10L 21s

↖ 9L 20s	↑ 10L 20s	11L 20s ↗
← 9L 21s	10L 21s	11L 21s →
↙ 9L 22s	↓ 10L 22s	11L 22s ↘

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Scale structure
Step pattern	LssLssLssLssLssLssLssLssLssLsss sssLssLssLssLssLssLssLssLssLssL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	3\31 to 1\10 (116.1¢ to 120.0¢)
Dark	9\10 to 28\31 (1080.0¢ to 1083.9¢)
TAMNAMS information
Descends from	1L 9s (antisinatonic)
Ancestor's step ratio range	1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent	10L 11s
Sister	21L 10s
Daughters	31L 10s, 10L 31s
Neutralized	20L 11s
2-Flought	41L 21s, 10L 52s
Equal tunings
Equalized (L:s = 1:1)	3\31 (116.1¢)
Supersoft (L:s = 4:3)	10\103 (116.5¢)
Soft (L:s = 3:2)	7\72 (116.7¢)
Semisoft (L:s = 5:3)	11\113 (116.8¢)
Basic (L:s = 2:1)	4\41 (117.1¢)
Semihard (L:s = 5:2)	9\92 (117.4¢)
Hard (L:s = 3:1)	5\51 (117.6¢)
Superhard (L:s = 4:1)	6\61 (118.0¢)
Collapsed (L:s = 1:0)	1\10 (120.0¢)

10L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 10 large steps and 21 small steps, repeating every octave. 10L 21s is a great-grandchild scale of 1L 9s, expanding it by 21 tones. Generators that produce this scale range from 116.1¢ to 120¢, or from 1080¢ to 1083.9¢.

Intervals

Intervals of 10L 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 38.7¢
	Major 1-mosstep	M1ms	L	38.7¢ to 120.0¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 77.4¢
	Major 2-mosstep	M2ms	L + s	77.4¢ to 120.0¢
3-mosstep	Diminished 3-mosstep	d3ms	3s	0.0¢ to 116.1¢
	Perfect 3-mosstep	P3ms	L + 2s	116.1¢ to 120.0¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	120.0¢ to 154.8¢
	Major 4-mosstep	M4ms	2L + 2s	154.8¢ to 240.0¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	120.0¢ to 193.5¢
	Major 5-mosstep	M5ms	2L + 3s	193.5¢ to 240.0¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	120.0¢ to 232.3¢
	Major 6-mosstep	M6ms	2L + 4s	232.3¢ to 240.0¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	240.0¢ to 271.0¢
	Major 7-mosstep	M7ms	3L + 4s	271.0¢ to 360.0¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	240.0¢ to 309.7¢
	Major 8-mosstep	M8ms	3L + 5s	309.7¢ to 360.0¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	240.0¢ to 348.4¢
	Major 9-mosstep	M9ms	3L + 6s	348.4¢ to 360.0¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	360.0¢ to 387.1¢
	Major 10-mosstep	M10ms	4L + 6s	387.1¢ to 480.0¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	360.0¢ to 425.8¢
	Major 11-mosstep	M11ms	4L + 7s	425.8¢ to 480.0¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	360.0¢ to 464.5¢
	Major 12-mosstep	M12ms	4L + 8s	464.5¢ to 480.0¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	480.0¢ to 503.2¢
	Major 13-mosstep	M13ms	5L + 8s	503.2¢ to 600.0¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	480.0¢ to 541.9¢
	Major 14-mosstep	M14ms	5L + 9s	541.9¢ to 600.0¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	480.0¢ to 580.6¢
	Major 15-mosstep	M15ms	5L + 10s	580.6¢ to 600.0¢
16-mosstep	Minor 16-mosstep	m16ms	5L + 11s	600.0¢ to 619.4¢
	Major 16-mosstep	M16ms	6L + 10s	619.4¢ to 720.0¢
17-mosstep	Minor 17-mosstep	m17ms	5L + 12s	600.0¢ to 658.1¢
	Major 17-mosstep	M17ms	6L + 11s	658.1¢ to 720.0¢
18-mosstep	Minor 18-mosstep	m18ms	5L + 13s	600.0¢ to 696.8¢
	Major 18-mosstep	M18ms	6L + 12s	696.8¢ to 720.0¢
19-mosstep	Minor 19-mosstep	m19ms	6L + 13s	720.0¢ to 735.5¢
	Major 19-mosstep	M19ms	7L + 12s	735.5¢ to 840.0¢
20-mosstep	Minor 20-mosstep	m20ms	6L + 14s	720.0¢ to 774.2¢
	Major 20-mosstep	M20ms	7L + 13s	774.2¢ to 840.0¢
21-mosstep	Minor 21-mosstep	m21ms	6L + 15s	720.0¢ to 812.9¢
	Major 21-mosstep	M21ms	7L + 14s	812.9¢ to 840.0¢
22-mosstep	Minor 22-mosstep	m22ms	7L + 15s	840.0¢ to 851.6¢
	Major 22-mosstep	M22ms	8L + 14s	851.6¢ to 960.0¢
23-mosstep	Minor 23-mosstep	m23ms	7L + 16s	840.0¢ to 890.3¢
	Major 23-mosstep	M23ms	8L + 15s	890.3¢ to 960.0¢
24-mosstep	Minor 24-mosstep	m24ms	7L + 17s	840.0¢ to 929.0¢
	Major 24-mosstep	M24ms	8L + 16s	929.0¢ to 960.0¢
25-mosstep	Minor 25-mosstep	m25ms	8L + 17s	960.0¢ to 967.7¢
	Major 25-mosstep	M25ms	9L + 16s	967.7¢ to 1080.0¢
26-mosstep	Minor 26-mosstep	m26ms	8L + 18s	960.0¢ to 1006.5¢
	Major 26-mosstep	M26ms	9L + 17s	1006.5¢ to 1080.0¢
27-mosstep	Minor 27-mosstep	m27ms	8L + 19s	960.0¢ to 1045.2¢
	Major 27-mosstep	M27ms	9L + 18s	1045.2¢ to 1080.0¢
28-mosstep	Perfect 28-mosstep	P28ms	9L + 19s	1080.0¢ to 1083.9¢
	Augmented 28-mosstep	A28ms	10L + 18s	1083.9¢ to 1200.0¢
29-mosstep	Minor 29-mosstep	m29ms	9L + 20s	1080.0¢ to 1122.6¢
	Major 29-mosstep	M29ms	10L + 19s	1122.6¢ to 1200.0¢
30-mosstep	Minor 30-mosstep	m30ms	9L + 21s	1080.0¢ to 1161.3¢
	Major 30-mosstep	M30ms	10L + 20s	1161.3¢ to 1200.0¢
31-mosstep	Perfect 31-mosstep	P31ms	10L + 21s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 10L 21s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\31						116.129	1083.871	1:1	1.000	Equalized 10L 21s
					16\165	116.364	1083.636	6:5	1.200
				13\134		116.418	1083.582	5:4	1.250
					23\237	116.456	1083.544	9:7	1.286
			10\103			116.505	1083.495	4:3	1.333	Supersoft 10L 21s
					27\278	116.547	1083.453	11:8	1.375
				17\175		116.571	1083.429	7:5	1.400
					24\247	116.599	1083.401	10:7	1.429
		7\72				116.667	1083.333	3:2	1.500	Soft 10L 21s
					25\257	116.732	1083.268	11:7	1.571
				18\185		116.757	1083.243	8:5	1.600
					29\298	116.779	1083.221	13:8	1.625
			11\113			116.814	1083.186	5:3	1.667	Semisoft 10L 21s
					26\267	116.854	1083.146	12:7	1.714
				15\154		116.883	1083.117	7:4	1.750
					19\195	116.923	1083.077	9:5	1.800
	4\41					117.073	1082.927	2:1	2.000	Basic 10L 21s Scales with tunings softer than this are proper
					17\174	117.241	1082.759	9:4	2.250
				13\133		117.293	1082.707	7:3	2.333
					22\225	117.333	1082.667	12:5	2.400
			9\92			117.391	1082.609	5:2	2.500	Semihard 10L 21s
					23\235	117.447	1082.553	13:5	2.600
				14\143		117.483	1082.517	8:3	2.667
					19\194	117.526	1082.474	11:4	2.750
		5\51				117.647	1082.353	3:1	3.000	Hard 10L 21s
					16\163	117.791	1082.209	10:3	3.333
				11\112		117.857	1082.143	7:2	3.500
					17\173	117.919	1082.081	11:3	3.667
			6\61			118.033	1081.967	4:1	4.000	Superhard 10L 21s
					13\132	118.182	1081.818	9:2	4.500
				7\71		118.310	1081.690	5:1	5.000
					8\81	118.519	1081.481	6:1	6.000
1\10						120.000	1080.000	1:0	→ ∞	Collapsed 10L 21s

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