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Re: [tuning] Re: questions about Paul's "Tuning, Tonality, & 22..."

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  • Kurt Bigler
    ... In support of Gene here, none of the discussion in this thread involved any clarification of possible contextual cues given by the presence of the word
    Message 1 of 109 , Nov 30, 2003
      on 11/30/03 8:20 PM, Gene Ward Smith <gwsmith@...> wrote:

      > --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
      >>> I know of no meaning for "5-limit interval" other than "5-prime-
      >> limit
      >>> interval". Note I say "interval", not "consonance".
      >> Well, take some time to re-read this thread and you might learn
      >> something.
      > 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?

      In support of Gene here, none of the discussion in this thread involved any
      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
      tuning dictionary.

    • Joseph Pehrson
      ... http://groups.yahoo.com/group/tuning/message/49322 ... that ... I m ... 5- ... on ... the ... prime ... ***Thanks, Paul. This helps! JP
      Message 109 of 109 , Dec 9, 2003
        --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:


        > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
        > > --- In tuning@yahoogroups.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!

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