2L 1s

← 1L 1s	2L 1s	3L 1s →
↙ 1L 2s	↓ 2L 2s	3L 2s ↘

┌╥╥┬┐ │║║││ │││││ └┴┴┴┘
Scale structure
Step pattern	LLs sLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\3 to 1\2 (400.0 ¢ to 600.0 ¢)
Dark	1\2 to 2\3 (600.0 ¢ to 800.0 ¢)
Related MOS scales
Parent	1L 1s
Sister	1L 2s
Daughters	3L 2s, 2L 3s
Neutralized	1L 2s
2-Flought	5L 1s, 2L 4s
Equal tunings
Equalized (L:s = 1:1)	1\3 (400.0 ¢)
Supersoft (L:s = 4:3)	4\11 (436.4 ¢)
Soft (L:s = 3:2)	3\8 (450.0 ¢)
Semisoft (L:s = 5:3)	5\13 (461.5 ¢)
Basic (L:s = 2:1)	2\5 (480.0 ¢)
Semihard (L:s = 5:2)	5\12 (500.0 ¢)
Hard (L:s = 3:1)	3\7 (514.3 ¢)
Superhard (L:s = 4:1)	4\9 (533.3 ¢)
Collapsed (L:s = 1:0)	1\2 (600.0 ¢)

2L 1s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 400 ¢ to 600 ¢, or from 600 ¢ to 800 ¢. Scales of this form are always proper because there is only one small step.

2L 1s is one of two halves in the tree of strict MOSes, the other being 1L 2s. It is the parent MOS of the pentic scale 2L 3s, which is itself the parent of the diatonic and antidiatonic scales, as well as the antipentic scale 3L 2s, which is itself the parent of the oneirotonic and checkertonic scales.

Names

TAMNAMS uses the name trial. Vector proposes the name fibotonic, as its series of soft children produces the Fibonacci numbers (3L 2s, 5L 3s, 8L 5s, 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 2L 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 400.0 ¢
	Perfect 1-mosstep	P1ms	L	400.0 ¢ to 600.0 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	600.0 ¢ to 800.0 ¢
	Augmented 2-mosstep	A2ms	2L	800.0 ¢ to 1200.0 ¢
3-mosstep	Perfect 3-mosstep	P3ms	2L + s	1200.0 ¢

Generator chain

Generator chain of 2L 1s

Bright gens	Scale degree	Abbrev.
4	Augmented 1-mosdegree	A1md
3	Augmented 0-mosdegree	A0md
2	Augmented 2-mosdegree	A2md
1	Perfect 1-mosdegree	P1md
0	Perfect 0-mosdegree Perfect 3-mosdegree	P0md P3md
−1	Perfect 2-mosdegree	P2md
−2	Diminished 1-mosdegree	d1md
−3	Diminished 3-mosdegree	d3md
−4	Diminished 2-mosdegree	d2md

Modes

Scale degrees of the modes of 2L 1s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3
2|0	1	LLs	Perf.	Perf.	Aug.	Perf.
1|1	2	LsL	Perf.	Perf.	Perf.	Perf.
0|2	3	sLL	Perf.	Dim.	Perf.	Perf.

Scale tree

Scale tree and tuning spectrum of 2L 1s

Generator(edo)						Cents		Step ratio		Comments(always proper)
						Bright	Dark	L:s	Hardness
1\3						400.000	800.000	1:1	1.000	Equalized 2L 1s
					6\17	423.529	776.471	6:5	1.200
				5\14		428.571	771.429	5:4	1.250
					9\25	432.000	768.000	9:7	1.286
			4\11			436.364	763.636	4:3	1.333	Supersoft 2L 1s
					11\30	440.000	760.000	11:8	1.375
				7\19		442.105	757.895	7:5	1.400
					10\27	444.444	755.556	10:7	1.429
		3\8				450.000	750.000	3:2	1.500	Soft 2L 1s
					11\29	455.172	744.828	11:7	1.571
				8\21		457.143	742.857	8:5	1.600
					13\34	458.824	741.176	13:8	1.625
			5\13			461.538	738.462	5:3	1.667	Semisoft 2L 1s
					12\31	464.516	735.484	12:7	1.714
				7\18		466.667	733.333	7:4	1.750
					9\23	469.565	730.435	9:5	1.800
	2\5					480.000	720.000	2:1	2.000	Basic 2L 1s
					9\22	490.909	709.091	9:4	2.250
				7\17		494.118	705.882	7:3	2.333
					12\29	496.552	703.448	12:5	2.400
			5\12			500.000	700.000	5:2	2.500	Semihard 2L 1s
					13\31	503.226	696.774	13:5	2.600
				8\19		505.263	694.737	8:3	2.667
					11\26	507.692	692.308	11:4	2.750
		3\7				514.286	685.714	3:1	3.000	Hard 2L 1s
					10\23	521.739	678.261	10:3	3.333
				7\16		525.000	675.000	7:2	3.500
					11\25	528.000	672.000	11:3	3.667
			4\9			533.333	666.667	4:1	4.000	Superhard 2L 1s
					9\20	540.000	660.000	9:2	4.500
				5\11		545.455	654.545	5:1	5.000
					6\13	553.846	646.154	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 1s