Re: [tuning-math] "The hypothesis" from a wedge product point of view

Okay, I've been waiting for this one... now, could somebody, maybe
somebody other than Gene, say the same thing and give some examples
*slowly*!

thanks,

--Dan Stearns

----- Original Message -----
From: "genewardsmith" <genewardsmith@juno.com>
To: <tuning-math@yahoogroups.com>
Sent: Wednesday, June 05, 2002 5:41 AM
Subject: [tuning-math] "The hypothesis" from a wedge product point of
view

> In the prime limit with k primes, take k commas in order from
largest to smallest,[c1, c2, ... , ck], defining a square matrix with
determinant +-1 (i.e., a "notation".) Leave off c1 and wedge the rest,
and you have a val "h" defining an et mapping, corresponding to a
Fokker block with h(2) notes to the octave. Suppose h linearly orders
the block; then leave off *both* c1 and c2 and wedge the rest, and you
have a linear temperament, which when applied to the block gives (when
the period is an octave) n contiguous
> (in the sense of the generator of the temperament) notes of a MOS,
and similarly with periods which are a fraction of an octave.
>
>
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--- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:

> Okay, I've been waiting for this one... now, could somebody, maybe
> somebody other than Gene, say the same thing and give some examples
> *slowly*!
>
>
> thanks,
>
> --Dan Stearns

i wish i could. unfortunately i haven't had the time to assimilate
the whole wedge product business. i'm pretty sure graham breed and
dave keenan have a handle on it. i'd say dave keenan might be the
best candidate to study gene's work here and translate it into a form
lots of us (especially people like you and me, who are familiar with
dave's language at least) could understand and visualize (i'm
thinking of dave's skill with graphics and diagrams) . . .

--- In tuning-math@y..., "emotionaljourney22" <paul@s...> wrote:
> --- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:
>
> > Okay, I've been waiting for this one... now, could somebody, maybe
> > somebody other than Gene, say the same thing and give some
examples
> > *slowly*!
> >
> >
> > thanks,
> >
> > --Dan Stearns
>
> i wish i could. unfortunately i haven't had the time to assimilate
> the whole wedge product business. i'm pretty sure graham breed and
> dave keenan have a handle on it. i'd say dave keenan might be the
> best candidate to study gene's work here and translate it into a
form
> lots of us (especially people like you and me, who are familiar with
> dave's language at least) could understand and visualize (i'm
> thinking of dave's skill with graphics and diagrams) . . .

Whew! That's flattering, but I don't have the time right now (end of
semester marking), but anyone who would hope to understand even my
explanation should first learn what the wedge product (a.k.a exterior
product) is all about, from another Australian, John Browne.

Gene found this excellent introduction some time ago. See the thread
starting at
/tuning-math/message/3754
or go straight to
http://www.ses.swin.edu.au/homes/browne/grassmannalgebra/book/
You might only need to read the first 6 pages of the introduction, to
get what it's all about.

--- In tuning-math@y..., "D.Stearns" <STEARNS@C...> wrote:

> Okay, I've been waiting for this one... now, could somebody, maybe
> somebody other than Gene, say the same thing and give some examples
> *slowly*!

I cancelled that about five minutes after posting, and I don't think it's a very good place to start. I'm thinking about how to remove the errors and get the basic idea to work, but I'm not there.