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
Related to 2L 7s (balzano)
With tunings 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 ¢)
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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 ¢.

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 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 ¢

Generator chain

Generator chain of 9L 11s
Bright gens Scale degree Abbrev.
28 Augmented 8-mosdegree A8md
27 Augmented 17-mosdegree A17md
26 Augmented 6-mosdegree A6md
25 Augmented 15-mosdegree A15md
24 Augmented 4-mosdegree A4md
23 Augmented 13-mosdegree A13md
22 Augmented 2-mosdegree A2md
21 Augmented 11-mosdegree A11md
20 Augmented 0-mosdegree A0md
19 Augmented 9-mosdegree A9md
18 Major 18-mosdegree M18md
17 Major 7-mosdegree M7md
16 Major 16-mosdegree M16md
15 Major 5-mosdegree M5md
14 Major 14-mosdegree M14md
13 Major 3-mosdegree M3md
12 Major 12-mosdegree M12md
11 Major 1-mosdegree M1md
10 Major 10-mosdegree M10md
9 Major 19-mosdegree M19md
8 Major 8-mosdegree M8md
7 Major 17-mosdegree M17md
6 Major 6-mosdegree M6md
5 Major 15-mosdegree M15md
4 Major 4-mosdegree M4md
3 Major 13-mosdegree M13md
2 Major 2-mosdegree M2md
1 Perfect 11-mosdegree P11md
0 Perfect 0-mosdegree
Perfect 20-mosdegree		 P0md
P20md
−1 Perfect 9-mosdegree P9md
−2 Minor 18-mosdegree m18md
−3 Minor 7-mosdegree m7md
−4 Minor 16-mosdegree m16md
−5 Minor 5-mosdegree m5md
−6 Minor 14-mosdegree m14md
−7 Minor 3-mosdegree m3md
−8 Minor 12-mosdegree m12md
−9 Minor 1-mosdegree m1md
−10 Minor 10-mosdegree m10md
−11 Minor 19-mosdegree m19md
−12 Minor 8-mosdegree m8md
−13 Minor 17-mosdegree m17md
−14 Minor 6-mosdegree m6md
−15 Minor 15-mosdegree m15md
−16 Minor 4-mosdegree m4md
−17 Minor 13-mosdegree m13md
−18 Minor 2-mosdegree m2md
−19 Diminished 11-mosdegree d11md
−20 Diminished 20-mosdegree d20md
−21 Diminished 9-mosdegree d9md
−22 Diminished 18-mosdegree d18md
−23 Diminished 7-mosdegree d7md
−24 Diminished 16-mosdegree d16md
−25 Diminished 5-mosdegree d5md
−26 Diminished 14-mosdegree d14md
−27 Diminished 3-mosdegree d3md
−28 Diminished 12-mosdegree d12md

Modes

Scale degrees of the modes of 9L 11s
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
19|0 1 LsLsLsLsLssLsLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Aug. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
18|1 12 LsLsLsLssLsLsLsLsLss Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf.
17|2 3 LsLsLsLssLsLsLsLssLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf.
16|3 14 LsLsLssLsLsLsLsLssLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf.
15|4 5 LsLsLssLsLsLsLssLsLs Perf. Maj. Maj. Maj. Maj. Maj. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf.
14|5 16 LsLssLsLsLsLsLssLsLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf.
13|6 7 LsLssLsLsLsLssLsLsLs Perf. Maj. Maj. Maj. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf.
12|7 18 LssLsLsLsLsLssLsLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf.
11|8 9 LssLsLsLsLssLsLsLsLs Perf. Maj. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf.
10|9 20 sLsLsLsLsLssLsLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Maj. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf.
9|10 11 sLsLsLsLssLsLsLsLsLs Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf.
8|11 2 sLsLsLsLssLsLsLsLssL Perf. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf.
7|12 13 sLsLsLssLsLsLsLsLssL Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf.
6|13 4 sLsLsLssLsLsLsLssLsL Perf. Min. Maj. Min. Maj. Min. Maj. Min. Min. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf.
5|14 15 sLsLssLsLsLsLsLssLsL Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf.
4|15 6 sLsLssLsLsLsLssLsLsL Perf. Min. Maj. Min. Maj. Min. Min. Min. Min. Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf.
3|16 17 sLssLsLsLsLsLssLsLsL Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf.
2|17 8 sLssLsLsLsLssLsLsLsL Perf. Min. Maj. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
1|18 19 ssLsLsLsLsLssLsLsLsL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf.
0|19 10 ssLsLsLsLssLsLsLsLsL Perf. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Dim. Min. Min. Min. Min. Min. Min. Min. Min. Perf.

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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