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

Intervals

Intervals of 7L 13s

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 60.0¢
	Major 1-mosstep	M1ms	L	60.0¢ to 171.4¢
2-mosstep	Minor 2-mosstep	m2ms	2s	0.0¢ to 120.0¢
	Major 2-mosstep	M2ms	L + s	120.0¢ to 171.4¢
3-mosstep	Perfect 3-mosstep	P3ms	L + 2s	171.4¢ to 180.0¢
	Augmented 3-mosstep	A3ms	2L + s	180.0¢ to 342.9¢
4-mosstep	Minor 4-mosstep	m4ms	L + 3s	171.4¢ to 240.0¢
	Major 4-mosstep	M4ms	2L + 2s	240.0¢ to 342.9¢
5-mosstep	Minor 5-mosstep	m5ms	L + 4s	171.4¢ to 300.0¢
	Major 5-mosstep	M5ms	2L + 3s	300.0¢ to 342.9¢
6-mosstep	Minor 6-mosstep	m6ms	2L + 4s	342.9¢ to 360.0¢
	Major 6-mosstep	M6ms	3L + 3s	360.0¢ to 514.3¢
7-mosstep	Minor 7-mosstep	m7ms	2L + 5s	342.9¢ to 420.0¢
	Major 7-mosstep	M7ms	3L + 4s	420.0¢ to 514.3¢
8-mosstep	Minor 8-mosstep	m8ms	2L + 6s	342.9¢ to 480.0¢
	Major 8-mosstep	M8ms	3L + 5s	480.0¢ to 514.3¢
9-mosstep	Minor 9-mosstep	m9ms	3L + 6s	514.3¢ to 540.0¢
	Major 9-mosstep	M9ms	4L + 5s	540.0¢ to 685.7¢
10-mosstep	Minor 10-mosstep	m10ms	3L + 7s	514.3¢ to 600.0¢
	Major 10-mosstep	M10ms	4L + 6s	600.0¢ to 685.7¢
11-mosstep	Minor 11-mosstep	m11ms	3L + 8s	514.3¢ to 660.0¢
	Major 11-mosstep	M11ms	4L + 7s	660.0¢ to 685.7¢
12-mosstep	Minor 12-mosstep	m12ms	4L + 8s	685.7¢ to 720.0¢
	Major 12-mosstep	M12ms	5L + 7s	720.0¢ to 857.1¢
13-mosstep	Minor 13-mosstep	m13ms	4L + 9s	685.7¢ to 780.0¢
	Major 13-mosstep	M13ms	5L + 8s	780.0¢ to 857.1¢
14-mosstep	Minor 14-mosstep	m14ms	4L + 10s	685.7¢ to 840.0¢
	Major 14-mosstep	M14ms	5L + 9s	840.0¢ to 857.1¢
15-mosstep	Minor 15-mosstep	m15ms	5L + 10s	857.1¢ to 900.0¢
	Major 15-mosstep	M15ms	6L + 9s	900.0¢ to 1028.6¢
16-mosstep	Minor 16-mosstep	m16ms	5L + 11s	857.1¢ to 960.0¢
	Major 16-mosstep	M16ms	6L + 10s	960.0¢ to 1028.6¢
17-mosstep	Diminished 17-mosstep	d17ms	5L + 12s	857.1¢ to 1020.0¢
	Perfect 17-mosstep	P17ms	6L + 11s	1020.0¢ to 1028.6¢
18-mosstep	Minor 18-mosstep	m18ms	6L + 12s	1028.6¢ to 1080.0¢
	Major 18-mosstep	M18ms	7L + 11s	1080.0¢ to 1200.0¢
19-mosstep	Minor 19-mosstep	m19ms	6L + 13s	1028.6¢ to 1140.0¢
	Major 19-mosstep	M19ms	7L + 12s	1140.0¢ to 1200.0¢
20-mosstep	Perfect 20-mosstep	P20ms	7L + 13s	1200.0¢

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

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