- on 11/30/03 8:20 PM, Gene Ward Smith <gwsmith@...> wrote:

> --- In tuning@yahoogroups.com, "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-

>> 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?

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.

-Kurt --- 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