Pseudo-Myhill's property

Dave Keenan and Carl Lumma have asked what this was in Scala on
21-7 and 23-7. My reply is late because a holiday and other
things came in between.
For lack of a better one, the term pseudo-Myhill's property was
chosen by me. Scales with this property can be considered
normalized scales with Myhill's property which didn't have pitches
in ascending order. With normalized I mean pitches brought within
the octave (or other interval of equivalence) and sorted.
For example take a 9-tone Pythagorean scale with generator 3/2.
In Scala:
PYTHAGOREAN
9
2/1
5
3/2
0
SHOW SCALE (shows pitches, they are not in ascending order)
SHOW DATA (shows Myhill's property)
NORMALIZE
SHOW DATA (shows pseudo-Myhill's property)

So it's kind of a degenerate form of Myhill's property. In terms
of intervals it means that interval class (generic interval) number
one doesn't have exactly two sizes, but three. The largest one
(in the example: 9/8) is equal to the smallest one (256/243) plus
the middle one (2187/2048). Other interval classes don't have to have
3 sizes.

Manuel Op de Coul coul@ezh.nl