1L 12s

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Todo: cleanup
Rewrite intro, add links to temperaments
↑1L 11s 2L 11s ↗
1L 12s 2L 12s →
↓1L 13s 2L 13s ↘
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern Lssssssssssss
ssssssssssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 12\13 to 1\1 (1107.7¢ to 1200.0¢)
Dark 0\1 to 1\13 (0.0¢ to 92.3¢)
TAMNAMS information
Descends from 1L 9s (antisinatonic)
Ancestor's step ratio range 4:1 to 1:0 (ultrahard)
Related MOS scales
Parent 1L 11s
Sister 12L 1s
Daughters 13L 1s, 1L 13s
Neutralized 2L 11s
2-Flought 14L 12s, 1L 25s
Equal tunings
Equalized (L:s = 1:1) 12\13 (1107.7¢)
Supersoft (L:s = 4:3) 37\40 (1110.0¢)
Soft (L:s = 3:2) 25\27 (1111.1¢)
Semisoft (L:s = 5:3) 38\41 (1112.2¢)
Basic (L:s = 2:1) 13\14 (1114.3¢)
Semihard (L:s = 5:2) 27\29 (1117.2¢)
Hard (L:s = 3:1) 14\15 (1120.0¢)
Superhard (L:s = 4:1) 15\16 (1125.0¢)
Collapsed (L:s = 1:0) 1\1 (1200.0¢)

1L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 12 small steps, repeating every octave. 1L 12s is a great-grandchild scale of 1L 9s, expanding it by 3 tones. Generators that produce this scale range from 1107.7¢ to 1200¢, or from 0¢ to 92.3¢. This MOS, also called the Happy tridecatonic scale, has its first harmonic entropy minimum at 1/14edo-3/40edo, where 3:2 is +8 generators (Octacot). However, the absolute harmonic entropy minimum is Nautilus (3:2=-6 generators), and that is not complete until 14 tones.

Modes

Modes of 1L 12s
UDP Rotational order Step pattern
12|0 1 Lssssssssssss
11|1 13 sLsssssssssss
10|2 12 ssLssssssssss
9|3 11 sssLsssssssss
8|4 10 ssssLssssssss
7|5 9 sssssLsssssss
6|6 8 ssssssLssssss
5|7 7 sssssssLsssss
4|8 6 ssssssssLssss
3|9 5 sssssssssLsss
2|10 4 ssssssssssLss
1|11 3 sssssssssssLs
0|12 2 ssssssssssssL

Scale tree

Scale Tree and Tuning Spectrum of 1L 12s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
12\13 1107.692 92.308 1:1 1.000 Equalized 1L 12s
61\66 1109.091 90.909 6:5 1.200
49\53 1109.434 90.566 5:4 1.250
86\93 1109.677 90.323 9:7 1.286
37\40 1110.000 90.000 4:3 1.333 Supersoft 1L 12s
99\107 1110.280 89.720 11:8 1.375
62\67 1110.448 89.552 7:5 1.400
87\94 1110.638 89.362 10:7 1.429
25\27 1111.111 88.889 3:2 1.500 Soft 1L 12s
88\95 1111.579 88.421 11:7 1.571
63\68 1111.765 88.235 8:5 1.600
101\109 1111.927 88.073 13:8 1.625
38\41 1112.195 87.805 5:3 1.667 Semisoft 1L 12s
89\96 1112.500 87.500 12:7 1.714
51\55 1112.727 87.273 7:4 1.750
64\69 1113.043 86.957 9:5 1.800
13\14 1114.286 85.714 2:1 2.000 Basic 1L 12s
Scales with tunings softer than this are proper
53\57 1115.789 84.211 9:4 2.250
40\43 1116.279 83.721 7:3 2.333
67\72 1116.667 83.333 12:5 2.400
27\29 1117.241 82.759 5:2 2.500 Semihard 1L 12s
68\73 1117.808 82.192 13:5 2.600
41\44 1118.182 81.818 8:3 2.667
55\59 1118.644 81.356 11:4 2.750
14\15 1120.000 80.000 3:1 3.000 Hard 1L 12s
43\46 1121.739 78.261 10:3 3.333
29\31 1122.581 77.419 7:2 3.500
44\47 1123.404 76.596 11:3 3.667
15\16 1125.000 75.000 4:1 4.000 Superhard 1L 12s
31\33 1127.273 72.727 9:2 4.500
16\17 1129.412 70.588 5:1 5.000
17\18 1133.333 66.667 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 12s