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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7L 1s, named pine in TAMNAMS, is a 2/1-equivalent (octave-equivalent) moment of symmetry scale containing 7 large steps and 1 small step, repeating every octave. Generators that produce this scale range from 150 ¢ to 171.4 ¢, or from 1028.6 ¢ to 1050 ¢. Scales of this form are always proper because there is only one small step. There are three notable harmonic entropy minima with this MOS pattern. The lowest accuracy one 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 and more accurate 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. Thirdly and finally, tempering S10/S11 so that (4/3)/(11/10)³ is tempered results in an unusually high accuracy & efficient rank 2 temperament in the 2.3.11/10 subgroup for which interpretation as a rank 3 temperament in 2.3.5.11 (the no-7's 11-limit) is natural, making 10/9 and 12/11 equidistant from 11/10 and offering many fruitful tempering opportunities. (Note therefore that porkypine can be seen as a trivial tuning of pine tempering 100/99 = S10 and 121/120 = S11.)

Modes

Mode names are from Porcupine temperament modal harmony. Descriptive mode names are based on using 1-4-7, i.e. 3+3 triads as a basis for harmony.

Mode	UDP	Mode name	Descriptive mode name
LLLLLLLs	7|0	octopus	Bright quartal
LLLLLLsL	6|1	mantis	Dark quartal
LLLLLsLL	5|2	dolphin	Bright major
LLLLsLLL	4|3	crab	Middle major
LLLsLLLL	3|4	tuna	Dark major
LLsLLLLL	2|5	salmon	Bright minor
LsLLLLLL	1|6	starfish	Middle minor
sLLLLLLL	0|7	whale	Dark major

Scale tree

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

Generator						Cents	Scale in EDO steps	Comments
1\7						171.43	1 1 1 1 1 1 1 0
					6\43	167.44	6 6 6 6 6 6 6 1
				5\36		166.67	5 5 5 5 5 5 5 1	pine is around here
			4\29			165.52	4 4 4 4 4 4 4 1	L/s = 4
						163.97	π π π π π π π 1	L/s = π
		3\22				163.64	3 3 3 3 3 3 3 1	L/s = 3
						162.87	e e e e e e e e 1	L/s = e
				8\59		162,71	8 8 8 8 8 8 8 3
					13\96	162.5	13 13 13 13 13 13 13 5
			5\37			162.16	5 5 5 5 5 5 5 2	Porcupine is in this general region
				7\52		161.54	7 7 7 7 7 7 7 3
	2\15					160	2 2 2 2 2 2 2 1	Optimum rank range (L/s=2/1) porcupine
						158.37	√3 √3 √3 √3 √3 √3 √3 1
			5\38			157.89	5 5 5 5 5 5 5 3
					13\99	157.58	13 13 13 13 13 13 13 8	Golden porcupine / golden hemikleismic
				8\61		157.38	8 8 8 8 8 8 8 5
					(11\84)	157.14)	11 11 11 11 11 11 11 7 π π π π π π π 2
		3\23				156.52	3 3 3 3 3 3 3 2
					10\77	155.84	10 10 10 10 10 10 10 7	Greeley is around here
				7\54		155.56	7 7 7 7 7 7 7 5
			4\31			154.84	4 4 4 4 4 4 4 3
				5\39		153.85	5 5 5 5 5 5 5 4
					6\47	153.19	6 6 6 6 6 6 6 5
1\8						150	1 1 1 1 1 1 1 1