8L 21s

↖7L 20s	↑8L 20s	9L 20s↗
←7L 21s	8L 21s	9L 21s→
↙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
Descends from	5L 3s (oneirotonic)
Related MOS scales
Parent	8L 13s
Sister	21L 8s
Daughters	29L 8s 8L 29s
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¢)

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¢.

Modes

Modes of 8L 21s

UDP	Rotational order	Step pattern
28|0	1	LssLsssLssLsssLsssLssLsssLsss
27|1	19	LssLsssLsssLssLsssLssLsssLsss
26|2	8	LssLsssLsssLssLsssLsssLssLsss
25|3	26	LsssLssLsssLssLsssLsssLssLsss
24|4	15	LsssLssLsssLsssLssLsssLssLsss
23|5	4	LsssLssLsssLsssLssLsssLsssLss
22|6	22	LsssLsssLssLsssLssLsssLsssLss
21|7	11	LsssLsssLssLsssLsssLssLsssLss
20|8	29	sLssLsssLssLsssLsssLssLsssLss
19|9	18	sLssLsssLsssLssLsssLssLsssLss
18|10	7	sLssLsssLsssLssLsssLsssLssLss
17|11	25	sLsssLssLsssLssLsssLsssLssLss
16|12	14	sLsssLssLsssLsssLssLsssLssLss
15|13	3	sLsssLssLsssLsssLssLsssLsssLs
14|14	21	sLsssLsssLssLsssLssLsssLsssLs
13|15	10	sLsssLsssLssLsssLsssLssLsssLs
12|16	28	ssLssLsssLssLsssLsssLssLsssLs
11|17	17	ssLssLsssLsssLssLsssLssLsssLs
10|18	6	ssLssLsssLsssLssLsssLsssLssLs
9|19	24	ssLsssLssLsssLssLsssLsssLssLs
8|20	13	ssLsssLssLsssLsssLssLsssLssLs
7|21	2	ssLsssLssLsssLsssLssLsssLsssL
6|22	20	ssLsssLsssLssLsssLssLsssLsssL
5|23	9	ssLsssLsssLssLsssLsssLssLsssL
4|24	27	sssLssLsssLssLsssLsssLssLsssL
3|25	16	sssLssLsssLsssLssLsssLssLsssL
2|26	5	sssLssLsssLsssLssLsssLsssLssL
1|27	23	sssLsssLssLsssLssLsssLsssLssL
0|28	12	sssLsssLssLsssLsssLssLsssLssL

Scale tree

Scale tree and tuning spectrum of 8L 21s

Generator (in steps of 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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