Re Fokker, In-Tuneness, Fractal Scales

Paul: We also generated at 25-limit table (in XH1), but I thought I
sent Fokker the larger one.
I just don't remember after all these years.

"In tuneness": Rothenberg's Equivalence Classes may give some
indication when a scale would be perceived as a mistuning or improved
tuning of a known scale. Scales in the same equivalence
class, defined as having the same rank-order matrix, tend to be heard
as retuning of each other. However, this perception depends upon one's
sensitivity to small pitch deviations in context. Some listeners in some
contexts might hear the Pythagorean, 12-tet, meantone, and 5-limit JI
versions of the major scale as the same scale.

(The rank-order matrix is derived from the difference matrix by
numbering each interval
class 1,2,.... in increasing order of size. Two scales whose ROM's are
the same are considered to be in the same equivalence class. The 4
different tunings of the major mode above fall into 4 distinct EC's.
Furthermore, the Pythagorean tuning is improper, the JI and Meantone (as
31-tet) are strictly proper, and the12- tet is proper. However, to one
not melodically sensitive to the syntonic and ditonic commas, these
tunings may be perceived as categorically identical.)

Similarly, raised leading tones and other expressive inflections might
or might not be considered out of tune, depending on context.
Rothenberg's Range and Blur functions are also relevant here as some
inflections are propriety-preserving modifications of the underlying
scale(s) and some are not. It's a very complex question, alas, with no
simple answers or rules.

Fractal scales: I've generated some more self-similar scales with a
simple program and will be happy to share the method and results with
anyone who wants it. Or I could post a brief description and some
examples of the output.

--John