Xenharmonic Wiki

12L 1s: Difference between revisions

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+Infobox, name still missing, misc. edits
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Line 1: Line 1:
{{Infobox MOS
{{Infobox MOS
| Name =  
| Other names = grumpy tridecatonic
| Periods = 1
| Periods = 1
| nLargeSteps = 12
| nLargeSteps = 12
Line 8: Line 8:
| Pattern = LLLLLLLLLLLLs
| Pattern = LLLLLLLLLLLLs
}}
}}
The '''12L 1s''' [[MOS scale]], the grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed 12ed scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24¢ of it), for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic ([[1L 11s]]) in the 1.75¢ above 1/13edo because the large and small steps register as identical to one another for human listeners).
The '''12L 1s''' [[MOS scale]], the grumpy tridecatonic, apparently belongs to no particularly important temperament. However, it becomes a compressed [[12edo]] scale when you ignore the octave (this obviously does not work when the generator is very near 12edo (within -7/24{{cent}} of it), for the 13th degree of the scale registers as identical to the octave for human listeners, and it becomes indistinct from 13edo or the Happy dodecatonic ([[1L 11s]]) in the 1.75{{cent}} above 1\13 because the large and small steps register as identical to one another for human listeners).


== Scale tree ==
== Scale tree ==
Line 14: Line 14:
|-
|-
! colspan="3" | Generator
! colspan="3" | Generator
! | Cents
! Cents
! | 12g
! 12g
! Comments
|-
|-
| | 1/13
| 1\13
| |  
|  
| |  
|  
| | 92.308
| 92.308
| | 1107.692
| 1107.692
|
|-
|-
| | 5/64
| 5\64
| |  
|  
| |  
|  
| | 93.75
| 93.75
| | 1125
| 1125
|  
|-
|-
| |  
|  
| | 9/115
| 9\115
| |  
|  
| | 93.913
| 93.913
| | 1126.9565
| 1126.9565
|
|-
|-
| |  
|  
| | 13/166
| 13\166
| |  
|  
| | 93.976
| 93.976
| | 1127.711
| 1127.711
|
|-
|-
| |  
|  
| | 17/217
| 17\217
| |  
|  
| | 94.009
| 94.009
| | 1128.111
| 1128.111
|
|-
|-
| | 4/51
| 4\51
| |  
|  
| |  
|  
| | 94.118
| 94.118
| | 1129.412
| 1129.412
|
|-
|-
| |  
|  
| | 15/191
| 15\191
| |  
|  
| | 94.241
| 94.241
| | 1130.89
| 1130.89
|
|-
|-
| |  
|  
| | 11/140
| 11\140
| |  
|  
| | 94.296
| 94.296
| | 1131 3/7
| 1131 3\7
|
|-
|-
| |  
|  
| | 7/89
| 7\89
| |  
|  
| | 94.382
| 94.382
| | 1132.584
| 1132.584
|
|-
|-
| |  
|  
| | 10/127
| 10\127
| |  
|  
| | 94.448
| 94.448
| | 1133.858
| 1133.858
|
|-
|-
| |  
|  
| | 13/165
| 13\165
| |  
|  
| | 94.5455
| 94.5455
| | 1134.5455
| 1134.5455
|
|-
|-
| |  
|  
| | 16/203
| 16\203
| |  
|  
| | 94.581
| 94.581
| | 1134.975
| 1134.975
|
|-
|-
| |  
|  
| | 19/241
| 19\241
| |  
|  
| | 94.606
| 94.606
| | 1135.27
| 1135.27
|
|-
|-
| | 3/38
| 3\38
| |  
|  
| |  
|  
| | 94.737
| 94.737
| | 1136.842
| 1136.842
|
|-
|-
| |  
|  
| | 26/329
| 26\329
| |  
|  
| | 94.8875
| 94.8875
| | 1137.6505
| 1137.6505
|
|-
|-
| |  
|  
| | 23/291
| 23\291
| |  
|  
| | 94.845
| 94.845
| | 1138.1443
| 1138.1443
|
|-
|-
| |  
|  
| | 20/253
| 20\253
| |  
|  
| | 94.862
| 94.862
| | 1138.34
| 1138.34
|
|-
|-
| |  
|  
| | 17/215
| 17\215
| |  
|  
| | 94.884
| 94.884
| | 1138.605
| 1138.605
|
|-
|-
| |  
|  
| | 14/177
| 14\177
| |  
|  
| | 94.915
| 94.915
| | 1138.983
| 1138.983
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 94.962
| 94.962
| | 1139.545
| 1139.545
|
|-
|-
| |  
|  
| | 11/139
| 11\139
| |  
|  
| | 94.964
| 94.964
| | 1139.568
| 1139.568
|
|-
|-
| |  
|  
| | 8/101
| 8\101
| |  
|  
| | 95.0495
| 95.0495
| | 1140.594
| 1140.594
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 95.102
| 95.102
| | 1141.224
| 1141.224
|
|-
|-
| |  
|  
| |  
|  
| | 13/164
| 13\164
| | 95.122
| 95.122
| | 1141.463
| 1141.463
|
|-
|-
| |  
|  
| | 5/63
| 5\63
| |  
|  
| | 95.238
| 95.238
| | 1142.714
| 1142.714
|
|-
|-
| |  
|  
| |  
|  
| | 17/214
| 17\214
| | 95.374
| 95.374
| | 1143.486
| 1143.486
|
|-
|-
| |  
|  
| |  
|  
| | 12/151
| 12\151
| | 95.362
| 95.362
| | 1144.371
| 1144.371
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 95.41
| 95.41
| | 1144.915
| 1144.915
|
|-
|-
| |  
|  
| | 7/88
| 7\88
| |  
|  
| | 95,4545
| 95,4545
| | 1145.4545
| 1145.4545
|
|-
|-
| |  
|  
| | 9/113
| 9\113
| |  
|  
| | 95.575
| 95.575
| | 1146.903
| 1146.903
|
|-
|-
| |  
|  
| | 11/138
| 11\138
| |  
|  
| | 95.652
| 95.652
| | 1147.826
| 1147.826
|
|-
|-
| |  
|  
| | 13/163
| 13\163
| |  
|  
| | 95.7055
| 95.7055
| | 1148.466
| 1148.466
|
|-
|-
| |  
|  
| | 15/188
| 15\188
| |  
|  
| | 95.745
| 95.745
| | 1148.936
| 1148.936
|
|-
|-
| |  
|  
| | 17/213
| 17\213
| |  
|  
| | 95.775
| 95.775
| | 1149.296
| 1149.296
|
|-
|-
| |  
|  
| | 19/238
| 19\238
| |  
|  
| | 95.798
| 95.798
| | 1149.58
| 1149.58
|
|-
|-
| |  
|  
| | 21/263
| 21\263
| |  
|  
| | 95.8175
| 95.8175
| | 1149.81
| 1149.81
|
|-
|-
| |  
|  
| | 23/288
| 23\288
| |  
|  
| | 95.833
| 95.833
| | 1150
| 1150
|  
|-
|-
| |  
|  
| | 25/313
| 25\313
| |  
|  
| | 95.847
| 95.847
| | 1150.16
| 1150.16
|
|-
|-
| |  
|  
| | 27/338
| 27\338
| |  
|  
| | 95.858
| 95.858
| | 1150.296
| 1150.296
|
|-
|-
| |  
|  
| | 29/363
| 29\363
| |  
|  
| | 95.868
| 95.868
| | 1150.467
| 1150.467
|
|-
|-
| |  
|  
| | 31/388
| 31\388
| |  
|  
| | 95.876
| 95.876
| | 1150.5155
| 1150.5155
|
|-
|-
| |  
|  
| | 33/413
| 33\413
| |  
|  
| | 95.884
| 95.884
| | 1150.605
| 1150.605
|
|-
|-
| |  
|  
| | 35/438
| 35\438
| |  
|  
| | 95.89
| 95.89
| | 1150.685
| 1150.685
|
|-
|-
| |  
|  
| | 37/463
| 37\463
| |  
|  
| | 95.896
| 95.896
| | 1150.75
| 1150.75
|
|-
|-
| |  
|  
| | 39/488
| 39\488
| |  
|  
| | 95.902
| 95.902
| | 1150.82
| 1150.82
|
|-
|-
| |  
|  
| | 41/513
| 41\513
| |  
|  
| | 95.906
| 95.906
| | 1150.877
| 1150.877
|
|-
|-
| |  
|  
| | 43/538
| 43\538
| |  
|  
| | 95.911
| 95.911
| | 1150.929
| 1150.929
|
|-
|-
| |  
|  
| | 45/563
| 45\563
| |  
|  
| | 95.915
| 95.915
| | 1150.977
| 1150.977
|
|-
|-
| |  
|  
| | 47/588
| 47\588
| |  
|  
| | 95.918
| 95.918
| | 1151.02
| 1151.02
|
|-
|-
| | 2/25
| 2\25
| |  
|  
| |  
|  
| | 96
| 96
| | 1152
| 1152
| Passion
|-
|-
| |  
|  
| | 25/312
| 25\312
| |  
|  
| | 96.154
| 96.154
| | 1153.846
| 1153.846
|
|-
|-
| |  
|  
| | 23/287
| 23\287
| |  
|  
| | 96.167
| 96.167
| | 1154.007
| 1154.007
|
|-
|-
| |  
|  
| | 21/262
| 21\262
| |  
|  
| | 96.183
| 96.183
| | 1154.1985
| 1154.1985
|
|-
|-
| |  
|  
| | 19/237
| 19\237
| |  
|  
| | 96.2025
| 96.2025
| | 1154,43
| 1154,43
|
|-
|-
| |  
|  
| | 17/212
| 17\212
| |  
|  
| | 96.226
| 96.226
| | 1154.717
| 1154.717
|
|-
|-
| |  
|  
| | 15/187
| 15\187
| |  
|  
| | 96.257
| 96.257
| | 1155.08
| 1155.08
|
|-
|-
| |  
|  
| | 13/162
| 13\162
| |  
|  
| | 96.296
| 96.296
| | 1155.556
| 1155.556
|
|-
|-
| |  
|  
| | 11/137
| 11\137
| |  
|  
| | 96.35
| 96.35
| | 1156.204
| 1156.204
|
|-
|-
| |  
|  
| | 9/112
| 9\112
| |  
|  
| | 96.429
| 96.429
| | 1157.143
| 1157.143
|
|-
|-
| |  
|  
| | 7/87
| 7\87
| |  
|  
| | 96.552
| 96.552
| | 1158.621
| 1158.621
|
|-
|-
| |  
|  
| |  
|  
| | 12/149
| 12\149
| | 96.644
| 96.644
| | 1159.7315
| 1159.7315
|
|-
|-
| |  
|  
| |  
|  
| | 17/211
| 17\211
| | 96.6825
| 96.6825
| | 1160.278
| 1160.278
|
|-
|-
| |  
|  
| | 5/62
| 5\62
| |  
|  
| | 96.774
| 96.774
| | 1161.29
| 1161.29
|
|-
|-
| |  
|  
| |  
|  
| | 13/161
| 13\161
| | 96.894
| 96.894
| | 1162.733
| 1162.733
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 96.915
| 96.915
| | 1162.982
| 1162.982
|
|-
|-
| |  
|  
| | 8/99
| 8\99
| |  
|  
| | 96.97
| 96.97
| | 1163.636
| 1163.636
|
|-
|-
| |  
|  
| | 11/136
| 11\136
| |  
|  
| | 97.059
| 97.059
| | 1164.706
| 1164.706
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 97.0255
| 97.0255
| | 1164.306
| 1164.306
|
|-
|-
| |  
|  
| | 14/173
| 14\173
| |  
|  
| | 97.11
| 97.11
| | 1165.318
| 1165.318
|
|-
|-
| |  
|  
| | 17/210
| 17\210
| |  
|  
| | 97.143
| 97.143
| | 1165.714
| 1165.714
|
|-
|-
| |  
|  
| | 20/247
| 20\247
| |  
|  
| | 97.166
| 97.166
| | 1165.992
| 1165.992
|
|-
|-
| |  
|  
| | 23/284
| 23\284
| |  
|  
| | 97.183
| 97.183
| | 1166.197
| 1166.197
|
|-
|-
| | 3/37
| 3\37
| |  
|  
| |  
|  
| | 97.297
| 97.297
| | 1167.568
| 1167.568
| Passion
|-
|-
| |  
|  
| | 25/308
| 25\308
| |  
|  
| | 97.403
| 97.403
| | 1168.831
| 1168.831
|
|-
|-
| |  
|  
| |  
|  
| |  
|  
| | 97.416
| 97.416
| | 1168.9915
| 1168.9915
|
|-
|-
| |  
|  
| | 22/271
| 22\271
| |  
|  
| | 97.417
| 97.417
| | 1169.004
| 1169.004
|
|-
|-
| |  
|  
| | 19/234
| 19\234
| |  
|  
| | 97.436
| 97.436
| | 1169.231
| 1169.231
|
|-
|-
| |  
|  
| | 16/197
| 16\197
| |  
|  
| | 97.462
| 97.462
| | 1169.543
| 1169.543
|
|-
|-
| |  
|  
| | 13/160
| 13\160
| |  
|  
| | 97.5
| 97.5
| | 1170
| 1170
|  
|-
|-
| |  
|  
| | 10/123
| 10\123
| |  
|  
| | 97.561
| 97.561
| | 1170.731
| 1170.731
|
|-
|-
| |  
|  
| |  
|  
| | 17/209
| 17\209
| | 97.608
| 97.608
| | 1171.292
| 1171.292
|
|-
|-
| |  
|  
| | 7/86
| 7\86
| |  
|  
| | 97.674
| 97.674
| | 1172.093
| 1172.093
|
|-
|-
| |  
|  
| | 11/135
| 11\135
| |  
|  
| | 97,778
| 97,778
| | 1173.333
| 1173.333
|
|-
|-
| |  
|  
| | 15/184
| 15\184
| |  
|  
| | 97.826
| 97.826
| | 1173.913
| 1173.913
|
|-
|-
| |  
|  
| | 19/233
| 19\233
| |  
|  
| | 97.854
| 97.854
| | 1174.249
| 1174.249
|
|-
|-
| | 4/49
| 4\49
| |  
|  
| |  
|  
| | 97.959
| 97.959
| | 1175.51
| 1175.51
|
|-
|-
| |  
|  
| | 17/208
| 17\208
| |  
|  
| | 98.077
| 98.077
| | 1176.923
| 1176.923
|
|-
|-
| |  
|  
| | 13/159
| 13\159
| |  
|  
| | 98.113
| 98.113
| | 1177.3585
| 1177.3585
|
|-
|-
| |  
|  
| | 9/110
| 9\110
| |  
|  
| | 98.182
| 98.182
| | 1178.182
| 1178.182
|
|-
|-
| |  
|  
| | 14/171
| 14\171
| |  
|  
| | 98.246
| 98.246
| | 1178.947
| 1178.947
|
|-
|-
| |  
|  
| | 19/232
| 19\232
| |  
|  
| | 98.276
| 98.276
| | 1179.31
| 1179.31
|
|-
|-
| | 5/61
| 5\61
| |  
|  
| |  
|  
| | 98.361
| 98.361
| | 1180.323
| 1180.323
|
|-
|-
| | 1/12
| 1\12
| |  
|  
| |  
|  
| | 100
| 100
| | 1200
| 1200
|}
|}


[[category:todo:unify precision]]
{{todo|unify precision}}
Retrieved from "https://en.xen.wiki/w/12L_1s"