11L 3s

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↖ 10L 2s ↑11L 2s 12L 2s ↗
← 10L 3s11L 3s 12L 3s →
↙ 10L 4s ↓11L 4s 12L 4s ↘
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐
│║║║║│║║║║│║║║││
││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLLLsLLLLsLLLs
sLLLsLLLLsLLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\14 to 4\11 (428.6¢ to 436.4¢)
Dark 7\11 to 9\14 (763.6¢ to 771.4¢)
TAMNAMS information
Descends from 3L 5s (checkertonic)
Descendant's step ratio range 2:1 to 3:1 (hypohard)
Other names
Name(s) Ketradektriatoh
Related MOS scales
Parent 3L 8s
Sister 3L 11s
Daughters 14L 11s, 11L 14s
Neutralized 8L 6s
2-Flought 25L 3s, 11L 17s
Equal tunings
Equalized (L:s = 1:1) 5\14 (428.6¢)
Supersoft (L:s = 4:3) 19\53 (430.2¢)
Soft (L:s = 3:2) 14\39 (430.8¢)
Semisoft (L:s = 5:3) 23\64 (431.2¢)
Basic (L:s = 2:1) 9\25 (432.0¢)
Semihard (L:s = 5:2) 22\61 (432.8¢)
Hard (L:s = 3:1) 13\36 (433.3¢)
Superhard (L:s = 4:1) 17\47 (434.0¢)
Collapsed (L:s = 1:0) 4\11 (436.4¢)

11L 3s, also called the Ketradektriatoh scale, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 11 large steps and 3 small steps, repeating every octave. 11L 3s is a grandchild scale of 3L 5s, expanding it by 6 tones. Generators that produce this scale range from 428.6¢ to 436.4¢, or from 763.6¢ to 771.4¢. This scale was named the "Ketradektriatoh scale" by Osmiorisbendi‎.

Scale tree

Scale Tree and Tuning Spectrum of 11L 3s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
5\14 428.571 771.429 1:1 1.000 Equalized 11L 3s
29\81 429.630 770.370 6:5 1.200
24\67 429.851 770.149 5:4 1.250
43\120 430.000 770.000 9:7 1.286
19\53 430.189 769.811 4:3 1.333 Supersoft 11L 3s
52\145 430.345 769.655 11:8 1.375
33\92 430.435 769.565 7:5 1.400
47\131 430.534 769.466 10:7 1.429
14\39 430.769 769.231 3:2 1.500 Soft 11L 3s
51\142 430.986 769.014 11:7 1.571
37\103 431.068 768.932 8:5 1.600
60\167 431.138 768.862 13:8 1.625
23\64 431.250 768.750 5:3 1.667 Semisoft 11L 3s
55\153 431.373 768.627 12:7 1.714
32\89 431.461 768.539 7:4 1.750
41\114 431.579 768.421 9:5 1.800
9\25 432.000 768.000 2:1 2.000 Basic 11L 3s
Scales with tunings softer than this are proper
40\111 432.432 767.568 9:4 2.250
31\86 432.558 767.442 7:3 2.333
53\147 432.653 767.347 12:5 2.400
22\61 432.787 767.213 5:2 2.500 Semihard 11L 3s
57\158 432.911 767.089 13:5 2.600
35\97 432.990 767.010 8:3 2.667
48\133 433.083 766.917 11:4 2.750
13\36 433.333 766.667 3:1 3.000 Hard 11L 3s
43\119 433.613 766.387 10:3 3.333
30\83 433.735 766.265 7:2 3.500
47\130 433.846 766.154 11:3 3.667
17\47 434.043 765.957 4:1 4.000 Superhard 11L 3s
38\105 434.286 765.714 9:2 4.500
21\58 434.483 765.517 5:1 5.000
25\69 434.783 765.217 6:1 6.000
4\11 436.364 763.636 1:0 → ∞ Collapsed 11L 3s