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12L 11s

Revision as of 00:20, 15 December 2024 by BudjarnLambeth (talk | contribs) (-todo:expand, already stub which is more accurate; add intervals)

12L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 11 small steps, repeating every octave. 12L 11s is a great-grandchild scale of 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 1095.7 ¢ to 1100 ¢, or from 100 ¢ to 104.3 ¢.

↖ 11L 10s ↑ 12L 10s 13L 10s ↗
← 11L 11s 12L 11s 13L 11s →
↙ 11L 12s ↓ 12L 12s 13L 12s ↘
Scale structure
Step pattern LLsLsLsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 21\23 to 11\12 (1095.7 ¢ to 1100.0 ¢)
Dark 1\12 to 2\23 (100.0 ¢ to 104.3 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 5:2 to 3:1 (quasihard)
Related MOS scales
Parent 11L 1s
Sister 11L 12s
Daughters 23L 12s, 12L 23s
Neutralized 1L 22s
2-Flought 35L 11s, 12L 34s
Equal tunings
Equalized (L:s = 1:1) 21\23 (1095.7 ¢)
Supersoft (L:s = 4:3) 74\81 (1096.3 ¢)
Soft (L:s = 3:2) 53\58 (1096.6 ¢)
Semisoft (L:s = 5:3) 85\93 (1096.8 ¢)
Basic (L:s = 2:1) 32\35 (1097.1 ¢)
Semihard (L:s = 5:2) 75\82 (1097.6 ¢)
Hard (L:s = 3:1) 43\47 (1097.9 ¢)
Superhard (L:s = 4:1) 54\59 (1098.3 ¢)
Collapsed (L:s = 1:0) 11\12 (1100.0 ¢)
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Modes

Modes of 12L 11s
UDP Cyclic
order		 Step
pattern
22|0 1 LLsLsLsLsLsLsLsLsLsLsLs
21|1 22 LsLLsLsLsLsLsLsLsLsLsLs
20|2 20 LsLsLLsLsLsLsLsLsLsLsLs
19|3 18 LsLsLsLLsLsLsLsLsLsLsLs
18|4 16 LsLsLsLsLLsLsLsLsLsLsLs
17|5 14 LsLsLsLsLsLLsLsLsLsLsLs
16|6 12 LsLsLsLsLsLsLLsLsLsLsLs
15|7 10 LsLsLsLsLsLsLsLLsLsLsLs
14|8 8 LsLsLsLsLsLsLsLsLLsLsLs
13|9 6 LsLsLsLsLsLsLsLsLsLLsLs
12|10 4 LsLsLsLsLsLsLsLsLsLsLLs
11|11 2 LsLsLsLsLsLsLsLsLsLsLsL
10|12 23 sLLsLsLsLsLsLsLsLsLsLsL
9|13 21 sLsLLsLsLsLsLsLsLsLsLsL
8|14 19 sLsLsLLsLsLsLsLsLsLsLsL
7|15 17 sLsLsLsLLsLsLsLsLsLsLsL
6|16 15 sLsLsLsLsLLsLsLsLsLsLsL
5|17 13 sLsLsLsLsLsLLsLsLsLsLsL
4|18 11 sLsLsLsLsLsLsLLsLsLsLsL
3|19 9 sLsLsLsLsLsLsLsLLsLsLsL
2|20 7 sLsLsLsLsLsLsLsLsLLsLsL
1|21 5 sLsLsLsLsLsLsLsLsLsLLsL
0|22 3 sLsLsLsLsLsLsLsLsLsLsLL

Intervals

Intervals of 12L 11s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Minor 1-mosstep m1ms s 0.0 ¢ to 52.2 ¢
Major 1-mosstep M1ms L 52.2 ¢ to 100.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 100.0 ¢ to 104.3 ¢
Augmented 2-mosstep A2ms 2L 104.3 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 100.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms 2L + s 156.5 ¢ to 200.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 200.0 ¢ to 208.7 ¢
Major 4-mosstep M4ms 3L + s 208.7 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 200.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 3L + 2s 260.9 ¢ to 300.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 300.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 4L + 2s 313.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 300.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms 4L + 3s 365.2 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 400.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 5L + 3s 417.4 ¢ to 500.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 400.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 5L + 4s 469.6 ¢ to 500.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 500.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 6L + 4s 521.7 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 500.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 6L + 5s 573.9 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 600.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 7L + 5s 626.1 ¢ to 700.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 7L + 6s 678.3 ¢ to 700.0 ¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 700.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 8L + 6s 730.4 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 700.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 8L + 7s 782.6 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 800.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 9L + 7s 834.8 ¢ to 900.0 ¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 800.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 9L + 8s 887.0 ¢ to 900.0 ¢
18-mosstep Minor 18-mosstep m18ms 9L + 9s 900.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 10L + 8s 939.1 ¢ to 1000.0 ¢
19-mosstep Minor 19-mosstep m19ms 9L + 10s 900.0 ¢ to 991.3 ¢
Major 19-mosstep M19ms 10L + 9s 991.3 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 10L + 10s 1000.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 11L + 9s 1043.5 ¢ to 1100.0 ¢
21-mosstep Diminished 21-mosstep d21ms 10L + 11s 1000.0 ¢ to 1095.7 ¢
Perfect 21-mosstep P21ms 11L + 10s 1095.7 ¢ to 1100.0 ¢
22-mosstep Minor 22-mosstep m22ms 11L + 11s 1100.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 12L + 10s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 12L + 11s 1200.0 ¢

Scale tree

  Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: 
{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}


The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.


Scale tree and tuning spectrum of 12L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
21\23 1095.652 104.348 1:1 1.000 Equalized 12L 11s
116\127 1096.063 103.937 6:5 1.200
95\104 1096.154 103.846 5:4 1.250
169\185 1096.216 103.784 9:7 1.286
74\81 1096.296 103.704 4:3 1.333 Supersoft 12L 11s
201\220 1096.364 103.636 11:8 1.375
127\139 1096.403 103.597 7:5 1.400
180\197 1096.447 103.553 10:7 1.429
53\58 1096.552 103.448 3:2 1.500 Soft 12L 11s
191\209 1096.651 103.349 11:7 1.571
138\151 1096.689 103.311 8:5 1.600
223\244 1096.721 103.279 13:8 1.625
85\93 1096.774 103.226 5:3 1.667 Semisoft 12L 11s
202\221 1096.833 103.167 12:7 1.714
117\128 1096.875 103.125 7:4 1.750
149\163 1096.933 103.067 9:5 1.800
32\35 1097.143 102.857 2:1 2.000 Basic 12L 11s
Scales with tunings softer than this are proper
139\152 1097.368 102.632 9:4 2.250
107\117 1097.436 102.564 7:3 2.333
182\199 1097.487 102.513 12:5 2.400
75\82 1097.561 102.439 5:2 2.500 Semihard 12L 11s
193\211 1097.630 102.370 13:5 2.600
118\129 1097.674 102.326 8:3 2.667
161\176 1097.727 102.273 11:4 2.750
43\47 1097.872 102.128 3:1 3.000 Hard 12L 11s
140\153 1098.039 101.961 10:3 3.333
97\106 1098.113 101.887 7:2 3.500
151\165 1098.182 101.818 11:3 3.667
54\59 1098.305 101.695 4:1 4.000 Superhard 12L 11s
119\130 1098.462 101.538 9:2 4.500
65\71 1098.592 101.408 5:1 5.000
76\83 1098.795 101.205 6:1 6.000
11\12 1100.000 100.000 1:0 → ∞ Collapsed 12L 11s


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