8L 7s

↖ 7L 6s	↑ 8L 6s	9L 6s ↗
← 7L 7s	8L 7s	9L 7s →
↙ 7L 8s	↓ 8L 8s	9L 8s ↘

┌╥╥┬╥┬╥┬╥┬╥┬╥┬╥┬┐ │║║│║│║│║│║│║│║││ │││││││││││││││││ └┴┴┴┴┴┴┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LLsLsLsLsLsLsLs sLsLsLsLsLsLsLL
Equave	2/1 (1200.0¢)
Period	2/1 (1200.0¢)
Generator size
Bright	13\15 to 7\8 (1040.0¢ to 1050.0¢)
Dark	1\8 to 2\15 (150.0¢ to 160.0¢)
TAMNAMS information
Descends from	7L 1s (pine)
Ancestor's step ratio range	1:1 to 2:1 (soft-of-basic)
Related MOS scales
Parent	7L 1s
Sister	7L 8s
Daughters	15L 8s, 8L 15s
Neutralized	1L 14s
2-Flought	23L 7s, 8L 22s
Equal tunings
Equalized (L:s = 1:1)	13\15 (1040.0¢)
Supersoft (L:s = 4:3)	46\53 (1041.5¢)
Soft (L:s = 3:2)	33\38 (1042.1¢)
Semisoft (L:s = 5:3)	53\61 (1042.6¢)
Basic (L:s = 2:1)	20\23 (1043.5¢)
Semihard (L:s = 5:2)	47\54 (1044.4¢)
Hard (L:s = 3:1)	27\31 (1045.2¢)
Superhard (L:s = 4:1)	34\39 (1046.2¢)
Collapsed (L:s = 1:0)	7\8 (1050.0¢)

8L 7s is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 8 large steps and 7 small steps, repeating every octave. 8L 7s is a child scale of 7L 1s, expanding it by 7 tones. Generators that produce this scale range from 1040¢ to 1050¢, or from 150¢ to 160¢.

This scale is the chromatic scale of opossum temperament, where the tetrad 1/1-6/5-10/7-12/7 (0¢-316¢-617¢-933¢) can be formed by by stacking the dark generator 2, 4, and 6 times above the root. 8L 7s approximates this tetrad from 0¢-300¢-600¢-900¢ to 0¢-320¢-640¢-960¢.

Modes

Modes of 8L 7s

UDP	Cyclic order	Step pattern
14|0	1	LLsLsLsLsLsLsLs
13|1	14	LsLLsLsLsLsLsLs
12|2	12	LsLsLLsLsLsLsLs
11|3	10	LsLsLsLLsLsLsLs
10|4	8	LsLsLsLsLLsLsLs
9|5	6	LsLsLsLsLsLLsLs
8|6	4	LsLsLsLsLsLsLLs
7|7	2	LsLsLsLsLsLsLsL
6|8	15	sLLsLsLsLsLsLsL
5|9	13	sLsLLsLsLsLsLsL
4|10	11	sLsLsLLsLsLsLsL
3|11	9	sLsLsLsLLsLsLsL
2|12	7	sLsLsLsLsLLsLsL
1|13	5	sLsLsLsLsLsLLsL
0|14	3	sLsLsLsLsLsLsLL

Intervals

Intervals of 8L 7s

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 80.0¢
	Major 1-mosstep	M1ms	L	80.0¢ to 150.0¢
2-mosstep	Perfect 2-mosstep	P2ms	L + s	150.0¢ to 160.0¢
	Augmented 2-mosstep	A2ms	2L	160.0¢ to 300.0¢
3-mosstep	Minor 3-mosstep	m3ms	L + 2s	150.0¢ to 240.0¢
	Major 3-mosstep	M3ms	2L + s	240.0¢ to 300.0¢
4-mosstep	Minor 4-mosstep	m4ms	2L + 2s	300.0¢ to 320.0¢
	Major 4-mosstep	M4ms	3L + s	320.0¢ to 450.0¢
5-mosstep	Minor 5-mosstep	m5ms	2L + 3s	300.0¢ to 400.0¢
	Major 5-mosstep	M5ms	3L + 2s	400.0¢ to 450.0¢
6-mosstep	Minor 6-mosstep	m6ms	3L + 3s	450.0¢ to 480.0¢
	Major 6-mosstep	M6ms	4L + 2s	480.0¢ to 600.0¢
7-mosstep	Minor 7-mosstep	m7ms	3L + 4s	450.0¢ to 560.0¢
	Major 7-mosstep	M7ms	4L + 3s	560.0¢ to 600.0¢
8-mosstep	Minor 8-mosstep	m8ms	4L + 4s	600.0¢ to 640.0¢
	Major 8-mosstep	M8ms	5L + 3s	640.0¢ to 750.0¢
9-mosstep	Minor 9-mosstep	m9ms	4L + 5s	600.0¢ to 720.0¢
	Major 9-mosstep	M9ms	5L + 4s	720.0¢ to 750.0¢
10-mosstep	Minor 10-mosstep	m10ms	5L + 5s	750.0¢ to 800.0¢
	Major 10-mosstep	M10ms	6L + 4s	800.0¢ to 900.0¢
11-mosstep	Minor 11-mosstep	m11ms	5L + 6s	750.0¢ to 880.0¢
	Major 11-mosstep	M11ms	6L + 5s	880.0¢ to 900.0¢
12-mosstep	Minor 12-mosstep	m12ms	6L + 6s	900.0¢ to 960.0¢
	Major 12-mosstep	M12ms	7L + 5s	960.0¢ to 1050.0¢
13-mosstep	Diminished 13-mosstep	d13ms	6L + 7s	900.0¢ to 1040.0¢
	Perfect 13-mosstep	P13ms	7L + 6s	1040.0¢ to 1050.0¢
14-mosstep	Minor 14-mosstep	m14ms	7L + 7s	1050.0¢ to 1120.0¢
	Major 14-mosstep	M14ms	8L + 6s	1120.0¢ to 1200.0¢
15-mosstep	Perfect 15-mosstep	P15ms	8L + 7s	1200.0¢

Scale tree

Scale Tree and Tuning Spectrum of 8L 7s

Generator(edo)						Cents		Step ratio		Comments
						Bright	Dark	L:s	Hardness
13\15						1040.000	160.000	1:1	1.000	Equalized 8L 7s
					72\83	1040.964	159.036	6:5	1.200
				59\68		1041.176	158.824	5:4	1.250
					105\121	1041.322	158.678	9:7	1.286
			46\53			1041.509	158.491	4:3	1.333	Supersoft 8L 7s
					125\144	1041.667	158.333	11:8	1.375
				79\91		1041.758	158.242	7:5	1.400
					112\129	1041.860	158.140	10:7	1.429
		33\38				1042.105	157.895	3:2	1.500	Soft 8L 7s
					119\137	1042.336	157.664	11:7	1.571
				86\99		1042.424	157.576	8:5	1.600
					139\160	1042.500	157.500	13:8	1.625
			53\61			1042.623	157.377	5:3	1.667	Semisoft 8L 7s
					126\145	1042.759	157.241	12:7	1.714
				73\84		1042.857	157.143	7:4	1.750
					93\107	1042.991	157.009	9:5	1.800
	20\23					1043.478	156.522	2:1	2.000	Basic 8L 7s Scales with tunings softer than this are proper
					87\100	1044.000	156.000	9:4	2.250
				67\77		1044.156	155.844	7:3	2.333
					114\131	1044.275	155.725	12:5	2.400
			47\54			1044.444	155.556	5:2	2.500	Semihard 8L 7s
					121\139	1044.604	155.396	13:5	2.600
				74\85		1044.706	155.294	8:3	2.667
					101\116	1044.828	155.172	11:4	2.750
		27\31				1045.161	154.839	3:1	3.000	Hard 8L 7s
					88\101	1045.545	154.455	10:3	3.333
				61\70		1045.714	154.286	7:2	3.500
					95\109	1045.872	154.128	11:3	3.667
			34\39			1046.154	153.846	4:1	4.000	Superhard 8L 7s
					75\86	1046.512	153.488	9:2	4.500
				41\47		1046.809	153.191	5:1	5.000
					48\55	1047.273	152.727	6:1	6.000
7\8						1050.000	150.000	1:0	→ ∞	Collapsed 8L 7s

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