Why are lists of vals often surrounded by a ket vector?

For example, meantone is [<1 1 0], <0 1 4]>. Why the [ > on the outside?

-Mike

--- In tuning-math@yahoogroups.com, Mike Battaglia <battaglia01@...> wrote:
>
> For example, meantone is [<1 1 0], <0 1 4]>. Why the [ > on the outside?
>
> -Mike
>

The experts will correct me if I am wrong but i believe that it merely makes the resultant vector a ket, in toto. I mean it has to be something (my ital.), right?

pgh

Mike Battaglia <battaglia01@gmail.com> wrote:
> For example, meantone is [<1 1 0], <0 1 4]>. Why the
> [ > on the outside?

It shows you have a matrix that transforms one set of
coordinates into another. The matrix itself doesn't have
interval-ness or val-ness.

If you multiply by [-1 1 0>, the vector for a perfect
fifth, you get

[<1 1 0], <0 1 4]>[-1 1 0>
= [<1 1 0|-1 1 0>, <0 1 4|-1 1 0>>
= [0, 1>

Which is the interval of a perfect fifth in terms of the
period and generator, and so looks like an interval.

Graham

Ah, OK. Thanks.
-Mike

On Tue, Sep 20, 2011 at 5:33 AM, Graham Breed <gbreed@gmail.com> wrote:
>
> Mike Battaglia <battaglia01@gmail.com> wrote:
> > For example, meantone is [<1 1 0], <0 1 4]>. Why the
> > [ > on the outside?
>
> It shows you have a matrix that transforms one set of
> coordinates into another. The matrix itself doesn't have
> interval-ness or val-ness.
>
> If you multiply by [-1 1 0>, the vector for a perfect
> fifth, you get
>
> [<1 1 0], <0 1 4]>[-1 1 0>
> = [<1 1 0|-1 1 0>, <0 1 4|-1 1 0>>
> = [0, 1>
>
> Which is the interval of a perfect fifth in terms of the
> period and generator, and so looks like an interval.
>
> Graham