9L 2s

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↖ 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
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, while Ganaram Inukshuk has suggested villatonic as a reference to the aforementioned Avila and Casablanca.

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"
  • 3|7 LsLLLLLsLLL "Ultradorian"
  • 2|8 LsLLLLsLLLL "Ultraaeolian"
  • 1|9 sLLLLLsLLLL "Ultraphrygian"
  • 0|10 sLLLLsLLLLL "Ultralocrian"

Mode degrees

Scale degrees of the modes of 9L 2s 
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.

Intervals

Intervals of 9L 2s
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 133.3¢
2-mosstep Minor 2-mosstep m2ms L + s 133.3¢ to 218.2¢
Major 2-mosstep M2ms 2L 218.2¢ to 266.7¢
3-mosstep Minor 3-mosstep m3ms 2L + s 266.7¢ to 327.3¢
Major 3-mosstep M3ms 3L 327.3¢ to 400.0¢
4-mosstep Minor 4-mosstep m4ms 3L + s 400.0¢ to 436.4¢
Major 4-mosstep M4ms 4L 436.4¢ to 533.3¢
5-mosstep Perfect 5-mosstep P5ms 4L + s 533.3¢ to 545.5¢
Augmented 5-mosstep A5ms 5L 545.5¢ to 666.7¢
6-mosstep Diminished 6-mosstep d6ms 4L + 2s 533.3¢ to 654.5¢
Perfect 6-mosstep P6ms 5L + s 654.5¢ to 666.7¢
7-mosstep Minor 7-mosstep m7ms 5L + 2s 666.7¢ to 763.6¢
Major 7-mosstep M7ms 6L + s 763.6¢ to 800.0¢
8-mosstep Minor 8-mosstep m8ms 6L + 2s 800.0¢ to 872.7¢
Major 8-mosstep M8ms 7L + s 872.7¢ to 933.3¢
9-mosstep Minor 9-mosstep m9ms 7L + 2s 933.3¢ to 981.8¢
Major 9-mosstep M9ms 8L + s 981.8¢ to 1066.7¢
10-mosstep Minor 10-mosstep m10ms 8L + 2s 1066.7¢ to 1090.9¢
Major 10-mosstep M10ms 9L + s 1090.9¢ to 1200.0¢
11-mosstep Perfect 11-mosstep P11ms 9L + 2s 1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 9L 2s
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
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