Interior product

Added to the Xenwiki: http://xenharmonic.wikispaces.com/Interior+product

On Tue, Nov 22, 2011 at 3:24 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> Added to the Xenwiki: http://xenharmonic.wikispaces.com/Interior+product

Wow, thanks. That makes perfect sense. So then if I want to compute
the interior product of 5-limit meantone ∨ 25/24, the answer is
basically

<meantone∨(2/1∧25/24) meantone∨(3/1∧25/24) meantone∨(5/1∧25/24)]

Right? I can't compute the numbers now, but I think I have that right.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> <meantone∨(2/1∧25/24) meantone∨(3/1∧25/24) meantone∨(5/1∧25/24)]
>
> Right? I can't compute the numbers now, but I think I have that right.

Who knows? It didn't arrive here in readable form.

On Tue, Nov 22, 2011 at 3:59 PM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > <meantone∨(2/1∧25/24) meantone∨(3/1∧25/24) meantone∨(5/1∧25/24)]
>
> >
> > Right? I can't compute the numbers now, but I think I have that right.
>
> Who knows? It didn't arrive here in readable form.

I was trying to use the fancy ASCII glyphs you used on the wiki, but
if ^ is exterior product and v is interior product, then

<meantone v (2/1^25/24) meantone v (3/1^25/24) meantone v (5/1^25/24)]

As in, first I take the wedge product of 2/1 and 25/24, dot product
with the meantone bival, that's the first coefficient, then repeat
with 3/1^25/24 and 5/1^25/24.

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:

> As in, first I take the wedge product of 2/1 and 25/24, dot product
> with the meantone bival, that's the first coefficient, then repeat
> with 3/1^25/24 and 5/1^25/24.

Right. Outputs <7 11 16|.

Woo hoo! I can't believe how many months I wasted not knowing how
simple this was. I'm just going to ask questions here from now on
instead of trying to parse Wikipedia. Thanks for this article.

-Mike

On Wed, Nov 23, 2011 at 6:23 AM, genewardsmith
<genewardsmith@sbcglobal.net> wrote:
>
> --- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> > As in, first I take the wedge product of 2/1 and 25/24, dot product
> > with the meantone bival, that's the first coefficient, then repeat
> > with 3/1^25/24 and 5/1^25/24.
>
> Right. Outputs <7 11 16|.