Re: series within a generalized periodicity

Dan Stearns wrote:

> These eight and eleven note "scales" are actually just an 8 - 16 and
> 11 - 22 over series where P = 2:5.

Would it be correct to describe these scales as harmonic fragments
with large amounts of "stretch tuning" applied?

--
David J. Finnamore
Nashville, TN, USA
http://personal.bna.bellsouth.net/bna/d/f/dfin/index.html
--

--- In tuning@egroups.com, "David J. Finnamore" <daeron@b...> wrote:
> Dan Stearns wrote:
>
> > These eight and eleven note "scales" are actually just an 8 - 16
and
> > 11 - 22 over series where P = 2:5.
>
> Would it be correct to describe these scales as harmonic fragments
> with large amounts of "stretch tuning" applied?
>
I think so!

David J. Finnamore,

> Would it be correct to describe these scales as harmonic fragments
with large amounts of "stretch tuning" applied?

Yes, in a way. But keep in mind that the two examples I gave were just
that, two examples, and "P" is generalized so that it can be any given
periodicity, so these harmonic fragments can just as easily occupy a
compressed "octave" as they can a stretched "octave"... and as the
stretching and compressing can be as radical as you like, I think
these tunings are conceptionally closer to something like the
Bohlen-Pierce, or the chromas of Moreno, or any of a number of other
non-octave tunings than they are to stretch tunings in the classic
sense; only these tunings are taken as pseudo over/under series rather
than equal temperaments.

--Dan Stearns

Paul Erlich wrote,

> I'm having trouble reproducing your results using the formula above.
Could you check the formula you're using?

In the formula "P" is generalized as any given periodicity in cents,
and in the two examples I gave P = (LOG(N)-LOG(D))*(1200/LOG(2)) where
D:N is 2:5.

--Dan Stearns

--- In tuning@egroups.com, "D.Stearns" <STEARNS@C...> wrote:
> David J. Finnamore,
>
> > Would it be correct to describe these scales as harmonic fragments
> with large amounts of "stretch tuning" applied?
>
> Yes, in a way.

Good! (And thanks to Paul for answering, too.)

> But keep in mind that the two examples I gave were
just
> that, two examples, and "P" is generalized so that it can be any
given
> periodicity, so these harmonic fragments can just as easily occupy a
> compressed "octave" as they can a stretched "octave"

Yes. I should have made it clear that I wasn't really interested in
viewing it as a stretched tuning, particularly. I just wasn't sure
whether I understood your first explanation so I thought of a way to
restate it as a question. It sounds very intersting and possibly
promising.

David Finnamore