2L 20s

↖ 1L 19s	↑ 2L 19s	3L 19s ↗
← 1L 20s	2L 20s	3L 20s →
↙ 1L 21s	↓ 2L 21s	3L 21s ↘

┌╥┬┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┐ │║││││││││││║│││││││││││ ││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssssssssLssssssssss ssssssssssLssssssssssL
Equave	2/1 (1200.0¢)
Period	1\2 (600.0¢)
Generator size
Bright	10\22 to 1\2 (545.5¢ to 600.0¢)
Dark	0\2 to 1\22 (0.0¢ to 54.5¢)
TAMNAMS information
Descends from	2L 8s (jaric)
Ancestor's step ratio range	7:1 to 1:0
Related MOS scales
Parent	2L 18s
Sister	20L 2s
Daughters	22L 2s, 2L 22s
Neutralized	4L 18s
2-Flought	24L 20s, 2L 42s
Equal tunings
Equalized (L:s = 1:1)	10\22 (545.5¢)
Supersoft (L:s = 4:3)	31\68 (547.1¢)
Soft (L:s = 3:2)	21\46 (547.8¢)
Semisoft (L:s = 5:3)	32\70 (548.6¢)
Basic (L:s = 2:1)	11\24 (550.0¢)
Semihard (L:s = 5:2)	23\50 (552.0¢)
Hard (L:s = 3:1)	12\26 (553.8¢)
Superhard (L:s = 4:1)	13\28 (557.1¢)
Collapsed (L:s = 1:0)	1\2 (600.0¢)

2L 20s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 20 small steps, with a period of 1 large step and 10 small steps that repeats every 600.0¢, or twice every octave. 2L 20s is related to 2L 8s, expanding it by 12 tones. Generators that produce this scale range from 545.5¢ to 600¢, or from 0¢ to 54.5¢.

This scale is the quarter tone scale of Shrutar

Modes

Modes of 2L 20s

UDP	Cyclic order	Step pattern
20|0(2)	1	LssssssssssLssssssssss
18|2(2)	11	sLssssssssssLsssssssss
16|4(2)	10	ssLssssssssssLssssssss
14|6(2)	9	sssLssssssssssLsssssss
12|8(2)	8	ssssLssssssssssLssssss
10|10(2)	7	sssssLssssssssssLsssss
8|12(2)	6	ssssssLssssssssssLssss
6|14(2)	5	sssssssLssssssssssLsss
4|16(2)	4	ssssssssLssssssssssLss
2|18(2)	3	sssssssssLssssssssssLs
0|20(2)	2	ssssssssssLssssssssssL

Intervals

Intervals of 2L 20s

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 54.5¢
	Augmented 1-mosstep	A1ms	L	54.5¢ to 600.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 109.1¢
	Major 2-mosstep	M2ms	L + s	109.1¢ to 600.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 163.6¢
	Major 3-mosstep	M3ms	L + 2s	163.6¢ to 600.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 218.2¢
	Major 4-mosstep	M4ms	L + 3s	218.2¢ to 600.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 272.7¢
	Major 5-mosstep	M5ms	L + 4s	272.7¢ to 600.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 327.3¢
	Major 6-mosstep	M6ms	L + 5s	327.3¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0¢ to 381.8¢
	Major 7-mosstep	M7ms	L + 6s	381.8¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0¢ to 436.4¢
	Major 8-mosstep	M8ms	L + 7s	436.4¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0¢ to 490.9¢
	Major 9-mosstep	M9ms	L + 8s	490.9¢ to 600.0¢
10-mosstep	Diminished 10-mosstep	d10ms	10s	0.0¢ to 545.5¢
	Perfect 10-mosstep	P10ms	L + 9s	545.5¢ to 600.0¢
11-mosstep	Perfect 11-mosstep	P11ms	L + 10s	600.0¢
12-mosstep	Perfect 12-mosstep	P12ms	L + 11s	600.0¢ to 654.5¢
	Augmented 12-mosstep	A12ms	2L + 10s	654.5¢ to 1200.0¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0¢ to 709.1¢
	Major 13-mosstep	M13ms	2L + 11s	709.1¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0¢ to 763.6¢
	Major 14-mosstep	M14ms	2L + 12s	763.6¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	600.0¢ to 818.2¢
	Major 15-mosstep	M15ms	2L + 13s	818.2¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	600.0¢ to 872.7¢
	Major 16-mosstep	M16ms	2L + 14s	872.7¢ to 1200.0¢
17-mosstep	Minor 17-mosstep	m17ms	L + 16s	600.0¢ to 927.3¢
	Major 17-mosstep	M17ms	2L + 15s	927.3¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	L + 17s	600.0¢ to 981.8¢
	Major 18-mosstep	M18ms	2L + 16s	981.8¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	L + 18s	600.0¢ to 1036.4¢
	Major 19-mosstep	M19ms	2L + 17s	1036.4¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	L + 19s	600.0¢ to 1090.9¢
	Major 20-mosstep	M20ms	2L + 18s	1090.9¢ to 1200.0¢
21-mosstep	Diminished 21-mosstep	d21ms	L + 20s	600.0¢ to 1145.5¢
	Perfect 21-mosstep	P21ms	2L + 19s	1145.5¢ to 1200.0¢
22-mosstep	Perfect 22-mosstep	P22ms	2L + 20s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 2L 20s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
10\22						545.455	54.545	1:1	1.000	Equalized 2L 20s
					51\112	546.429	53.571	6:5	1.200
				41\90		546.667	53.333	5:4	1.250
					72\158	546.835	53.165	9:7	1.286
			31\68			547.059	52.941	4:3	1.333	Supersoft 2L 20s
					83\182	547.253	52.747	11:8	1.375
				52\114		547.368	52.632	7:5	1.400
					73\160	547.500	52.500	10:7	1.429
		21\46				547.826	52.174	3:2	1.500	Soft 2L 20s
					74\162	548.148	51.852	11:7	1.571
				53\116		548.276	51.724	8:5	1.600
					85\186	548.387	51.613	13:8	1.625
			32\70			548.571	51.429	5:3	1.667	Semisoft 2L 20s
					75\164	548.780	51.220	12:7	1.714
				43\94		548.936	51.064	7:4	1.750
					54\118	549.153	50.847	9:5	1.800
	11\24					550.000	50.000	2:1	2.000	Basic 2L 20s Scales with tunings softer than this are proper
					45\98	551.020	48.980	9:4	2.250
				34\74		551.351	48.649	7:3	2.333
					57\124	551.613	48.387	12:5	2.400
			23\50			552.000	48.000	5:2	2.500	Semihard 2L 20s
					58\126	552.381	47.619	13:5	2.600
				35\76		552.632	47.368	8:3	2.667
					47\102	552.941	47.059	11:4	2.750
		12\26				553.846	46.154	3:1	3.000	Hard 2L 20s
					37\80	555.000	45.000	10:3	3.333
				25\54		555.556	44.444	7:2	3.500
					38\82	556.098	43.902	11:3	3.667
			13\28			557.143	42.857	4:1	4.000	Superhard 2L 20s
					27\58	558.621	41.379	9:2	4.500
				14\30		560.000	40.000	5:1	5.000
					15\32	562.500	37.500	6:1	6.000
1\2						600.000	0.000	1:0	→ ∞	Collapsed 2L 20s

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