12L 11s

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↖ 11L 10s ↑ 12L 10s 13L 10s ↗
← 11L 11s 12L 11s 13L 11s →
↙ 11L 12s ↓ 12L 12s 13L 12s ↘
┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐
│║║│║│║│║│║│║│║│║│║│║│║││
│││││││││││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LLsLsLsLsLsLsLsLsLsLsLs
sLsLsLsLsLsLsLsLsLsLsLL
Equave 2/1 (1200.0 ¢)
Period 2/1 (1200.0 ¢)
Generator size
Bright 21\23 to 11\12 (1095.7 ¢ to 1100.0 ¢)
Dark 1\12 to 2\23 (100.0 ¢ to 104.3 ¢)
TAMNAMS information
Related to 1L 9s (antisinatonic)
With tunings 5:2 to 3:1 (quasihard)
Related MOS scales
Parent 11L 1s
Sister 11L 12s
Daughters 23L 12s, 12L 23s
Neutralized 1L 22s
2-Flought 35L 11s, 12L 34s
Equal tunings
Equalized (L:s = 1:1) 21\23 (1095.7 ¢)
Supersoft (L:s = 4:3) 74\81 (1096.3 ¢)
Soft (L:s = 3:2) 53\58 (1096.6 ¢)
Semisoft (L:s = 5:3) 85\93 (1096.8 ¢)
Basic (L:s = 2:1) 32\35 (1097.1 ¢)
Semihard (L:s = 5:2) 75\82 (1097.6 ¢)
Hard (L:s = 3:1) 43\47 (1097.9 ¢)
Superhard (L:s = 4:1) 54\59 (1098.3 ¢)
Collapsed (L:s = 1:0) 11\12 (1100.0 ¢)

12L 11s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 12 large steps and 11 small steps, repeating every octave. 12L 11s is a great-grandchild scale of 1L 9s, expanding it by 13 tones. Generators that produce this scale range from 1095.7 ¢ to 1100 ¢, or from 100 ¢ to 104.3 ¢.

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

Intervals of 12L 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 52.2 ¢
Major 1-mosstep M1ms L 52.2 ¢ to 100.0 ¢
2-mosstep Perfect 2-mosstep P2ms L + s 100.0 ¢ to 104.3 ¢
Augmented 2-mosstep A2ms 2L 104.3 ¢ to 200.0 ¢
3-mosstep Minor 3-mosstep m3ms L + 2s 100.0 ¢ to 156.5 ¢
Major 3-mosstep M3ms 2L + s 156.5 ¢ to 200.0 ¢
4-mosstep Minor 4-mosstep m4ms 2L + 2s 200.0 ¢ to 208.7 ¢
Major 4-mosstep M4ms 3L + s 208.7 ¢ to 300.0 ¢
5-mosstep Minor 5-mosstep m5ms 2L + 3s 200.0 ¢ to 260.9 ¢
Major 5-mosstep M5ms 3L + 2s 260.9 ¢ to 300.0 ¢
6-mosstep Minor 6-mosstep m6ms 3L + 3s 300.0 ¢ to 313.0 ¢
Major 6-mosstep M6ms 4L + 2s 313.0 ¢ to 400.0 ¢
7-mosstep Minor 7-mosstep m7ms 3L + 4s 300.0 ¢ to 365.2 ¢
Major 7-mosstep M7ms 4L + 3s 365.2 ¢ to 400.0 ¢
8-mosstep Minor 8-mosstep m8ms 4L + 4s 400.0 ¢ to 417.4 ¢
Major 8-mosstep M8ms 5L + 3s 417.4 ¢ to 500.0 ¢
9-mosstep Minor 9-mosstep m9ms 4L + 5s 400.0 ¢ to 469.6 ¢
Major 9-mosstep M9ms 5L + 4s 469.6 ¢ to 500.0 ¢
10-mosstep Minor 10-mosstep m10ms 5L + 5s 500.0 ¢ to 521.7 ¢
Major 10-mosstep M10ms 6L + 4s 521.7 ¢ to 600.0 ¢
11-mosstep Minor 11-mosstep m11ms 5L + 6s 500.0 ¢ to 573.9 ¢
Major 11-mosstep M11ms 6L + 5s 573.9 ¢ to 600.0 ¢
12-mosstep Minor 12-mosstep m12ms 6L + 6s 600.0 ¢ to 626.1 ¢
Major 12-mosstep M12ms 7L + 5s 626.1 ¢ to 700.0 ¢
13-mosstep Minor 13-mosstep m13ms 6L + 7s 600.0 ¢ to 678.3 ¢
Major 13-mosstep M13ms 7L + 6s 678.3 ¢ to 700.0 ¢
14-mosstep Minor 14-mosstep m14ms 7L + 7s 700.0 ¢ to 730.4 ¢
Major 14-mosstep M14ms 8L + 6s 730.4 ¢ to 800.0 ¢
15-mosstep Minor 15-mosstep m15ms 7L + 8s 700.0 ¢ to 782.6 ¢
Major 15-mosstep M15ms 8L + 7s 782.6 ¢ to 800.0 ¢
16-mosstep Minor 16-mosstep m16ms 8L + 8s 800.0 ¢ to 834.8 ¢
Major 16-mosstep M16ms 9L + 7s 834.8 ¢ to 900.0 ¢
17-mosstep Minor 17-mosstep m17ms 8L + 9s 800.0 ¢ to 887.0 ¢
Major 17-mosstep M17ms 9L + 8s 887.0 ¢ to 900.0 ¢
18-mosstep Minor 18-mosstep m18ms 9L + 9s 900.0 ¢ to 939.1 ¢
Major 18-mosstep M18ms 10L + 8s 939.1 ¢ to 1000.0 ¢
19-mosstep Minor 19-mosstep m19ms 9L + 10s 900.0 ¢ to 991.3 ¢
Major 19-mosstep M19ms 10L + 9s 991.3 ¢ to 1000.0 ¢
20-mosstep Minor 20-mosstep m20ms 10L + 10s 1000.0 ¢ to 1043.5 ¢
Major 20-mosstep M20ms 11L + 9s 1043.5 ¢ to 1100.0 ¢
21-mosstep Diminished 21-mosstep d21ms 10L + 11s 1000.0 ¢ to 1095.7 ¢
Perfect 21-mosstep P21ms 11L + 10s 1095.7 ¢ to 1100.0 ¢
22-mosstep Minor 22-mosstep m22ms 11L + 11s 1100.0 ¢ to 1147.8 ¢
Major 22-mosstep M22ms 12L + 10s 1147.8 ¢ to 1200.0 ¢
23-mosstep Perfect 23-mosstep P23ms 12L + 11s 1200.0 ¢

Generator chain

Generator chain of 12L 11s
Bright gens Scale degree Abbrev.
34 Augmented 1-mosdegree A1md
33 Augmented 3-mosdegree A3md
32 Augmented 5-mosdegree A5md
31 Augmented 7-mosdegree A7md
30 Augmented 9-mosdegree A9md
29 Augmented 11-mosdegree A11md
28 Augmented 13-mosdegree A13md
27 Augmented 15-mosdegree A15md
26 Augmented 17-mosdegree A17md
25 Augmented 19-mosdegree A19md
24 Augmented 21-mosdegree A21md
23 Augmented 0-mosdegree A0md
22 Augmented 2-mosdegree A2md
21 Major 4-mosdegree M4md
20 Major 6-mosdegree M6md
19 Major 8-mosdegree M8md
18 Major 10-mosdegree M10md
17 Major 12-mosdegree M12md
16 Major 14-mosdegree M14md
15 Major 16-mosdegree M16md
14 Major 18-mosdegree M18md
13 Major 20-mosdegree M20md
12 Major 22-mosdegree M22md
11 Major 1-mosdegree M1md
10 Major 3-mosdegree M3md
9 Major 5-mosdegree M5md
8 Major 7-mosdegree M7md
7 Major 9-mosdegree M9md
6 Major 11-mosdegree M11md
5 Major 13-mosdegree M13md
4 Major 15-mosdegree M15md
3 Major 17-mosdegree M17md
2 Major 19-mosdegree M19md
1 Perfect 21-mosdegree P21md
0 Perfect 0-mosdegree
Perfect 23-mosdegree
P0md
P23md
−1 Perfect 2-mosdegree P2md
−2 Minor 4-mosdegree m4md
−3 Minor 6-mosdegree m6md
−4 Minor 8-mosdegree m8md
−5 Minor 10-mosdegree m10md
−6 Minor 12-mosdegree m12md
−7 Minor 14-mosdegree m14md
−8 Minor 16-mosdegree m16md
−9 Minor 18-mosdegree m18md
−10 Minor 20-mosdegree m20md
−11 Minor 22-mosdegree m22md
−12 Minor 1-mosdegree m1md
−13 Minor 3-mosdegree m3md
−14 Minor 5-mosdegree m5md
−15 Minor 7-mosdegree m7md
−16 Minor 9-mosdegree m9md
−17 Minor 11-mosdegree m11md
−18 Minor 13-mosdegree m13md
−19 Minor 15-mosdegree m15md
−20 Minor 17-mosdegree m17md
−21 Minor 19-mosdegree m19md
−22 Diminished 21-mosdegree d21md
−23 Diminished 23-mosdegree d23md
−24 Diminished 2-mosdegree d2md
−25 Diminished 4-mosdegree d4md
−26 Diminished 6-mosdegree d6md
−27 Diminished 8-mosdegree d8md
−28 Diminished 10-mosdegree d10md
−29 Diminished 12-mosdegree d12md
−30 Diminished 14-mosdegree d14md
−31 Diminished 16-mosdegree d16md
−32 Diminished 18-mosdegree d18md
−33 Diminished 20-mosdegree d20md
−34 Diminished 22-mosdegree d22md

Modes

Scale degrees of the modes of 12L 11s
UDP Cyclic
order
Step
pattern
Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23
22|0 1 LLsLsLsLsLsLsLsLsLsLsLs Perf. Maj. Aug. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
21|1 22 LsLLsLsLsLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
20|2 20 LsLsLLsLsLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
19|3 18 LsLsLsLLsLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
18|4 16 LsLsLsLsLLsLsLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
17|5 14 LsLsLsLsLsLLsLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
16|6 12 LsLsLsLsLsLsLLsLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
15|7 10 LsLsLsLsLsLsLsLLsLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
14|8 8 LsLsLsLsLsLsLsLsLLsLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Maj. Maj. Perf. Maj. Perf.
13|9 6 LsLsLsLsLsLsLsLsLsLLsLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Maj. Perf. Maj. Perf.
12|10 4 LsLsLsLsLsLsLsLsLsLsLLs Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Maj. Perf.
11|11 2 LsLsLsLsLsLsLsLsLsLsLsL Perf. Maj. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
10|12 23 sLLsLsLsLsLsLsLsLsLsLsL Perf. Min. Perf. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
9|13 21 sLsLLsLsLsLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
8|14 19 sLsLsLLsLsLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
7|15 17 sLsLsLsLLsLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
6|16 15 sLsLsLsLsLLsLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
5|17 13 sLsLsLsLsLsLLsLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
4|18 11 sLsLsLsLsLsLsLLsLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
3|19 9 sLsLsLsLsLsLsLsLLsLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Maj. Min. Perf. Min. Perf.
2|20 7 sLsLsLsLsLsLsLsLsLLsLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Maj. Min. Perf. Min. Perf.
1|21 5 sLsLsLsLsLsLsLsLsLsLLsL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Perf. Min. Perf.
0|22 3 sLsLsLsLsLsLsLsLsLsLsLL Perf. Min. Perf. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Min. Dim. Min. Perf.

Scale tree

Scale tree and tuning spectrum of 12L 11s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
21\23 1095.652 104.348 1:1 1.000 Equalized 12L 11s
116\127 1096.063 103.937 6:5 1.200
95\104 1096.154 103.846 5:4 1.250
169\185 1096.216 103.784 9:7 1.286
74\81 1096.296 103.704 4:3 1.333 Supersoft 12L 11s
201\220 1096.364 103.636 11:8 1.375
127\139 1096.403 103.597 7:5 1.400
180\197 1096.447 103.553 10:7 1.429
53\58 1096.552 103.448 3:2 1.500 Soft 12L 11s
191\209 1096.651 103.349 11:7 1.571
138\151 1096.689 103.311 8:5 1.600
223\244 1096.721 103.279 13:8 1.625
85\93 1096.774 103.226 5:3 1.667 Semisoft 12L 11s
202\221 1096.833 103.167 12:7 1.714
117\128 1096.875 103.125 7:4 1.750
149\163 1096.933 103.067 9:5 1.800
32\35 1097.143 102.857 2:1 2.000 Basic 12L 11s
Scales with tunings softer than this are proper
139\152 1097.368 102.632 9:4 2.250
107\117 1097.436 102.564 7:3 2.333
182\199 1097.487 102.513 12:5 2.400
75\82 1097.561 102.439 5:2 2.500 Semihard 12L 11s
193\211 1097.630 102.370 13:5 2.600
118\129 1097.674 102.326 8:3 2.667
161\176 1097.727 102.273 11:4 2.750
43\47 1097.872 102.128 3:1 3.000 Hard 12L 11s
140\153 1098.039 101.961 10:3 3.333
97\106 1098.113 101.887 7:2 3.500
151\165 1098.182 101.818 11:3 3.667
54\59 1098.305 101.695 4:1 4.000 Superhard 12L 11s
119\130 1098.462 101.538 9:2 4.500
65\71 1098.592 101.408 5:1 5.000
76\83 1098.795 101.205 6:1 6.000
11\12 1100.000 100.000 1:0 → ∞ Collapsed 12L 11s
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