9L 13s

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↖ 8L 12s ↑ 9L 12s 10L 12s ↗
← 8L 13s 9L 13s 10L 13s →
↙ 8L 14s ↓ 9L 14s 10L 14s ↘ 
┌╥┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬╥┬╥┬┬┐
│║│║│║││║│║││║│║││║│║│││
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└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
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)
Ancestor's 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¢.

Modes

Modes of 9L 13s
UDP Cyclic
order		 Step
pattern
21|0 1 LsLsLssLsLssLsLssLsLss
20|1 18 LsLssLsLsLssLsLssLsLss
19|2 13 LsLssLsLssLsLsLssLsLss
18|3 8 LsLssLsLssLsLssLsLsLss
17|4 3 LsLssLsLssLsLssLsLssLs
16|5 20 LssLsLsLssLsLssLsLssLs
15|6 15 LssLsLssLsLsLssLsLssLs
14|7 10 LssLsLssLsLssLsLsLssLs
13|8 5 LssLsLssLsLssLsLssLsLs
12|9 22 sLsLsLssLsLssLsLssLsLs
11|10 17 sLsLssLsLsLssLsLssLsLs
10|11 12 sLsLssLsLssLsLsLssLsLs
9|12 7 sLsLssLsLssLsLssLsLsLs
8|13 2 sLsLssLsLssLsLssLsLssL
7|14 19 sLssLsLsLssLsLssLsLssL
6|15 14 sLssLsLssLsLsLssLsLssL
5|16 9 sLssLsLssLsLssLsLsLssL
4|17 4 sLssLsLssLsLssLsLssLsL
3|18 21 ssLsLsLssLsLssLsLssLsL
2|19 16 ssLsLssLsLsLssLsLssLsL
1|20 11 ssLsLssLsLssLsLsLssLsL
0|21 6 ssLsLssLsLssLsLssLsLsL

Intervals

Intervals of 9L 13s
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 54.5¢
Major 1-mosstep M1ms L 54.5¢ to 133.3¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 109.1¢
Major 2-mosstep M2ms L + s 109.1¢ to 133.3¢
3-mosstep Minor 3-mosstep m3ms L + 2s 133.3¢ to 163.6¢
Major 3-mosstep M3ms 2L + s 163.6¢ to 266.7¢
4-mosstep Minor 4-mosstep m4ms L + 3s 133.3¢ to 218.2¢
Major 4-mosstep M4ms 2L + 2s 218.2¢ to 266.7¢
5-mosstep Perfect 5-mosstep P5ms 2L + 3s 266.7¢ to 272.7¢
Augmented 5-mosstep A5ms 3L + 2s 272.7¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 266.7¢ to 327.3¢
Major 6-mosstep M6ms 3L + 3s 327.3¢ to 400.0¢
7-mosstep Minor 7-mosstep m7ms 2L + 5s 266.7¢ to 381.8¢
Major 7-mosstep M7ms 3L + 4s 381.8¢ to 400.0¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 400.0¢ to 436.4¢
Major 8-mosstep M8ms 4L + 4s 436.4¢ to 533.3¢
9-mosstep Minor 9-mosstep m9ms 3L + 6s 400.0¢ to 490.9¢
Major 9-mosstep M9ms 4L + 5s 490.9¢ to 533.3¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 533.3¢ to 545.5¢
Major 10-mosstep M10ms 5L + 5s 545.5¢ to 666.7¢
11-mosstep Minor 11-mosstep m11ms 4L + 7s 533.3¢ to 600.0¢
Major 11-mosstep M11ms 5L + 6s 600.0¢ to 666.7¢
12-mosstep Minor 12-mosstep m12ms 4L + 8s 533.3¢ to 654.5¢
Major 12-mosstep M12ms 5L + 7s 654.5¢ to 666.7¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 666.7¢ to 709.1¢
Major 13-mosstep M13ms 6L + 7s 709.1¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms 5L + 9s 666.7¢ to 763.6¢
Major 14-mosstep M14ms 6L + 8s 763.6¢ to 800.0¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 800.0¢ to 818.2¢
Major 15-mosstep M15ms 7L + 8s 818.2¢ to 933.3¢
16-mosstep Minor 16-mosstep m16ms 6L + 10s 800.0¢ to 872.7¢
Major 16-mosstep M16ms 7L + 9s 872.7¢ to 933.3¢
17-mosstep Diminished 17-mosstep d17ms 6L + 11s 800.0¢ to 927.3¢
Perfect 17-mosstep P17ms 7L + 10s 927.3¢ to 933.3¢
18-mosstep Minor 18-mosstep m18ms 7L + 11s 933.3¢ to 981.8¢
Major 18-mosstep M18ms 8L + 10s 981.8¢ to 1066.7¢
19-mosstep Minor 19-mosstep m19ms 7L + 12s 933.3¢ to 1036.4¢
Major 19-mosstep M19ms 8L + 11s 1036.4¢ to 1066.7¢
20-mosstep Minor 20-mosstep m20ms 8L + 12s 1066.7¢ to 1090.9¢
Major 20-mosstep M20ms 9L + 11s 1090.9¢ to 1200.0¢
21-mosstep Minor 21-mosstep m21ms 8L + 13s 1066.7¢ to 1145.5¢
Major 21-mosstep M21ms 9L + 12s 1145.5¢ to 1200.0¢
22-mosstep Perfect 22-mosstep P22ms 9L + 13s 1200.0¢

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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