[tuning] new John Chalmers 19-limit lattice

John Chalmers just emailed me a terrific lattice diagram
he made of the 1.3.5.7.11.13.17.19 Euler genus. I put it
at the bottom of the "John Chalmers Lattice Diagrams" page:

http://www.ixpres.com/interval/chalmers/diagrams.htm

Awesome!

-monz
http://www.monz.org
"All roads lead to n^0"

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> Subject: new John Chalmers 19-limit lattice
>
> http://www.ixpres.com/interval/chalmers/diagrams.htm

Joe, On your website John's comment states "Here's a 7-D
hypercube interpreted as a 19-limit scale with 1/1 in the
middle (and the point 1*3*5*7*11*13*17*19 on top of it)". I
guess this means that in 2-D form these two points simply
overlap, ie. they are not the same pitch. It would be nice
to compare this with Euler Genus model Erv Wilson made at
MicroFest using the zometools. From memory wasn't that an
Euler Genus 1*3*5*7*11*13*15*17 ? It's interesting how a
lattice generated using all-primes and all-primes with one
odd-number can look so radically different. What will that
tell us about the scales ?

Greg S

Greg!
http://www.anaphoria.com/images/euler01.gif
This structure is distinct from the factors one uses. one could replace 1,3,5,7,9,11 with
a,b,c,d,e,f,g and use what you wish. This diagram shows how they these geometric structures
appear.

Greg Schiemer wrote:

> > Subject: new John Chalmers 19-limit lattice
> >
> > http://www.ixpres.com/interval/chalmers/diagrams.htm
>
> Joe, On your website John's comment states "Here's a 7-D
> hypercube interpreted as a 19-limit scale with 1/1 in the
> middle (and the point 1*3*5*7*11*13*17*19 on top of it)". I
> guess this means that in 2-D form these two points simply
> overlap, ie. they are not the same pitch. It would be nice
> to compare this with Euler Genus model Erv Wilson made at
> MicroFest using the zometools. From memory wasn't that an
> Euler Genus 1*3*5*7*11*13*15*17 ? It's interesting how a
> lattice generated using all-primes and all-primes with one
> odd-number can look so radically different. What will that
> tell us about the scales ?

-- Kraig Grady
North American Embassy of Anaphoria island
http://www.anaphoria.com

The Wandering Medicine Show
Wed. 8-9 KXLU 88.9 fm

Hi Greg,

> ----- Original Message -----
> From: Greg Schiemer <gregs@conmusic.usyd.edu.au>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, June 23, 2001 6:03 PM
> Subject: [tuning] Re: new John Chalmers 19-limit lattice
>
>
> > Subject: new John Chalmers 19-limit lattice
> >
> > http://www.ixpres.com/interval/chalmers/diagrams.htm
>
> Joe, On your website John's comment states "Here's a 7-D
> hypercube interpreted as a 19-limit scale with 1/1 in the
> middle (and the point 1*3*5*7*11*13*17*19 on top of it)". I
> guess this means that in 2-D form these two points simply
> overlap, ie. they are not the same pitch.

Right, that's what I took it to mean. John?

> ... It would be nice
> to compare this with Euler Genus model Erv Wilson made at
> MicroFest using the zometools. From memory wasn't that an
> Euler Genus 1*3*5*7*11*13*15*17 ?

Hmmm... your memory about that is a lot better than mine.

> ... It's interesting how a
> lattice generated using all-primes and all-primes with one
> odd-number can look so radically different. What will that
> tell us about the scales ?

Well, I *think* this makes sense to me. The "one odd-number"
is going to be composed of two or more of the primes, so it
will not introduce another dimension, whereas the lattice with
all primes is going to have a unique dimension for every prime.

I dunno... I could be making a mistake here, because Erv's
lattices frequently have separate dimensions for all the
*odd* numbers, don't they?...

(I really hope that one of these days I can sit down for
a few months with the Complete Writings of Erv Wilson, and
do nothing else but study them until I understand it all...)

-monz
http://www.monz.org
"All roads lead to n^0"

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Get your free @yahoo.com address at http://mail.yahoo.com

> ----- Original Message -----
> From: monz <joemonz@yahoo.com>
> To: <tuning@yahoogroups.com>
> Sent: Saturday, June 23, 2001 10:49 PM
> Subject: Re: [tuning] Re: new John Chalmers 19-limit lattice
>
>
> ... The "one odd-number"
> is going to be composed of two or more of the primes,

Oops... my bad. Of course, some odd-numbers are made
up of only *one* prime, multiplied by itself various
numbers of times. I.e., 9 = 3^2, 27 = 3^3, 25 = 5^2, etc.

-monz
http://www.monz.org
"All roads lead to n^0"

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--- In tuning@y..., "Greg Schiemer" <gregs@c...> wrote:

> It's interesting how a
> lattice generated using all-primes and all-primes with one
> odd-number can look so radically different.

It depends how you construct the lattice. Erv Wilson often gives
composite odd numbers their own distinct axes, which can sometimes
make the musical relationships clearer.

> > ... It would be nice
> > to compare this with Euler Genus model Erv Wilson made
> at
> > MicroFest using the zometools. From memory wasn't that
> an
> > Euler Genus 1*3*5*7*11*13*15*17 ?
>
> Hmmm... your memory about that is a lot better than mine.

Jo,

It's only my memory so I wouldn't hang too much on that. So
I hope I'm not putting words into Erv's mouth here. I
couldn't check this at the time as my copy of his handout is
in a file at work.

> I dunno... I could be making a mistake here, because
> Erv's
> lattices frequently have separate dimensions for all the
> *odd* numbers, don't they?...
>

I hope this is not a question for me as I don't really know
either. If only more would acknowledge what they don't
understand !

> (I really hope that one of these days I can sit down for
> a few months with the Complete Writings of Erv Wilson,
> and
> do nothing else but study them until I understand it
> all...)

Yeah. Me too!! Incidentally, several of my students find
your website a fantastic source of information particularly
on lattices. And I too will use it, along with
anaphoria.com, as I attempt to get my head around his
theories.

Greg S

Paul Erlich wrote:

> It depends how you construct the lattice. Erv Wilson often gives
> composite odd numbers their own distinct axes, which can sometimes
> make the musical relationships clearer.
>

Paul,

Exactly!

GZ