Why wedge products?

If you take the minors of the matrix constructed by stacking two
5-limit vals on top of one another, and then you take the result and
flip it sideways, and also invert the sign of the middle number, you
can turn two vals into a comma or two commas into a val. Therefore,
this random procedure that I had coded to check for torsion is
actually checking to see if you've tempered out the square of a comma
(or cube, etc) instead of the comma itself. The whole thing is
apparently related to something called Grassmann algebra, according to
Wikipedia. Why does this work?

Can you turn one val into two commas this way, somehow?

-Mike

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

> Can you turn one val into two commas this way, somehow?

I've been thinking of adding a section to this page:

http://xenharmonic.wikispaces.com/Abstract+regular+temperament

on how you can translate between these various ways of denoting an abstract regular temperament. Don't know if that would help, but if you convert the val method of denoting a rank one temperament to commas, you of course get commas. Trouble is, for a p-limit val you get pi(p)-1 commas; in general rank n means pi(p)-n commas.