czhenry at gmail.com
Fri Nov 23 21:22:12 CET 2007
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))
Then, we have a way to deform one spectrum into the other. Anyhow, see
what you think...
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