3-D representation of 7-limit JI

Hi all,
I've been working on a project to see the relationships between 5-
limit JI and 12-eT - and thought you might be interested in this:
http://www.skytopia.com/project/scale/ji5.html

I think I might have already seen a few diagrams which displayed 5-
limit as a 2 dimensional picture, but not the comparison bit. Notice
the blue-orange-white bars in the picture; this represents how close
the pitch is to the nearest 12-eT equivalent. I find it interesting
how the diagonal from top-left to bottom-right is 'close' (almost all
5 bars), while the diagonal from bottom-left to top-right is 'far'
from 12-equal (almost 0 bars).
What would the diagram look like if I used more iterations?

Then I thought of an idea to repesent 7-limit in a 3 dimensional cube
(or even 9-limit in 4 dimensions). Has this ever been done before?
If so, then I would be very interested to see the comparison with 12-
eT in the same implementation as the above picture.

Finally, and on a different topic, does anyone know of a utility to
convert an MP3 or wav from 12-eT temperament to 3 or 5 limit JI (or
vice versa).
Perhaps such a program would need to 'seperate' all the instruments,
tune them slightly, and then recombine them. Or perhaps all it would
need to do is perform a 'frequency sweep' and change the mp3/wav on
the fly. Any thoughts?

Cheers,
Daniel
http://www.skytopia.com

--- In tuning@yahoogroups.com, "Daniel White" <soundburst@l...> wrote:

>
> Then I thought of an idea to repesent 7-limit in a 3 dimensional
> (or even 9-limit in 4 dimensions). Has this ever been done before?

yes, such pictures are called lattices around here and you'll find
them littering the archives and files folder of this list. there have
probably been more 3-dimensional, 7-limit lattices posted on this
list than people who ever have, and ever will, read it.