[PD] tabread4~~

[Mathieu Bouchard]

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.

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| Mathieu Bouchard - tél:+1.514.383.3801, Montréal QC Canada