2L 9s

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↖ 1L 8s ↑2L 8s 3L 8s ↗
← 1L 9s2L 9s 3L 9s →
↙ 1L 10s ↓2L 10s 3L 10s ↘
┌╥┬┬┬┬╥┬┬┬┬┬┐
│║││││║││││││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLsssss
sssssLssssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 5\11 to 1\2 (545.5¢ to 600.0¢)
Dark 1\2 to 6\11 (600.0¢ to 654.5¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Required step ratio range 2:1 to 1:0 (hard-of-basic)
Related MOS scales
Parent 2L 7s
Sister 9L 2s
Daughters 11L 2s, 2L 11s
Neutralized 4L 7s
2-Flought 13L 9s, 2L 20s
Equal tunings
Equalized (L:s = 1:1) 5\11 (545.5¢)
Supersoft (L:s = 4:3) 16\35 (548.6¢)
Soft (L:s = 3:2) 11\24 (550.0¢)
Semisoft (L:s = 5:3) 17\37 (551.4¢)
Basic (L:s = 2:1) 6\13 (553.8¢)
Semihard (L:s = 5:2) 13\28 (557.1¢)
Hard (L:s = 3:1) 7\15 (560.0¢)
Superhard (L:s = 4:1) 8\17 (564.7¢)
Collapsed (L:s = 1:0) 1\2 (600.0¢)

2L 9s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 9 small steps, repeating every octave. 2L 9s is a child scale of 2L 7s, expanding it by 2 tones. Generators that produce this scale range from 545.5¢ to 600¢, or from 600¢ to 654.5¢. This MOS reaches a harmonic entropy minimum when the generator is 7/5. It represents temperaments like Tritonic, Triton, Heinz and Liese.

Modes

Modes of 2L 9s
UDP Rotational order Step pattern
10|0 1 LssssLsssss
9|1 6 LsssssLssss
8|2 11 sLssssLssss
7|3 5 sLsssssLsss
6|4 10 ssLssssLsss
5|5 4 ssLsssssLss
4|6 9 sssLssssLss
3|7 3 sssLsssssLs
2|8 8 ssssLssssLs
1|9 2 ssssLsssssL
0|10 7 sssssLssssL

Scale tree

Scale Tree and Tuning Spectrum of 2L 9s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
5\11 545.455 654.545 1:1 1.000 Equalized 2L 9s
26\57 547.368 652.632 6:5 1.200
21\46 547.826 652.174 5:4 1.250 Heinz
37\81 548.148 651.852 9:7 1.286
16\35 548.571 651.429 4:3 1.333 Supersoft 2L 9s
43\94 548.936 651.064 11:8 1.375
27\59 549.153 650.847 7:5 1.400
38\83 549.398 650.602 10:7 1.429
11\24 550.000 650.000 3:2 1.500 Soft 2L 9s
39\85 550.588 649.412 11:7 1.571
28\61 550.820 649.180 8:5 1.600
45\98 551.020 648.980 13:8 1.625
17\37 551.351 648.649 5:3 1.667 Semisoft 2L 9s
40\87 551.724 648.276 12:7 1.714
23\50 552.000 648.000 7:4 1.750
29\63 552.381 647.619 9:5 1.800
6\13 553.846 646.154 2:1 2.000 Basic 2L 9s
Scales with tunings softer than this are proper
25\54 555.556 644.444 9:4 2.250
19\41 556.098 643.902 7:3 2.333
32\69 556.522 643.478 12:5 2.400
13\28 557.143 642.857 5:2 2.500 Semihard 2L 9s
33\71 557.746 642.254 13:5 2.600
20\43 558.140 641.860 8:3 2.667
27\58 558.621 641.379 11:4 2.750
7\15 560.000 640.000 3:1 3.000 Hard 2L 9s
22\47 561.702 638.298 10:3 3.333
15\32 562.500 637.500 7:2 3.500
23\49 563.265 636.735 11:3 3.667
8\17 564.706 635.294 4:1 4.000 Superhard 2L 9s
17\36 566.667 633.333 9:2 4.500
9\19 568.421 631.579 5:1 5.000 Triton / liese
10\21 571.429 628.571 6:1 6.000 Tritonic
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 9s