2L 21s

↖ 1L 20s	↑ 2L 20s	3L 20s ↗
← 1L 21s	2L 21s	3L 21s →
↙ 1L 22s	↓ 2L 22s	3L 22s ↘

┌╥┬┬┬┬┬┬┬┬┬┬╥┬┬┬┬┬┬┬┬┬┬┬┐ │║││││││││││║││││││││││││ │││││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LssssssssssLsssssssssss sssssssssssLssssssssssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	11\23 to 1\2 (573.9¢ to 600.0¢)
Dark	1\2 to 12\23 (600.0¢ to 626.1¢)
TAMNAMS information
Descends from	2L 7s (balzano)
Ancestor's step ratio range	8:1 to 1:0
Related MOS scales
Parent	2L 19s
Sister	21L 2s
Daughters	23L 2s, 2L 23s
Neutralized	4L 19s
2-Flought	25L 21s, 2L 44s
Equal tunings
Equalized (L:s = 1:1)	11\23 (573.9¢)
Supersoft (L:s = 4:3)	34\71 (574.6¢)
Soft (L:s = 3:2)	23\48 (575.0¢)
Semisoft (L:s = 5:3)	35\73 (575.3¢)
Basic (L:s = 2:1)	12\25 (576.0¢)
Semihard (L:s = 5:2)	25\52 (576.9¢)
Hard (L:s = 3:1)	13\27 (577.8¢)
Superhard (L:s = 4:1)	14\29 (579.3¢)
Collapsed (L:s = 1:0)	1\2 (600.0¢)

2L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 2 large steps and 21 small steps, repeating every octave. 2L 21s is related to 2L 7s, expanding it by 14 tones. Generators that produce this scale range from 573.9¢ to 600¢, or from 600¢ to 626.1¢.

Modes

Modes of 2L 21s

UDP	Cyclic order	Step pattern
22|0	1	LssssssssssLsssssssssss
21|1	12	LsssssssssssLssssssssss
20|2	23	sLssssssssssLssssssssss
19|3	11	sLsssssssssssLsssssssss
18|4	22	ssLssssssssssLsssssssss
17|5	10	ssLsssssssssssLssssssss
16|6	21	sssLssssssssssLssssssss
15|7	9	sssLsssssssssssLsssssss
14|8	20	ssssLssssssssssLsssssss
13|9	8	ssssLsssssssssssLssssss
12|10	19	sssssLssssssssssLssssss
11|11	7	sssssLsssssssssssLsssss
10|12	18	ssssssLssssssssssLsssss
9|13	6	ssssssLsssssssssssLssss
8|14	17	sssssssLssssssssssLssss
7|15	5	sssssssLsssssssssssLsss
6|16	16	ssssssssLssssssssssLsss
5|17	4	ssssssssLsssssssssssLss
4|18	15	sssssssssLssssssssssLss
3|19	3	sssssssssLsssssssssssLs
2|20	14	ssssssssssLssssssssssLs
1|21	2	ssssssssssLsssssssssssL
0|22	13	sssssssssssLssssssssssL

Intervals

Intervals of 2L 21s

Intervals			Steps subtended	Range in cents
Generic	Specific	Abbrev.
0-mosstep	Perfect 0-mosstep	P0ms	0	0.0¢
1-mosstep	Minor 1-mosstep	m1ms	s	0.0¢ to 52.2¢
	Major 1-mosstep	M1ms	L	52.2¢ to 600.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 104.3¢
	Major 2-mosstep	M2ms	L + s	104.3¢ to 600.0¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0¢ to 156.5¢
	Major 3-mosstep	M3ms	L + 2s	156.5¢ to 600.0¢
4-mosstep	Minor 4-mosstep	m4ms	4s	0.0¢ to 208.7¢
	Major 4-mosstep	M4ms	L + 3s	208.7¢ to 600.0¢
5-mosstep	Minor 5-mosstep	m5ms	5s	0.0¢ to 260.9¢
	Major 5-mosstep	M5ms	L + 4s	260.9¢ to 600.0¢
6-mosstep	Minor 6-mosstep	m6ms	6s	0.0¢ to 313.0¢
	Major 6-mosstep	M6ms	L + 5s	313.0¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	7s	0.0¢ to 365.2¢
	Major 7-mosstep	M7ms	L + 6s	365.2¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	8s	0.0¢ to 417.4¢
	Major 8-mosstep	M8ms	L + 7s	417.4¢ to 600.0¢
9-mosstep	Minor 9-mosstep	m9ms	9s	0.0¢ to 469.6¢
	Major 9-mosstep	M9ms	L + 8s	469.6¢ to 600.0¢
10-mosstep	Minor 10-mosstep	m10ms	10s	0.0¢ to 521.7¢
	Major 10-mosstep	M10ms	L + 9s	521.7¢ to 600.0¢
11-mosstep	Diminished 11-mosstep	d11ms	11s	0.0¢ to 573.9¢
	Perfect 11-mosstep	P11ms	L + 10s	573.9¢ to 600.0¢
12-mosstep	Perfect 12-mosstep	P12ms	L + 11s	600.0¢ to 626.1¢
	Augmented 12-mosstep	A12ms	2L + 10s	626.1¢ to 1200.0¢
13-mosstep	Minor 13-mosstep	m13ms	L + 12s	600.0¢ to 678.3¢
	Major 13-mosstep	M13ms	2L + 11s	678.3¢ to 1200.0¢
14-mosstep	Minor 14-mosstep	m14ms	L + 13s	600.0¢ to 730.4¢
	Major 14-mosstep	M14ms	2L + 12s	730.4¢ to 1200.0¢
15-mosstep	Minor 15-mosstep	m15ms	L + 14s	600.0¢ to 782.6¢
	Major 15-mosstep	M15ms	2L + 13s	782.6¢ to 1200.0¢
16-mosstep	Minor 16-mosstep	m16ms	L + 15s	600.0¢ to 834.8¢
	Major 16-mosstep	M16ms	2L + 14s	834.8¢ to 1200.0¢
17-mosstep	Minor 17-mosstep	m17ms	L + 16s	600.0¢ to 887.0¢
	Major 17-mosstep	M17ms	2L + 15s	887.0¢ to 1200.0¢
18-mosstep	Minor 18-mosstep	m18ms	L + 17s	600.0¢ to 939.1¢
	Major 18-mosstep	M18ms	2L + 16s	939.1¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	L + 18s	600.0¢ to 991.3¢
	Major 19-mosstep	M19ms	2L + 17s	991.3¢ to 1200.0¢
20-mosstep	Minor 20-mosstep	m20ms	L + 19s	600.0¢ to 1043.5¢
	Major 20-mosstep	M20ms	2L + 18s	1043.5¢ to 1200.0¢
21-mosstep	Minor 21-mosstep	m21ms	L + 20s	600.0¢ to 1095.7¢
	Major 21-mosstep	M21ms	2L + 19s	1095.7¢ to 1200.0¢
22-mosstep	Minor 22-mosstep	m22ms	L + 21s	600.0¢ to 1147.8¢
	Major 22-mosstep	M22ms	2L + 20s	1147.8¢ to 1200.0¢
23-mosstep	Perfect 23-mosstep	P23ms	2L + 21s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 2L 21s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\23						573.913	626.087	1:1	1.000	Equalized 2L 21s
					56\117	574.359	625.641	6:5	1.200
				45\94		574.468	625.532	5:4	1.250
					79\165	574.545	625.455	9:7	1.286
			34\71			574.648	625.352	4:3	1.333	Supersoft 2L 21s
					91\190	574.737	625.263	11:8	1.375
				57\119		574.790	625.210	7:5	1.400
					80\167	574.850	625.150	10:7	1.429
		23\48				575.000	625.000	3:2	1.500	Soft 2L 21s
					81\169	575.148	624.852	11:7	1.571
				58\121		575.207	624.793	8:5	1.600
					93\194	575.258	624.742	13:8	1.625
			35\73			575.342	624.658	5:3	1.667	Semisoft 2L 21s
					82\171	575.439	624.561	12:7	1.714
				47\98		575.510	624.490	7:4	1.750
					59\123	575.610	624.390	9:5	1.800
	12\25					576.000	624.000	2:1	2.000	Basic 2L 21s Scales with tunings softer than this are proper
					49\102	576.471	623.529	9:4	2.250
				37\77		576.623	623.377	7:3	2.333
					62\129	576.744	623.256	12:5	2.400
			25\52			576.923	623.077	5:2	2.500	Semihard 2L 21s
					63\131	577.099	622.901	13:5	2.600
				38\79		577.215	622.785	8:3	2.667
					51\106	577.358	622.642	11:4	2.750
		13\27				577.778	622.222	3:1	3.000	Hard 2L 21s
					40\83	578.313	621.687	10:3	3.333
				27\56		578.571	621.429	7:2	3.500
					41\85	578.824	621.176	11:3	3.667
			14\29			579.310	620.690	4:1	4.000	Superhard 2L 21s
					29\60	580.000	620.000	9:2	4.500
				15\31		580.645	619.355	5:1	5.000
					16\33	581.818	618.182	6:1	6.000
1\2						600.000	600.000	1:0	→ ∞	Collapsed 2L 21s

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