9L 13s

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↖ 8L 12s ↑9L 12s 10L 12s ↗
← 8L 13s9L 13s 10L 13s →
↙ 8L 14s ↓9L 14s 10L 14s ↘
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║││║│║││║│║│││
││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLssLsLssLsLssLsLss
ssLsLssLsLssLsLssLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 17\22 to 7\9 (927.3¢ to 933.3¢)
Dark 2\9 to 5\22 (266.7¢ to 272.7¢)
TAMNAMS information
Descends from 4L 5s (gramitonic)
Required step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 9L 4s
Sister 13L 9s
Daughters 22L 9s, 9L 22s
Neutralized 18L 4s
2-Flought 31L 13s, 9L 35s
Equal tunings
Equalized (L:s = 1:1) 17\22 (927.3¢)
Supersoft (L:s = 4:3) 58\75 (928.0¢)
Soft (L:s = 3:2) 41\53 (928.3¢)
Semisoft (L:s = 5:3) 65\84 (928.6¢)
Basic (L:s = 2:1) 24\31 (929.0¢)
Semihard (L:s = 5:2) 55\71 (929.6¢)
Hard (L:s = 3:1) 31\40 (930.0¢)
Superhard (L:s = 4:1) 38\49 (930.6¢)
Collapsed (L:s = 1:0) 7\9 (933.3¢)

9L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 13 small steps, repeating every octave. 9L 13s is a grandchild scale of 4L 5s, expanding it by 13 tones. Generators that produce this scale range from 927.3¢ to 933.3¢, or from 266.7¢ to 272.7¢.

Scale tree

Scale Tree and Tuning Spectrum of 9L 13s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
17\22 927.273 272.727 1:1 1.000 Equalized 9L 13s
92\119 927.731 272.269 6:5 1.200
75\97 927.835 272.165 5:4 1.250
133\172 927.907 272.093 9:7 1.286
58\75 928.000 272.000 4:3 1.333 Supersoft 9L 13s
157\203 928.079 271.921 11:8 1.375
99\128 928.125 271.875 7:5 1.400
140\181 928.177 271.823 10:7 1.429
41\53 928.302 271.698 3:2 1.500 Soft 9L 13s
147\190 928.421 271.579 11:7 1.571
106\137 928.467 271.533 8:5 1.600
171\221 928.507 271.493 13:8 1.625
65\84 928.571 271.429 5:3 1.667 Semisoft 9L 13s
154\199 928.643 271.357 12:7 1.714
89\115 928.696 271.304 7:4 1.750
113\146 928.767 271.233 9:5 1.800
24\31 929.032 270.968 2:1 2.000 Basic 9L 13s
Scales with tunings softer than this are proper
103\133 929.323 270.677 9:4 2.250
79\102 929.412 270.588 7:3 2.333
134\173 929.480 270.520 12:5 2.400
55\71 929.577 270.423 5:2 2.500 Semihard 9L 13s
141\182 929.670 270.330 13:5 2.600
86\111 929.730 270.270 8:3 2.667
117\151 929.801 270.199 11:4 2.750
31\40 930.000 270.000 3:1 3.000 Hard 9L 13s
100\129 930.233 269.767 10:3 3.333
69\89 930.337 269.663 7:2 3.500
107\138 930.435 269.565 11:3 3.667
38\49 930.612 269.388 4:1 4.000 Superhard 9L 13s
83\107 930.841 269.159 9:2 4.500
45\58 931.034 268.966 5:1 5.000
52\67 931.343 268.657 6:1 6.000
7\9 933.333 266.667 1:0 → ∞ Collapsed 9L 13s
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