12L 10s

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↖ 11L 9s ↑ 12L 9s 13L 9s ↗
← 11L 10s 12L 10s 13L 10s →
↙ 11L 11s ↓ 12L 11s 13L 11s ↘ 
┌╥╥┬╥┬╥┬╥┬╥┬╥╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║│║║│║│║│║│║││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLLsLsLsLsLs
sLsLsLsLsLLsLsLsLsLsLL
Equave 2/1 (1200.0¢)
Period 1\2 (600.0¢)
Generator size
Bright 9\22 to 5\12 (490.9¢ to 500.0¢)
Dark 1\12 to 2\22 (100.0¢ to 109.1¢)
TAMNAMS information
Descends from 2L 8s
Ancestor's step ratio range 3:2 to 2:1 (hyposoft)
Related MOS scales
Parent 10L 2s
Sister 10L 12s
Daughters 22L 12s, 12L 22s
Neutralized 2L 20s
2-Flought 34L 10s, 12L 32s
Equal tunings
Equalized (L:s = 1:1) 9\22 (490.9¢)
Supersoft (L:s = 4:3) 32\78 (492.3¢)
Soft (L:s = 3:2) 23\56 (492.9¢)
Semisoft (L:s = 5:3) 37\90 (493.3¢)
Basic (L:s = 2:1) 14\34 (494.1¢)
Semihard (L:s = 5:2) 33\80 (495.0¢)
Hard (L:s = 3:1) 19\46 (495.7¢)
Superhard (L:s = 4:1) 24\58 (496.6¢)
Collapsed (L:s = 1:0) 5\12 (500.0¢)

12L 10s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 10 small steps, with a period of 6 large steps and 5 small steps that repeats every 600.0¢, or twice every octave. 12L 10s is a grandchild scale of 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 490.9¢ to 500¢, or from 100¢ to 109.1¢.

This scale is the quartertone scale of diaschismic temperament with dark generators above 100¢ (around the upper range of a diatonic semitone). This maps 5/4 (386¢) to one period (600¢) minus two dark generators.

Modes

Modes of 12L 10s
UDP Cyclic
order		 Step
pattern
20|0(2) 1 LLsLsLsLsLsLLsLsLsLsLs
18|2(2) 10 LsLLsLsLsLsLsLLsLsLsLs
16|4(2) 8 LsLsLLsLsLsLsLsLLsLsLs
14|6(2) 6 LsLsLsLLsLsLsLsLsLLsLs
12|8(2) 4 LsLsLsLsLLsLsLsLsLsLLs
10|10(2) 2 LsLsLsLsLsLLsLsLsLsLsL
8|12(2) 11 sLLsLsLsLsLsLLsLsLsLsL
6|14(2) 9 sLsLLsLsLsLsLsLLsLsLsL
4|16(2) 7 sLsLsLLsLsLsLsLsLLsLsL
2|18(2) 5 sLsLsLsLLsLsLsLsLsLLsL
0|20(2) 3 sLsLsLsLsLLsLsLsLsLsLL

Intervals

Intervals of 12L 10s
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 54.5¢
Major 1-mosstep M1ms L 54.5¢ to 100.0¢
2-mosstep Perfect 2-mosstep P2ms L + s 100.0¢ to 109.1¢
Augmented 2-mosstep A2ms 2L 109.1¢ to 200.0¢
3-mosstep Minor 3-mosstep m3ms L + 2s 100.0¢ to 163.6¢
Major 3-mosstep M3ms 2L + s 163.6¢ to 200.0¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 200.0¢ to 218.2¢
Major 4-mosstep M4ms 3L + s 218.2¢ to 300.0¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 200.0¢ to 272.7¢
Major 5-mosstep M5ms 3L + 2s 272.7¢ to 300.0¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 300.0¢ to 327.3¢
Major 6-mosstep M6ms 4L + 2s 327.3¢ to 400.0¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 300.0¢ to 381.8¢
Major 7-mosstep M7ms 4L + 3s 381.8¢ to 400.0¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 400.0¢ to 436.4¢
Major 8-mosstep M8ms 5L + 3s 436.4¢ to 500.0¢
9-mosstep Diminished 9-mosstep d9ms 4L + 5s 400.0¢ to 490.9¢
Perfect 9-mosstep P9ms 5L + 4s 490.9¢ to 500.0¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 500.0¢ to 545.5¢
Major 10-mosstep M10ms 6L + 4s 545.5¢ to 600.0¢
11-mosstep Perfect 11-mosstep P11ms 6L + 5s 600.0¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 600.0¢ to 654.5¢
Major 12-mosstep M12ms 7L + 5s 654.5¢ to 700.0¢
13-mosstep Perfect 13-mosstep P13ms 7L + 6s 700.0¢ to 709.1¢
Augmented 13-mosstep A13ms 8L + 5s 709.1¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 700.0¢ to 763.6¢
Major 14-mosstep M14ms 8L + 6s 763.6¢ to 800.0¢
15-mosstep Minor 15-mosstep m15ms 8L + 7s 800.0¢ to 818.2¢
Major 15-mosstep M15ms 9L + 6s 818.2¢ to 900.0¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 800.0¢ to 872.7¢
Major 16-mosstep M16ms 9L + 7s 872.7¢ to 900.0¢
17-mosstep Minor 17-mosstep m17ms 9L + 8s 900.0¢ to 927.3¢
Major 17-mosstep M17ms 10L + 7s 927.3¢ to 1000.0¢
18-mosstep Minor 18-mosstep m18ms 9L + 9s 900.0¢ to 981.8¢
Major 18-mosstep M18ms 10L + 8s 981.8¢ to 1000.0¢
19-mosstep Minor 19-mosstep m19ms 10L + 9s 1000.0¢ to 1036.4¢
Major 19-mosstep M19ms 11L + 8s 1036.4¢ to 1100.0¢
20-mosstep Diminished 20-mosstep d20ms 10L + 10s 1000.0¢ to 1090.9¢
Perfect 20-mosstep P20ms 11L + 9s 1090.9¢ to 1100.0¢
21-mosstep Minor 21-mosstep m21ms 11L + 10s 1100.0¢ to 1145.5¢
Major 21-mosstep M21ms 12L + 9s 1145.5¢ to 1200.0¢
22-mosstep Perfect 22-mosstep P22ms 12L + 10s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 12L 10s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
9\22 490.909 109.091 1:1 1.000 Equalized 12L 10s
50\122 491.803 108.197 6:5 1.200
41\100 492.000 108.000 5:4 1.250
73\178 492.135 107.865 9:7 1.286
32\78 492.308 107.692 4:3 1.333 Supersoft 12L 10s
87\212 492.453 107.547 11:8 1.375
55\134 492.537 107.463 7:5 1.400
78\190 492.632 107.368 10:7 1.429
23\56 492.857 107.143 3:2 1.500 Soft 12L 10s
83\202 493.069 106.931 11:7 1.571
60\146 493.151 106.849 8:5 1.600
97\236 493.220 106.780 13:8 1.625
37\90 493.333 106.667 5:3 1.667 Semisoft 12L 10s
88\214 493.458 106.542 12:7 1.714
51\124 493.548 106.452 7:4 1.750
65\158 493.671 106.329 9:5 1.800
14\34 494.118 105.882 2:1 2.000 Basic 12L 10s
Scales with tunings softer than this are proper
61\148 494.595 105.405 9:4 2.250
47\114 494.737 105.263 7:3 2.333
80\194 494.845 105.155 12:5 2.400
33\80 495.000 105.000 5:2 2.500 Semihard 12L 10s
85\206 495.146 104.854 13:5 2.600
52\126 495.238 104.762 8:3 2.667
71\172 495.349 104.651 11:4 2.750
19\46 495.652 104.348 3:1 3.000 Hard 12L 10s
62\150 496.000 104.000 10:3 3.333
43\104 496.154 103.846 7:2 3.500 Diaschismic
67\162 496.296 103.704 11:3 3.667
24\58 496.552 103.448 4:1 4.000 Superhard 12L 10s
53\128 496.875 103.125 9:2 4.500
29\70 497.143 102.857 5:1 5.000
34\82 497.561 102.439 6:1 6.000
5\12 500.000 100.000 1:0 → ∞ Collapsed 12L 10s
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