1L 2s

1L 2s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 1 large step and 2 small steps, repeating every octave. Generators that produce this scale range from 800 ¢ to 1200 ¢, or from 0 ¢ to 400 ¢.

	↑ 1L 1s	2L 1s ↗
	1L 2s	2L 2s →
	↓ 1L 3s	2L 3s ↘

Scale structure
Step pattern	Lss ssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	2\3 to 1\1 (800.0 ¢ to 1200.0 ¢)
Dark	0\1 to 1\3 (0.0 ¢ to 400.0 ¢)
Related MOS scales
Parent	1L 1s
Sister	2L 1s
Daughters	3L 1s, 1L 3s
Neutralized	2L 1s
2-Flought	4L 2s, 1L 5s
Equal tunings
Equalized (L:s = 1:1)	2\3 (800.0 ¢)
Supersoft (L:s = 4:3)	7\10 (840.0 ¢)
Soft (L:s = 3:2)	5\7 (857.1 ¢)
Semisoft (L:s = 5:3)	8\11 (872.7 ¢)
Basic (L:s = 2:1)	3\4 (900.0 ¢)
Semihard (L:s = 5:2)	7\9 (933.3 ¢)
Hard (L:s = 3:1)	4\5 (960.0 ¢)
Superhard (L:s = 4:1)	5\6 (1000.0 ¢)
Collapsed (L:s = 1:0)	1\1 (1200.0 ¢)
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This MOS is the parent of tetric (3L 1s) and antetric (1L 3s), the former being the parent of mosh (3L 4s) and smitonic (4L 3s), and the latter being the predecessor of other MOS scales such as semiquartal (5L 4s), gramitonic (4L 5s), and other 1L ns MOS scales.

Names

TAMNAMS uses the name antrial. Vector proposes lucatonic, as its series of soft children produces the Lucas numbers (3L 1s, 4L 3s, 7L 4s, etc).

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 1L 2s

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 400.0 ¢
	Augmented 1-mosstep	A1ms	L	400.0 ¢ to 1200.0 ¢
2-mosstep	Diminished 2-mosstep	d2ms	2s	0.0 ¢ to 800.0 ¢
	Perfect 2-mosstep	P2ms	L + s	800.0 ¢ to 1200.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	1200.0 ¢

Generator chain

Generator chain of 1L 2s

Bright gens	Scale degree	Abbrev.
3	Augmented 0-mosdegree	A0md
2	Augmented 1-mosdegree	A1md
1	Perfect 2-mosdegree	P2md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md
−1	Perfect 1-mosdegree	P1md
−2	Diminished 2-mosdegree	d2md
−3	Diminished 3-mosdegree	d3md

Modes

Scale degrees of the modes of 1L 2s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3
2|0	1	Lss	Perf.	Aug.	Perf.	Perf.
1|1	3	sLs	Perf.	Perf.	Perf.	Perf.
0|2	2	ssL	Perf.	Perf.	Dim.	Perf.

Scale tree

Scale tree and tuning spectrum of 1L 2s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
2\3						800.000	400.000	1:1	1.000	Equalized 1L 2s
					11\16	825.000	375.000	6:5	1.200
				9\13		830.769	369.231	5:4	1.250
					16\23	834.783	365.217	9:7	1.286
			7\10			840.000	360.000	4:3	1.333	Supersoft 1L 2s
					19\27	844.444	355.556	11:8	1.375
				12\17		847.059	352.941	7:5	1.400
					17\24	850.000	350.000	10:7	1.429
		5\7				857.143	342.857	3:2	1.500	Soft 1L 2s
					18\25	864.000	336.000	11:7	1.571
				13\18		866.667	333.333	8:5	1.600
					21\29	868.966	331.034	13:8	1.625
			8\11			872.727	327.273	5:3	1.667	Semisoft 1L 2s
					19\26	876.923	323.077	12:7	1.714
				11\15		880.000	320.000	7:4	1.750
					14\19	884.211	315.789	9:5	1.800
	3\4					900.000	300.000	2:1	2.000	Basic 1L 2s Scales with tunings softer than this are proper
					13\17	917.647	282.353	9:4	2.250
				10\13		923.077	276.923	7:3	2.333
					17\22	927.273	272.727	12:5	2.400
			7\9			933.333	266.667	5:2	2.500	Semihard 1L 2s
					18\23	939.130	260.870	13:5	2.600
				11\14		942.857	257.143	8:3	2.667
					15\19	947.368	252.632	11:4	2.750
		4\5				960.000	240.000	3:1	3.000	Hard 1L 2s
					13\16	975.000	225.000	10:3	3.333
				9\11		981.818	218.182	7:2	3.500
					14\17	988.235	211.765	11:3	3.667
			5\6			1000.000	200.000	4:1	4.000	Superhard 1L 2s
					11\13	1015.385	184.615	9:2	4.500
				6\7		1028.571	171.429	5:1	5.000
					7\8	1050.000	150.000	6:1	6.000
1\1						1200.000	0.000	1:0	→ ∞	Collapsed 1L 2s