distorted lattices

> Chalmers lattices dont do anything for me I'm afraid.
> Bending to show pitch radially loses too much other
> info for my liking.
>
> However, these prompted me to draw (by hand) a similar
> distorted lattice for Lumma's scale...<snip>
>
> It is much easier to understand it as a periodic
> (i.e. repeating) 3D lattice...<big snip>

Hey Dave, I was just reading this again and realized
that you were tossing something out here and hoping,
in addition to whomever else's, to also get my feedback.

I've been really busy working on website pages and
the Euler, and on my software, but I've just gotten
over two huge hurdles in the same day on that,
so I can relax a bit.

Your whole post was interesting, as was Paul's response,
but it was that comment you made about the periodic tiling
of the 3D lattice that really got me thinking.

My ears and my years of composing, playing,
writing about, and listening to music tell me
that the kind of tetrahedral lattices we usually
use here to portray tuning systems does not
represent enough of what I'm hearing in the music.

The unique vector-lengths and angles I use in
my diagrams give me the ability to portray multiple
dimensions, which is how I think we relate to
harmonic pitch information, possibly melodic too.

But then, on the other hand . . .

In numerous arguments with Paul Erlich I've had
to concede that the evidence was on his side,
and what he mainly refutes is exactly what I talked
about above.

Also, the 'direct lattice connections' I've
been talking about (see TD 132) seem to refute my
prime-factor theories to some extent.

Maybe what I'll learn after making my lattices
more and more complex is, finally, that the
reason we humans impose finity on the musical
systems in the first place is because we just have
too much of a problem conceiving of and understanding
a spatial relationship that is more than 3-dimensional.

But I don't think so.

I think a really imaginative approach to graphing
pitch relationships will aid in our understanding
of the questions we pursue in this forum.

Certainly, the tetrahedral lattices are important, too.
They may be more important.

But I've been thinking of so many wild and varied ways
to graph pitch that there may end up being something in
it anyway. Who knows? - maybe those unusual lattices
John Chalmers made recently fit together like Mandelbrot
pieces. Maybe Mandelbrot shapes are the ones that
ultimately graph music the best.

As I begin to imagine the kinds of lattice-graphing
my software will do, I can picture something like the
light-show at a Hendrix concert.

(I bet Sarn's gonna resond to that one...)

-monz

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html
|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |
--------------------------------------------------

___________________________________________________________________
You don't need to buy Internet access to use free Internet e-mail.
Get completely free e-mail from Juno at http://www.juno.com/getjuno.html
or call Juno at (800) 654-JUNO [654-5866]

Joe Monzo wrote,

>My ears and my years of composing, playing,
>writing about, and listening to music tell me
>that the kind of tetrahedral lattices we usually
>use here to portray tuning systems does not
>represent enough of what I'm hearing in the music.
>
>The unique vector-lengths and angles I use in
>my diagrams give me the ability to portray multiple
>dimensions, which is how I think we relate to
>harmonic pitch information, possibly melodic too.

Joe, there's nothing to prevent you from using unique vector-lengths and
angles in the triangular lattices (a better term than tetrahedral, since the
3-d triangular lattice is filled with both tetrahedra _and_ octahedra, and
the higher-dimensional triangular lattices have higher-dimensional figures).
As you may recall from our discussions on Erv Wilson's diagrams when you
came over, they started out as triangular lattices with many identical
angles, but then Erv distorted the angles slightly so that the resulting
plots would look more three-dimensional. I independently came to the same
approach in my paper (http://www-math.cudenver.edu/~jstarret/22ALL.pdf, pp.
29-31), where I show a tetrahedral lattice as it would appear if rotated 1
degree from the plane of projection (mentioned on p. 21), resulting in
slightly distorted angles and clearer 3-d visualization. Giving the
different vectors radically different lengths was the topic of recent
discussions here between Paul H., Carl, and me. The reason Graham, Dave,
Carl, Paul H. and I don't do these things when we draw lattices here is
simple: ASCII. As for melodic information, Canright's approach can work with
either of our methods to show interval sizes.

> Who knows? - maybe those unusual lattices
>John Chalmers made recently fit together like Mandelbrot
>pieces. Maybe Mandelbrot shapes are the ones that
>ultimately graph music the best.

What are Mandelbrot pieces and Mandelbrot shapes? Mandelbrot is the fractal
guy -- maybe youre thinking of Penrose? In that case, Chalmers' lattices are
not going to do it, but Erv Wilson has already created pitch systems based
on Penrose tilings in his approach.