RE: color plots

On Tue, 10 Oct 2000, Paul H. Erlich wrote:

> The color one is all yellow, with red points for major triads and blue
> points for minor triads. I did announce that.

I meant this one, which I just came across by accident without having seen
it before: http://www.egroups.com/files/tuning/enttriad.jpg

I misread the date on the file and thought it had just been posted this
weekend.

I can't figure out why there's a minimum at 9:12:16 (498,498) which looks
at least as important as, say, the one at 3:4:5. Is the interval between
the outer voices also taken into account into your calculation?

> Please, let's keep this discussion on the harmonic entropy list. I look
> forward to continuing discussions with you there.
>
> -Paul
>
> -----Original Message-----
> From: jon wild [mailto:wild@...]
> Sent: Tuesday, October 10, 2000 4:33 PM
> To: Paul H. Erlich
> Subject: color plots
>
>
> Hey - have your colour triadic entropy plots in the files area been
> announced on the list yet, and I missed it? I just downloaded them, they
[snip]

Hi Jon.

That file (http://www.egroups.com/files/tuning/enttriad.jpg) was calculated
using the Farey-series based harmonic entropy. The outer interval is taken
into consideration, but there is a downward slop on the Farey-based curve,
making wider intervals look more consonant than narrow intervals with equal
ratio-complexity. Thus, since the 9:12:16 has wider intervals than 3:4:5 but
the three intervals are comparable in complexity, 9:12:16 gets at least as
low a total dyadic entropy value as 3:4:5.

I should redo this using (a) the Tenney-based rather than Farey-based dyadic
h.e., and (b) the triagular rather than square plot.

Paul.