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.

Name

TAMNAMS suggests the temperament-agnostic name pine, in reference to porcupine temperament.

Theory

Low harmonic entropy scales

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

Scale degrees of the modes of 7L 1s
UDP	Cyclic order	Step pattern	Scale degree (pinedegree)
UDP	Cyclic order	Step pattern	0	1	2	3	4	5	6	7	8
7\|0	1	LLLLLLLs	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Aug.	Perf.
6\|1	2	LLLLLLsL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Maj.	Perf.	Perf.
5\|2	3	LLLLLsLL	Perf.	Perf.	Maj.	Maj.	Maj.	Maj.	Min.	Perf.	Perf.
4\|3	4	LLLLsLLL	Perf.	Perf.	Maj.	Maj.	Maj.	Min.	Min.	Perf.	Perf.
3\|4	5	LLLsLLLL	Perf.	Perf.	Maj.	Maj.	Min.	Min.	Min.	Perf.	Perf.
2\|5	6	LLsLLLLL	Perf.	Perf.	Maj.	Min.	Min.	Min.	Min.	Perf.	Perf.
1\|6	7	LsLLLLLL	Perf.	Perf.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.
0\|7	8	sLLLLLLL	Perf.	Dim.	Min.	Min.	Min.	Min.	Min.	Perf.	Perf.

Proposed Names

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

Template: Scale tree is deprecated. Please use Template: MOS tuning spectrum instead. Details:
Use of a single Comments parameter has become unmaintainable. Existing scale trees should be migrated to the new template, where comments are entered using a step ratio p/q as a parameter:

{{MOS tuning spectrum
| 3/2 = Example comment
| 4/3 = Another example comment
}}

The parameters tuning and depth have been replaced with Scale Signature and Depth, respectively.

Scale tree and tuning spectrum of 7L 1s
Generator^(edo)						Cents		Step ratio		Comments^{(always proper)}
Generator^(edo)						Bright	Dark	L:s	Hardness	Comments^{(always proper)}
1\8						150.000	1050.000	1:1	1.000	Equalized 7L 1s
					6\47	153.191	1046.809	6:5	1.200
				5\39		153.846	1046.154	5:4	1.250
					9\70	154.286	1045.714	9:7	1.286
			4\31			154.839	1045.161	4:3	1.333	Supersoft 7L 1s
					11\85	155.294	1044.706	11:8	1.375
				7\54		155.556	1044.444	7:5	1.400
					10\77	155.844	1044.156	10:7	1.429
		3\23				156.522	1043.478	3:2	1.500	Soft 7L 1s
					11\84	157.143	1042.857	11:7	1.571
				8\61		157.377	1042.623	8:5	1.600
					13\99	157.576	1042.424	13:8	1.625
			5\38			157.895	1042.105	5:3	1.667	Semisoft 7L 1s
					12\91	158.242	1041.758	12:7	1.714
				7\53		158.491	1041.509	7:4	1.750
					9\68	158.824	1041.176	9:5	1.800
	2\15					160.000	1040.000	2:1	2.000	Basic 7L 1s
					9\67	161.194	1038.806	9:4	2.250
				7\52		161.538	1038.462	7:3	2.333
					12\89	161.798	1038.202	12:5	2.400
			5\37			162.162	1037.838	5:2	2.500	Semihard 7L 1s
					13\96	162.500	1037.500	13:5	2.600
				8\59		162.712	1037.288	8:3	2.667
					11\81	162.963	1037.037	11:4	2.750
		3\22				163.636	1036.364	3:1	3.000	Hard 7L 1s
					10\73	164.384	1035.616	10:3	3.333
				7\51		164.706	1035.294	7:2	3.500
					11\80	165.000	1035.000	11:3	3.667
			4\29			165.517	1034.483	4:1	4.000	Superhard 7L 1s
					9\65	166.154	1033.846	9:2	4.500
				5\36		166.667	1033.333	5:1	5.000
					6\43	167.442	1032.558	6:1	6.000
1\7						171.429	1028.571	1:0	→ ∞	Collapsed 7L 1s