editing disabled

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





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


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 father




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) father



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