Yahoo has been bouncing my messages back to me lately.

i'm trying this one again.

-monz

----- Original Message -----

From: "monz" <monz@attglobal.net>

To: <tuning-math@yahoogroups.com>

Sent: Friday, October 18, 2002 1:37 AM

Subject: Re: [tuning-math] Re: mathematical model of torsion-block symmetry?

> hi Gene,

>

> > From: "Gene Ward Smith" <genewardsmith@juno.com>

> > To: <tuning-math@yahoogroups.com>

> > Sent: Tuesday, October 15, 2002 8:27 PM

> > Subject: [tuning-math] Re: mathematical model of torsion-block symmetry?

> >

> >

> > --- In tuning-math@y..., "Hans Straub" <straub@d...> wrote:

> >

> > > > > Now, the quotient module being finite...

> > > >

> > > > Whups--you are sticking "2" into the mix when you conclude this.

> > > > The math is more straightforward if you treat 2 as just another

prime

> number.

> > > >

> > >

> > > 2 is just another prime number, sure - but where exactly do you think

I

> > > confuse something?

> >

> > Monzo's example was the block defined by 2048/2025 and 648/625;

> > if we mod out the free group on three generators {2,3,5} by the

> > subgroup defined by the above, we produce a mapping onto Z x Z/2Z.

> > This has a nontrivial torsion part, so the block is a torsion block.

> >

> > Using wedge products, which in the 5-limit we can identify with

> > the cross-product, we have 2048/2025 ^ 648/625 = [11 -4 -2] ^ [3 4 -4] =

> > [24 38 56] = 2 * [12 19 28], showing the 2-torsion. For this to work,

> > the vectors need to be defined using the 2; Monzo unfortunately left

> > this off and the page should be changed.

>

>

>

> hmmm ... somewhere on this list, about a month or two back, you

> wrote a post explaining how to do the wedgie, and i had set up

> a spreadsheet to do the calculation according to your formula.

> the answer i just got for this one was: [0 0 24 56 -38 0].

>

>

> regarding the webpage:

> /tuning-math/files/dict/torsion.htm

>

> ... not really knowing how to edit down what i already have

> in the "torsion" definition, which is now quite confusing to me,

> i simply added the above quote to the bottom of the "real"

> definition (around the middle of the page).

>

> Gene, is there any way that you could edit this mess into

> one good solid definition? perhaps with commentary after

> it, but *useful* commentary?

>

>

>

> -monz

>

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