Re: [tuning] Re: questions about Paul's "Tuning, Tonality, & 22..."
- on 11/30/03 6:12 PM, monz <monz@...> wrote:
> try the updated version now.I don't think so. The "form" being defined is actually the linguistic form
> i decided to keep "n-limit" because i didn't like
> the look of "o-limit" for the odd-limit definition.
> (confusion with zero, etc.)
> if there's enough consensus that i should change
> the descriptions in the definitions to "p-limit"
> and "o-limit", then i will.
The issue is that the form n-limit is actually ambiguous, and using p versus
o for the variable name in different contexts would serve to obscure rather
than clarifying the fact of this ambiguity.
Personally I would like to see something like 11-olimit or 11-plimit come
into use. If we can have utones and otones then why not olimits and
plimits? But the history of language can not be changed, and so except in
special cases language can not be changed readily by design.
N in n-limit should be perhaps be in italic to indicate that it is a
variable. At least that is one common use for italics in metalinguistic
contexts. The limit page is inconsistent on this admittedly minor point.
The "Concordance" link on the limit page is broken. Or maybe monz is
working on this as we speak.
--- In firstname.lastname@example.org, "Paul Erlich" <paul@s...> wrote:
> --- In email@example.com, "Joseph Pehrson" <jpehrson@r...>
> > --- In firstname.lastname@example.org, "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!