: 97 Split-φ
8 8 8 5 8 8 8 8 5 8 8 8 8 5: 103 φ
8 8 8 7 8 8 8 8 7 8 8 8 8 7: 109
9 9 9 1 9 9 9 9 1 9 9 9 9 1: 102
9 9 9 2 9 9 9 9 2 9 9 9 9 2: 105
9 9 9 4 9 9 9 9 4 9 9 9 9 4: 111
9 9 9 5 9 9 9 9 5 9 9 9 9 5: 114
9 9 9 7 9 9 9 9 7 9 9 9 9 7: 120
9 9 9 8 9 9 9 9 8 9 9 9 9 8: 123
10 10 10 1 10 10 10 10 1 10 10 10 10 1:113
10 10 10 3 10 10 10 10 3 10 10 10 10 3: 119
10 10 10 7 10 10 10 10 7 10 10 10 10 7: 131
10 10 10 9 10 10 10 10 9 10 10 10 10 9: 137
11 11 11 1 11 11 11 11 1 11 11 11 11 1: 124
11 11 11 2 11 11 11 11 2 11 11 11 11 2: 127
11 11 11 3 11 11 11 11 3 11 11 11 11 3: 130
11 11 11 4 11 11 11 11 4 11 11 11 11 4: 133
11 11 11 5 11 11 11 11 5 11 11 11 11 5: 136
11 11 11 6 11 11 11 11 6 11 11 11 11 6: 139
11 11 11 7 11 11 11 11 7 11 11 11 11 7: 142
11 11 11 8 11 11 11 11 8 11 11 11 11 8: 145
11 11 11 9 11 11 11 11 9 11 11 11 11 9 :148
11 11 11 10 11 11 11 11 10 11 11 11 11 10: 151
12 12 12 1 12 12 12 12 1 12 12 12 12 1: 135
12 12 12 5 12 12 12 12 5 12 12 12 12 5: 147
12 12 12 7 12 12 12 12 7 12 12 12 12 7: 153
12 12 12 11 12 12 12 12 11 12 12 12 12 11: 165
13 13 13 1 13 13 13 13 1 13 13 13 13 1: 146
13 13 13 2 13 13 13 13 2 13 13 13 13 2: 149
13 13 13 3 13 13 13 13 3 13 13 13 13 3: 152
13 13 13 4 13 13 13 13 4 13 13 13 13 4: 155
13 13 13 5 13 13 13 13 5 13 13 13 13 5: 158 Split-φ
13 13 13 6 13 13 13 13 6 13 13 13 13 6: 161
13 13 13 7 13 13 13 13 7 13 13 13 13 7: 164
13 13 13 8 13 13 13 13 8 13 13 13 13 8: 167 φ
13 13 13 9 13 13 13 13 9 13 13 13 13 9: 170
13 13 13 10 13 13 13 13 10 13 13 13 13 10: 173
13 13 13 11 13 13 13 13 11 13 13 13 13 11: 176
13 13 13 12 13 13 13 13 12 13 13 13 13 12: 179
14 14 14 1 14 14 14 14 1 14 14 14 14 1: 157
14 14 14 3 14 14 14 14 3 14 14 14 14 3: 163
14 14 14 5 14 14 14 14 5 14 14 14 14 5: 169
14 14 14 9 14 14 14 14 9 14 14 14 14 9: 181
14 14 14 11 14 14 14 14 11 14 14 14 14 11: 187
14 14 14 13 14 14 14 14 13 14 14 14 14 13: 193
15 15 15 1 15 15 15 15 1 15 15 15 15 1: 168
15 15 15 2 15 15 15 15 2 15 15 15 15 2: 171
15 15 15 4 15 15 15 15 4 15 15 15 15 4: 177
15 15 15 7 15 15 15 15 7 15 15 15 15 7: 186
15 15 15 8 15 15 15 15 8 15 15 15 15 8: 189
15 15 15 11 15 15 15 15 11 15 15 15 15 11: 198
15 15 15 13 15 15 15 15 13 15 15 15 15 13: 204
15 15 15 14 15 15 15 15 14 15 15 15 15 14: 207
16 16 16 1 16 16 16 16 1 16 16 16 16 1: 179
16 16 16 3 16 16 16 16 3 16 16 16 16 3: 185
16 16 16 5 16 16 16 16 5 16 16 16 16 5: 191
16 16 16 7 16 16 16 16 7 16 16 16 16 7: 197
16 16 16 9 16 16 16 16 9 16 16 16 16 9: 203
16 16 16 11 16 16 16 16 11 16 16 16 16 11: 209
16 16 16 13 16 16 16 16 13 16 16 16 16 13: 215
16 16 16 15 16 16 16 16 15 16 16 16 16 15: 221
17 17 17 1 17 17 17 17 1 17 17 17 17 1: 190
17 17 17 2 17 17 17 17 2 17 17 17 17 2: 193
17 17 17 3 17 17 17 17 3 17 17 17 17 3: 196
17 17 17 4 17 17 17 17 4 17 17 17 17 4: 199
17 17 17 5 17 17 17 17 5 17 17 17 17 5: 202 (Top limit for Lufsur range)
17 17 17 6 17 17 17 17 6 17 17 17 17 6: 205
17 17 17 7 17 17 17 17 7 17 17 17 17 7: 208
17 17 17 8 17 17 17 17 8 17 17 17 17 8: 211
17 17 17 9 17 17 17 17 9 17 17 17 17 9: 214
17 17 17 10 17 17 17 17 10 17 17 17 17 10: 217
17 17 17 11 17 17 17 17 11 17 17 17 17 11: 220
17 17 17 12 17 17 17 17 12 17 17 17 17 12: 223 (Top limit for Fuslur range)
17 17 17 13 17 17 17 17 13 17 17 17 17 13: 226
17 17 17 14 17 17 17 17 14 17 17 17 17 14: 229
17 17 17 15 17 17 17 17 15 17 17 17 17 15: 232
17 17 17 16 17 17 17 17 16 17 17 17 17 16: 235