7L 1s

← 6L 1s	7L 1s	8L 1s →
↙ 6L 2s	↓ 7L 2s	8L 2s ↘

Scale structure
Step pattern	LLLLLLLs sLLLLLLL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	1\8 to 1\7 (150.0 ¢ to 171.4 ¢)
Dark	6\7 to 7\8 (1028.6 ¢ to 1050.0 ¢)
TAMNAMS information
Name	pine
Prefix	pine-
Abbrev.	p
Related MOS scales
Parent	1L 6s
Sister	1L 7s
Daughters	8L 7s, 7L 8s
Neutralized	6L 2s
2-Flought	15L 1s, 7L 9s
Equal tunings
Equalized (L:s = 1:1)	1\8 (150.0 ¢)
Supersoft (L:s = 4:3)	4\31 (154.8 ¢)
Soft (L:s = 3:2)	3\23 (156.5 ¢)
Semisoft (L:s = 5:3)	5\38 (157.9 ¢)
Basic (L:s = 2:1)	2\15 (160.0 ¢)
Semihard (L:s = 5:2)	5\37 (162.2 ¢)
Hard (L:s = 3:1)	3\22 (163.6 ¢)
Superhard (L:s = 4:1)	4\29 (165.5 ¢)
Collapsed (L:s = 1:0)	1\7 (171.4 ¢)
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There are two notable harmonic entropy minima with this MOS pattern. The first is porcupine, in which two generators make a 6/5 and three make a 4/3. The range of porcupine tunings is about 2\15 to 3\22. Less well-known is greeley, in which two generators are still 6/5 but three fall quite short of a 4/3, but the scale happens to closely approximate a lot of higher-complexity intervals like 10/7, 11/7, etc.

Scales of this form are always proper, because there is only one small step.

Modes

Mode names are from Porcupine temperament modal harmony.

Mode	UDP	Mode name
LLLLLLLs	7|0	octopus
LLLLLLsL	6|1	mantis
LLLLLsLL	5|2	dolphin
LLLLsLLL	4|3	crab
LLLsLLLL	3|4	tuna
LLsLLLLL	2|5	salmon
LsLLLLLL	1|6	starfish
sLLLLLLL	0|7	whale

Scale tree

Generator						Cents	Remainder	Scale in EDO steps	Comments
1\7						171.43	0.00	1 1 1 1 1 1 1 0
					6\43	167.44	27.91	6 6 6 6 6 6 6 1
				5\36		166.67	33.32	5 5 5 5 5 5 5 1
			4\29			165.52	41.38	4 4 4 4 4 4 4 1	L/s = 4
						163.97	52.19	π π π π π π π 1	L/s = π
		3\22				163.64	54.55	3 3 3 3 3 3 3 1	L/s = 3
						162.87	59.92	e e e e e e e e 1	L/s = e
				8\59		162.71	61.02	8 8 8 8 8 8 8 3
					13\96	162.5	62.5	[13 13 13 13 13 13|13 13 13 13 13 13 13] 5
			5\37			162.16	64.86	5 5 5 5 5 5 5 2	Porcupine is in this general region
				7\52		161.54	69.23	7 7 7 7 7 7 7 3
	2\15					160	80	2 2 2 2 2 2 2 1	Optimum rank range (L/s=2/1) porcupine
						158.37	91.43	√3 √3 √3 √3 √3 √3 √3 1
			5\38			157.89	94.73	5 5 5 5 5 5 5 3
					13\99	157.58	96.97	[13 13 13 13 13 13|13 13 13 13 13 13 13] 8	Golden porcupine / golden hemikleismic
				8\61		157.38	98.36	8 8 8 8 8 8 8 5
					(11\84)	(157.14)	(100)	[11 11 11 11 11 11|11 11 11 11 11 11 11] 7 π π π π π π π 2
		3\23				156.52	104.348	3 3 3 3 3 3 3 2
					10\77	155.84	109.09	[10 10 10 10 10 10|10 10 10 10 10 10 10] 7	Greeley is around here
				7\54		155.56	111.11	7 7 7 7 7 7 7 5
			4\31			154.84	116.13	4 4 4 4 4 4 4 3
				5\39		153.85	123.08	5 5 5 5 5 5 5 4
					6\47	153.19	127.66	6 6 6 6 6 6 6 5
1\8						150	150	1 1 1 1 1 1 1 1