8L 21s

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 ¢.

↖ 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
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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Modes

Modes of 8L 21s

UDP	Cyclic 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

Tuning spectrum

generator								L	s	L/s	gen (cents)	comment
3\8								1	0		450.000
							32\85	8	1	8.000	451.765
						29\77		7	1	7.000	451.948
							55\146	13	2	6.500	452.055
					26\69			6	1	6.000	452.174
							75\199	17	3	5.667	452.261
						49\130		11	2	5.500	452.308
							72\191	16	3	5.333	452.356
				23\61				5	1	5.000	452.459
						66\175		14	3	4.667	452.571
					43\114			9	2	4.500	452.632
						63\167		13	3	4.333	452.695
			20\53					4	1	4.000	452.830
					57\151			11	3	3.667	452.980
				37\98				7	2	3.500	453.061
					54\143			10	3	3.333	453.147
						71\188		13	4	3.250	453.191
		17\45						3	1	3.000	453.333
					65\172			11	4	2.750	453.488
				48\127				8	3	2.667	453.543
			31\82					5	2	2.500	453.659
				45\119				7	3	2.333	453.782
					59\156			9	4	2.250	453.846
						73\193		11	5	2.200	453.886
	14\37							2	1	2.000	454.054
					67\177			9	5	1.800	454.237
				53\140				7	4	1.750	454.286
			39\103					5	3	1.667	454.369
				64\169				8	5	1.600	454.438
		25\66						3	2	1.500	454.545
				61\161				7	5	1.400	454.658
			36\95					4	3	1.333	454.737
				47\124				5	4	1.250	454.839
					58\153			6	5	1.200	454.902
						69\182		7	6	1.167	454.945
							80\211	8	7	1.143	454.976
11\29								1	1	1.000	455.172