- At 02:12 PM 12/1/2003, you wrote:
>--- In tuning@yahoogroups.com, "Paul Erlich" <paul@s...> wrote:

"audibly indistinguishable" comes from the Just Intonation link.

>> --- 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.

Don't tell me you want to get back into the defining JI thing...

:)

-Carl --- 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