9L 11s

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↖ 8L 10s ↑ 9L 10s 10L 10s ↗
← 8L 11s 9L 11s 10L 11s →
↙ 8L 12s ↓ 9L 12s 10L 12s ↘ 
┌╥┬╥┬╥┬╥┬╥┬┬╥┬╥┬╥┬╥┬┬┐
│║│║│║│║│║││║│║│║│║│││
││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsLsLsLsLssLsLsLsLss
ssLsLsLsLssLsLsLsLsL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 11\20 to 5\9 (660.0¢ to 666.7¢)
Dark 4\9 to 9\20 (533.3¢ to 540.0¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 1:1 to 3:2 (soft)
Related MOS scales
Parent 9L 2s
Sister 11L 9s
Daughters 20L 9s, 9L 20s
Neutralized 18L 2s
2-Flought 29L 11s, 9L 31s
Equal tunings
Equalized (L:s = 1:1) 11\20 (660.0¢)
Supersoft (L:s = 4:3) 38\69 (660.9¢)
Soft (L:s = 3:2) 27\49 (661.2¢)
Semisoft (L:s = 5:3) 43\78 (661.5¢)
Basic (L:s = 2:1) 16\29 (662.1¢)
Semihard (L:s = 5:2) 37\67 (662.7¢)
Hard (L:s = 3:1) 21\38 (663.2¢)
Superhard (L:s = 4:1) 26\47 (663.8¢)
Collapsed (L:s = 1:0) 5\9 (666.7¢)

9L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 11 small steps, repeating every octave. 9L 11s is a grandchild scale of 2L 7s, expanding it by 11 tones. Generators that produce this scale range from 660¢ to 666.7¢, or from 533.3¢ to 540¢.

Modes

Modes of 9L 11s
UDP Cyclic
order		 Step
pattern
19|0 1 LsLsLsLsLssLsLsLsLss
18|1 12 LsLsLsLssLsLsLsLsLss
17|2 3 LsLsLsLssLsLsLsLssLs
16|3 14 LsLsLssLsLsLsLsLssLs
15|4 5 LsLsLssLsLsLsLssLsLs
14|5 16 LsLssLsLsLsLsLssLsLs
13|6 7 LsLssLsLsLsLssLsLsLs
12|7 18 LssLsLsLsLsLssLsLsLs
11|8 9 LssLsLsLsLssLsLsLsLs
10|9 20 sLsLsLsLsLssLsLsLsLs
9|10 11 sLsLsLsLssLsLsLsLsLs
8|11 2 sLsLsLsLssLsLsLsLssL
7|12 13 sLsLsLssLsLsLsLsLssL
6|13 4 sLsLsLssLsLsLsLssLsL
5|14 15 sLsLssLsLsLsLsLssLsL
4|15 6 sLsLssLsLsLsLssLsLsL
3|16 17 sLssLsLsLsLsLssLsLsL
2|17 8 sLssLsLsLsLssLsLsLsL
1|18 19 ssLsLsLsLsLssLsLsLsL
0|19 10 ssLsLsLsLssLsLsLsLsL

Intervals

Intervals of 9L 11s
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 60.0¢
Major 1-mosstep M1ms L 60.0¢ to 133.3¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0¢ to 120.0¢
Major 2-mosstep M2ms L + s 120.0¢ to 133.3¢
3-mosstep Minor 3-mosstep m3ms L + 2s 133.3¢ to 180.0¢
Major 3-mosstep M3ms 2L + s 180.0¢ to 266.7¢
4-mosstep Minor 4-mosstep m4ms L + 3s 133.3¢ to 240.0¢
Major 4-mosstep M4ms 2L + 2s 240.0¢ to 266.7¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 266.7¢ to 300.0¢
Major 5-mosstep M5ms 3L + 2s 300.0¢ to 400.0¢
6-mosstep Minor 6-mosstep m6ms 2L + 4s 266.7¢ to 360.0¢
Major 6-mosstep M6ms 3L + 3s 360.0¢ to 400.0¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 400.0¢ to 420.0¢
Major 7-mosstep M7ms 4L + 3s 420.0¢ to 533.3¢
8-mosstep Minor 8-mosstep m8ms 3L + 5s 400.0¢ to 480.0¢
Major 8-mosstep M8ms 4L + 4s 480.0¢ to 533.3¢
9-mosstep Perfect 9-mosstep P9ms 4L + 5s 533.3¢ to 540.0¢
Augmented 9-mosstep A9ms 5L + 4s 540.0¢ to 666.7¢
10-mosstep Minor 10-mosstep m10ms 4L + 6s 533.3¢ to 600.0¢
Major 10-mosstep M10ms 5L + 5s 600.0¢ to 666.7¢
11-mosstep Diminished 11-mosstep d11ms 4L + 7s 533.3¢ to 660.0¢
Perfect 11-mosstep P11ms 5L + 6s 660.0¢ to 666.7¢
12-mosstep Minor 12-mosstep m12ms 5L + 7s 666.7¢ to 720.0¢
Major 12-mosstep M12ms 6L + 6s 720.0¢ to 800.0¢
13-mosstep Minor 13-mosstep m13ms 5L + 8s 666.7¢ to 780.0¢
Major 13-mosstep M13ms 6L + 7s 780.0¢ to 800.0¢
14-mosstep Minor 14-mosstep m14ms 6L + 8s 800.0¢ to 840.0¢
Major 14-mosstep M14ms 7L + 7s 840.0¢ to 933.3¢
15-mosstep Minor 15-mosstep m15ms 6L + 9s 800.0¢ to 900.0¢
Major 15-mosstep M15ms 7L + 8s 900.0¢ to 933.3¢
16-mosstep Minor 16-mosstep m16ms 7L + 9s 933.3¢ to 960.0¢
Major 16-mosstep M16ms 8L + 8s 960.0¢ to 1066.7¢
17-mosstep Minor 17-mosstep m17ms 7L + 10s 933.3¢ to 1020.0¢
Major 17-mosstep M17ms 8L + 9s 1020.0¢ to 1066.7¢
18-mosstep Minor 18-mosstep m18ms 8L + 10s 1066.7¢ to 1080.0¢
Major 18-mosstep M18ms 9L + 9s 1080.0¢ to 1200.0¢
19-mosstep Minor 19-mosstep m19ms 8L + 11s 1066.7¢ to 1140.0¢
Major 19-mosstep M19ms 9L + 10s 1140.0¢ to 1200.0¢
20-mosstep Perfect 20-mosstep P20ms 9L + 11s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 9L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
11\20 660.000 540.000 1:1 1.000 Equalized 9L 11s
60\109 660.550 539.450 6:5 1.200
49\89 660.674 539.326 5:4 1.250
87\158 660.759 539.241 9:7 1.286
38\69 660.870 539.130 4:3 1.333 Supersoft 9L 11s
103\187 660.963 539.037 11:8 1.375
65\118 661.017 538.983 7:5 1.400
92\167 661.078 538.922 10:7 1.429
27\49 661.224 538.776 3:2 1.500 Soft 9L 11s
97\176 661.364 538.636 11:7 1.571
70\127 661.417 538.583 8:5 1.600
113\205 661.463 538.537 13:8 1.625
43\78 661.538 538.462 5:3 1.667 Semisoft 9L 11s
102\185 661.622 538.378 12:7 1.714
59\107 661.682 538.318 7:4 1.750
75\136 661.765 538.235 9:5 1.800
16\29 662.069 537.931 2:1 2.000 Basic 9L 11s
Scales with tunings softer than this are proper
69\125 662.400 537.600 9:4 2.250
53\96 662.500 537.500 7:3 2.333
90\163 662.577 537.423 12:5 2.400
37\67 662.687 537.313 5:2 2.500 Semihard 9L 11s
95\172 662.791 537.209 13:5 2.600
58\105 662.857 537.143 8:3 2.667
79\143 662.937 537.063 11:4 2.750
21\38 663.158 536.842 3:1 3.000 Hard 9L 11s
68\123 663.415 536.585 10:3 3.333
47\85 663.529 536.471 7:2 3.500
73\132 663.636 536.364 11:3 3.667
26\47 663.830 536.170 4:1 4.000 Superhard 9L 11s
57\103 664.078 535.922 9:2 4.500
31\56 664.286 535.714 5:1 5.000
36\65 664.615 535.385 6:1 6.000
5\9 666.667 533.333 1:0 → ∞ Collapsed 9L 11s


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