RE: Re: RE: A gentle introduction to Fokker periodicity blocks, par...

Daniel Wolf wrote,

>Thanks for reiterating this, a non-trivial point. The unison vectors have
to
>be chosen for some musical utility and I'd like to see more discussion of
>that in postings about the topic.

In my original postings in this thread, I specifically identified the
impetus for choosing a unison vector to be this (adapted from Kees van
Prooijen): given the potentially unlimited set of pitches that n-dimensional
JI provides, the simplest n intervals that are too small to represent a
meaningful musical difference (in whatever musical context one may be
operating) should be chosen as the unison vectors. My 1-D examples were: the
limma; and then, given that the limma is to large to function as a UV in
most contexts, a Pythagorean comma. My 2-D examples were: the syntonic comma
and chromatic semitone; and then, given that the chromatic semitone is too
large to function as a UV in most contexts, the syntonic comma and lesser
diesis. If one wishes to recognize subcommatic distinctions, one would
simply move on to the next periodicity blocks in the tables Kees has
compiled (http://www.kees.cc/tuning/perbl.html). Also, I've mentioned that
Kees' tables miss some musically viable periodicity blocks in which no two
notes are separated by an intervals smaller than any of the UVs.