# 3L 3s

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.