Re: [tuning] More Voronoi plots

> From: "Paul H. Erlich" <PERLICH@ACADIAN-ASSET.COM>
>
> Spurred by Darren Burgess' request, I made Voronoi plots for the triads
> available in a bunch of JI scales -- they're at
> http://lumma.org/erlich/voronoi/. 5-limit major triads are shown in red
and
> 5-limit minor triads are shown in blue.
>
> wolf.jpg 17-Mar-2000 01:37 134k
> (3,6)1�3�5�7�9�11 Eikosany -- for Daniel Wolf
>

Thanks for the thought. Could you run the (3,6)1�3�7�9�11�15 Eikosany? (I
usually use that one).

These plots are extremely interesting, I look forward to seeing what you do
with them -- you may well be on the way to solving the musical equivalent of
the three-body problem.

Once you make the modifications you mentioned previously, would it be
possible to make a table of the spaces ordered by the size?

Daniel Wolf wrote,

>These plots are extremely interesting, I look forward to seeing what you do
>with them -- you may well be on the way to solving the musical equivalent
of
>the three-body problem.

As I said, only the harmonic series plots will be useful for harmonic
entropy. The calculations involved will be long and arduous, even for my 550
MHz computer.

>Once you make the modifications you mentioned previously,

Meaning doing the (3,6)1·3·7·9·11·15 Eikosany?

>would it be
>possible to make a table of the spaces ordered by the size?

Right -- calculating the area of these regions will be necessary for
harmonic entropy work, so once I figure out how to do it, I'll apply it to
your Eikosany plot.

Daniel Wolf wrote,

>Once you make the modifications you mentioned previously,

Not sure which modifications you mean.

As for (3,6)1·3·7·9·11·15 Eikosany, I'm about to send that to you.

The total number of kinds of triads spanning no more than one octave
(including degenerate ones) in either this or the (3,6)1·3·5·7·9·11 Eikosany
is 2494.

>would it be
>possible to make a table of the spaces ordered by the size?

That's not looking like it's going to be easy. Maybe someone familiar with
Delaunay triangulation can help me out.