New Paper on Optimal Tuning Systems

Larry Polansky asked me to forward this message about his recent paper "A Mathematical Model for Optimal Tuning Systems" to the Tuning list. I've taken the liberty of cross-posting it to both Tuning and Tuning math as I think it is of sufficient interest for both lists.

Polansky, L.; Rockmore, D; Johnson, K., Repetto, D. "A Mathematical Model for Optimal Tuning Systems," is now posted as 08-05-023 at

http://www.santafe.edu/research/publications/wplist/2008

Software: MatLab and Java tools for this framework are available at:

http://eamusic.dartmouth.edu/~larry/owt/index.html

Musical Examples are available here:

http://eamusic.dartmouth.edu/~larry/owt/Optimal_well_temperament_examples.html

--John

At 10:35 AM 5/8/2008, you wrote:
>Larry Polansky asked me to forward this message about his recent paper
>"A Mathematical Model for Optimal Tuning Systems" to the Tuning
>list. I've taken the liberty of cross-posting it to both Tuning and
>Tuning math as I think it is of sufficient interest for both lists.
>
>Polansky, L.; Rockmore, D; Johnson, K., Repetto, D. "A Mathematical
>Model for Optimal Tuning Systems," is now posted as 08-05-023 at
>
> http://www.santafe.edu/research/publications/wplist/2008

Wow, Sante Fe, I didn't know he was active there! Thanks John!

-Carl

--- In tuning-math@yahoogroups.com, John Chalmers <JHCHALMERS@...>
wrote:
>
> Larry Polansky asked me to forward this message about his recent
paper
> "A Mathematical Model for Optimal Tuning Systems" to the Tuning
> list. I've taken the liberty of cross-posting it to both Tuning
and
> Tuning math as I think it is of sufficient interest for both lists.
>
> Polansky, L.; Rockmore, D; Johnson, K., Repetto, D. "A
Mathematical
> Model for Optimal Tuning Systems," is now posted as 08-05-023 at
>
> http://www.santafe.edu/research/publications/wplist/2008
>
>
> Software: MatLab and Java tools for this framework are available at:
>
> http://eamusic.dartmouth.edu/~larry/owt/index.html
>
> Musical Examples are available here:
>
>
http://eamusic.dartmouth.edu/~larry/owt/Optimal_well_temperament_examp
les.html
>
>
> --John
> I read this paper with interest and the only conclusion which I can
draw is that it appears to focus on these chords: 0-267-702, 0-386-
702, 0-408-702 and by implication 0-316-702 and 0-435-702. These
figures suggest 53tet. I offer no criticism--just an
observation.
robert

--- In tuning-math@yahoogroups.com, "robert thomas martin"
<robertthomasmartin@...> wrote:
>
> --- In tuning-math@yahoogroups.com, John Chalmers <JHCHALMERS@>
> wrote:
> >
> > Larry Polansky asked me to forward this message about his recent
> paper
> > "A Mathematical Model for Optimal Tuning Systems" to the Tuning
> > list. I've taken the liberty of cross-posting it to both Tuning
> and
> > Tuning math as I think it is of sufficient interest for both
lists.
> >
> > Polansky, L.; Rockmore, D; Johnson, K., Repetto, D. "A
> Mathematical
> > Model for Optimal Tuning Systems," is now posted as 08-05-023 at
> >
> > http://www.santafe.edu/research/publications/wplist/2008
> >
> >
> > Software: MatLab and Java tools for this framework are available
at:
> >
> > http://eamusic.dartmouth.edu/~larry/owt/index.html
> >
> > Musical Examples are available here:
> >
> >
>
http://eamusic.dartmouth.edu/~larry/owt/Optimal_well_temperament_examp
> les.html
> >
> >
> > --John
> > I read this paper with interest and the only conclusion which I
can
> draw is that it appears to focus on these chords: 0-267-702, 0-386-
> 702, 0-408-702 and by implication 0-316-702 and 0-435-702. These
> figures suggest 53tet. I offer no criticism--just an
>
observation.
> robert
> I left out 0-294-702. I hope that American awe of the Santa Fe
Institute doesn't cloud the
issue.

Robert.

robert thomas martin wrote:

>> I read this paper with interest and the only conclusion which I can > draw is that it appears to focus on these chords: 0-267-702, 0-386-
> 702, 0-408-702 and by implication 0-316-702 and 0-435-702. These > figures suggest 53tet. I offer no criticism--just an > observation. > robert

I don't know where you get a 408 out of this. The ideal intervals in the examples are 7/6 (266.87 cents), 5/4 (386.31), 3/2 (701.96), and 7/4 (968.83). Without 408, 72-tet is a much better approximation. But if you're looking for ET approximations of these intervals, you've missed the point of the article.

Some basic familiarity with musical theory and historical tunings would be helpful.

http://en.wikipedia.org/wiki/Well_temperament
http://en.wikipedia.org/wiki/Werckmeister_temperament
http://en.wikipedia.org/wiki/Musical_tuning
http://en.wikipedia.org/wiki/Consonance_and_dissonance

--- In tuning-math@yahoogroups.com, Herman Miller <hmiller@...> wrote:
>
> robert thomas martin wrote:
>
> >> I read this paper with interest and the only conclusion which I
can
> > draw is that it appears to focus on these chords: 0-267-702, 0-
386-
> > 702, 0-408-702 and by implication 0-316-702 and 0-435-702. These
> > figures suggest 53tet. I offer no criticism--just an
> >
observation.
> > robert
>
> I don't know where you get a 408 out of this. The ideal intervals
in the
> examples are 7/6 (266.87 cents), 5/4 (386.31), 3/2 (701.96), and
7/4
> (968.83). Without 408, 72-tet is a much better approximation. But
if
> you're looking for ET approximations of these intervals, you've
missed
> the point of the article.
>
> Some basic familiarity with musical theory and historical tunings
would
> be helpful.
>
> http://en.wikipedia.org/wiki/Well_temperament
> http://en.wikipedia.org/wiki/Werckmeister_temperament
> http://en.wikipedia.org/wiki/Musical_tuning
> http://en.wikipedia.org/wiki/Consonance_and_dissonance
>
From Robert. Perhaps I did misunderstand but on page 8 both 294 and
408 are mentioned.Robert.