2L 11s

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↖ 1L 10s ↑ 2L 10s 3L 10s ↗
← 1L 11s 2L 11s 3L 11s →
↙ 1L 12s ↓ 2L 12s 3L 12s ↘ 
┌╥┬┬┬┬┬╥┬┬┬┬┬┬┐
│║│││││║│││││││
│││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LsssssLssssss
ssssssLsssssL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 6\13 to 1\2 (553.8 ¢ to 600.0 ¢)
Dark 1\2 to 7\13 (600.0 ¢ to 646.2 ¢)
TAMNAMS information
Descends from 2L 7s (balzano)
Ancestor's step ratio range 3:1 to 1:0 (hard)
Related MOS scales
Parent 2L 9s
Sister 11L 2s
Daughters 13L 2s, 2L 13s
Neutralized 4L 9s
2-Flought 15L 11s, 2L 24s
Equal tunings
Equalized (L:s = 1:1) 6\13 (553.8 ¢)
Supersoft (L:s = 4:3) 19\41 (556.1 ¢)
Soft (L:s = 3:2) 13\28 (557.1 ¢)
Semisoft (L:s = 5:3) 20\43 (558.1 ¢)
Basic (L:s = 2:1) 7\15 (560.0 ¢)
Semihard (L:s = 5:2) 15\32 (562.5 ¢)
Hard (L:s = 3:1) 8\17 (564.7 ¢)
Superhard (L:s = 4:1) 9\19 (568.4 ¢)
Collapsed (L:s = 1:0) 1\2 (600.0 ¢)

2L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 11 small steps, repeating every octave. 2L 11s is a grandchild scale of 2L 7s, expanding it by 4 tones. Generators that produce this scale range from 553.8 ¢ to 600 ¢, or from 600 ¢ to 646.2 ¢.

This MOS is the minimal truly chromatic scale[clarification needed] of Liese, Triton, and Tritonic temperaments.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

The intervals of 2L 11s are named after the number of mossteps (L and s) they subtend. Each interval, apart from the root and octave (perfect 0-mosstep and perfect 13-mosstep), has two varieties, or sizes, each. Interval varieties are named major and minor for the large and small sizes, respectively, and augmented, perfect, and diminished for the scale's generators.

Intervals of 2L 11s
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 92.3 ¢
Major 1-mosstep M1ms L 92.3 ¢ to 600.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 184.6 ¢
Major 2-mosstep M2ms L + s 184.6 ¢ to 600.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 276.9 ¢
Major 3-mosstep M3ms L + 2s 276.9 ¢ to 600.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 369.2 ¢
Major 4-mosstep M4ms L + 3s 369.2 ¢ to 600.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 461.5 ¢
Major 5-mosstep M5ms L + 4s 461.5 ¢ to 600.0 ¢
6-mosstep Diminished 6-mosstep d6ms 6s 0.0 ¢ to 553.8 ¢
Perfect 6-mosstep P6ms L + 5s 553.8 ¢ to 600.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 600.0 ¢ to 646.2 ¢
Augmented 7-mosstep A7ms 2L + 5s 646.2 ¢ to 1200.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 600.0 ¢ to 738.5 ¢
Major 8-mosstep M8ms 2L + 6s 738.5 ¢ to 1200.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 600.0 ¢ to 830.8 ¢
Major 9-mosstep M9ms 2L + 7s 830.8 ¢ to 1200.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 600.0 ¢ to 923.1 ¢
Major 10-mosstep M10ms 2L + 8s 923.1 ¢ to 1200.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 600.0 ¢ to 1015.4 ¢
Major 11-mosstep M11ms 2L + 9s 1015.4 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 600.0 ¢ to 1107.7 ¢
Major 12-mosstep M12ms 2L + 10s 1107.7 ¢ to 1200.0 ¢
13-mosstep Perfect 13-mosstep P13ms 2L + 11s 1200.0 ¢

Generator chain

A chain of bright generators, each a perfect 6-mosstep, produces the following scale degrees. A chain of 13 bright generators contains the scale degrees of one of the modes of 2L 11s. Expanding the chain to 15 scale degrees produces the modes of either 13L 2s (for soft-of-basic tunings) or 2L 13s (for hard-of-basic tunings).

Generator chain of 2L 11s
Bright gens Scale degree Abbrev.
14 Augmented 6-mosdegree A6md
13 Augmented 0-mosdegree A0md
12 Augmented 7-mosdegree A7md
11 Major 1-mosdegree M1md
10 Major 8-mosdegree M8md
9 Major 2-mosdegree M2md
8 Major 9-mosdegree M9md
7 Major 3-mosdegree M3md
6 Major 10-mosdegree M10md
5 Major 4-mosdegree M4md
4 Major 11-mosdegree M11md
3 Major 5-mosdegree M5md
2 Major 12-mosdegree M12md
1 Perfect 6-mosdegree P6md
0 Perfect 0-mosdegree
Perfect 13-mosdegree		 P0md
P13md
−1 Perfect 7-mosdegree P7md
−2 Minor 1-mosdegree m1md
−3 Minor 8-mosdegree m8md
−4 Minor 2-mosdegree m2md
−5 Minor 9-mosdegree m9md
−6 Minor 3-mosdegree m3md
−7 Minor 10-mosdegree m10md
−8 Minor 4-mosdegree m4md
−9 Minor 11-mosdegree m11md
−10 Minor 5-mosdegree m5md
−11 Minor 12-mosdegree m12md
−12 Diminished 6-mosdegree d6md
−13 Diminished 13-mosdegree d13md
−14 Diminished 7-mosdegree d7md

Modes

Scale degrees of the modes of 2L 11s 
UDP Cyclic
order		 Step
pattern		 Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13
12|0 1 LsssssLssssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Aug. Maj. Maj. Maj. Maj. Maj. Perf.
11|1 7 LssssssLsssss Perf. Maj. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
10|2 13 sLsssssLsssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Perf. Maj. Maj. Maj. Maj. Maj. Perf.
9|3 6 sLssssssLssss Perf. Min. Maj. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Perf.
8|4 12 ssLsssssLssss Perf. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Maj. Maj. Maj. Maj. Perf.
7|5 5 ssLssssssLsss Perf. Min. Min. Maj. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Perf.
6|6 11 sssLsssssLsss Perf. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Maj. Maj. Maj. Perf.
5|7 4 sssLssssssLss Perf. Min. Min. Min. Maj. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Perf.
4|8 10 ssssLsssssLss Perf. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Maj. Maj. Perf.
3|9 3 ssssLssssssLs Perf. Min. Min. Min. Min. Maj. Perf. Perf. Min. Min. Min. Min. Maj. Perf.
2|10 9 sssssLsssssLs Perf. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Maj. Perf.
1|11 2 sssssLssssssL Perf. Min. Min. Min. Min. Min. Perf. Perf. Min. Min. Min. Min. Min. Perf.
0|12 8 ssssssLsssssL Perf. Min. Min. Min. Min. Min. Dim. Perf. Min. Min. Min. Min. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 2L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
6\13 553.846 646.154 1:1 1.000 Equalized 2L 11s
31\67 555.224 644.776 6:5 1.200
25\54 555.556 644.444 5:4 1.250
44\95 555.789 644.211 9:7 1.286
19\41 556.098 643.902 4:3 1.333 Supersoft 2L 11s
51\110 556.364 643.636 11:8 1.375
32\69 556.522 643.478 7:5 1.400
45\97 556.701 643.299 10:7 1.429
13\28 557.143 642.857 3:2 1.500 Soft 2L 11s
46\99 557.576 642.424 11:7 1.571
33\71 557.746 642.254 8:5 1.600
53\114 557.895 642.105 13:8 1.625
20\43 558.140 641.860 5:3 1.667 Semisoft 2L 11s
47\101 558.416 641.584 12:7 1.714
27\58 558.621 641.379 7:4 1.750
34\73 558.904 641.096 9:5 1.800
7\15 560.000 640.000 2:1 2.000 Basic 2L 11s
Scales with tunings softer than this are proper
29\62 561.290 638.710 9:4 2.250
22\47 561.702 638.298 7:3 2.333
37\79 562.025 637.975 12:5 2.400
15\32 562.500 637.500 5:2 2.500 Semihard 2L 11s
38\81 562.963 637.037 13:5 2.600
23\49 563.265 636.735 8:3 2.667
31\66 563.636 636.364 11:4 2.750
8\17 564.706 635.294 3:1 3.000 Hard 2L 11s
25\53 566.038 633.962 10:3 3.333
17\36 566.667 633.333 7:2 3.500
26\55 567.273 632.727 11:3 3.667
9\19 568.421 631.579 4:1 4.000 Superhard 2L 11s
19\40 570.000 630.000 9:2 4.500
10\21 571.429 628.571 5:1 5.000
11\23 573.913 626.087 6:1 6.000
1\2 600.000 600.000 1:0 → ∞ Collapsed 2L 11s
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