Re: [tuning] Re: questions about Paul's "Tuning, Tonality, & 22..."
- on 11/30/03 8:20 PM, Gene Ward Smith <gwsmith@...> wrote:
> --- In firstname.lastname@example.org, "Carl Lumma" <ekin@l...> wrote:In support of Gene here, none of the discussion in this thread involved any
>>> I know of no meaning for "5-limit interval" other than "5-prime-
>>> interval". Note I say "interval", not "consonance".
>> Well, take some time to re-read this thread and you might learn
> That is less than helpful. Do you mean something other than either
> "5-prime-limit interval" (redundent) or "5-odd-limit consonance"
> (pleonastic) and if so, what?
clarification of possible contextual cues given by the presence of the word
"interval", so rereading it would not add anything.
Such cues would be very counter-intuitive to me however. From the outside
it looks like all of this is about intervals. So "limit" is about
intervals, whether odd or prime. I just want to point out the non-arcane
side of this. If the presence of the word "interval" or "consonance" is
truly contextually relevant, then it would be good to have that noted in a
place where everyone using this language will be referring to it. One of
the best places for that to happpen (at least for starters) is the monz
--- In email@example.com, "Paul Erlich" <paul@s...> wrote:
> --- In firstname.lastname@example.org, "Joseph Pehrson" <jpehrson@r...>
> > --- In email@example.com, "Paul Erlich" <paul@s...> wrote:
> > http://groups.yahoo.com/group/tuning/message/48992
> > > >
> > > > ***Looking over Monz' page again, it seems pretty evident
> > the
> > > > *odd* limit is what I have been familiar with, in the Doty
> > primer,
> > > in
> > > > Partch, and in discussions on this list.
> > >
> > > No, Doty only uses prime limit, as I recall.
> > ***Hmmm. I can't believe I'm still not understanding this, but
> > past embarassment, so I'll plow forward... :)
> > So, the *ODD* limit looks like it's the more *inclusive* one, or,
> > rather, it contains more sonorities because it uses all the odd
> > numbers rather than just "primes..." ??
> No, it's quite exclusive, giving *only* the ratios listed in the
> Tonality Diamond diagram for each odd limit (Partch's book has the
> limit, 11-limit, and I believe 13-limit Tonality Diamonds -- take a
> look -- you can easily construct the 7-limit and 9-limit ones now,
> your own . . .)
> > And the *PRIME* limit is the restrictive one that focuses on the
> > basic intervals of just like the perfect fifth for the 3-limit,
> > major third for the 5-limit and the minor seventh for the 7-limit.
> It's less restrictive (even 3-limit, but also all higher prime
> limits, contain an infinite number of ratios between any two ratios
> you care to name, no matter how close), since all conceivable
> combinations of multiplying and dividing 1/1 by these 'basic'
> intervals, using each as many times as you wish, still yield ratios
> belonging to the same prime limit -- in this case, the largest
> factor of all the ratios is still 7. You'll see Doty uses this
> definition of limit.
***Thanks, Paul. This helps!