3L 12s

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↖ 2L 11s↑ 3L 11s 4L 11s ↗
← 2L 12s3L 12s4L 12s →
↙ 2L 13s↓ 3L 13s 4L 13s ↘
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│║││││║││││║│││││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLssssLssss
ssssLssssLssssL
Equave 2/1 (1200.0¢)
Period 1\3 (400.0¢)
Generator size
Bright 4\15 to 1\3 (320.0¢ to 400.0¢)
Dark 0\3 to 1\15 (0.0¢ to 80.0¢)
TAMNAMS information
Descends from 3L 6s (tcherepnin)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 3L 9s
Sister 12L 3s
Daughters 15L 3s, 3L 15s
Neutralized 6L 9s
2-Flought 18L 12s, 3L 27s
Equal tunings
Equalized (L:s = 1:1) 4\15 (320.0¢)
Supersoft (L:s = 4:3) 13\48 (325.0¢)
Soft (L:s = 3:2) 9\33 (327.3¢)
Semisoft (L:s = 5:3) 14\51 (329.4¢)
Basic (L:s = 2:1) 5\18 (333.3¢)
Semihard (L:s = 5:2) 11\39 (338.5¢)
Hard (L:s = 3:1) 6\21 (342.9¢)
Superhard (L:s = 4:1) 7\24 (350.0¢)
Collapsed (L:s = 1:0) 1\3 (400.0¢)

3L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 12 small steps, with a period of 1 large step and 4 small steps that repeats every 400.0¢, or 3 times every octave. 3L 12s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 320¢ to 400¢, or from 0¢ to 80¢. It is the MOS of Inflated[15].

Modes

Modes of 3L 12s
UDP Cyclic
order
Step
pattern
12|0(3) 1 LssssLssssLssss
9|3(3) 5 sLssssLssssLsss
6|6(3) 4 ssLssssLssssLss
3|9(3) 3 sssLssssLssssLs
0|12(3) 2 ssssLssssLssssL

Scale tree

Scale Tree and Tuning Spectrum of 3L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\15 320.000 80.000 1:1 1.000 Equalized 3L 12s
21\78 323.077 76.923 6:5 1.200
17\63 323.810 76.190 5:4 1.250
30\111 324.324 75.676 9:7 1.286
13\48 325.000 75.000 4:3 1.333 Supersoft 3L 12s
35\129 325.581 74.419 11:8 1.375
22\81 325.926 74.074 7:5 1.400
31\114 326.316 73.684 10:7 1.429
9\33 327.273 72.727 3:2 1.500 Soft 3L 12s
32\117 328.205 71.795 11:7 1.571
23\84 328.571 71.429 8:5 1.600
37\135 328.889 71.111 13:8 1.625
14\51 329.412 70.588 5:3 1.667 Semisoft 3L 12s
33\120 330.000 70.000 12:7 1.714
19\69 330.435 69.565 7:4 1.750
24\87 331.034 68.966 9:5 1.800
5\18 333.333 66.667 2:1 2.000 Basic 3L 12s
Scales with tunings softer than this are proper
21\75 336.000 64.000 9:4 2.250
16\57 336.842 63.158 7:3 2.333
27\96 337.500 62.500 12:5 2.400
11\39 338.462 61.538 5:2 2.500 Semihard 3L 12s
28\99 339.394 60.606 13:5 2.600
17\60 340.000 60.000 8:3 2.667
23\81 340.741 59.259 11:4 2.750
6\21 342.857 57.143 3:1 3.000 Hard 3L 12s
19\66 345.455 54.545 10:3 3.333
13\45 346.667 53.333 7:2 3.500
20\69 347.826 52.174 11:3 3.667
7\24 350.000 50.000 4:1 4.000 Superhard 3L 12s
15\51 352.941 47.059 9:2 4.500
8\27 355.556 44.444 5:1 5.000
9\30 360.000 40.000 6:1 6.000
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 12s