11L 3s

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↖ 10L 2s ↑ 11L 2s 12L 2s ↗
← 10L 3s 11L 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)
Ancestor'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.

Modes

Modes of 11L 3s
UDP Cyclic
order		 Step
pattern
13|0 1 LLLLsLLLLsLLLs
12|1 6 LLLLsLLLsLLLLs
11|2 11 LLLsLLLLsLLLLs
10|3 2 LLLsLLLLsLLLsL
9|4 7 LLLsLLLsLLLLsL
8|5 12 LLsLLLLsLLLLsL
7|6 3 LLsLLLLsLLLsLL
6|7 8 LLsLLLsLLLLsLL
5|8 13 LsLLLLsLLLLsLL
4|9 4 LsLLLLsLLLsLLL
3|10 9 LsLLLsLLLLsLLL
2|11 14 sLLLLsLLLLsLLL
1|12 5 sLLLLsLLLsLLLL
0|13 10 sLLLsLLLLsLLLL

Intervals

Intervals of 11L 3s
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 85.7¢
Major 1-mosstep M1ms L 85.7¢ to 109.1¢
2-mosstep Minor 2-mosstep m2ms L + s 109.1¢ to 171.4¢
Major 2-mosstep M2ms 2L 171.4¢ to 218.2¢
3-mosstep Minor 3-mosstep m3ms 2L + s 218.2¢ to 257.1¢
Major 3-mosstep M3ms 3L 257.1¢ to 327.3¢
4-mosstep Minor 4-mosstep m4ms 3L + s 327.3¢ to 342.9¢
Major 4-mosstep M4ms 4L 342.9¢ to 436.4¢
5-mosstep Diminished 5-mosstep d5ms 3L + 2s 327.3¢ to 428.6¢
Perfect 5-mosstep P5ms 4L + s 428.6¢ to 436.4¢
6-mosstep Minor 6-mosstep m6ms 4L + 2s 436.4¢ to 514.3¢
Major 6-mosstep M6ms 5L + s 514.3¢ to 545.5¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 545.5¢ to 600.0¢
Major 7-mosstep M7ms 6L + s 600.0¢ to 654.5¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 654.5¢ to 685.7¢
Major 8-mosstep M8ms 7L + s 685.7¢ to 763.6¢
9-mosstep Perfect 9-mosstep P9ms 7L + 2s 763.6¢ to 771.4¢
Augmented 9-mosstep A9ms 8L + s 771.4¢ to 872.7¢
10-mosstep Minor 10-mosstep m10ms 7L + 3s 763.6¢ to 857.1¢
Major 10-mosstep M10ms 8L + 2s 857.1¢ to 872.7¢
11-mosstep Minor 11-mosstep m11ms 8L + 3s 872.7¢ to 942.9¢
Major 11-mosstep M11ms 9L + 2s 942.9¢ to 981.8¢
12-mosstep Minor 12-mosstep m12ms 9L + 3s 981.8¢ to 1028.6¢
Major 12-mosstep M12ms 10L + 2s 1028.6¢ to 1090.9¢
13-mosstep Minor 13-mosstep m13ms 10L + 3s 1090.9¢ to 1114.3¢
Major 13-mosstep M13ms 11L + 2s 1114.3¢ to 1200.0¢
14-mosstep Perfect 14-mosstep P14ms 11L + 3s 1200.0¢

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
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