# 9L 2s

 ↖ 8L 1s ↑ 9L 1s 10L 1s ↗ ← 8L 2s 9L 2s 10L 2s → ↙ 8L 3s ↓ 9L 3s 10L 3s ↘
```┌╥╥╥╥╥┬╥╥╥╥┬┐
│║║║║║│║║║║││
│││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┘```
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¢)

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

Modes of 9L 2s
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"
• 2|8 LsLLLLsLLLL "Ultraaeolian"
• 1|9 sLLLLLsLLLL "Ultraphrygian"
• 0|10 sLLLLsLLLLL "Ultralocrian"

## Scale tree

Scale Tree and Tuning Spectrum of 9L 2s
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