11L 3s
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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¢)
| ↖ 10L 2s | ↑ 11L 2s | 12L 2s ↗ |
| ← 10L 3s | 11L 3s | 12L 3s → |
| ↙ 10L 4s | ↓ 11L 4s | 12L 4s ↘ |
┌╥╥╥╥┬╥╥╥╥┬╥╥╥┬┐ │║║║║│║║║║│║║║││ ││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
sLLLsLLLLsLLLL
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
| 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 | |||||