stellation

Is there a good explanation of "stellation" in regard to CPS's somewhere?

The entry in the Tuning Dictionary (taken from the glossary of
"Divisions") is a litle to brief.

What is the n-ad? What is a "facet"?

Thanks for any assistance. . .

***From: Christopher Bailey******************

http://music.columbia.edu/~chris

**********************************************

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:
>
>
> Is there a good explanation of "stellation" in regard to CPS's
somewhere?
>
> The entry in the Tuning Dictionary (taken from the glossary of
> "Divisions") is a litle to brief.
>
> What is the n-ad? What is a "facet"?
>
> Thanks for any assistance. . .

hi chris,

have you read this?

http://sonic-arts.org/td/erlich/paul-cps.htm

please let me know if this doesn't make john's definition crystal
clear.

also you will find many postings in the archives of this list on
these subjects helpful, including those by manuel, john, and carl.

--- In tuning@yahoogroups.com, Christopher Bailey <cb202@c...> wrote:
>
>
> Is there a good explanation of "stellation" in regard to CPS's
somewhere?

The term comes from geometry. Coxeter on polytopes would be a source.

chris, you might also want to check out

http://tunesmithy.netfirms.com/tunes/cps.htm

a search on stellation in these archives brings up a bunch of posts
that don't mention it, for some strange reason . . .

>
> From: Christopher Bailey <cb202@columbia.edu>
> Subject: stellation
>
> Is there a good explanation of "stellation" in regard to CPS's somewhere?

An example works best. if you take a hexany which has it various triads and you complete them as tetrads you have done stellation. In otherwords in any particular CPS set you have your generating set and it mirror (or inversion ) which unfolds in partial expression throughout the CPS structure. Stellation is the process of completing these partial expressions with your master set of generating set or mirror which ever applies.

>
>
> The entry in the Tuning Dictionary (taken from the glossary of
> "Divisions") is a litle to brief.
>
> What is the n-ad? What is a "facet"?

Do not recognize the first term. By Facet, i know only a referance to a lattice. By example again. Starting with the lattice of the eikosany with the center hexad ( which forms a 10 sided object). If you look at the generating hexads, more often than not, it is pictured with the factor 1 in the center. As it is posssible to rotate all these factors how one wishes, each of these permutation shows a different "facet" of the eikosany. In this particular case what one places in the center will have the most influence on using
this lattice in that every dyad will involve this this ratio. In this way a piece like "the creation of the Worlds" will have different versions that expose different "facets" of the structure

>
>
> Thanks for any assistance. . .
>
> ***From: Christopher Bailey******************
>
> http://music.columbia.edu/~chris
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> >
> > From: Christopher Bailey <cb202@c...>
> > Subject: stellation
> >
> > Is there a good explanation of "stellation" in regard to CPS's
somewhere?
>
> An example works best. if you take a hexany which has it various
triads and you complete them as tetrads you have done stellation. In
otherwords in any particular CPS set you have your generating set and
it mirror (or inversion ) which unfolds in partial expression
throughout the CPS structure. Stellation is the process of completing
these partial expressions with your master set of generating set or
mirror which ever applies.
>
> >
> >
> > The entry in the Tuning Dictionary (taken from the glossary of
> > "Divisions") is a litle to brief.
> >
> > What is the n-ad? What is a "facet"?

for the hexany example, each facet is a triad, or an n-ad where n=3.
the generating "chord", or set of factors, for the hexany is actually
a tetrad, or n-ad with n=4. so stellating a hexany means adding a
note to each of the triadic facets so that each becomes a tetrad,
expressing (or mirroring) the original set of factors. hope this is
not too abstract and that the writeups that robert and i put together
help you make sense out of this. if not, i'll be happy to start over
and take it more slowly.

>

>

The hexany maps onto a octohedron with it eight sides, each side or "face" (being a triad) is a "face"t.

>
> From: "wallyesterpaulrus" <wallyesterpaulrus@yahoo.com>
> Subject: Re: stellation
>
> for the hexany example, each facet is a triad, or an n-ad where n=3.
> the generating "chord", or set of factors, for the hexany is actually
> a tetrad, or n-ad with n=4. so stellating a hexany means adding a
> note to each of the triadic facets so that each becomes a tetrad,
> expressing (or mirroring) the original set of factors. hope this is
> not too abstract and that the writeups that robert and i put together
> help you make sense out of this. if not, i'll be happy to start over
> and take it more slowly.
>
>

-- -Kraig Grady
North American Embassy of Anaphoria Island
http://www.anaphoria.com
The Wandering Medicine Show
KXLU 88.9 FM WED 8-9PM PST

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43712.html#43726

<wallyesterpaulrus@y...> wrote:
> chris, you might also want to check out
>
> http://tunesmithy.netfirms.com/tunes/cps.htm
>
> a search on stellation in these archives brings up a bunch of posts
> that don't mention it, for some strange reason . . .

***Monzo has a *short* entry on this that kind makes sense...:

http://sonic-arts.org/dict/stellat.htm

JP

--- In tuning@yahoogroups.com, "wallyesterpaulrus"

/tuning/topicId_43712.html#43738

<wallyesterpaulrus@y...> wrote:
> --- In tuning@yahoogroups.com, Kraig Grady <kraiggrady@a...> wrote:
> > >
> > > From: Christopher Bailey <cb202@c...>
> > > Subject: stellation
> > >
> > > Is there a good explanation of "stellation" in regard to CPS's
> somewhere?
> >
> > An example works best. if you take a hexany which has it various
> triads and you complete them as tetrads you have done stellation.
In
> otherwords in any particular CPS set you have your generating set
and
> it mirror (or inversion ) which unfolds in partial expression
> throughout the CPS structure. Stellation is the process of
completing
> these partial expressions with your master set of generating set
or
> mirror which ever applies.
> >
> > >
> > >
> > > The entry in the Tuning Dictionary (taken from the glossary of
> > > "Divisions") is a litle to brief.
> > >
> > > What is the n-ad? What is a "facet"?
>
> for the hexany example, each facet is a triad, or an n-ad where
n=3.
> the generating "chord", or set of factors, for the hexany is
actually
> a tetrad, or n-ad with n=4. so stellating a hexany means adding a
> note to each of the triadic facets so that each becomes a tetrad,
> expressing (or mirroring) the original set of factors. hope this is
> not too abstract and that the writeups that robert and i put
together
> help you make sense out of this. if not, i'll be happy to start
over
> and take it more slowly.

***I think more needs to be added to the Monzo definition, which is a
bit brief and has no examples...

JP