NOT all "ethnic" scales

Reprinted from the nonoctave forum:

The researchers did not restrict themselves to "ethnic" scales, but simply used all 7-limit scales they found in the archive. This is good in a way, as the concept of a convex "ethnic" scale is problematical to the point of being meaningless. However, it ignores the fact that many of the systems of scale construction automatically produce convex scales, and they are aware, at least, that Fokker blocks do. Moreover since it is obvious and since they have read Euler, it must have been clear to them an Euler genus is convex. Moreover, they also ignore the possibility that scale creators deliberately set out to make the scale convex, which they sometimes do.

The reason convexity for "ethnic" scales is more or less meaningless is that if you temper a 7-limit scale in a regular temperament, it is very likely the result will no longer be convex. Think of tempering a 7-limit scale to meantone or miracle, and you will see that "holes" in the chain of generators are likely to appear. This remains true for planar temperaments--tempering the 9-limit tonality diamond in 225/224 "marvel" temperament produces two holes where the secor and 2/secor go. Tempering with 2401/2400 "breed" is almost impossible without introducing non-convexity, and it is so accurate that it is hard to argue an "ethnic" scale must be in JI and not in breed temperament. Who is to say, and on what basis?