Diatonic and Pentatonic Microtonality

In my PNM Article, I made it clear that diatonic and pentatonic scales are
an abstract shape built from integer ratios, and that EDOs 'quantize' the
infinite pitch-space to give a resource-constrained view of that infinite
pitch-space. But is also important to see how other abstract shapes can be
formed using the EDOs themselves, and how these are quantizing other ratio
relationships than the 5/4 6/5 of traditional diatony.

I feel that EDOs and ratios are related through diatonic scales, each
giving a new perspective on the other. In some EDOs, certain relationships
are telescoped (such as #=b), whilst others are retained. Meantone scales
lie halfway between them, being both infinite and constrained at the same
time.

EDOs may only /represent/ diatonic or 'pentatonic' scales, but sometimes
the representation itself can be an interesting musical object.

>sounds very much like my aim (and work)! one of my basic
>philosophical differences with you (i think) and with the academic
>community, is that i feel that diatony and pentatony are in no way
>connected with the equal tempered scale of 12 notes in the first
>place. but i hope we'll keep communicating as much as possible . . .