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

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  • Carl Lumma
    ... audibly indistinguishable comes from the Just Intonation link. Don t tell me you want to get back into the defining JI thing... ... -Carl
    Message 1 of 109 , Dec 1, 2003
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      At 02:12 PM 12/1/2003, you wrote:
      >--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:
      >> --- In tuning@yahoogroups.com, "Carl Lumma" <ekin@l...> wrote:
      >
      >> > That looks good, except I'd take out "Just Intonation"
      >> > under 1.. We often use things like "7-limit" to mean
      >> > approximations that are not "audibly indistinguishable"
      >> > from JI.
      >
      >> How about "A pitch system in Just Intonation, or an approximation
      >> thereto, where . . ."
      >
      >I don't think audible distinguishibility is the point; a meantone
      >triad is audibly distinct from a JI triad, but still a 5-limit
      >entity.

      "audibly indistinguishable" comes from the Just Intonation link.
      Don't tell me you want to get back into the defining JI thing...
      :)

      -Carl
    • 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
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        --- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

        http://groups.yahoo.com/group/tuning/message/49322

        > --- In tuning@yahoogroups.com, "Joseph Pehrson" <jpehrson@r...>
        wrote:
        > > --- 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
        that
        > > 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
        I'm
        > > 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
        5-
        > 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,
        on
        > 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,
        the
        > > 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
        prime
        > factor of all the ratios is still 7. You'll see Doty uses this
        > definition of limit.

        ***Thanks, Paul. This helps!

        JP
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