4L 3s

4L 3s refers to the structure of moment of symmetry scales with generators ranging from 1\4edo (one degree of 4edo, 300¢) to 2\7edo (two degrees of 7edo, or approx. 342.857¢).

Scale tree

The spectrum looks like this:

Generator								Tetrachord	g in cents	2g	3g	4g	Comments
1\4								1 0 1	300	600	900	0
							9\35	8 1 8	308.571	617.143	925.714	34.286
						8\31		7 1 7	309.677	619.355	929.023	38.71	Myna is around here
					7\27			6 1 6	311.111	622.222	933.333	44.444
				6\23				5 1 5	313.043	626.087	939.13	52.174
			5\19					4 1 4	315.789	631.579	947.368	63.158	L/s = 4
				9\34				7 2 7	317.647	634.294	951.941	70.588	Hanson/Keemun is around here
								pi 1 pi	319.272	638.545	957.817	77.089	L/s = pi
		4\15						3 1 3	320	640	960	80	L/s = 3
								e 1 e	321.6245	641.249	964.874	86.498	L/s = e
				11\41				8 3 8	321.951	643.902	965.854	87.805
						29\108		21 8 21	322.222	644.444	966.667	88.889
					18\67			13 5 13	322.388	644.776	967.364	89.522
			7\26					5 2 5	323.077	646.154	969.231	92.308	Orgone is around here
	3\11							2 1 2	327.273	654.545	981.818	109.091	Boundary of propriety (generators larger than this are proper)
								√3 1 √3	330.217	660.434	990.651	120.868
			8\29					5 3 5	331.034	662.069	993.013	124.138
					21\76			13 8 13	331.579	663.158	994.739	126.316
							34\123	21 13 21	331.707	663.415	995.122	126.829	Unnamed golden temperament
				13\47				8 5 8	331.915	663.83	995.745	127.66
								pi 2 pi	332.3165	664.633	996.9495	129.266
		5\18						3 2 3	333.333	666.667	1000	133.333	Optimum rank range (L/s=3/2)
			7\25					4 3 4	336	672	1008	144
				9\32				5 4 5	337.5	675	1012.5	150	Sixix
					11\39			6 5 6	338.462	676.923	1015.385	153.846	Sixix
						13\46		7 6 7	339.13	678.261	1017.391	156.522	(17/14)^3=9/5
							15\53	8 7 8	339.623	679.245	1018.868	158.491	Amity is around here
2\7								1 1 1	342.857	685.714	1028.571	171.429

There are two notable harmonic entropy minima: hanson/keemun, in which the generator is 6/5 and 6 of them make a 3/1, and myna, in which the generator is also 6/5 but now 10 of them make a 6/1 (so no 4/3's or 3/2's appear in this scale).