| Morphing
Given 2 soundfiles, S1 and S2. There is a unique transformation function
, T, such that
S1 x T = S2 (1)
T can simply be derived:
T = S2 / S1
This means that any soundfile can be converted to any other soundfile.
Given an appropriate T function The Black Dog's "Spanners" can be
converted into Stravinsky's "Requiem Canticles" using a process of
multplication. (Copyrighters could go crazy on this one).
There must be a function, Tm ,that will create a soundfile Sm, that is
part way between S2 and S3. So, if
S1 x T1 = S2, and
S1 x T2 = S3
maybe Tm = (k x T1) + ( (1-k) x T2). So
S1 x Tm = Sm
If k was a linear function between 0 and 1, then we would have a morph
right?
I implemented this a few years ago, in Csound and in C. Turns out that
the resultant "morph" is just a straight mix of the 2 soundfiles :-(
I hoped that by fiddling with Tm (or substituting S1) I could create new
soundfile variants. It turns out that T is VERY sensitive to
modifications - you can easily get samples wildly out of range or a lot
of noise.
Any comments? A mathematically literate friend has told me that in (1)
the spectrum of S2 is the convolution of the spectra of S1 and T.
Practical or not, transformationists may enjoy the knowledge that any
sound can be derived or converted into any other. And you don't even
have to hear that to appreciate the elegance. |