1L 3s

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↑ 1L 2s 2L 2s ↗
1L 3s2L 3s →
↓ 1L 4s 2L 4s ↘
┌╥┬┬┬┐
│║││││
││││││
└┴┴┴┴┘
Scale structure
Step pattern Lsss
sssL
Equave 2/1 (1200.0¢)
Period 2/1 (1200.0¢)
Generator size
Bright 3\4 to 1\1 (900.0¢ to 1200.0¢)
Dark 0\1 to 1\4 (0.0¢ to 300.0¢)
Related MOS scales
Parent 1L 2s
Sister 3L 1s
Daughters 4L 1s, 1L 4s
Neutralized 2L 2s
2-Flought 5L 3s, 1L 7s
Equal tunings
Equalized (L:s = 1:1) 3\4 (900.0¢)
Supersoft (L:s = 4:3) 10\13 (923.1¢)
Soft (L:s = 3:2) 7\9 (933.3¢)
Semisoft (L:s = 5:3) 11\14 (942.9¢)
Basic (L:s = 2:1) 4\5 (960.0¢)
Semihard (L:s = 5:2) 9\11 (981.8¢)
Hard (L:s = 3:1) 5\6 (1000.0¢)
Superhard (L:s = 4:1) 6\7 (1028.6¢)
Collapsed (L:s = 1:0) 1\1 (1200.0¢)

1L 3s, also called antetric, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 3 small steps, repeating every octave. Generators that produce this scale range from 900¢ to 1200¢, or from 0¢ to 300¢.

In South Africa, the San use a tetratonic scale which can be approximated by basic 1L 3s.[1]

Modes

Scale degrees of the modes of 1L 3s 
UDP Cyclic
Order
Step
Pattern
Scale Degree (mosdegree)
0 1 2 3 4
3|0 1 Lsss Perf. Aug. Maj. Perf. Perf.
2|1 4 sLss Perf. Perf. Maj. Perf. Perf.
1|2 3 ssLs Perf. Perf. Min. Perf. Perf.
0|3 2 sssL Perf. Perf. Min. Dim. Perf.

Scale tree

Generator ranges:

  • Chroma-positive generator: 900 cents (3\4) to 1200 cents (1\1)
  • Chroma-negative generator: 0 cents (0\1) to 300 cents (1\4)


Scale Tree and Tuning Spectrum of 1L 3s
Generator(edo) Cents Step Ratio Comments
Bright Dark L:s Hardness
3\4 900.000 300.000 1:1 1.000 Equalized 1L 3s
16\21 914.286 285.714 6:5 1.200
13\17 917.647 282.353 5:4 1.250
23\30 920.000 280.000 9:7 1.286
10\13 923.077 276.923 4:3 1.333 Supersoft 1L 3s
27\35 925.714 274.286 11:8 1.375
17\22 927.273 272.727 7:5 1.400
24\31 929.032 270.968 10:7 1.429 Orson/Orwell
7\9 933.333 266.667 3:2 1.500 Soft 1L 3s
25\32 937.500 262.500 11:7 1.571
18\23 939.130 260.870 8:5 1.600
29\37 940.541 259.459 13:8 1.625
11\14 942.857 257.143 5:3 1.667 Semisoft 1L 3s
26\33 945.455 254.545 12:7 1.714
15\19 947.368 252.632 7:4 1.750
19\24 950.000 250.000 9:5 1.800 Godzilla
4\5 960.000 240.000 2:1 2.000 Basic 1L 3s
Scales with tunings softer than this are proper
17\21 971.429 228.571 9:4 2.250 Laconic/gorgo
13\16 975.000 225.000 7:3 2.333
22\27 977.778 222.222 12:5 2.400
9\11 981.818 218.182 5:2 2.500 Semihard 1L 3s
23\28 985.714 214.286 13:5 2.600 Unnamed golden tuning (213.5979¢
14\17 988.235 211.765 8:3 2.667
19\23 991.304 208.696 11:4 2.750
5\6 1000.000 200.000 3:1 3.000 Hard 1L 3s
16\19 1010.526 189.474 10:3 3.333 Isra/deutone
11\13 1015.385 184.615 7:2 3.500
17\20 1020.000 180.000 11:3 3.667
6\7 1028.571 171.429 4:1 4.000 Superhard 1L 3s
13\15 1040.000 160.000 9:2 4.500 Porcupine
7\8 1050.000 150.000 5:1 5.000
8\9 1066.667 133.333 6:1 6.000
1\1 1200.000 0.000 1:0 → ∞ Collapsed 1L 3s

Sources

  1. Wikipedia contributors. (2022, November 21). Tetratonic scale. In Wikipedia, The Free Encyclopedia. Retrieved 09:40, August 13, 2024, from https://en.wikipedia.org/w/index.php?title=Tetratonic_scale&oldid=1123114247