3L 1s

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← 2L 1s3L 1s4L 1s →
↙ 2L 2s↓ 3L 2s 4L 2s ↘
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│║║║││
││││││
└┴┴┴┴┘
Scale structure
Step pattern LLLs
sLLL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 1\4 to 1\3 (300.0¢ to 400.0¢)
Dark 2\3 to 3\4 (800.0¢ to 900.0¢)
Related MOS scales
Parent 1L 2s
Sister 1L 3s
Daughters 4L 3s, 3L 4s
Neutralized 2L 2s
2-Flought 7L 1s, 3L 5s
Equal tunings
Equalized (L:s = 1:1) 1\4 (300.0¢)
Supersoft (L:s = 4:3) 4\15 (320.0¢)
Soft (L:s = 3:2) 3\11 (327.3¢)
Semisoft (L:s = 5:3) 5\18 (333.3¢)
Basic (L:s = 2:1) 2\7 (342.9¢)
Semihard (L:s = 5:2) 5\17 (352.9¢)
Hard (L:s = 3:1) 3\10 (360.0¢)
Superhard (L:s = 4:1) 4\13 (369.2¢)
Collapsed (L:s = 1:0) 1\3 (400.0¢)

3L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 3 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 300¢ to 400¢, or from 800¢ to 900¢. Scales of this form are always proper because there is only one small step.

Modes

Scale degrees of the modes of 3L 1s 
UDP Cyclic
Order
Step
Pattern
Scale Degree (mosdegree)
0 1 2 3 4
3|0 1 LLLs Perf. Perf. Maj. Aug. Perf.
2|1 2 LLsL Perf. Perf. Maj. Perf. Perf.
1|2 3 LsLL Perf. Perf. Min. Perf. Perf.
0|3 4 sLLL Perf. Dim. Min. Perf. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 300 cents (1\4) to 400 cents (1\3)
  • Chroma-negative generator: 800 cents (2\3) to 900 cents (3\4)
Scale Tree and Tuning Spectrum of 3L 1s
Generator(edo) Cents Step Ratio Comments(always proper)
Bright Dark L:s Hardness
1\4 300.000 900.000 1:1 1.000 Equalized 3L 1s
6\23 313.043 886.957 6:5 1.200
5\19 315.789 884.211 5:4 1.250
9\34 317.647 882.353 9:7 1.286 Hanson/keemun
4\15 320.000 880.000 4:3 1.333 Supersoft 3L 1s
11\41 321.951 878.049 11:8 1.375 Superkleismic
7\26 323.077 876.923 7:5 1.400
10\37 324.324 875.676 10:7 1.429 Hyperkleismic
3\11 327.273 872.727 3:2 1.500 Soft 3L 1s
11\40 330.000 870.000 11:7 1.571
8\29 331.034 868.966 8:5 1.600
13\47 331.915 868.085 13:8 1.625 Golden dicot (331.672 cents)
5\18 333.333 866.667 5:3 1.667 Semisoft 3L 1s
12\43 334.884 865.116 12:7 1.714
7\25 336.000 864.000 7:4 1.750
9\32 337.500 862.500 9:5 1.800 Sixix
2\7 342.857 857.143 2:1 2.000 Basic 3L 1s
9\31 348.387 851.613 9:4 2.250 Mohaha/mohajira
7\24 350.000 850.000 7:3 2.333
12\41 351.220 848.780 12:5 2.400 Hemif/hemififths
5\17 352.941 847.059 5:2 2.500 Semihard 3L 1s
13\44 354.545 845.455 13:5 2.600
8\27 355.556 844.444 8:3 2.667
11\37 356.757 843.243 11:4 2.750 Beatles
3\10 360.000 840.000 3:1 3.000 Hard 3L 1s
10\33 363.636 836.364 10:3 3.333
7\23 365.217 834.783 7:2 3.500
11\36 366.667 833.333 11:3 3.667
4\13 369.231 830.769 4:1 4.000 Superhard 3L 1s
9\29 372.414 827.586 9:2 4.500 Sephiroth
5\16 375.000 825.000 5:1 5.000
6\19 378.947 821.053 6:1 6.000 Magic
1\3 400.000 800.000 1:0 → ∞ Collapsed 3L 1s