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Associated with the augmented family, which comprises the only significant minimum of harmonic entropy for these scales.
Generator
Cents
Comments
0\3




0




1\15

80
L/s = 4




2\27
88.88
Optimal augmented is around here





400/(1+pi)



1\12


100
L/s = 3





400/(1+e)





3\33
109.09






400/(2+phi)




2\21

114.29


1\9



133.33
Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS





400/(1+sqrt(3))




3\24

150






400/(1+phi)
Golden triforce




5\39
153.85






400/(1+pi/2)



2\15


160

1\6




200

The true MOS is LsLsLs but interesting near-MOSs include LLsLss and LLssLs. The MOS is always proper but the other forms are only proper if the generator is larger than 1\9 of an octave (so not augmented).

Out of all proper six-note MOS scales, this augmented scale probably has the lowest harmonic entropy.