Prime and odd limit

Joel Rodrigues wrote:
>Manuel further says:

>"The prime limit definition should NOT be the default, despite
>its utility in
>describing a tuning system. The odd limit definition is not intended to
>describe a tuning system; it is intended to describe musical practice.
>Despite what Jonathan Walker said, one does not consider music in
>Pythagorean tuning to be a 531441-limit system under the odd
>definition of
>limit. Even under Partch's own (odd) definition, Partch's music was
>11-limit, not 33-limit nor some product of powers of numbers through 11.
>Partch listened carefully and came up with the most useful
>definition for
>the ear and for musical practice, not for studying the
>mathematics of tuning
>systems.

>The definition is: A piece of music is N-limit if all intervals whose
>(heard) rational approximations use odd numbers up to N, and all chords
>containing only such intervals, are considered consonant, while
>intervals
>which cannot be so approximated, or any chord containg at least one such
>interval, are considered dissonant. In other words, it's how high up the
>harmonic series (or how far down the subharmonic series) the ear
>is asked to
>go in a particular piece."

>Manuel, I need to research & ponder further, but do you still
>stand by this ? Because this seems to make the most sense to me.
>Though, I would use "harmonic" and "inharmonic" instead of
>"consonant" and "dissonant".

It was Paul Erlich who wrote that i.i.r.c. That time I forwarded some
of his posts because of an email problem.
Personally I have no problem with prime limit being the default
meaning.

Manuel