distributional evenness

I apprecaite Paul Erlich's clarification re maximal evenness (ME) and
distributional evenness (DE). I had not realized that what Paul had called
ME is equivalent to DE, as defined a few years ago (in conference
presentations) by Nora Engebretsen and me. For those interested, our
paper covering evenness and related features will be coming out soon in
_Music Theory Spectrum_:

J. Clough, J. Kochavi, and N. Engebretsen, "Scales, Sets, and Interval
Cycles: A Taxonomy.".

John Clough
SUNY at Buffalo

John Clough wrote,

>I apprecaite Paul Erlich's clarification re maximal evenness (ME) and
>distributional evenness (DE). I had not realized that what Paul had called
>ME is equivalent to DE, as defined a few years ago (in conference
>presentations) by Nora Engebretsen and me. For those interested, our
>paper covering evenness and related features will be coming out soon in
>_Music Theory Spectrum_:

>J. Clough, J. Kochavi, and N. Engebretsen, "Scales, Sets, and Interval
>Cycles: A Taxonomy.".

The distinction between your ME and your DE does not matter for the scales
discussed in my paper. But for 7-out-of-31, ME does not yield either the
standard Western diatonic or Arabic/Chinese heptatonic scales (both of which
are represented excellently in 31), but rather a rare Arabic scale. The
standard Western diatonic scale in 31 is DE, though.