Re: [tuning] Digest Number 3335

Hi Aaron!
First i have to know exactly which diagram you are referring to. Parallel line in the key below will coincide with the intervals in most of the full eikosany lattices ( there are a few exceptions)
If one is a factor in every other note , it sounds like you are referring to the centered Pentagon lattice. One could place any factor in the middle, say 7 and then every other tone would include 7. using the factor 1 is what separates Erv's work from Eulers, who would use one as a start but not as a product in a full set. It prevented Euler from discovering the hexany. If one preserves the notation ofthe three factors it is much easier to move around the structure and to pick out all the cross relations.
I recommend reading the letter to John Chalmers on this subject

>
>OTOH, I do notice a certain pattern in the rotational symmetry of the 'star' >figure, where for instance, the '1' factor occurs as every other vertex on >the outside, etc. But that seems arbitrary. And wouldn't it be better to do >this diagram with the actual resultant ratios listed, and not the generating >factors, so that we might intuit the pentachords which are formed as a result >of the process?
>
>Kraig? Carl? Monz? Gene? Paul, if you are lurking? Othere experts on Wilson >out there lurking, who I have neglected to mention?
> >-A.
>
> >

--
Kraig Grady
North American Embassy of Anaphoria Island <http://anaphoria.com/>
The Wandering Medicine Show
KXLU <http://www.kxlu.com/main.html> 88.9 FM Wed 8-9 pm Los Angeles

On Friday 03 December 2004 09:40 pm, Kraig Grady wrote:
> Hi Aaron!
> First i have to know exactly which diagram you are referring to.
> Parallel line in the key below will coincide with the intervals in most
> of the full eikosany lattices ( there are a few exceptions)
> If one is a factor in every other note , it sounds like you are
> referring to the centered Pentagon lattice. One could place any factor
> in the middle, say 7 and then every other tone would include 7. using
> the factor 1 is what separates Erv's work from Eulers, who would use one
> as a start but not as a product in a full set. It prevented Euler from
> discovering the hexany. If one preserves the notation ofthe three
> factors it is much easier to move around the structure and to pick out
> all the cross relations.
> I recommend reading the letter to John Chalmers on this subject

Thanks Kraig for your response. All is becoming clear, thanks to you Carl, and
Paul Erlich, who I spoke with on the phone tonight.I will check out the
Chalmers letter, I assume it's on your site?

Incidentally, I am intrigued that Paul told me you are getting into some
non-JI tunings! Anything in particular you are finding attractive or
promising?

All best,
Aaron Krister Johnson
http://www.akjmusic.com
http://www.dividebypi.com

> Thanks Kraig for your response. All is becoming clear,
> thanks to you Carl, and Paul Erlich, who I spoke with
> on the phone tonight. I will check out the Chalmers
> letter, I assume it's on your site?

I do wish Paul would step out of the woodwork and
present his latest tonespace diagrams.

-Carl