7L 6s

↖ 6L 5s	↑ 7L 5s	8L 5s ↗
← 6L 6s	7L 6s	8L 6s →
↙ 6L 7s	↓ 7L 7s	8L 7s ↘

┌╥╥┬╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║│║││ │││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLsLsLsLs sLsLsLsLsLsLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	11\13 to 6\7 (1015.4 ¢ to 1028.6 ¢)
Dark	1\7 to 2\13 (171.4 ¢ to 184.6 ¢)
TAMNAMS information
Descends from	6L 1s (archaeotonic)
Ancestor's step ratio range	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	6L 1s
Sister	6L 7s
Daughters	13L 7s, 7L 13s
Neutralized	1L 12s
2-Flought	20L 6s, 7L 19s
Equal tunings
Equalized (L:s = 1:1)	11\13 (1015.4 ¢)
Supersoft (L:s = 4:3)	39\46 (1017.4 ¢)
Soft (L:s = 3:2)	28\33 (1018.2 ¢)
Semisoft (L:s = 5:3)	45\53 (1018.9 ¢)
Basic (L:s = 2:1)	17\20 (1020.0 ¢)
Semihard (L:s = 5:2)	40\47 (1021.3 ¢)
Hard (L:s = 3:1)	23\27 (1022.2 ¢)
Superhard (L:s = 4:1)	29\34 (1023.5 ¢)
Collapsed (L:s = 1:0)	6\7 (1028.6 ¢)

7L 6s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 6 small steps, repeating every octave. 7L 6s is a child scale of 6L 1s, expanding it by 6 tones. Generators that produce this scale range from 1015.4 ¢ to 1028.6 ¢, or from 171.4 ¢ to 184.6 ¢.

Scale properties

This article uses TAMNAMS conventions for the names of this scale's intervals and scale degrees. The use of 1-indexed ordinal names is reserved for diatonic interval categories.

Intervals

Intervals of 7L 6s

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 92.3 ¢
	Major 1-mosstep	M1ms	L	92.3 ¢ to 171.4 ¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	171.4 ¢ to 184.6 ¢
	Augmented 2-mosstep	A2ms	2L	184.6 ¢ to 342.9 ¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	171.4 ¢ to 276.9 ¢
	Major 3-mosstep	M3ms	2L + s	276.9 ¢ to 342.9 ¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	342.9 ¢ to 369.2 ¢
	Major 4-mosstep	M4ms	3L + s	369.2 ¢ to 514.3 ¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	342.9 ¢ to 461.5 ¢
	Major 5-mosstep	M5ms	3L + 2s	461.5 ¢ to 514.3 ¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	514.3 ¢ to 553.8 ¢
	Major 6-mosstep	M6ms	4L + 2s	553.8 ¢ to 685.7 ¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	514.3 ¢ to 646.2 ¢
	Major 7-mosstep	M7ms	4L + 3s	646.2 ¢ to 685.7 ¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	685.7 ¢ to 738.5 ¢
	Major 8-mosstep	M8ms	5L + 3s	738.5 ¢ to 857.1 ¢
9-mosstep	Minor 9-mosstep	m9ms	4L + 5s	685.7 ¢ to 830.8 ¢
	Major 9-mosstep	M9ms	5L + 4s	830.8 ¢ to 857.1 ¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	857.1 ¢ to 923.1 ¢
	Major 10-mosstep	M10ms	6L + 4s	923.1 ¢ to 1028.6 ¢
11-mosstep	Diminished 11-mosstep	d11ms	5L + 6s	857.1 ¢ to 1015.4 ¢
	Perfect 11-mosstep	P11ms	6L + 5s	1015.4 ¢ to 1028.6 ¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	1028.6 ¢ to 1107.7 ¢
	Major 12-mosstep	M12ms	7L + 5s	1107.7 ¢ to 1200.0 ¢
13-mosstep	Perfect 13-mosstep	P13ms	7L + 6s	1200.0 ¢

Generator chain

Generator chain of 7L 6s

Bright gens	Scale degree	Abbrev.
19	Augmented 1-mosdegree	A1md
18	Augmented 3-mosdegree	A3md
17	Augmented 5-mosdegree	A5md
16	Augmented 7-mosdegree	A7md
15	Augmented 9-mosdegree	A9md
14	Augmented 11-mosdegree	A11md
13	Augmented 0-mosdegree	A0md
12	Augmented 2-mosdegree	A2md
11	Major 4-mosdegree	M4md
10	Major 6-mosdegree	M6md
9	Major 8-mosdegree	M8md
8	Major 10-mosdegree	M10md
7	Major 12-mosdegree	M12md
6	Major 1-mosdegree	M1md
5	Major 3-mosdegree	M3md
4	Major 5-mosdegree	M5md
3	Major 7-mosdegree	M7md
2	Major 9-mosdegree	M9md
1	Perfect 11-mosdegree	P11md
0	Perfect 0-mosdegree Perfect 13-mosdegree	P0md P13md
−1	Perfect 2-mosdegree	P2md
−2	Minor 4-mosdegree	m4md
−3	Minor 6-mosdegree	m6md
−4	Minor 8-mosdegree	m8md
−5	Minor 10-mosdegree	m10md
−6	Minor 12-mosdegree	m12md
−7	Minor 1-mosdegree	m1md
−8	Minor 3-mosdegree	m3md
−9	Minor 5-mosdegree	m5md
−10	Minor 7-mosdegree	m7md
−11	Minor 9-mosdegree	m9md
−12	Diminished 11-mosdegree	d11md
−13	Diminished 13-mosdegree	d13md
−14	Diminished 2-mosdegree	d2md
−15	Diminished 4-mosdegree	d4md
−16	Diminished 6-mosdegree	d6md
−17	Diminished 8-mosdegree	d8md
−18	Diminished 10-mosdegree	d10md
−19	Diminished 12-mosdegree	d12md

Modes

Scale degrees of the modes of 7L 6s

UDP	Cyclic order	Step pattern	Scale degree (mosdegree)
			0	1	2	3	4	5	6	7	8	9	10	11	12	13
12|0	1	LLsLsLsLsLsLs	Perf.	Maj.	Aug.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
11|1	12	LsLLsLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
10|2	10	LsLsLLsLsLsLs	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
9|3	8	LsLsLsLLsLsLs	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Maj.	Maj.	Perf.	Maj.	Perf.
8|4	6	LsLsLsLsLLsLs	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Maj.	Perf.	Maj.	Perf.
7|5	4	LsLsLsLsLsLLs	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Maj.	Perf.
6|6	2	LsLsLsLsLsLsL	Perf.	Maj.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.
5|7	13	sLLsLsLsLsLsL	Perf.	Min.	Perf.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.
4|8	11	sLsLLsLsLsLsL	Perf.	Min.	Perf.	Min.	Min.	Maj.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.
3|9	9	sLsLsLLsLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Maj.	Min.	Maj.	Min.	Perf.	Min.	Perf.
2|10	7	sLsLsLsLLsLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Maj.	Min.	Perf.	Min.	Perf.
1|11	5	sLsLsLsLsLLsL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Perf.	Min.	Perf.
0|12	3	sLsLsLsLsLsLL	Perf.	Min.	Perf.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Min.	Dim.	Min.	Perf.

Tuning spectrum

Enipucrop range. See also 7L 6s, 7L 13s, and 13L 7s.

Scale tree and tuning spectrum of 7L 6s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
11\13						1015.385	184.615	1:1	1.000	Equalized 7L 6s
					61\72	1016.667	183.333	6:5	1.200
				50\59		1016.949	183.051	5:4	1.250
					89\105	1017.143	182.857	9:7	1.286
			39\46			1017.391	182.609	4:3	1.333	Supersoft 7L 6s Mitonic
					106\125	1017.600	182.400	11:8	1.375
				67\79		1017.722	182.278	7:5	1.400
					95\112	1017.857	182.143	10:7	1.429
		28\33				1018.182	181.818	3:2	1.500	Soft 7L 6s
					101\119	1018.487	181.513	11:7	1.571
				73\86		1018.605	181.395	8:5	1.600
					118\139	1018.705	181.295	13:8	1.625
			45\53			1018.868	181.132	5:3	1.667	Semisoft 7L 6s
					107\126	1019.048	180.952	12:7	1.714
				62\73		1019.178	180.822	7:4	1.750
					79\93	1019.355	180.645	9:5	1.800
	17\20					1020.000	180.000	2:1	2.000	Basic 7L 6s Scales with tunings softer than this are proper
					74\87	1020.690	179.310	9:4	2.250
				57\67		1020.896	179.104	7:3	2.333
					97\114	1021.053	178.947	12:5	2.400
			40\47			1021.277	178.723	5:2	2.500	Semihard 7L 6s
					103\121	1021.488	178.512	13:5	2.600
				63\74		1021.622	178.378	8:3	2.667
					86\101	1021.782	178.218	11:4	2.750
		23\27				1022.222	177.778	3:1	3.000	Hard 7L 6s
					75\88	1022.727	177.273	10:3	3.333	Wollemia, Ponens
				52\61		1022.951	177.049	7:2	3.500	Modus
					81\95	1023.158	176.842	11:3	3.667
			29\34			1023.529	176.471	4:1	4.000	Superhard 7L 6s Tetracot is in this range
					64\75	1024.000	176.000	9:2	4.500
				35\41		1024.390	175.610	5:1	5.000	Sesquiquartififths, Monkey, Bunya
					41\48	1025.000	175.000	6:1	6.000
6\7						1028.571	171.429	1:0	→ ∞	Collapsed 7L 6s

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