9L 13s

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↖ 8L 12s ↑ 9L 12s 10L 12s ↗
← 8L 13s 9L 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
Related to 4L 5s (gramitonic)
With tunings 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 properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 9L 13s
Bright gens Scale degree Abbrev.
30 Augmented 4-mosdegree A4md
29 Augmented 9-mosdegree A9md
28 Augmented 14-mosdegree A14md
27 Augmented 19-mosdegree A19md
26 Augmented 2-mosdegree A2md
25 Augmented 7-mosdegree A7md
24 Augmented 12-mosdegree A12md
23 Augmented 17-mosdegree A17md
22 Augmented 0-mosdegree A0md
21 Augmented 5-mosdegree A5md
20 Major 10-mosdegree M10md
19 Major 15-mosdegree M15md
18 Major 20-mosdegree M20md
17 Major 3-mosdegree M3md
16 Major 8-mosdegree M8md
15 Major 13-mosdegree M13md
14 Major 18-mosdegree M18md
13 Major 1-mosdegree M1md
12 Major 6-mosdegree M6md
11 Major 11-mosdegree M11md
10 Major 16-mosdegree M16md
9 Major 21-mosdegree M21md
8 Major 4-mosdegree M4md
7 Major 9-mosdegree M9md
6 Major 14-mosdegree M14md
5 Major 19-mosdegree M19md
4 Major 2-mosdegree M2md
3 Major 7-mosdegree M7md
2 Major 12-mosdegree M12md
1 Perfect 17-mosdegree P17md
0 Perfect 0-mosdegree
Perfect 22-mosdegree		 P0md
P22md
−1 Perfect 5-mosdegree P5md
−2 Minor 10-mosdegree m10md
−3 Minor 15-mosdegree m15md
−4 Minor 20-mosdegree m20md
−5 Minor 3-mosdegree m3md
−6 Minor 8-mosdegree m8md
−7 Minor 13-mosdegree m13md
−8 Minor 18-mosdegree m18md
−9 Minor 1-mosdegree m1md
−10 Minor 6-mosdegree m6md
−11 Minor 11-mosdegree m11md
−12 Minor 16-mosdegree m16md
−13 Minor 21-mosdegree m21md
−14 Minor 4-mosdegree m4md
−15 Minor 9-mosdegree m9md
−16 Minor 14-mosdegree m14md
−17 Minor 19-mosdegree m19md
−18 Minor 2-mosdegree m2md
−19 Minor 7-mosdegree m7md
−20 Minor 12-mosdegree m12md
−21 Diminished 17-mosdegree d17md
−22 Diminished 22-mosdegree d22md
−23 Diminished 5-mosdegree d5md
−24 Diminished 10-mosdegree d10md
−25 Diminished 15-mosdegree d15md
−26 Diminished 20-mosdegree d20md
−27 Diminished 3-mosdegree d3md
−28 Diminished 8-mosdegree d8md
−29 Diminished 13-mosdegree d13md
−30 Diminished 18-mosdegree d18md

Modes

Scale degrees of the modes of 9L 13s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
21|0 1 LsLsLssLsLssLsLssLsLss Perf. Maj. Maj. Maj. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
20|1 18 LsLssLsLsLssLsLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
19|2 13 LsLssLsLssLsLsLssLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
18|3 8 LsLssLsLssLsLssLsLsLss Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Perf.
17|4 3 LsLssLsLssLsLssLsLssLs Perf. Maj. Maj. Maj. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
16|5 20 LssLsLsLssLsLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
15|6 15 LssLsLssLsLsLssLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
14|7 10 LssLsLssLsLssLsLsLssLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Perf.
13|8 5 LssLsLssLsLssLsLssLsLs Perf. Maj. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
12|9 22 sLsLsLssLsLssLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
11|10 17 sLsLssLsLsLssLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
10|11 12 sLsLssLsLssLsLsLssLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Perf.
9|12 7 sLsLssLsLssLsLssLsLsLs Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Perf.
8|13 2 sLsLssLsLssLsLssLsLssL Perf. Min. Maj. Min. Maj. Perf. Min. Maj. Min. Maj. Min. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
7|14 19 sLssLsLsLssLsLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Maj. Min. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
6|15 14 sLssLsLssLsLsLssLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Maj. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Perf.
5|16 9 sLssLsLssLsLssLsLsLssL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Perf.
4|17 4 sLssLsLssLsLssLsLssLsL Perf. Min. Maj. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
3|18 21 ssLsLsLssLsLssLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Maj. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
2|19 16 ssLsLssLsLsLssLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
1|20 11 ssLsLssLsLssLsLsLssLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Perf.
0|21 6 ssLsLssLsLssLsLssLsLsL Perf. Min. Min. Min. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Min. Min. Min. Perf.

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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