9L 2s
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Scale structure
Step pattern
LLLLLsLLLLs
sLLLLsLLLLL
Equave
2/1 (1200.0¢)
Period
2/1 (1200.0¢)
Generator size
Bright
6\11 to 5\9 (654.5¢ to 666.7¢)
Dark
4\9 to 5\11 (533.3¢ to 545.5¢)
TAMNAMS information
Descends from
2L 7s (balzano)
Ancestor's step ratio range
1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent
2L 7s
Sister
2L 9s
Daughters
11L 9s, 9L 11s
Neutralized
7L 4s
2-Flought
20L 2s, 9L 13s
Equal tunings
Equalized (L:s = 1:1)
6\11 (654.5¢)
Supersoft (L:s = 4:3)
23\42 (657.1¢)
Soft (L:s = 3:2)
17\31 (658.1¢)
Semisoft (L:s = 5:3)
28\51 (658.8¢)
Basic (L:s = 2:1)
11\20 (660.0¢)
Semihard (L:s = 5:2)
27\49 (661.2¢)
Hard (L:s = 3:1)
16\29 (662.1¢)
Superhard (L:s = 4:1)
21\38 (663.2¢)
Collapsed (L:s = 1:0)
5\9 (666.7¢)
| ↖ 8L 1s | ↑ 9L 1s | 10L 1s ↗ |
| ← 8L 2s | 9L 2s | 10L 2s → |
| ↙ 8L 3s | ↓ 9L 3s | 10L 3s ↘ |
┌╥╥╥╥╥┬╥╥╥╥┬┐ │║║║║║│║║║║││ │││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┘
sLLLLsLLLLL
9L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 9 large steps and 2 small steps, repeating every octave. 9L 2s is a child scale of 2L 7s, expanding it by 2 tones. Generators that produce this scale range from 654.5¢ to 666.7¢, or from 533.3¢ to 545.5¢. It represents temperaments like Avila (narrow generator) and Casablanca (wide). CompactStar has suggested the names ultradiatonic and superarmotonic by analogy to 7L 2s's name of superdiatonic.
Modes
| UDP | Cyclic order |
Step pattern |
Scale degree (mosdegree) | |||||||||||
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | |||
| 10|0 | 1 | LLLLLsLLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Aug. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 9|1 | 7 | LLLLsLLLLLs | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. |
| 8|2 | 2 | LLLLsLLLLsL | Perf. | Maj. | Maj. | Maj. | Maj. | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. |
| 7|3 | 8 | LLLsLLLLLsL | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. | Maj. | Maj. | Maj. | Min. | Perf. |
| 6|4 | 3 | LLLsLLLLsLL | Perf. | Maj. | Maj. | Maj. | Min. | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Perf. |
| 5|5 | 9 | LLsLLLLLsLL | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Perf. | Maj. | Maj. | Min. | Min. | Perf. |
| 4|6 | 4 | LLsLLLLsLLL | Perf. | Maj. | Maj. | Min. | Min. | Perf. | Perf. | Maj. | Min. | Min. | Min. | Perf. |
| 3|7 | 10 | LsLLLLLsLLL | Perf. | Maj. | Min. | Min. | Min. | Perf. | Perf. | Maj. | Min. | Min. | Min. | Perf. |
| 2|8 | 5 | LsLLLLsLLLL | Perf. | Maj. | Min. | Min. | Min. | Perf. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 1|9 | 11 | sLLLLLsLLLL | Perf. | Min. | Min. | Min. | Min. | Perf. | Perf. | Min. | Min. | Min. | Min. | Perf. |
| 0|10 | 6 | sLLLLsLLLLL | Perf. | Min. | Min. | Min. | Min. | Perf. | Dim. | Min. | Min. | Min. | Min. | Perf. |
| UDP | Cyclic order |
Step pattern |
|---|---|---|
| 10|0 | 1 | LLLLLsLLLLs |
| 9|1 | 7 | LLLLsLLLLLs |
| 8|2 | 2 | LLLLsLLLLsL |
| 7|3 | 8 | LLLsLLLLLsL |
| 6|4 | 3 | LLLsLLLLsLL |
| 5|5 | 9 | LLsLLLLLsLL |
| 4|6 | 4 | LLsLLLLsLLL |
| 3|7 | 10 | LsLLLLLsLLL |
| 2|8 | 5 | LsLLLLsLLLL |
| 1|9 | 11 | sLLLLLsLLLL |
| 0|10 | 6 | sLLLLsLLLLL |
Proposed Names
- 10|0 LLLLLsLLLLs "Ultralydian"
- 9|1 LLLLsLLLLLs "Ultraionian"
- 8|2 LLLLsLLLLsL "Ultramixolydian"
- 7|3 LLLsLLLLLsL "Ultracorinthian"
- 6|4 LLLsLLLLsLL "Ultraolympian"
- 5|5 LLsLLLLLsLL "Ultralycian"
- 4|6 LLsLLLLsLLL "Ultrapisidian"
- 3|7 LsLLLLLsLLL "Ultradorian"
- 2|8 LsLLLLsLLLL "Ultraaeolian"
- 1|9 sLLLLLsLLLL "Ultraphrygian"
- 0|10 sLLLLsLLLLL "Ultralocrian"
Scale tree
| Generator(edo) | Cents | Step ratio | Comments | |||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Bright | Dark | L:s | Hardness | |||||||
| 6\11 | 654.545 | 545.455 | 1:1 | 1.000 | Equalized 9L 2s | |||||
| 35\64 | 656.250 | 543.750 | 6:5 | 1.200 | ||||||
| 29\53 | 656.604 | 543.396 | 5:4 | 1.250 | ||||||
| 52\95 | 656.842 | 543.158 | 9:7 | 1.286 | ||||||
| 23\42 | 657.143 | 542.857 | 4:3 | 1.333 | Supersoft 9L 2s | |||||
| 63\115 | 657.391 | 542.609 | 11:8 | 1.375 | ||||||
| 40\73 | 657.534 | 542.466 | 7:5 | 1.400 | ||||||
| 57\104 | 657.692 | 542.308 | 10:7 | 1.429 | ||||||
| 17\31 | 658.065 | 541.935 | 3:2 | 1.500 | Soft 9L 2s | |||||
| 62\113 | 658.407 | 541.593 | 11:7 | 1.571 | ||||||
| 45\82 | 658.537 | 541.463 | 8:5 | 1.600 | ||||||
| 73\133 | 658.647 | 541.353 | 13:8 | 1.625 | ||||||
| 28\51 | 658.824 | 541.176 | 5:3 | 1.667 | Semisoft 9L 2s | |||||
| 67\122 | 659.016 | 540.984 | 12:7 | 1.714 | ||||||
| 39\71 | 659.155 | 540.845 | 7:4 | 1.750 | ||||||
| 50\91 | 659.341 | 540.659 | 9:5 | 1.800 | ||||||
| 11\20 | 660.000 | 540.000 | 2:1 | 2.000 | Basic 9L 2s Scales with tunings softer than this are proper | |||||
| 49\89 | 660.674 | 539.326 | 9:4 | 2.250 | ||||||
| 38\69 | 660.870 | 539.130 | 7:3 | 2.333 | ||||||
| 65\118 | 661.017 | 538.983 | 12:5 | 2.400 | ||||||
| 27\49 | 661.224 | 538.776 | 5:2 | 2.500 | Semihard 9L 2s | |||||
| 70\127 | 661.417 | 538.583 | 13:5 | 2.600 | ||||||
| 43\78 | 661.538 | 538.462 | 8:3 | 2.667 | ||||||
| 59\107 | 661.682 | 538.318 | 11:4 | 2.750 | ||||||
| 16\29 | 662.069 | 537.931 | 3:1 | 3.000 | Hard 9L 2s | |||||
| 53\96 | 662.500 | 537.500 | 10:3 | 3.333 | ||||||
| 37\67 | 662.687 | 537.313 | 7:2 | 3.500 | ||||||
| 58\105 | 662.857 | 537.143 | 11:3 | 3.667 | ||||||
| 21\38 | 663.158 | 536.842 | 4:1 | 4.000 | Superhard 9L 2s | |||||
| 47\85 | 663.529 | 536.471 | 9:2 | 4.500 | ||||||
| 26\47 | 663.830 | 536.170 | 5:1 | 5.000 | ||||||
| 31\56 | 664.286 | 535.714 | 6:1 | 6.000 | ||||||
| 5\9 | 666.667 | 533.333 | 1:0 | → ∞ | Collapsed 9L 2s | |||||