RE: [tuning] Re: Triadic topography

Joseph Pehrson wrote,

>http://www.egroups.com/message/tuning/14282
>That's a great graphic, Paul. Now if we could only combine that with
>the kind of 3-dimensional stuff that Jon Wild has been doing, we'd
>have a great masterwork!

Done: http://www.egroups.com/files/tuning/terrain/waves.jpg. I decided that
for this dyadic model, much more detail would be visible if consonance
corresponded to mountains and dissonance corresponded to depressions. Since
we are just summing the dyadic concordance values, there is a noticeable
ridge corresponding to each consonant interval, and peaks on each ridge
where the other two intervals in the triad are consonant. Also, because we
are summing, mathematically the surface is equivalent to what would happen
if we had three linear wave patterns, corresponding to each of the dyadic
concordance functions, with wave fronts parallel to the corresponding side
of triangle. So I chose a blue-green colormap to make the picture more
suggestive of waves.

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/146

Wow! This is the best graphic I've seen yet! Now were cooking with
entropy!
__________ ___ __ _
Joseph Pehrson

Joseph wrote,

>Wow! This is the best graphic I've seen yet! Now were cooking with
>entropy!

Thanks.

Joseph, can you identify which interval each wave front corresponds to, and
which chords happen where they intersect?

It would be nice to have a Java applet where a little "surfer" cruises these
waves and plays the triad corresponding to whatever point he's at.

I've redone http://www.egroups.com/files/tuning/terrain/waves.jpg to use the
same color scheme as
http://www.egroups.com/files/tuning/perlich/triangle_01.jpg, for easier
reference. Now the poor surfer will be in a pool of liquid acid, but oh
well.

--- In harmonic_entropy@egroups.com, "Paul H. Erlich" <PERLICH@A...>
wrote:

http://www.egroups.com/message/harmonic_entropy/148

>
> Joseph, can you identify which interval each wave front corresponds
to, and which chords happen where they intersect?
>

Well, this would be a good exercise! I would guess I could try to
place some of the labeled intersections from the 2-D "snowflake."
That would be a good way to proceed, yes??
___________ _____ __
Joseph Pehrson

--- In harmonic_entropy@egroups.com, "Joseph Pehrson" <pehrson@p...>
>
> Well, this would be a good exercise! I would guess I could try to
> place some of the labeled intersections from the 2-D "snowflake."
> That would be a good way to proceed, yes??

Yes, or even better, look at the colored "triangle_01" file.

> Joseph, can you identify which interval each wave front corresponds
to, and
> which chords happen where they intersect?

I've taken a stab at this, on the triangle_01 pic. I labeled 6
additional triads in white, in order to distinguish them, and
uploaded it to:

http://www.egroups.com/files/harmonic_entropy/Finnamore/triangle_01dfi
nn_01.jpg

How'd I do, Teach'?

David Finnamore

Doh! It broke the link. I'll try it without word wrap checked this
time. 8>/

http://www.egroups.com/files/harmonic_entropy/Finnamore/triangle_01dfi
nn_01.jpg

If it's still broken, I guess we'll have to copy and paste the thing
together in the address field.

--- In harmonic_entropy@egroups.com, "David Finnamore" <daeron@b...>
wrote:

> How'd I do, Teach'?

You did great -- even at matching the font. You solved
this "crosschord puzzle".

--- In harmonic_entropy@egroups.com, "Paul Erlich" <PERLICH@A...>
wrote:
> --- In harmonic_entropy@egroups.com, "David Finnamore"
<daeron@b...>
> wrote:
>
> > How'd I do, Teach'?
>
> You did great -- even at matching the font. You solved
> this "crosschord puzzle".

Duh. I'm not getting it. I'm glad David did this rather than me,
for that reason... Sorry to be getting behind, but WHAT's going on
here with the 2-D pizza slice again??