prime vs. odd (vs. integer) -limit

Dante Rosati wrote [TD 64]:

> Im a little confused. Are ratios usually
> catagorized by prime limit or odd limit?

Funny that Dante should bring this up
right now. I had already written the following
before reading his post:
--------------------------------------

For the purposes of accuracy
and updating in my book, I would
like to know which of you agree
to the following (mutually-exclusive)
choices regarding the important
aspects of tuning/ musical perception,
etc. If you feel that different
aspects are important for different
considerations, please express that
fact.

1) Integer factors of ratios
2) Odd factors of ratios
3) Prime factors of ratios

Please feel free to add to this list
and to explain in more detail.

Also, if you know about historical
feelings about these aspects by
other theorists, please illuminate.

I'll get the ball rolling by saying
that I place supreme importance on
the prime factors for all the important
harmonic/ timbral considerations.

Paul Erlich places importance on
the odd factors for consideration of
the consonance of chords, scales, etc.
(Paul has already given a pretty
good elaboration in answer to Dante).

Partch placed importance on the odd
factors for chord consonance and for
delineation of a tonality. However,
he seems to place importance on prime
factors for other (admittedly more
ephemeral) considerations (Partch
scholars please elaborate).

My book has a lot of historical
tuning information, and I'd like
to include as much of contemporary
thought on the subject as possible,
so I'd appreciate lots of response
to this. I particularly need more
info in more exotic tunings, like
those based on pi, non-octave, etc.

- Monzo

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