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2L 11s (3/1-equivalent)

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2L 11s⟨3/1⟩ is a 3/1-equivalent (tritave-equivalent) moment of symmetry scale containing 2 large steps and 11 small steps, repeating every interval of 3/1 (1902.0 ¢). Generators that produce this scale range from 877.8 ¢ to 951 ¢, or from 951 ¢ to 1024.1 ¢.

↖ 1L 10s⟨3/1⟩ ↑ 2L 10s⟨3/1⟩ 3L 10s⟨3/1⟩ ↗
← 1L 11s⟨3/1⟩ 2L 11s (3/1-equivalent) 3L 11s⟨3/1⟩ →
↙ 1L 12s⟨3/1⟩ ↓ 2L 12s⟨3/1⟩ 3L 12s⟨3/1⟩ ↘
Scale structure
Step pattern LsssssLssssss
ssssssLsssssL
Equave 3/1 (1902.0 ¢)
Period 3/1 (1902.0 ¢)
Generator size(edt)
Bright 6\13 to 1\2 (877.8 ¢ to 951.0 ¢)
Dark 1\2 to 7\13 (951.0 ¢ to 1024.1 ¢)
Related MOS scales
Parent 2L 9s⟨3/1⟩
Sister 11L 2s⟨3/1⟩
Daughters 13L 2s⟨3/1⟩, 2L 13s⟨3/1⟩
Neutralized 4L 9s⟨3/1⟩
2-Flought 15L 11s⟨3/1⟩, 2L 24s⟨3/1⟩
Equal tunings(edt)
Equalized (L:s = 1:1) 6\13 (877.8 ¢)
Supersoft (L:s = 4:3) 19\41 (881.4 ¢)
Soft (L:s = 3:2) 13\28 (883.1 ¢)
Semisoft (L:s = 5:3) 20\43 (884.6 ¢)
Basic (L:s = 2:1) 7\15 (887.6 ¢)
Semihard (L:s = 5:2) 15\32 (891.5 ¢)
Hard (L:s = 3:1) 8\17 (895.0 ¢)
Superhard (L:s = 4:1) 9\19 (900.9 ¢)
Collapsed (L:s = 1:0) 1\2 (951.0 ¢)
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This MOS is most notable for representing the 13-note Trithagorean scale generated by 5/3.

Modes

Modes of 2L 11s⟨3/1⟩
UDP Cyclic
order		 Step
pattern
12|0 1 LsssssLssssss
11|1 7 LssssssLsssss
10|2 13 sLsssssLsssss
9|3 6 sLssssssLssss
8|4 12 ssLsssssLssss
7|5 5 ssLssssssLsss
6|6 11 sssLsssssLsss
5|7 4 sssLssssssLss
4|8 10 ssssLsssssLss
3|9 3 ssssLssssssLs
2|10 9 sssssLsssssLs
1|11 2 sssssLssssssL
0|12 8 ssssssLsssssL

Scale degrees

Scale degrees of the modes of 2L 11s⟨3/1⟩
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.

Intervals

Intervals of 2L 11s⟨3/1⟩
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 146.3 ¢
Major 1-mosstep M1ms L 146.3 ¢ to 951.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 292.6 ¢
Major 2-mosstep M2ms L + s 292.6 ¢ to 951.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 438.9 ¢
Major 3-mosstep M3ms L + 2s 438.9 ¢ to 951.0 ¢
4-mosstep Minor 4-mosstep m4ms 4s 0.0 ¢ to 585.2 ¢
Major 4-mosstep M4ms L + 3s 585.2 ¢ to 951.0 ¢
5-mosstep Minor 5-mosstep m5ms 5s 0.0 ¢ to 731.5 ¢
Major 5-mosstep M5ms L + 4s 731.5 ¢ to 951.0 ¢
6-mosstep Diminished 6-mosstep d6ms 6s 0.0 ¢ to 877.8 ¢
Perfect 6-mosstep P6ms L + 5s 877.8 ¢ to 951.0 ¢
7-mosstep Perfect 7-mosstep P7ms L + 6s 951.0 ¢ to 1024.1 ¢
Augmented 7-mosstep A7ms 2L + 5s 1024.1 ¢ to 1902.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 951.0 ¢ to 1170.4 ¢
Major 8-mosstep M8ms 2L + 6s 1170.4 ¢ to 1902.0 ¢
9-mosstep Minor 9-mosstep m9ms L + 8s 951.0 ¢ to 1316.7 ¢
Major 9-mosstep M9ms 2L + 7s 1316.7 ¢ to 1902.0 ¢
10-mosstep Minor 10-mosstep m10ms L + 9s 951.0 ¢ to 1463.0 ¢
Major 10-mosstep M10ms 2L + 8s 1463.0 ¢ to 1902.0 ¢
11-mosstep Minor 11-mosstep m11ms L + 10s 951.0 ¢ to 1609.3 ¢
Major 11-mosstep M11ms 2L + 9s 1609.3 ¢ to 1902.0 ¢
12-mosstep Minor 12-mosstep m12ms L + 11s 951.0 ¢ to 1755.7 ¢
Major 12-mosstep M12ms 2L + 10s 1755.7 ¢ to 1902.0 ¢
13-mosstep Perfect 13-mosstep P13ms 2L + 11s 1902.0 ¢

Scale tree

Scale tree and tuning spectrum of 2L 11s⟨3/1⟩
Generator(edt) Cents Step ratio Comments
Bright Dark L:s Hardness
6\13 877.825 1024.130 1:1 1.000 Equalized 2L 11s⟨3/1⟩
31\67 880.009 1021.946 6:5 1.200
25\54 880.535 1021.420 5:4 1.250
44\95 880.905 1021.050 9:7 1.286
19\41 881.394 1020.561 4:3 1.333 Supersoft 2L 11s⟨3/1⟩
51\110 881.816 1020.140 11:8 1.375
32\69 882.066 1019.889 7:5 1.400
45\97 882.350 1019.605 10:7 1.429
13\28 883.051 1018.904 3:2 1.500 Soft 2L 11s⟨3/1⟩
46\99 883.737 1018.218 11:7 1.571
33\71 884.007 1017.948 8:5 1.600
53\114 884.242 1017.713 13:8 1.625
20\43 884.630 1017.325 5:3 1.667 Semisoft 2L 11s⟨3/1⟩
47\101 885.068 1016.887 12:7 1.714
27\58 885.393 1016.562 7:4 1.750
34\73 885.842 1016.113 9:5 1.800
7\15 887.579 1014.376 2:1 2.000 Basic 2L 11s⟨3/1⟩
Scales with tunings softer than this are proper
29\62 889.624 1012.331 9:4 2.250
22\47 890.277 1011.678 7:3 2.333
37\79 890.789 1011.166 12:5 2.400
15\32 891.541 1010.414 5:2 2.500 Semihard 2L 11s⟨3/1⟩
38\81 892.275 1009.680 13:5 2.600
23\49 892.754 1009.201 8:3 2.667
31\66 893.343 1008.613 11:4 2.750
8\17 895.038 1006.917 3:1 3.000 Hard 2L 11s⟨3/1⟩
25\53 897.149 1004.806 10:3 3.333
17\36 898.145 1003.810 7:2 3.500
26\55 899.106 1002.849 11:3 3.667
9\19 900.926 1001.029 4:1 4.000 Superhard 2L 11s⟨3/1⟩
19\40 903.429 998.526 9:2 4.500
10\21 905.693 996.262 5:1 5.000
11\23 909.631 992.324 6:1 6.000
1\2 950.978 950.978 1:0 → ∞ Collapsed 2L 11s⟨3/1⟩
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