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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