12L 4s

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↖ 11L 3s↑ 12L 3s 13L 3s ↗
← 11L 4s12L 4s13L 4s →
↙ 11L 5s↓ 12L 5s 13L 5s ↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLsLLLsLLLsLLLs
sLLLsLLLsLLLsLLL
Equave 2/1 (1200.0¢)
Period 1\4 (300.0¢)
Generator size
Bright 1\16 to 1\12 (75.0¢ to 100.0¢)
Dark 2\12 to 3\16 (200.0¢ to 225.0¢)
TAMNAMS information
Descends from 4L 4s (tetrawood)
Ancestor's step ratio range 2:1 to 3:1 (hypohard)
Related MOS scales
Parent 4L 8s
Sister 4L 12s
Daughters 16L 12s, 12L 16s
Neutralized 8L 8s
2-Flought 28L 4s, 12L 20s
Equal tunings
Equalized (L:s = 1:1) 1\16 (75.0¢)
Supersoft (L:s = 4:3) 4\60 (80.0¢)
Soft (L:s = 3:2) 3\44 (81.8¢)
Semisoft (L:s = 5:3) 5\72 (83.3¢)
Basic (L:s = 2:1) 2\28 (85.7¢)
Semihard (L:s = 5:2) 5\68 (88.2¢)
Hard (L:s = 3:1) 3\40 (90.0¢)
Superhard (L:s = 4:1) 4\52 (92.3¢)
Collapsed (L:s = 1:0) 1\12 (100.0¢)

12L 4s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 4 small steps, with a period of 3 large steps and 1 small step that repeats every 300.0¢, or 4 times every octave. 12L 4s is a grandchild scale of 4L 4s, expanding it by 8 tones. Generators that produce this scale range from 75¢ to 100¢, or from 200¢ to 225¢. Scales of the true MOS form, where every period is the same, are proper because there is only one small step per period.

Modes

Modes of 12L 4s
UDP Cyclic
order
Step
pattern
12|0(4) 1 LLLsLLLsLLLsLLLs
8|4(4) 2 LLsLLLsLLLsLLLsL
4|8(4) 3 LsLLLsLLLsLLLsLL
0|12(4) 4 sLLLsLLLsLLLsLLL

Scale tree

Scale Tree and Tuning Spectrum of 12L 4s
Generator(edo) Cents Step ratio Comments(always proper)
Bright Dark L:s Hardness
1\16 75.000 225.000 1:1 1.000 Equalized 12L 4s
6\92 78.261 221.739 6:5 1.200
5\76 78.947 221.053 5:4 1.250
9\136 79.412 220.588 9:7 1.286
4\60 80.000 220.000 4:3 1.333 Supersoft 12L 4s
11\164 80.488 219.512 11:8 1.375
7\104 80.769 219.231 7:5 1.400
10\148 81.081 218.919 10:7 1.429
3\44 81.818 218.182 3:2 1.500 Soft 12L 4s
11\160 82.500 217.500 11:7 1.571
8\116 82.759 217.241 8:5 1.600
13\188 82.979 217.021 13:8 1.625
5\72 83.333 216.667 5:3 1.667 Semisoft 12L 4s
12\172 83.721 216.279 12:7 1.714
7\100 84.000 216.000 7:4 1.750
9\128 84.375 215.625 9:5 1.800
2\28 85.714 214.286 2:1 2.000 Basic 12L 4s
9\124 87.097 212.903 9:4 2.250
7\96 87.500 212.500 7:3 2.333
12\164 87.805 212.195 12:5 2.400
5\68 88.235 211.765 5:2 2.500 Semihard 12L 4s
13\176 88.636 211.364 13:5 2.600
8\108 88.889 211.111 8:3 2.667
11\148 89.189 210.811 11:4 2.750
3\40 90.000 210.000 3:1 3.000 Hard 12L 4s
10\132 90.909 209.091 10:3 3.333
7\92 91.304 208.696 7:2 3.500
11\144 91.667 208.333 11:3 3.667
4\52 92.308 207.692 4:1 4.000 Superhard 12L 4s
9\116 93.103 206.897 9:2 4.500
5\64 93.750 206.250 5:1 5.000
6\76 94.737 205.263 6:1 6.000
1\12 100.000 200.000 1:0 → ∞ Collapsed 12L 4s