1L 3s

	↑ 1L 2s	2L 2s ↗
	1L 3s	2L 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.

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.

Intervals

Intervals of 1L 3s

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 300.0 ¢
	Augmented 1-mosstep	A1ms	L	300.0 ¢ to 1200.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 600.0 ¢
	Major 2-mosstep	M2ms	L + s	600.0 ¢ to 1200.0 ¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0 ¢ to 900.0 ¢
	Perfect 3-mosstep	P3ms	L + 2s	900.0 ¢ to 1200.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	L + 3s	1200.0 ¢

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)

Sources

Todo: expand