13L 7s

↖ 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

Scale tree

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details: Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter: {{MOS tuning spectrum | 3/2 = Example comment | 4/3 = Another example comment }} The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 13L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
3\20						180.000	1020.000	1:1	1.000	Equalized 13L 7s
					17\113	180.531	1019.469	6:5	1.200
				14\93		180.645	1019.355	5:4	1.250
					25\166	180.723	1019.277	9:7	1.286
			11\73			180.822	1019.178	4:3	1.333	Supersoft 13L 7s
					30\199	180.905	1019.095	11:8	1.375
				19\126		180.952	1019.048	7:5	1.400
					27\179	181.006	1018.994	10:7	1.429
		8\53				181.132	1018.868	3:2	1.500	Soft 13L 7s
					29\192	181.250	1018.750	11:7	1.571
				21\139		181.295	1018.705	8:5	1.600
					34\225	181.333	1018.667	13:8	1.625
			13\86			181.395	1018.605	5:3	1.667	Semisoft 13L 7s
					31\205	181.463	1018.537	12:7	1.714
				18\119		181.513	1018.487	7:4	1.750
					23\152	181.579	1018.421	9:5	1.800
	5\33					181.818	1018.182	2:1	2.000	Basic 13L 7s Scales with tunings softer than this are proper
					22\145	182.069	1017.931	9:4	2.250
				17\112		182.143	1017.857	7:3	2.333
					29\191	182.199	1017.801	12:5	2.400
			12\79			182.278	1017.722	5:2	2.500	Semihard 13L 7s
					31\204	182.353	1017.647	13:5	2.600
				19\125		182.400	1017.600	8:3	2.667
					26\171	182.456	1017.544	11:4	2.750
		7\46				182.609	1017.391	3:1	3.000	Hard 13L 7s Mitonic / Minortone
					23\151	182.781	1017.219	10:3	3.333
				16\105		182.857	1017.143	7:2	3.500
					25\164	182.927	1017.073	11:3	3.667
			9\59			183.051	1016.949	4:1	4.000	Superhard 13L 7s
					20\131	183.206	1016.794	9:2	4.500
				11\72		183.333	1016.667	5:1	5.000
					13\85	183.529	1016.471	6:1	6.000
2\13						184.615	1015.385	1:0	→ ∞	Collapsed 13L 7s

See also

• 7L 6s 7L 13s and 13L 7s