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.
Intervals
| 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 109.1¢ |
| Major 1-mosstep | M1ms | L | 109.1¢ to 600.0¢ | |
| 2-mosstep | Minor 2-mosstep | m2ms | 2s | 0.0¢ to 218.2¢ |
| Major 2-mosstep | M2ms | L + s | 218.2¢ to 600.0¢ | |
| 3-mosstep | Minor 3-mosstep | m3ms | 3s | 0.0¢ to 327.3¢ |
| Major 3-mosstep | M3ms | L + 2s | 327.3¢ to 600.0¢ | |
| 4-mosstep | Minor 4-mosstep | m4ms | 4s | 0.0¢ to 436.4¢ |
| Major 4-mosstep | M4ms | L + 3s | 436.4¢ to 600.0¢ | |
| 5-mosstep | Diminished 5-mosstep | d5ms | 5s | 0.0¢ to 545.5¢ |
| Perfect 5-mosstep | P5ms | L + 4s | 545.5¢ to 600.0¢ | |
| 6-mosstep | Perfect 6-mosstep | P6ms | L + 5s | 600.0¢ to 654.5¢ |
| Augmented 6-mosstep | A6ms | 2L + 4s | 654.5¢ to 1200.0¢ | |
| 7-mosstep | Minor 7-mosstep | m7ms | L + 6s | 600.0¢ to 763.6¢ |
| Major 7-mosstep | M7ms | 2L + 5s | 763.6¢ to 1200.0¢ | |
| 8-mosstep | Minor 8-mosstep | m8ms | L + 7s | 600.0¢ to 872.7¢ |
| Major 8-mosstep | M8ms | 2L + 6s | 872.7¢ to 1200.0¢ | |
| 9-mosstep | Minor 9-mosstep | m9ms | L + 8s | 600.0¢ to 981.8¢ |
| Major 9-mosstep | M9ms | 2L + 7s | 981.8¢ to 1200.0¢ | |
| 10-mosstep | Minor 10-mosstep | m10ms | L + 9s | 600.0¢ to 1090.9¢ |
| Major 10-mosstep | M10ms | 2L + 8s | 1090.9¢ to 1200.0¢ | |
| 11-mosstep | Perfect 11-mosstep | P11ms | 2L + 9s | 1200.0¢ |
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 | |||||