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 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¢). 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	Orwell is around here
		5\22			2 3 2 3 2 3 2 3 2	272.727	Optimum rank range (L/s=3/2) orwell
					2 pi 2 pi 2 pi 2 pi 2	273.412
				13\57	5 8 5 8 5 8 5 8 5	273.684	Golden orwell (bad tuning)
			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

Note that between 7\31 and 5\22, g approximates frequency ratio 7:6, 2g approximates 11:8, and 3g approximates 8:5. This defines the range of Orwell Temperament, which is the only notable harmonic entropy minimum with this MOS pattern. 4L 5s scales outside of that range are not suitable for Orwell.