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There are 4 different near-MOSes such that multiples of the period are the only generic intervals with more than two specific representatives: LLsLsLss, LLsLssLs, LLssLLss, LLssLsLs. However, none are strictly proper in 12edo. (They are only proper if the generator is larger than 100 cents, which unfortunately is the wrong direction for good diminished tunings.)

Optimum rank range (L/s=2/1) for MOS