Re: [tuning] Re: questions about Paul's "Tuning, Tonality, & 22..."
- At 02:12 PM 12/1/2003, you wrote:
>--- In email@example.com, "Paul Erlich" <paul@s...> wrote:"audibly indistinguishable" comes from the Just Intonation link.
>> --- In firstname.lastname@example.org, "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
Don't tell me you want to get back into the defining JI thing...
--- 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!