8L 21s

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↙ 7L 22s	↓ 8L 22s	9L 22s ↘

Scale structure
Step pattern	LssLsssLssLsssLsssLssLsssLsss sssLsssLssLsssLsssLssLsssLssL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	18\29 to 5\8 (744.8 ¢ to 750.0 ¢)
Dark	3\8 to 11\29 (450.0 ¢ to 455.2 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	1:1 to 4:3 (ultrasoft)
Related MOS scales
Parent	8L 13s
Sister	21L 8s
Daughters	29L 8s, 8L 29s
Neutralized	16L 13s
2-Flought	37L 21s, 8L 50s
Equal tunings
Equalized (L:s = 1:1)	18\29 (744.8 ¢)
Supersoft (L:s = 4:3)	59\95 (745.3 ¢)
Soft (L:s = 3:2)	41\66 (745.5 ¢)
Semisoft (L:s = 5:3)	64\103 (745.6 ¢)
Basic (L:s = 2:1)	23\37 (745.9 ¢)
Semihard (L:s = 5:2)	51\82 (746.3 ¢)
Hard (L:s = 3:1)	28\45 (746.7 ¢)
Superhard (L:s = 4:1)	33\53 (747.2 ¢)
Collapsed (L:s = 1:0)	5\8 (750.0 ¢)
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8L 21s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 21 small steps, repeating every octave. 8L 21s is a great-grandchild scale of 5L 3s, expanding it by 21 tones. Generators that produce this scale range from 744.8 ¢ to 750 ¢, or from 450 ¢ to 455.2 ¢.

Intervals

Intervals of 8L 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 41.4 ¢
	Major 1-mosstep	M1ms	L	41.4 ¢ to 150.0 ¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0 ¢ to 82.8 ¢
	Major 2-mosstep	M2ms	L + s	82.8 ¢ to 150.0 ¢
3-mosstep	Minor 3-mosstep	m3ms	3s	0.0 ¢ to 124.1 ¢
	Major 3-mosstep	M3ms	L + 2s	124.1 ¢ to 150.0 ¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	150.0 ¢ to 165.5 ¢
	Major 4-mosstep	M4ms	2L + 2s	165.5 ¢ to 300.0 ¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	150.0 ¢ to 206.9 ¢
	Major 5-mosstep	M5ms	2L + 3s	206.9 ¢ to 300.0 ¢
6-mosstep	Minor 6-mosstep	m6ms	L + 5s	150.0 ¢ to 248.3 ¢
	Major 6-mosstep	M6ms	2L + 4s	248.3 ¢ to 300.0 ¢
7-mosstep	Minor 7-mosstep	m7ms	L + 6s	150.0 ¢ to 289.7 ¢
	Major 7-mosstep	M7ms	2L + 5s	289.7 ¢ to 300.0 ¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	300.0 ¢ to 331.0 ¢
	Major 8-mosstep	M8ms	3L + 5s	331.0 ¢ to 450.0 ¢
9-mosstep	Minor 9-mosstep	m9ms	2L + 7s	300.0 ¢ to 372.4 ¢
	Major 9-mosstep	M9ms	3L + 6s	372.4 ¢ to 450.0 ¢
10-mosstep	Minor 10-mosstep	m10ms	2L + 8s	300.0 ¢ to 413.8 ¢
	Major 10-mosstep	M10ms	3L + 7s	413.8 ¢ to 450.0 ¢
11-mosstep	Perfect 11-mosstep	P11ms	3L + 8s	450.0 ¢ to 455.2 ¢
	Augmented 11-mosstep	A11ms	4L + 7s	455.2 ¢ to 600.0 ¢
12-mosstep	Minor 12-mosstep	m12ms	3L + 9s	450.0 ¢ to 496.6 ¢
	Major 12-mosstep	M12ms	4L + 8s	496.6 ¢ to 600.0 ¢
13-mosstep	Minor 13-mosstep	m13ms	3L + 10s	450.0 ¢ to 537.9 ¢
	Major 13-mosstep	M13ms	4L + 9s	537.9 ¢ to 600.0 ¢
14-mosstep	Minor 14-mosstep	m14ms	3L + 11s	450.0 ¢ to 579.3 ¢
	Major 14-mosstep	M14ms	4L + 10s	579.3 ¢ to 600.0 ¢
15-mosstep	Minor 15-mosstep	m15ms	4L + 11s	600.0 ¢ to 620.7 ¢
	Major 15-mosstep	M15ms	5L + 10s	620.7 ¢ to 750.0 ¢
16-mosstep	Minor 16-mosstep	m16ms	4L + 12s	600.0 ¢ to 662.1 ¢
	Major 16-mosstep	M16ms	5L + 11s	662.1 ¢ to 750.0 ¢
17-mosstep	Minor 17-mosstep	m17ms	4L + 13s	600.0 ¢ to 703.4 ¢
	Major 17-mosstep	M17ms	5L + 12s	703.4 ¢ to 750.0 ¢
18-mosstep	Diminished 18-mosstep	d18ms	4L + 14s	600.0 ¢ to 744.8 ¢
	Perfect 18-mosstep	P18ms	5L + 13s	744.8 ¢ to 750.0 ¢
19-mosstep	Minor 19-mosstep	m19ms	5L + 14s	750.0 ¢ to 786.2 ¢
	Major 19-mosstep	M19ms	6L + 13s	786.2 ¢ to 900.0 ¢
20-mosstep	Minor 20-mosstep	m20ms	5L + 15s	750.0 ¢ to 827.6 ¢
	Major 20-mosstep	M20ms	6L + 14s	827.6 ¢ to 900.0 ¢
21-mosstep	Minor 21-mosstep	m21ms	5L + 16s	750.0 ¢ to 869.0 ¢
	Major 21-mosstep	M21ms	6L + 15s	869.0 ¢ to 900.0 ¢
22-mosstep	Minor 22-mosstep	m22ms	6L + 16s	900.0 ¢ to 910.3 ¢
	Major 22-mosstep	M22ms	7L + 15s	910.3 ¢ to 1050.0 ¢
23-mosstep	Minor 23-mosstep	m23ms	6L + 17s	900.0 ¢ to 951.7 ¢
	Major 23-mosstep	M23ms	7L + 16s	951.7 ¢ to 1050.0 ¢
24-mosstep	Minor 24-mosstep	m24ms	6L + 18s	900.0 ¢ to 993.1 ¢
	Major 24-mosstep	M24ms	7L + 17s	993.1 ¢ to 1050.0 ¢
25-mosstep	Minor 25-mosstep	m25ms	6L + 19s	900.0 ¢ to 1034.5 ¢
	Major 25-mosstep	M25ms	7L + 18s	1034.5 ¢ to 1050.0 ¢
26-mosstep	Minor 26-mosstep	m26ms	7L + 19s	1050.0 ¢ to 1075.9 ¢
	Major 26-mosstep	M26ms	8L + 18s	1075.9 ¢ to 1200.0 ¢
27-mosstep	Minor 27-mosstep	m27ms	7L + 20s	1050.0 ¢ to 1117.2 ¢
	Major 27-mosstep	M27ms	8L + 19s	1117.2 ¢ to 1200.0 ¢
28-mosstep	Minor 28-mosstep	m28ms	7L + 21s	1050.0 ¢ to 1158.6 ¢
	Major 28-mosstep	M28ms	8L + 20s	1158.6 ¢ to 1200.0 ¢
29-mosstep	Perfect 29-mosstep	P29ms	8L + 21s	1200.0 ¢

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 8L 21s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
18\29						744.828	455.172	1:1	1.000	Equalized 8L 21s
					95\153	745.098	454.902	6:5	1.200
				77\124		745.161	454.839	5:4	1.250
					136\219	745.205	454.795	9:7	1.286
			59\95			745.263	454.737	4:3	1.333	Supersoft 8L 21s
					159\256	745.312	454.688	11:8	1.375
				100\161		745.342	454.658	7:5	1.400
					141\227	745.374	454.626	10:7	1.429
		41\66				745.455	454.545	3:2	1.500	Soft 8L 21s
					146\235	745.532	454.468	11:7	1.571
				105\169		745.562	454.438	8:5	1.600
					169\272	745.588	454.412	13:8	1.625
			64\103			745.631	454.369	5:3	1.667	Semisoft 8L 21s
					151\243	745.679	454.321	12:7	1.714
				87\140		745.714	454.286	7:4	1.750
					110\177	745.763	454.237	9:5	1.800
	23\37					745.946	454.054	2:1	2.000	Basic 8L 21s Scales with tunings softer than this are proper
					97\156	746.154	453.846	9:4	2.250
				74\119		746.218	453.782	7:3	2.333
					125\201	746.269	453.731	12:5	2.400
			51\82			746.341	453.659	5:2	2.500	Semihard 8L 21s
					130\209	746.411	453.589	13:5	2.600
				79\127		746.457	453.543	8:3	2.667
					107\172	746.512	453.488	11:4	2.750
		28\45				746.667	453.333	3:1	3.000	Hard 8L 21s
					89\143	746.853	453.147	10:3	3.333
				61\98		746.939	453.061	7:2	3.500
					94\151	747.020	452.980	11:3	3.667
			33\53			747.170	452.830	4:1	4.000	Superhard 8L 21s
					71\114	747.368	452.632	9:2	4.500
				38\61		747.541	452.459	5:1	5.000
					43\69	747.826	452.174	6:1	6.000
5\8						750.000	450.000	1:0	→ ∞	Collapsed 8L 21s

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