3L 1s

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← 2L 1s3L 1s 4L 1s →
↙ 2L 2s ↓3L 2s 4L 2s ↘
┌╥╥╥┬┐
│║║║││
││││││
└┴┴┴┴┘
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

  • 3|0 LLLs
  • 2|1 LLsL
  • 1|2 LsLL
  • 0|3 sLLL

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