7L 13s

↖ 6L 12s	↑ 7L 12s	8L 12s ↗
← 6L 13s	7L 13s	8L 13s →
↙ 6L 14s	↓ 7L 14s	8L 14s ↘

┌╥┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬╥┬┬┐ │║│║││║││║││║││║││║│││ ││││││││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLssLssLssLssLssLss ssLssLssLssLssLssLsL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	17\20 to 6\7 (1020.0¢ to 1028.6¢)
Dark	1\7 to 3\20 (171.4¢ to 180.0¢)
TAMNAMS information
Descends from	6L 1s (archaeotonic)
Ancestor's step ratio range	1:1 to 3:2 (soft)
Related MOS scales
Parent	7L 6s
Sister	13L 7s
Daughters	20L 7s, 7L 20s
Neutralized	14L 6s
2-Flought	27L 13s, 7L 33s
Equal tunings
Equalized (L:s = 1:1)	17\20 (1020.0¢)
Supersoft (L:s = 4:3)	57\67 (1020.9¢)
Soft (L:s = 3:2)	40\47 (1021.3¢)
Semisoft (L:s = 5:3)	63\74 (1021.6¢)
Basic (L:s = 2:1)	23\27 (1022.2¢)
Semihard (L:s = 5:2)	52\61 (1023.0¢)
Hard (L:s = 3:1)	29\34 (1023.5¢)
Superhard (L:s = 4:1)	35\41 (1024.4¢)
Collapsed (L:s = 1:0)	6\7 (1028.6¢)

7L 13s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 13 small steps, repeating every octave. 7L 13s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 1020¢ to 1028.6¢, or from 171.4¢ to 180¢.

Modes

Modes of 7L 13s

UDP	Cyclic order	Step pattern
19|0	1	LsLssLssLssLssLssLss
18|1	18	LssLsLssLssLssLssLss
17|2	15	LssLssLsLssLssLssLss
16|3	12	LssLssLssLsLssLssLss
15|4	9	LssLssLssLssLsLssLss
14|5	6	LssLssLssLssLssLsLss
13|6	3	LssLssLssLssLssLssLs
12|7	20	sLsLssLssLssLssLssLs
11|8	17	sLssLsLssLssLssLssLs
10|9	14	sLssLssLsLssLssLssLs
9|10	11	sLssLssLssLsLssLssLs
8|11	8	sLssLssLssLssLsLssLs
7|12	5	sLssLssLssLssLssLsLs
6|13	2	sLssLssLssLssLssLssL
5|14	19	ssLsLssLssLssLssLssL
4|15	16	ssLssLsLssLssLssLssL
3|16	13	ssLssLssLsLssLssLssL
2|17	10	ssLssLssLssLsLssLssL
1|18	7	ssLssLssLssLssLsLssL
0|19	4	ssLssLssLssLssLssLsL

Tuning spectrum

Todo: review Review entries from past page revision and enter them into the scale tree.

Tetracot / enipucrop range. See also 7L 6s 7L 13s and 13L 7s.

Scale Tree and Tuning Spectrum of 7L 13s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
17\20						1020.000	180.000	1:1	1.000	Equalized 7L 13s
					91\107	1020.561	179.439	6:5	1.200
				74\87		1020.690	179.310	5:4	1.250
					131\154	1020.779	179.221	9:7	1.286
			57\67			1020.896	179.104	4:3	1.333	Supersoft 7L 13s
					154\181	1020.994	179.006	11:8	1.375
				97\114		1021.053	178.947	7:5	1.400
					137\161	1021.118	178.882	10:7	1.429
		40\47				1021.277	178.723	3:2	1.500	Soft 7L 13s
					143\168	1021.429	178.571	11:7	1.571
				103\121		1021.488	178.512	8:5	1.600
					166\195	1021.538	178.462	13:8	1.625
			63\74			1021.622	178.378	5:3	1.667	Semisoft 7L 13s
					149\175	1021.714	178.286	12:7	1.714
				86\101		1021.782	178.218	7:4	1.750
					109\128	1021.875	178.125	9:5	1.800
	23\27					1022.222	177.778	2:1	2.000	Basic 7L 13s Scales with tunings softer than this are proper
					98\115	1022.609	177.391	9:4	2.250
				75\88		1022.727	177.273	7:3	2.333
					127\149	1022.819	177.181	12:5	2.400
			52\61			1022.951	177.049	5:2	2.500	Semihard 7L 13s
					133\156	1023.077	176.923	13:5	2.600
				81\95		1023.158	176.842	8:3	2.667
					110\129	1023.256	176.744	11:4	2.750
		29\34				1023.529	176.471	3:1	3.000	Hard 7L 13s
					93\109	1023.853	176.147	10:3	3.333
				64\75		1024.000	176.000	7:2	3.500
					99\116	1024.138	175.862	11:3	3.667
			35\41			1024.390	175.610	4:1	4.000	Superhard 7L 13s
					76\89	1024.719	175.281	9:2	4.500
				41\48		1025.000	175.000	5:1	5.000
					47\55	1025.455	174.545	6:1	6.000
6\7						1028.571	171.429	1:0	→ ∞	Collapsed 7L 13s