3L 2s

The only notable low-harmonic-entropy scale for this MOS pattern is sensi, in which two generators make a 5/3. The harmonic entropy of sensi[5] is still fairly high relative to other pentatonic scales, such as meantone. It's also improper.

Generator							Cents	s	L-s	Comments
1\3							400	0	400
						8\23	417.39	52.18	365.21	8ed(14/11) is near here
					7\20		420	60	300
				6\17			423.53	70.59	282.35	Skwares is around here
						17\48	425	75	275	Squares is around here
					11\31		425.81	77.42	270.97
			5\14				428.57	85.71	257.14	L/s = 4
							435.01	105.035	224.91	L/s = pi, essentially perfect 9/7
		4\11					436.36	109.09	218.18	L/s = 3
							439.39	118.17	203.05	L/s = e
				11/30			440	120	200
							440.59	121.78	197.04
			7/19				442.11	126.32	189.47	Sensi is around here
	3\8						450	150	150	Boundary of propriety (larger generators than this are proper)
							455.59	166.76	122.07
			8\21				457.14	171.43	114.29
					21\55		458.18	174.55	109.09
							1200/(1+phi)	175.08	108.20	Golden petrtri
				13\34			458.82	176.47	105.88
							459.59	178.77	102.04
		5\13					461.54	184.62	92.31	Optimum rank range (L/s=3/2) oneirotonic[5]
			7\18				466.67	200	66.67
				9\23			469.57	208.70	52.17
					11\28		471.43	214.29	42.86
						13\33	472.73	218.18	36.36	Slendro-like scales in this region
2\5							480	240	0