4L 1s (5/3-equivalent)

←3L 1s⟨5/3⟩	4L 1s (5/3-equivalent)	5L 1s⟨5/3⟩→
↙3L 2s⟨5/3⟩	↓4L 2s⟨5/3⟩	5L 2s⟨5/3⟩↘

┌╥╥╥╥┬┐ │║║║║││ │││││││ └┴┴┴┴┴┘
Scale structure
Step pattern	LLLLs sLLLL
Equave	5/3 (884.4¢)
Period	5/3 (884.4¢)
Generator size(ed5/3)
Bright	1\5 to 1\4 (176.9¢ to 221.1¢)
Dark	3\4 to 4\5 (663.3¢ to 707.5¢)
Related MOS scales
Parent	1L 3s⟨5/3⟩
Sister	1L 4s⟨5/3⟩
Daughters	5L 4s⟨5/3⟩ 4L 5s⟨5/3⟩
Equal tunings(ed5/3)
Equalized (L:s = 1:1)	1\5 (176.9¢)
Supersoft (L:s = 4:3)	4\19 (186.2¢)
Soft (L:s = 3:2)	3\14 (189.5¢)
Semisoft (L:s = 5:3)	5\23 (192.3¢)
Basic (L:s = 2:1)	2\9 (196.5¢)
Semihard (L:s = 5:2)	5\22 (201.0¢)
Hard (L:s = 3:1)	3\13 (204.1¢)
Superhard (L:s = 4:1)	4\17 (208.1¢)
Collapsed (L:s = 1:0)	1\4 (221.1¢)

4L 1s⟨5/3⟩ is a 5/3-equivalent (non-octave) moment of symmetry scale containing 4 large steps and 1 small step, repeating every interval of 5/3 (884.4¢). Generators that produce this scale range from 176.9¢ to 221.1¢, or from 663.3¢ to 707.5¢. Scales of this form are always proper because there is only one small step.

Modes

Modes of 4L 1s⟨5/3⟩

UDP	Rotational order	Step pattern
4|0	1	LLLLs
3|1	2	LLLsL
2|2	3	LLsLL
1|3	4	LsLLL
0|4	5	sLLLL

Scale tree

Scale tree and tuning spectrum of 4L 1s⟨5/3⟩

Generator (in steps of ed5/3)						Cents		Step ratio		Comments (Every tuning produces a proper scale)
						Bright	Dark	L:s	Hardness
1\5						176.872	707.487	1:1	1.000	Equalized 4L 1s⟨5/3⟩
					6\29	182.971	701.388	6:5	1.200
				5\24		184.241	700.117	5:4	1.250
					9\43	185.098	699.260	9:7	1.286
			4\19			186.181	698.178	4:3	1.333	Supersoft 4L 1s⟨5/3⟩
					11\52	187.076	697.283	11:8	1.375
				7\33		187.591	696.767	7:5	1.400
					10\47	188.161	696.197	10:7	1.429
		3\14				189.505	694.853	3:2	1.500	Soft 4L 1s⟨5/3⟩
					11\51	190.744	693.615	11:7	1.571
				8\37		191.213	693.146	8:5	1.600
					13\60	191.611	692.748	13:8	1.625
			5\23			192.252	692.107	5:3	1.667	Semisoft 4L 1s⟨5/3⟩
					12\55	192.951	691.408	12:7	1.714
				7\32		193.453	690.905	7:4	1.750
					9\41	194.128	690.231	9:5	1.800
	2\9					196.524	687.835	2:1	2.000	Basic 4L 1s⟨5/3⟩
					9\40	198.981	685.378	9:4	2.250
				7\31		199.694	684.665	7:3	2.333
					12\53	200.232	684.127	12:5	2.400
			5\22			200.991	683.368	5:2	2.500	Semihard 4L 1s⟨5/3⟩
					13\57	201.696	682.663	13:5	2.600
				8\35		202.139	682.220	8:3	2.667
					11\48	202.666	681.693	11:4	2.750
		3\13				204.083	680.276	3:1	3.000	Hard 4L 1s⟨5/3⟩
					10\43	205.665	678.694	10:3	3.333
				7\30		206.350	678.008	7:2	3.500
					11\47	206.978	677.381	11:3	3.667
			4\17			208.084	676.274	4:1	4.000	Superhard 4L 1s⟨5/3⟩
					9\38	209.453	674.905	9:2	4.500
				5\21		210.562	673.797	5:1	5.000
					6\25	212.246	672.113	6:1	6.000
1\4						221.090	663.269	1:0	→ ∞	Collapsed 4L 1s⟨5/3⟩