3L 12s

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↖ 2L 11s ↑ 3L 11s 4L 11s ↗
← 2L 12s 3L 12s 4L 12s →
↙ 2L 13s ↓ 3L 13s 4L 13s ↘ 
┌╥┬┬┬┬╥┬┬┬┬╥┬┬┬┬┐
│║││││║││││║│││││
│││││││││││││││││
└┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern LssssLssssLssss
ssssLssssLssssL
Equave 2/1 (1200.0 ¢)
Period 1\3 (400.0 ¢)
Generator size
Bright 4\15 to 1\3 (320.0 ¢ to 400.0 ¢)
Dark 0\3 to 1\15 (0.0 ¢ to 80.0 ¢)
TAMNAMS information
Related to 3L 6s (tcherepnin)
With tunings 3:1 to 1:0 (hard)
Related MOS scales
Parent 3L 9s
Sister 12L 3s
Daughters 15L 3s, 3L 15s
Neutralized 6L 9s
2-Flought 18L 12s, 3L 27s
Equal tunings
Equalized (L:s = 1:1) 4\15 (320.0 ¢)
Supersoft (L:s = 4:3) 13\48 (325.0 ¢)
Soft (L:s = 3:2) 9\33 (327.3 ¢)
Semisoft (L:s = 5:3) 14\51 (329.4 ¢)
Basic (L:s = 2:1) 5\18 (333.3 ¢)
Semihard (L:s = 5:2) 11\39 (338.5 ¢)
Hard (L:s = 3:1) 6\21 (342.9 ¢)
Superhard (L:s = 4:1) 7\24 (350.0 ¢)
Collapsed (L:s = 1:0) 1\3 (400.0 ¢)

3L 12s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 12 small steps, with a period of 1 large step and 4 small steps that repeats every 400.0 ¢, or 3 times every octave. 3L 12s is a grandchild scale of 3L 6s, expanding it by 6 tones. Generators that produce this scale range from 320 ¢ to 400 ¢, or from 0 ¢ to 80 ¢.

It is the MOS of Inflated[15].

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 interval regions.

Intervals

Intervals of 3L 12s
Intervals Steps
subtended 		Range in cents
Generic Specific Abbrev.
0-mosstep Perfect 0-mosstep P0ms 0 0.0 ¢
1-mosstep Perfect 1-mosstep P1ms s 0.0 ¢ to 80.0 ¢
Augmented 1-mosstep A1ms L 80.0 ¢ to 400.0 ¢
2-mosstep Minor 2-mosstep m2ms 2s 0.0 ¢ to 160.0 ¢
Major 2-mosstep M2ms L + s 160.0 ¢ to 400.0 ¢
3-mosstep Minor 3-mosstep m3ms 3s 0.0 ¢ to 240.0 ¢
Major 3-mosstep M3ms L + 2s 240.0 ¢ to 400.0 ¢
4-mosstep Diminished 4-mosstep d4ms 4s 0.0 ¢ to 320.0 ¢
Perfect 4-mosstep P4ms L + 3s 320.0 ¢ to 400.0 ¢
5-mosstep Perfect 5-mosstep P5ms L + 4s 400.0 ¢
6-mosstep Perfect 6-mosstep P6ms L + 5s 400.0 ¢ to 480.0 ¢
Augmented 6-mosstep A6ms 2L + 4s 480.0 ¢ to 800.0 ¢
7-mosstep Minor 7-mosstep m7ms L + 6s 400.0 ¢ to 560.0 ¢
Major 7-mosstep M7ms 2L + 5s 560.0 ¢ to 800.0 ¢
8-mosstep Minor 8-mosstep m8ms L + 7s 400.0 ¢ to 640.0 ¢
Major 8-mosstep M8ms 2L + 6s 640.0 ¢ to 800.0 ¢
9-mosstep Diminished 9-mosstep d9ms L + 8s 400.0 ¢ to 720.0 ¢
Perfect 9-mosstep P9ms 2L + 7s 720.0 ¢ to 800.0 ¢
10-mosstep Perfect 10-mosstep P10ms 2L + 8s 800.0 ¢
11-mosstep Perfect 11-mosstep P11ms 2L + 9s 800.0 ¢ to 880.0 ¢
Augmented 11-mosstep A11ms 3L + 8s 880.0 ¢ to 1200.0 ¢
12-mosstep Minor 12-mosstep m12ms 2L + 10s 800.0 ¢ to 960.0 ¢
Major 12-mosstep M12ms 3L + 9s 960.0 ¢ to 1200.0 ¢
13-mosstep Minor 13-mosstep m13ms 2L + 11s 800.0 ¢ to 1040.0 ¢
Major 13-mosstep M13ms 3L + 10s 1040.0 ¢ to 1200.0 ¢
14-mosstep Diminished 14-mosstep d14ms 2L + 12s 800.0 ¢ to 1120.0 ¢
Perfect 14-mosstep P14ms 3L + 11s 1120.0 ¢ to 1200.0 ¢
15-mosstep Perfect 15-mosstep P15ms 3L + 12s 1200.0 ¢

Generator chain

Generator chain of 3L 12s
Bright gens Scale degree Abbrev. Scale degree Abbrev. Scale degree Abbrev.
5 Augmented 0-mosdegree A0md Augmented 5-mosdegree A5md Augmented 10-mosdegree A10md
4 Augmented 1-mosdegree A1md Augmented 6-mosdegree A6md Augmented 11-mosdegree A11md
3 Major 2-mosdegree M2md Major 7-mosdegree M7md Major 12-mosdegree M12md
2 Major 3-mosdegree M3md Major 8-mosdegree M8md Major 13-mosdegree M13md
1 Perfect 4-mosdegree P4md Perfect 9-mosdegree P9md Perfect 14-mosdegree P14md
0 Perfect 0-mosdegree
Perfect 5-mosdegree		 P0md
P5md		 Perfect 5-mosdegree
Perfect 10-mosdegree		 P5md
P10md		 Perfect 10-mosdegree
Perfect 15-mosdegree		 P10md
P15md
−1 Perfect 1-mosdegree P1md Perfect 6-mosdegree P6md Perfect 11-mosdegree P11md
−2 Minor 2-mosdegree m2md Minor 7-mosdegree m7md Minor 12-mosdegree m12md
−3 Minor 3-mosdegree m3md Minor 8-mosdegree m8md Minor 13-mosdegree m13md
−4 Diminished 4-mosdegree d4md Diminished 9-mosdegree d9md Diminished 14-mosdegree d14md
−5 Diminished 5-mosdegree d5md Diminished 10-mosdegree d10md Diminished 15-mosdegree d15md

Modes

Scale degrees of the modes of 3L 12s
UDP Cyclic
order 		Step
pattern 		Scale degree (mosdegree)
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
12|0(3) 1 LssssLssssLssss Perf. Aug. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Perf. Perf. Aug. Maj. Maj. Perf. Perf.
9|3(3) 5 sLssssLssssLsss Perf. Perf. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Perf. Perf. Perf. Maj. Maj. Perf. Perf.
6|6(3) 4 ssLssssLssssLss Perf. Perf. Min. Maj. Perf. Perf. Perf. Min. Maj. Perf. Perf. Perf. Min. Maj. Perf. Perf.
3|9(3) 3 sssLssssLssssLs Perf. Perf. Min. Min. Perf. Perf. Perf. Min. Min. Perf. Perf. Perf. Min. Min. Perf. Perf.
0|12(3) 2 ssssLssssLssssL Perf. Perf. Min. Min. Dim. Perf. Perf. Min. Min. Dim. Perf. Perf. Min. Min. Dim. Perf.

Scale tree

Scale tree and tuning spectrum of 3L 12s
Generator(edo) Cents Step ratio Comments
Bright Dark L:s Hardness
4\15 320.000 80.000 1:1 1.000 Equalized 3L 12s
21\78 323.077 76.923 6:5 1.200
17\63 323.810 76.190 5:4 1.250
30\111 324.324 75.676 9:7 1.286
13\48 325.000 75.000 4:3 1.333 Supersoft 3L 12s
35\129 325.581 74.419 11:8 1.375
22\81 325.926 74.074 7:5 1.400
31\114 326.316 73.684 10:7 1.429
9\33 327.273 72.727 3:2 1.500 Soft 3L 12s
32\117 328.205 71.795 11:7 1.571
23\84 328.571 71.429 8:5 1.600
37\135 328.889 71.111 13:8 1.625
14\51 329.412 70.588 5:3 1.667 Semisoft 3L 12s
33\120 330.000 70.000 12:7 1.714
19\69 330.435 69.565 7:4 1.750
24\87 331.034 68.966 9:5 1.800
5\18 333.333 66.667 2:1 2.000 Basic 3L 12s
Scales with tunings softer than this are proper
21\75 336.000 64.000 9:4 2.250
16\57 336.842 63.158 7:3 2.333
27\96 337.500 62.500 12:5 2.400
11\39 338.462 61.538 5:2 2.500 Semihard 3L 12s
28\99 339.394 60.606 13:5 2.600
17\60 340.000 60.000 8:3 2.667
23\81 340.741 59.259 11:4 2.750
6\21 342.857 57.143 3:1 3.000 Hard 3L 12s
19\66 345.455 54.545 10:3 3.333
13\45 346.667 53.333 7:2 3.500
20\69 347.826 52.174 11:3 3.667
7\24 350.000 50.000 4:1 4.000 Superhard 3L 12s
15\51 352.941 47.059 9:2 4.500
8\27 355.556 44.444 5:1 5.000
9\30 360.000 40.000 6:1 6.000
1\3 400.000 0.000 1:0 → ∞ Collapsed 3L 12s
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