2L 9s
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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)
Ancestor's 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¢)
| ↖ 1L 8s | ↑ 2L 8s | 3L 8s ↗ |
| ← 1L 9s | 2L 9s | 3L 9s → |
| ↙ 1L 10s | ↓ 2L 10s | 3L 10s ↘ |
┌╥┬┬┬┬╥┬┬┬┬┬┐ │║││││║││││││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sssssLssssL
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
| UDP | Cyclic 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
| 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 | |||||