Harry Partch related scales

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The famous Partch scale is his 43 note Genesis or "pure" scale. The Wikipedia article on it is here, and the scale itself here. Other Partch scales are his 29-note adapted viola scale, his 37-note draft exposition scale, his 41 note exposition scale and his 43-note exposition scale.

By removing 11/10 and 20/11 from the Genesis scale, we obtain a 41 note epimorphic scale which has been called Genesis Minus; this scale is close to being a Fokker block, tempering to a MOS in cassandra, magic and rodan temperaments, for each of which the generators range from -20 to 20, leading to a symmetrical scale. Paul Erlich constructed this Fokker block which is also a MOS in octacot temperament, with generator range -20 to 20. By chosing other linearly independent temperaments supported by the 11-limit patent val for 41edo to add to cassandra, magic and rodan and requiring the range of generators to be -20 to 20 for that temperament also, we can find other alternatives to Genesis Minus based on monkey, superkleismic, or miracle, which do equally well measured by differences from Genesis Minus.

A 58 note scale is as small as is possible for an epimorphic scale containing Genesis, for example this one. By way of comparison, here is a Fokker block containing 35 of the 43 notes of Genesis: mynadiaechhemi. Mynadiaechhemi also contains a complete 11-limit tonality diamond, and 58 is the smallest size of epimorphic scale for which that is possible

see also Harry Partch