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