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

Tuning ranges

Parasoft

Parasoft tunings of orwelloid have a step ratio between 4/3 and 3/2, implying a generator sharper than 7\31 = 270.97¢ and flatter than 5\22 = 272.73¢.

In parasoft orwelloid, the generator (major mosthird) is an approximate 7/6, the major mosfifth is an approximate but rather flat 11/8, the minor mosfourth is an approximate 5/4, and the major mossixth is an approximate 3/2.

Parasoft orwelloid EDOs include 22edo, 31edo, 53edo, and 84edo.

• 22edo can be used to make large and small steps more distinct (the step ratio is 3/2).
• 31edo can be used for its nearly pure 5/4.
• 53edo can be used for its nearly pure 3/2 and good 5/4.

The sizes of the generator, large step and small step of orwelloid are as follows in various parasoft orwelloid tunings.

	22edo	31edo	53edo	84edo	JI intervals represented
generator (g)	5\22, 272.73	7\31, 270.97	12\53, 271.70	19\84, 271.43	7/6
L (5g - octave)	3\22, 163.64	4\31, 154.84	7\53, 158.49	11\84, 157.14	12/11, 11/10
s (octave - 4g)	2\22, 109.09	3\31, 116.13	5\53, 113.21	8\84, 114.29	16/15, 15/14

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
				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
				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
		4\17			1 3 1 3 1 3 1 3 1	282.353	L/s = 3
				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