3L 1s

← 2L 1s	3L 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

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.

Intervals

Intervals of 3L 1s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0 ¢
1-mosstep	Diminished 1-mosstep	d1ms	s	0.0 ¢ to 300.0 ¢
	Perfect 1-mosstep	P1ms	L	300.0 ¢ to 400.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	L + s	400.0 ¢ to 600.0 ¢
	Major 2-mosstep	M2ms	2L	600.0 ¢ to 800.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	800.0 ¢ to 900.0 ¢
	Augmented 3-mosstep	A3ms	3L	900.0 ¢ to 1200.0 ¢
4-mosstep	Perfect 4-mosstep	P4ms	3L + s	1200.0 ¢

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)