7L 1s

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

Brightest mode	LLLLLLLs
Period	2/1
Range for bright generator	1\8 (150¢) to 1\7 (171.4¢)
Range for dark generator	6\7 (1028.6¢) to 7\8 (1050¢)
TAMNAMS name	pine
TAMNAMS prefix	pine-
Parent MOS	1L 6s
Sister MOS	1L 7s
Daughter MOSes	8L 7s, 7L 8s
Equal tunings
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¢)
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¢)

7L 1s, also called pine, is a moment of symmetry scale consisting of 7 large steps and 1 small step, repeating every octave. This scale is made using a generator ranging from 150¢ to 171.429¢, or from 1028.571¢ to 1050¢.

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