4L 5s

↖ 3L 4s	↑ 4L 4s	5L 4s ↗
← 3L 5s	4L 5s	5L 5s →
↙ 3L 6s	↓ 4L 6s	5L 6s ↘

┌╥┬╥┬╥┬╥┬┬┐ │║│║│║│║│││ │││││││││││ └┴┴┴┴┴┴┴┴┴┘
Scale structure
Step pattern	LsLsLsLss ssLsLsLsL
Equave	2/1 (1200.0 ¢)
Period	2/1 (1200.0 ¢)
Generator size
Bright	2\9 to 1\4 (266.7 ¢ to 300.0 ¢)
Dark	3\4 to 7\9 (900.0 ¢ to 933.3 ¢)
TAMNAMS information
Name	gramitonic
Prefix	gram-
Abbrev.	gm
Related MOS scales
Parent	4L 1s
Sister	5L 4s
Daughters	9L 4s, 4L 9s
Neutralized	8L 1s
2-Flought	13L 5s, 4L 14s
Equal tunings
Equalized (L:s = 1:1)	2\9 (266.7 ¢)
Supersoft (L:s = 4:3)	7\31 (271.0 ¢)
Soft (L:s = 3:2)	5\22 (272.7 ¢)
Semisoft (L:s = 5:3)	8\35 (274.3 ¢)
Basic (L:s = 2:1)	3\13 (276.9 ¢)
Semihard (L:s = 5:2)	7\30 (280.0 ¢)
Hard (L:s = 3:1)	4\17 (282.4 ¢)
Superhard (L:s = 4:1)	5\21 (285.7 ¢)
Collapsed (L:s = 1:0)	1\4 (300.0 ¢)

4L 5s or orwelloid (named after the abstract temperament orwell) refers to the structure of MOS scales whose generator falls between 2\9 (two degrees of 9edo = approx. 266.667¢) and 1\4 (one degree of 4edo = 300¢).

Notation

The notation used in this article is LsLsLsLss = JKLMNOPQRJ unless specified otherwise. We denote raising and lowering by a chroma (L − s) by & "amp" and @ "at". (Mnemonics: & "and" means additional pitch. @ "at" rhymes with "flat".)

Thus the 13edo gamut is as follows:

J/R& J&/K@ K/L@ L/K& L&/M@ M/N@ N/M& N&/O@ O/P@ P/O& P&/Q@ Q/R@ R/Q&/J@ J

Scale tree

In the case of 9edo, L and s are the same size; in the case of 4edo, s is so small it disappears. The spectrum, then, goes something like:

Generator					Scale	Generator in cents	Comments
2\9					1 1 1 1 1 1 1 1 1	266.667
				9\40	4 5 4 5 4 5 4 5 4	270
			7\31		3 4 3 4 3 4 3 4 3	270.968
				12\53	5 7 5 7 5 7 5 7 5	271.698
		5\22			2 3 2 3 2 3 2 3 2	272.727
					2 pi 2 pi 2 pi 2 pi 2	273.412
				13\57	5 8 5 8 5 8 5 8 5	273.684
			8\35		3 5 3 5 3 5 3 5 3	274.286
					1 √3 1 √3 1 √3 1 √3 1	274.85
				11\48	4 7 4 7 4 7 4 7 4	275
	3\13				1 2 1 2 1 2 1 2 1	276.923	Boundary of propriety: generators smaller than this are proper
				10\43	3 7 3 7 3 7 3 7 3	279.07
			7\30		2 5 2 5 2 5 2 5 2	280.000
				11\47	3 8 3 8 3 8 3 8 3	280.851
					1 e 1 e 1 e 1 e 1	281.100	L/s = e
		4\17			1 3 1 3 1 3 1 3 1	282.353	L/s = 3
					1 pi 1 pi 1 pi 1 pi 1	282.922	L/s = pi
				9\38	2 7 2 7 2 7 2 7 2	284.2105
			5\21		1 4 1 4 1 4 1 4 1	285.714	L/s = 4
				6\25	1 5 1 5 1 5 1 5 1	288
1\4					0 1 0 1 0 1 0 1 0	300.000