Behaviour, Structure and Causality in Procedural Audio - Game Sound Technology and Player Interaction: Concepts and Developments - page 331

artistic direction, as Randy Thom likes to remind
us, the narrative is paramount. Knowing this, such
insight can equally be applied to the performance
of a synthetic model. In Vicario's (2001) example
it is not until further sensible data is obtained that
an identification error is revealed. The apparent
sound of rain on the window is experienced as
rain until the curtain is drawn back to reveal a
cloudless sky and leaves brushing against the
window in a breeze.
Let's turn to the physical domain now, and we
can see the source of the confusion. A motorbike
and a tuba share much in common, with a long
tubular exhaust system driven by acoustic pulses.
Any source, whatever its mechanism, that happens
to coincide with the spectrum of the motorbike
will, when taken entirely in isolation as a static
spectrum, be a motorbike. The moment of truth
comes when we attempt to move one of the gen-
erative parameters. The error, that a correct causal
model (in terms of structure and scale) exists, is
revealed. Structure is wrong for all other points in
the behavioural parameter space. As soon as the
pitch speeds up, the motorbike transforms into a
tuba again and the deception is exposed.
We can almost always find isolated matches to
static examples. That is to say, given an arbitrary
synthesiser with a small number of arbitrary pa-
rameters and a timbre space that includes the target
sound, there are successful methods of converging
on the parameter set necessary to mimic the target
(Yee-King & Roth, 2008) One of the fascinating
things about the system of Yee-King and Roth,
which uses genetic algorithms to approach the best
approximation for a given time domain example,
is that it can find unlikely candidates within the
timbre space. It can find islands that are entirely
brittle and bear no resemblance to the target
sound. One question I have put to Roth (with
whom I currently share a laboratory) is whether,
given a structurally and causally well-formed
trumpet model and a target snapshot of a trumpet
note, the system would converge on a parameter
set congruent with the performance space of the

trumpet. I strongly suspect the answer is no (given
just one example). Roth agrees, but suggests that
convergent parameter estimation may work for
higher dimensional performance spaces too and
that given two or more examples of trumpet notes,
and thus the ability to form lines then planes within
the performance parameter space, it would do so.
Indeed, this is what we would expect of such a
multi-dimensional adaptive system. We call them
neural networks. It's what the brain of a musician
does while learning to play an instrument.

Parameters and Performance

Let's distinguish time invariant or fixed parameters
from behavioural parameters. These parameters
for a particular piano note are generally taken as
fixed within the duration/lifetime of that sound
(although they may themselves have time vari-
ance such as envelope settings). In music we
sometimes call the behavioural parameters the
performance setup, for instance pedal pressure
or keyboard scaling. These describe how higher
order parameter changes affect each note or each
instance of a sound. The fixed parameters would
be the oscillator levels, filter settings and such-
like, while the behavioural parameters are those
that change during performance. A well-formed
parameter space provides a behaviour captured
by the fewest salient variables while allowing
the greatest sensible range. For a piano, it's how
hard you hit the key. That's all, no need to alter
the weight per unit length of the string or the
size of the sound board. A pianist doesn't need
to know that. It interfaces to the performance use
case giving no more or less control than required.
Imagine if a piano offered an array of levers for
string tension and hammer hardness that had to
be set up before pressing each note!
A model for raindrops offering ten filter values
at its interface would be less useful than one offer-
ing only two relevant controls for size and velocity,
provided that the size and velocity controls work
over a proper range of values. Part of the work