Propriety and Maximal Evennness

Although I do think propriety is a more reasonable property than maximal
evenness, I think it's too restrictive. My favorite example over the years
has been the Pythagorean diatonic scale, which is not proper. Although the
deviation from propriety is a mere comma involving the tritone, a 22-tET
version of the scale (where the thirds are septimal) has a more severe
impropriety yet is quite melodically satisfying to my ear.

I have advocated a weaker version of propriety which only enforces the
non-contradiction between generic size and specific size when it involves
consonant intervals.

Next I have to point out that the definition of maximal evenness used in my
paper is not quite right. What I call maximal evenness turns out to be
equivalent to what John Clough and a colleague (Nora somebody) have called
"distributional evenness." I should really have fixed my paper more
throughly -- I took the easy way out and indicated in a footnote that my
definition of ME is different from Clough's. A distributional even scale
satisfies what I call maximal evenness (given two step sizes, the notes are
arranged in as close as possible an approximation to a scale with the same
number of notes and only one step size), and an equivalent condition is that
every generic interval comes in at most two specific sizes.

So let's use Clough's definitions of maximal evenness and distributional
evenness, and pretend my paper says "distributional evenness", shall we?

Paul Erlich wrote:
>So let's use Clough's definitions of maximal evenness and distributional
>evenness, and pretend my paper says "distributional evenness", shall we?

In Scala, when the command FIT/MODE indicates "ME", there is indeed maximal
evenness. But when SHOW DATA says "Scale is maximally even" it is
distributionally even under Clough's definition. I will change the term in
the next version.

Manuel Op de Coul coul@ezh.nl

I wrote,

>>So let's use Clough's definitions of maximal evenness and distributional
>>evenness, and pretend my paper says "distributional evenness", shall we?

I would like to put up a new version of the paper. Can anyone help convert a
.doc file to a .pdf file?