12L 1s: Difference between revisions

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{{Infobox MOS
{{Infobox MOS}}
| Other names = grumpy tridecatonic
 
| Periods = 1
{{MOS intro|Other Names=quasidozenal}}
| nLargeSteps = 12
 
| nSmallSteps = 1
Quasidozenal does not have many [[regular temperament]] applications.  
| Equalized = 1
 
| Collapsed = 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 [[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).
 
== Modes ==
{{MOS modes}}
 
== Intervals ==
{{MOS intervals}}


== Scale tree ==
== Scale tree ==
{| class="wikitable"
{{MOS tuning spectrum}}
|-
! colspan="3" | Generator
! Cents
! 12g
! Comments
|-
| 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
| Passion
|-
|
| 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
| Passion
|-
|
| 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
|}


{{todo|unify precision}}
{{Todo|cleanup|add etymology|inline=1|text=Clean up lead section, find out who first proposed the name quasidozenal}}


[[Category:13-tone scales]]
[[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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