On Fri, 23 Nov 2007, Charles Henry wrote:
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.
This is because you have trained yourself to recognise the violin, and you
have trained yourself to recognise the trumpet. There is nothing inherent
to the timbre that enables you to say that. There is not even something
that you can find in one spectrum to tell whether it is a single note or
several of them -- you can only guess, and some spectra may look more
"chordish", but still any spectrum can be considered as a possibly
infinite number of sine wave instruments played at once.
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...
There are two definitions of timbre in use: one that is equivalent to
spectrum, and one which is everything except amplitude and frequency, the
latter of which can include the evolution of the relative spectrum of a
note over time, as well as the envelope of the amplitude, etc. This makes
a lot more details that you can train yourself with, and makes it easier
to distinguish two sounds.
There is no way you can play a single note that glides from a timbre
(of the latter kind) to another and retain the full characteristics
of both. It will only keep the attack of the first timbre, and as the
attacks tend to be more special than the rest of the spectra, it's much
more difficult to recognise the second timbre (of the latter kind).
For plain spectra (timbres of the first kind), I fully understand what you
mean, though 0^anything is pretty much nothing at all, and just as much if
you multiply it with anything else, and furthermore, Jethro Tull has
computed that one white duck divided by 0^10 is also nothing at all.
Somehow, you can't ramp decibels linearly (raw amplitudes exponentially)
from minus infinity to anything, so, you will have to give up on that and
find something else, like ramping raw amplitudes linearly or according to
phons or another kind of pseudo-log.
_ _ __ ___ _____ ________ _____________ _____________________ ...
| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada
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