3L 1s

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.

← 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 ¢)
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Names

TAMNAMS suggests the temperament-agnostic name tetric for this MOS pattern. User:MisterShafXen calls this scale quasi-tritonic, as this scale has 3 large steps and only a single small step.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for interval regions.

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 ¢

Generator chain

Generator chain of 3L 1s

Bright gens	Scale degree	Abbrev.
6	Augmented 2-mosdegree	A2md
5	Augmented 1-mosdegree	A1md
4	Augmented 0-mosdegree	A0md
3	Augmented 3-mosdegree	A3md
2	Major 2-mosdegree	M2md
1	Perfect 1-mosdegree	P1md
0	Perfect 0-mosdegree Perfect 4-mosdegree	P0md P4md
−1	Perfect 3-mosdegree	P3md
−2	Minor 2-mosdegree	m2md
−3	Diminished 1-mosdegree	d1md
−4	Diminished 4-mosdegree	d4md
−5	Diminished 3-mosdegree	d3md
−6	Diminished 2-mosdegree	d2md

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.

Trivia

This scale can be considered the neutral analogue to pentatonic, as the hard descendants of this scale include neutral[7] {3L 4s) and dicot[10] (dicoid/3L 7s).

Scale tree

Generator ranges:

• Chroma-positive generator: 300 ¢ (1\4) to 400 ¢ (1\3)
• Chroma-negative generator: 800 ¢ (2\3) to 900 ¢ (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	Lucas generator (331.672 ¢)
			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	Golden suhajira (354.823 ¢)
				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