[PD] tabread4~~

[Charles Henry]

On Nov 23, 2007 10:16 AM, Charles Henry <czhenry at gmail.com> wrote:
> > > I feel absolutely certain that I can convince you that timbre is *not* a
> > > vector space, using only the defining properties of a vector space.
> >
> > Ok, let's do that. How do you prove it?
>
> With another little thought experiment.  If I can't convince you, I'll
> eat my words (yum)

When I look at that previous post, I realize that the
notation/concepts were confusing at the least, and abusive at the
worst.  It's not an easy topic to work with.  A more concrete example:
we could take a trumpt and violin, two instruments with distinct
timbres.  We cannot mix them together as signals to produce a new,
unified timbre.  You would perceive them as a combination of two
timbres, that cannot be condensed into a single instrument, because
they are so distant from one another in timbre.
However, we could deform one instrument to another.  Suppose we had a
good phase unwrap function, unwrap(G(f))
Example:
z(t,a)=ifft(unwrap(X(f))^a*unwrap(Y(f))^(1-a))
Then, we have a way to deform one spectrum into the other. Anyhow, see
what you think...

Chuck