On Nov 23, 2007 10:16 AM, Charles Henry <[EMAIL PROTECTED]> 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 _______________________________________________ PD-list@iem.at mailing list UNSUBSCRIBE and account-management -> http://lists.puredata.info/listinfo/pd-list
