"microtemperament" definition (was: Interval Database Experiences)

hi Gene,

> From: "Gene Ward Smith" <gwsmith@svpal.org>
> To: <tuning-math@yahoogroups.com>
> Sent: Sunday, June 15, 2003 7:11 PM
> Subject: [tuning-math] Re: Interval Database Experiences
>
>
> --- In tuning-math@yahoogroups.com, "monz" <monz@a...> wrote:
>
> > you were never very specific about what's wrong
> > with it.
>
> What I mean by a "microtemperament" is something like this: one where
> all of the relevant consonant intervals are within a cent of being
> pure. What you've defined is a regular temperament of dimension
> greater than or equal to one, so I think it should not be used as a
> definition of microtemperament.
>
> I'd first define "regular temperament" as the expression of musical
> intervals by means of a set of generators g1, ..., gn such that each
> interval is represented as a number of the form g1^e1 ... gn^en, then
> the dimension of the regular temperament as the number of generators
> minus one. An equal temperament, with one generator, would be regular
> of dimension zero; p-limit just intonation would be regular with
> dimension pi(p), which is the number of primes <= p. A linear
> temperament, or temperament of dimension one, has two generators.

OK, thanks. umm ... i'm still real busy with "regular life"
(meaning that i have to do other work to make money), so i'll
still need more help with this.

so, should i put your second paragraph in my "temperament"
definition, and then the first paragraph in "microtemperament"?
please advise.

-monz