6L 1s
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There are two notable harmonic entropy minima with this MOS pattern. The first is tetracot, in which four generators make a 3/2, and the second is known as roulette7, the seven note albitonic scale for the 2.5.7.11.13 subgroup temperament roulette. (Other temperaments like "luna", "hemithird", and "hemiwürschmidt" have very similar 7-note MOSes.)
The 6L+1s pattern also houses a temperament of the 11th and 13th harmonics, for example L=7 s=4 (46 edo) is such a scale.
Scales of this form are always proper, because there is only one small step.
| Generator | Cents | Comments | |||||
|---|---|---|---|---|---|---|---|
| 1\7 | 171.43 | ||||||
| 6\41 | 175.61 | Enipucrop is between here and 1\7 | |||||
| 5\34 | 176.47 | Tetracot is around here | |||||
| 4\27 | 177.78 | ||||||
| 3\20 | 180 | ||||||
| 180.815 | |||||||
| 8\53 | 181.13 | ||||||
| 1200/(5+phi) | Unnamed golden temperament (discussed in this thread) | ||||||
| 5\33 | 181.82 | ||||||
| 182.44 | |||||||
| 7\46 | 182.61 | ||||||
| 2\13 | 184.62 | Optimum rank range glacial (L/s=2/1) | |||||
| 5\32 | 187.5 | ||||||
| 188.03 | |||||||
| 8\51 | 188.235 | ||||||
| 188.45 | L/s = e | ||||||
| 3\19 | 189.47 | L/s = 3 | |||||
| 189.92 | L/s = pi | ||||||
| 4\25 | 192 | L/s = 4 | |||||
| 5\31 | 193.55 | Luna/hemithird/roulette is around here | |||||
| 1\6 | 200 | ||||||