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 184.108.40.206.13 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.
|6\41||175.61||Enipucrop is between here and 1\7|
|5\34||176.47||Tetracot is around here|
|1200/(5+phi)||Unnamed golden temperament (discussed in this thread)|
|2\13||184.62||Optimum rank range glacial (L/s=2/1)|
|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|