12L 1s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Name =
 
| Periods = 1
{{MOS intro|Other Names=quasidozenal}}
| nLargeSteps = 12
 
| nSmallSteps = 1
Quasidozenal does not have many [[regular temperament]] applications.  
| Equalized = 1
 
| Paucitonic = 1
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.
| Pattern = LLLLLLLLLLLLs
 
}}
And it becomes indistinct from [[13edo]] or [[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).
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).
 
== Modes ==
{{MOS modes}}
 
== Intervals ==
{{MOS intervals}}


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


[[category:todo:unify precision]]
[[Category:13-tone scales]]

Latest revision as of 16:43, 28 February 2025

← 11L 1s 12L 1s 13L 1s →
↙ 11L 2s ↓ 12L 2s 13L 2s ↘
Scale structure
Step pattern LLLLLLLLLLLLs
sLLLLLLLLLLLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 1\13 to 1\12 (92.3 ¢ to 100.0 ¢)
Dark 11\12 to 12\13 (1100.0 ¢ to 1107.7 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 3:1 to 4:1 (parahard)
Related MOS scales
Parent 1L 11s
Sister 1L 12s
Daughters 13L 12s, 12L 13s
Neutralized 11L 2s
2-Flought 25L 1s, 12L 14s
Equal tunings
Equalized (L:s = 1:1) 1\13 (92.3 ¢)
Supersoft (L:s = 4:3) 4\51 (94.1 ¢)
Soft (L:s = 3:2) 3\38 (94.7 ¢)
Semisoft (L:s = 5:3) 5\63 (95.2 ¢)
Basic (L:s = 2:1) 2\25 (96.0 ¢)
Semihard (L:s = 5:2) 5\62 (96.8 ¢)
Hard (L:s = 3:1) 3\37 (97.3 ¢)
Superhard (L:s = 4:1) 4\49 (98.0 ¢)
Collapsed (L:s = 1:0) 1\12 (100.0 ¢)
View • Talk • Edit

12L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 1 small step, repeating every octave. 12L 1s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 92.3 ¢ to 100 ¢, or from 1100 ¢ to 1107.7 ¢. Scales of this form are always proper because there is only one small step.

Quasidozenal does not have many regular temperament applications.

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 ¢ 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 1L 11s in the 1.75 ¢ above 1\13 because the large and small steps register as identical to one another for human listeners).

Modes

Modes of 12L 1s
UDP Cyclic
order		 Step
pattern
12|0 1 LLLLLLLLLLLLs
11|1 2 LLLLLLLLLLLsL
10|2 3 LLLLLLLLLLsLL
9|3 4 LLLLLLLLLsLLL
8|4 5 LLLLLLLLsLLLL
7|5 6 LLLLLLLsLLLLL
6|6 7 LLLLLLsLLLLLL
5|7 8 LLLLLsLLLLLLL
4|8 9 LLLLsLLLLLLLL
3|9 10 LLLsLLLLLLLLL
2|10 11 LLsLLLLLLLLLL
1|11 12 LsLLLLLLLLLLL
0|12 13 sLLLLLLLLLLLL

Intervals

Intervals of 12L 1s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Diminished 1-mosstep d1ms s 0.0 ¢ to 92.3 ¢
Perfect 1-mosstep P1ms L 92.3 ¢ to 100.0 ¢
2-mosstep Minor 2-mosstep m2ms L + s 100.0 ¢ to 184.6 ¢
Major 2-mosstep M2ms 2L 184.6 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms 2L + s 200.0 ¢ to 276.9 ¢
Major 3-mosstep M3ms 3L 276.9 ¢ to 300.0 ¢
4-mosstep Minor 4-mosstep m4ms 3L + s 300.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms 4L 369.2 ¢ to 400.0 ¢
5-mosstep Minor 5-mosstep m5ms 4L + s 400.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms 5L 461.5 ¢ to 500.0 ¢
6-mosstep Minor 6-mosstep m6ms 5L + s 500.0 ¢ to 553.8 ¢
Major 6-mosstep M6ms 6L 553.8 ¢ to 600.0 ¢
7-mosstep Minor 7-mosstep m7ms 6L + s 600.0 ¢ to 646.2 ¢
Major 7-mosstep M7ms 7L 646.2 ¢ to 700.0 ¢
8-mosstep Minor 8-mosstep m8ms 7L + s 700.0 ¢ to 738.5 ¢
Major 8-mosstep M8ms 8L 738.5 ¢ to 800.0 ¢
9-mosstep Minor 9-mosstep m9ms 8L + s 800.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 9L 830.8 ¢ to 900.0 ¢
10-mosstep Minor 10-mosstep m10ms 9L + s 900.0 ¢ to 923.1 ¢
Major 10-mosstep M10ms 10L 923.1 ¢ to 1000.0 ¢
11-mosstep Minor 11-mosstep m11ms 10L + s 1000.0 ¢ to 1015.4 ¢
Major 11-mosstep M11ms 11L 1015.4 ¢ to 1100.0 ¢
12-mosstep Perfect 12-mosstep P12ms 11L + s 1100.0 ¢ to 1107.7 ¢
Augmented 12-mosstep A12ms 12L 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 12L + s 1200.0 ¢

Scale tree

Scale tree and tuning spectrum of 12L 1s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\13 92.308 1107.692 1:1 1.000 Equalized 12L 1s
6\77 93.506 1106.494 6:5 1.200
5\64 93.750 1106.250 5:4 1.250
9\115 93.913 1106.087 9:7 1.286
4\51 94.118 1105.882 4:3 1.333 Supersoft 12L 1s
11\140 94.286 1105.714 11:8 1.375
7\89 94.382 1105.618 7:5 1.400
10\127 94.488 1105.512 10:7 1.429
3\38 94.737 1105.263 3:2 1.500 Soft 12L 1s
11\139 94.964 1105.036 11:7 1.571
8\101 95.050 1104.950 8:5 1.600
13\164 95.122 1104.878 13:8 1.625
5\63 95.238 1104.762 5:3 1.667 Semisoft 12L 1s
12\151 95.364 1104.636 12:7 1.714
7\88 95.455 1104.545 7:4 1.750
9\113 95.575 1104.425 9:5 1.800
2\25 96.000 1104.000 2:1 2.000 Basic 12L 1s
9\112 96.429 1103.571 9:4 2.250
7\87 96.552 1103.448 7:3 2.333
12\149 96.644 1103.356 12:5 2.400
5\62 96.774 1103.226 5:2 2.500 Semihard 12L 1s
13\161 96.894 1103.106 13:5 2.600
8\99 96.970 1103.030 8:3 2.667
11\136 97.059 1102.941 11:4 2.750
3\37 97.297 1102.703 3:1 3.000 Hard 12L 1s
10\123 97.561 1102.439 10:3 3.333
7\86 97.674 1102.326 7:2 3.500
11\135 97.778 1102.222 11:3 3.667
4\49 97.959 1102.041 4:1 4.000 Superhard 12L 1s
9\110 98.182 1101.818 9:2 4.500
5\61 98.361 1101.639 5:1 5.000
6\73 98.630 1101.370 6:1 6.000
1\12 100.000 1100.000 1:0 → ∞ Collapsed 12L 1s
Todo: cleanup, add etymology

Clean up lead section, find out who first proposed the name quasidozenal

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