5L 1s

5L 1s refers to MOS scales with 5 large steps and 1 small step. When L=s we have 6edo, the equal-tempered "whole tone scale" of impressionistic fame. At the other end of the spectrum, we approach 5edo, with five equal whole tones of 240 cents. In between, we find relatively even hexatonic scales with one irregularity: a "whole tone" which is smaller than all the others — perhaps not a "whole tone" at all.

The only notable low-harmonic-entropy scale with this MOS pattern is slendric, in which the large step is 8/7 and three of them make a 3/2.

Scales with this pattern are always proper, because there is only one small step.

generator							scale	large step (L)	small step (s)	comments
1\5							1 1 1 1 1 0	240	0
						7\36	7 7 7 7 7 1	233.3	33.3	Slendric is around here
					6\31		6 6 6 6 6 1	232.3	38.7
				5\26			5 5 5 5 5 1	230.8	46.2
			4\21				4 4 4 4 4 1	228.6	57.1	L/s = 4
				7\37			7 7 7 7 7 2	227.0	64.9
							pi pi pi pi pi 1	225.6	71.8	L/s = pi
		3\16					3 3 3 3 3 1	225	75	Gorgo is around here L/s = 3
							e e e e e 1	223.55	82.2	L/s = e
				8\43			8 8 8 8 8 3	223.3	83.7
							phi+1 phi+1 phi+1 phi+1 phi+1 1	223	85.2
			5\27				5 5 5 5 5 2	222.2	88.9
				7\38			7 7 7 7 7 3	221.1	94.7
	2\11						2 2 2 2 2 1	218.2	109.1	Optimum rank range (L/s=2/1) machine
				7\39			7 7 7 7 7 4	215.4	123.1
							√3 √3 √3 √3 √3 1	215.2	124.2
			5\28				5 5 5 5 5 3	214.3	128.6
					13\73		13 13 13 13 8	213.7	131.5
							phi phi phi phi phi 1	213.6	1200/(1+5phi)	Golden machine
				8\45			8 8 8 8 8 5	213.3	133.3
							pi pi pi pi pi 2	212.9	135.5
		3\17					3 3 3 3 3 2	211.8	141.2
				7\40			7 7 7 7 7 5	210	150
			4\23				4 4 4 4 4 3	208.7	156.5
				5\29			5 5 5 5 5 4	206.9	165.5
					6\35		6 6 6 6 6 5	205.7	171.4	Whole tone scales proper begin here
						7\41	7 7 7 7 7 6	204.9	175.6
1\6							1 1 1 1 1 1	200