new Chalmers/Monzo lattices

[Keenan:]
> Chalmers lattices dont do anything for me I'm afraid.
> Bending to show pitch radially loses too much other info
> for my liking.

Dave is referring to 5 webpages of new lattices which begin at:
http://www.ixpres.com/interval/monzo/w-jchalm/1999-3-29/oc-red1.htm

Well... I'll have to take the brunt of the criticism here.

John Chalmers did the calculating and plotting,
but those lattices are actually based on some ideas
I had about a month ago.

(John even changed the name of his 'New Chalmers Plot'
to 'Doubly Proportional Monzo Plot', so when you see
NCP and DPMP on the webpages, they refer to the same method.)

They didn't turn out anything like what I had expected.

I got the idea one day to make the vector-lengths of
all the different primes give the same radial distance
from 1/1, to show the cents value of the ratios/lattice-points
on the same scale for all the primes.

After I had mentioned that idea to Chalmers, I had another
idea to octave-reduce the whole lattice.

I tried drawing both of these by hand, but without
doing calculatons and without using rulers, protractors, etc.
Needless to say, they came out looking horrible.

I thought that it would be fairly straightforward to
get someone conversant with the math (Chalmers) to
plot them on a computer, and these are the result.

John has mentioned to me the idea of actually putting
those webpages and commentary together in a coherent
manner, but I don't think I can do it. I leave it for him.
Or anyone else who understands what he did (perhaps you?)

Actually, because I don't fully understand how he did them,
I'm not even sure how well they represent what I orignally
thought of. I *think* we're both on the same track,
but not completely sure.

I had imagined that the lattices would more-or-less
retain the familiar shape that my 'regular' ones have.
I never expected them to have such weird angles.
But then again, I know absolutely nothing about trigonometry.

The one I called '7-Limit Diamond,
Scaled Proportional Monzo Plot', at:
http://www.ixpres.com/interval/monzo/w-jchalm/1999-4-7/message2/transitio
nal-lattices.htm
is pretty close to what I originally drew.

It's not so easy to know what's happening without data
labels either. I'll try to remedy that when I have time.

-monz

Joseph L. Monzo....................monz@juno.com
http://www.ixpres.com/interval/monzo/homepage.html

|"...I had broken thru the lattice barrier..."|
| - Erv Wilson |

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