Nomenclature

James Kukula wrote:

> For the phonemic analogy - well, phonemes are really language specific. There
> is no universal set of phonemes. For an overarching theory of the musical
> analogue of phonemes, probably some kind of mathematical system might
> work. Group theory would work if every interval could be combined with every
> other interval to form another legal interval. But this strong a rule drives
> one to equal temperament. Category theory is like group theory, but it
> restricts what elements can be combined with what other elements. But it
> probably wouldn't work for music.

I don't know the specifics of either group or category theory, but
this is definitely something like what I do with matrices. You can
define scale "families" by a basis (primitive group?) and define a
practical scale as a finite subset, usually octave repeating. This
works for ETs, linear temperaments and JIs. Beyond that, you just
have to specify all the intervals in cents.

The matrices are used to convert between bases. Beyond that,
scales really aren't complicated enough to justify bringing in
standard mathematical theory.



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