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
Related to	6L 1s (archaeotonic)
With tunings	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 ¢)
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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 interval regions.

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.

Theory

The only notable harmonic entropy minimum corresponds to Tetracot temperament, where 1 generator is a "minor whole tone" that approximates 10/9 and 11/10, and 4 generators stack to a perfect fifth (~3/2).

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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