8L 13s

↖ 7L 12s	↑ 8L 12s	9L 12s ↗
← 7L 13s	8L 13s	9L 13s →
↙ 7L 14s	↓ 8L 14s	9L 14s ↘

Scale structure
Step pattern	LsLssLsLssLssLsLssLss ssLssLsLssLssLsLssLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	13\21 to 5\8 (742.9 ¢ to 750.0 ¢)
Dark	3\8 to 8\21 (450.0 ¢ to 457.1 ¢)
TAMNAMS information
Related to	5L 3s (oneirotonic)
With tunings	1:1 to 3:2 (soft)
Related MOS scales
Parent	8L 5s
Sister	13L 8s
Daughters	21L 8s, 8L 21s
Neutralized	16L 5s
2-Flought	29L 13s, 8L 34s
Equal tunings
Equalized (L:s = 1:1)	13\21 (742.9 ¢)
Supersoft (L:s = 4:3)	44\71 (743.7 ¢)
Soft (L:s = 3:2)	31\50 (744.0 ¢)
Semisoft (L:s = 5:3)	49\79 (744.3 ¢)
Basic (L:s = 2:1)	18\29 (744.8 ¢)
Semihard (L:s = 5:2)	41\66 (745.5 ¢)
Hard (L:s = 3:1)	23\37 (745.9 ¢)
Superhard (L:s = 4:1)	28\45 (746.7 ¢)
Collapsed (L:s = 1:0)	5\8 (750.0 ¢)
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8L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 13 small steps, repeating every octave. 8L 13s is a grandchild scale of 5L 3s, expanding it by 13 tones. Generators that produce this scale range from 742.9 ¢ to 750 ¢, or from 450 ¢ to 457.1 ¢.

Modes

Modes of 8L 13s

UDP	Cyclic order	Step pattern
20|0	1	LsLssLsLssLssLsLssLss
19|1	14	LsLssLssLsLssLsLssLss
18|2	6	LsLssLssLsLssLssLsLss
17|3	19	LssLsLssLsLssLssLsLss
16|4	11	LssLsLssLssLsLssLsLss
15|5	3	LssLsLssLssLsLssLssLs
14|6	16	LssLssLsLssLsLssLssLs
13|7	8	LssLssLsLssLssLsLssLs
12|8	21	sLsLssLsLssLssLsLssLs
11|9	13	sLsLssLssLsLssLsLssLs
10|10	5	sLsLssLssLsLssLssLsLs
9|11	18	sLssLsLssLsLssLssLsLs
8|12	10	sLssLsLssLssLsLssLsLs
7|13	2	sLssLsLssLssLsLssLssL
6|14	15	sLssLssLsLssLsLssLssL
5|15	7	sLssLssLsLssLssLsLssL
4|16	20	ssLsLssLsLssLssLsLssL
3|17	12	ssLsLssLssLsLssLsLssL
2|18	4	ssLsLssLssLsLssLssLsL
1|19	17	ssLssLsLssLsLssLssLsL
0|20	9	ssLssLsLssLssLsLssLsL

Scale tree

generator								L	s	L/s	gen (cents)	comment
3\8								1	0		450.000
							29\77	8	1	8.000	451.948
						26\69		7	1	7.000	452.174
							49\130	13	2	6.500	452.308
					23\61			6	1	6.000	452.459
						43\114		11	2	5.500	452.632
				20\53				5	1	5.000	452.830
					37\98			9	2	4.500	453.061
						54\143		13	3	4.333	453.147
			17\45					4	1	4.000	453.333
					48\127			11	3	3.667	453.543
				31\82				7	2	3.500	453.659
					45\119			10	3	3.333	453.782
		14\37						3	1	3.000	454.054
					53\140			11	4	2.750	454.286
				39\103				8	3	2.667	454.369
			25\66					5	2	2.500	454.545
				36\95				7	3	2.333	454.737
					47\124			9	4	2.250	454.839
	11\29							2	1	2.000	455.172
					52\137			9	5	1.800	455.474
				41\108				7	4	1.750	455.556
			30\79					5	3	1.667	455.696
				49\129				8	5	1.600	455.814
		19\50						3	2	1.500	456.000
				46\121				7	5	1.400	456.198
			27\71					4	3	1.333	456.338
				35\92				5	4	1.250	456.522
					43\113			6	5	1.200	456.637
						51\134		7	6	1.167	456.716
							59\155	8	7	1.143	456.774
8\21								1	1	1.000	457.143