13L 7s

Todo: cleanup Swap scale tree for template, transfer entries

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

Scale structure
Step pattern	LLsLLsLLsLLsLLsLLsLs sLsLLsLLsLLsLLsLLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	3\20 to 2\13 (180.0 ¢ to 184.6 ¢)
Dark	11\13 to 17\20 (1015.4 ¢ to 1020.0 ¢)
TAMNAMS information
Related to	6L 1s (archaeotonic)
With tunings	3:2 to 2:1 (hyposoft)
Related MOS scales
Parent	7L 6s
Sister	7L 13s
Daughters	20L 13s, 13L 20s
Neutralized	6L 14s
2-Flought	33L 7s, 13L 27s
Equal tunings
Equalized (L:s = 1:1)	3\20 (180.0 ¢)
Supersoft (L:s = 4:3)	11\73 (180.8 ¢)
Soft (L:s = 3:2)	8\53 (181.1 ¢)
Semisoft (L:s = 5:3)	13\86 (181.4 ¢)
Basic (L:s = 2:1)	5\33 (181.8 ¢)
Semihard (L:s = 5:2)	12\79 (182.3 ¢)
Hard (L:s = 3:1)	7\46 (182.6 ¢)
Superhard (L:s = 4:1)	9\59 (183.1 ¢)
Collapsed (L:s = 1:0)	2\13 (184.6 ¢)
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13L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 13 large steps and 7 small steps, repeating every octave. 13L 7s is a grandchild scale of 6L 1s, expanding it by 13 tones. Generators that produce this scale range from 180 ¢ to 184.6 ¢, or from 1015.4 ¢ to 1020 ¢.

Modes

Modes of 13L 7s

UDP	Cyclic order	Step pattern
19|0	1	LLsLLsLLsLLsLLsLLsLs
18|1	4	LLsLLsLLsLLsLLsLsLLs
17|2	7	LLsLLsLLsLLsLsLLsLLs
16|3	10	LLsLLsLLsLsLLsLLsLLs
15|4	13	LLsLLsLsLLsLLsLLsLLs
14|5	16	LLsLsLLsLLsLLsLLsLLs
13|6	19	LsLLsLLsLLsLLsLLsLLs
12|7	2	LsLLsLLsLLsLLsLLsLsL
11|8	5	LsLLsLLsLLsLLsLsLLsL
10|9	8	LsLLsLLsLLsLsLLsLLsL
9|10	11	LsLLsLLsLsLLsLLsLLsL
8|11	14	LsLLsLsLLsLLsLLsLLsL
7|12	17	LsLsLLsLLsLLsLLsLLsL
6|13	20	sLLsLLsLLsLLsLLsLLsL
5|14	3	sLLsLLsLLsLLsLLsLsLL
4|15	6	sLLsLLsLLsLLsLsLLsLL
3|16	9	sLLsLLsLLsLsLLsLLsLL
2|17	12	sLLsLLsLsLLsLLsLLsLL
1|18	15	sLLsLsLLsLLsLLsLLsLL
0|19	18	sLsLLsLLsLLsLLsLLsLL

Tuning spectrum

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

generator								L	s	L/s	gen (cents)	comment
2\13								1	0		184.615
							17\111	8	1	8.000	183.784
						15\98		7	1	7.000	183.673
					13\85			6	1	6.000	183.529
				11\72				5	1	5.000	183.333
			9\59					4	1	4.000	183.051
				16\105				7	2	3.500	182.857
		7\46						3	1	3.000	182.609	Mitonic, Minortone
			12\79					5	2	2.500	182.278
				17\112				7	3	2.333	182.143
	5\33							2	1	2.000	181.818
				18\119				7	4	1.750	181.513
			13\86					5	3	1.667	181.395
		8\53						3	2	1.500	181.132
			11\73					4	3	1.333	180.822
				14\93				5	4	1.250	180.645
					17\113			6	5	1.200	180.531
						20\133		7	6	1.167	180.451
							23\153	8	7	1.143	180.392
3\20								1	1	1.000	180.000