There are three scales with this MOS pattern that are significant minima of harmonic entropy.
The first is antikythera, or no-3's srutal/pajara, which is srutal/pajara without any intervals containing 3 in their prime factorization, so it becomes a 2.5.9 or 188.8.131.52 subgroup temperament. This means that the generator is twice that of srutal/pajara (210-220 cents rather than 105-110), since odd numbers of generators are only needed for intervals with 3. So this is a basically "whole tone" scale, but made uneven so some 2-step intervals are 5/4 and others are 9/7.
In addition to the true MOS with pattern LLsLLs, all these scales also come in a near-MOS version, LLLsLs, in which the period is the only generic interval that has more than two specific representatives. The true MOS is always proper, but the near-MOS is only proper if the generator is smaller than 2\10 of an octave (240 cents).
|5\28||214.29||Antikythera is around here|
|7\36||233.33||Lemba is around here|
|2\10||240||Boundary of propriety for near-MOS
Optimum rank range (L/s=2/1) for MOS
|5\24||250||Decimal is around here|
|253.39||L/s = e|
|3\14||257.14||L/s = 3|
|258.81||L/s = pi|
|4\18||266.67||L/s = 4|
|11\46||286.96||Doublewide is around here|