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are all psychoacoustic sound design tricks that
work at the sensation or perceptual level. They
are stock tricks known to sound designers rather
than features of a well-modelled reality.
computer graphics (in procedural geometry and
textures) and will certainly yield new audio syn-
thesis methods in time. In some cases they seem
to accord with natural processes in an uncanny
way. In practice, exact relations to clearly stated
and understood natural processes are often open
mathematical questions. Many operate on the
coarse-grained, emergent level, which is not to
say purely aleatoric/stochastic. Contrast this with
the precision of the wave equation methods. For
this reason there is some overlap in use with the
phenomenal approach (it works but we don't care
why), though their ideologies are different.
Metaphysical (Purely Abstract)
The metaphysicists would have it that there is a
deeper order lying behind even the hard essen-
tialist position, that ultimately mathematics alone
can provide what we need, often from simple and
elegant roots. The seductive idea that a formula
can fall out the air to replace thousands of cycles
of computation provokes intense debate. This
ranges from comparatively concrete, order await-
ing discovery (within geometry and topology with
the effect of furthering understanding of signals),
from the “bigger things” of which Gauss (1882)
speaks, or Feynman's “chequer board”, to the
frankly mystical. If our bouncing ball can obtain
a shortcut to spherical modes by Riemann, and
a handy computable identity leading to a fast
way of making struck solid sphere sounds, that's
wonderful progress. Maybe things turn out to be
simple in the end. My bet is that we'll need to
work hard for results for a lot longer yet.
But elegant formulas don't always give el-
egant methods. The arbiter is computability: not
mathematics but, to the extent our Von Neumann
machines are able; algorithmic complexity.
Waveguide and finite difference methods may
be expensive, but they are reliable and provable.
When stability becomes an issue in such systems,
at least they are able to assert good behaviour for
proper conditions. A series that converges too
slowly, grows too fast for a set of variables, or has
too many expensive terms might never match a
crude bunch of heuristics stored in a lookup table
in terms of reliability. Ideas of innateness, intrinsic
order and Platonic truths give promise of natural
models with little computational work. They
include self similar fractal geometry, L-systems,
cellular and genetic autonoma, recursive noise,
and chaotic systems. All have all found use in
Pragmatic
A pragmatic stance admits all of the above think-
ing, using every tool in the box to achieve a goal.
Bringing together all of the above, but without
insistence on purity of method or on some over-
arching ideology. This requires the synthesist
to understand at least a little of each and their
relationships. What influences adherence to one
or another way of thinking are the constraints
imposed by a production context. For animation
and movies, one may, in the spirit of Takala &
Hahn (1992), prefer to adopt full-blown physical
modelling with the luxury of powerful computers,
plentiful budgets, and an offline deadline . On
the other hand, an embedded musical greetings
card may harness unusual, shallow processes
like shift register composition and direct binary
instruction (Miranda, 2002) to create useful sound
with negligible CPU cost/complexity. Computer
games, for the next decade will probably exploit
procedural audio techniques with a behavioural
slant towards signal/parametric methods, with es-
sential/source methods appearing as cost allows.
It will be driven by the need for a compromise
between deep process and efficient code that may
run in real-time. Open frameworks that allow
artists to play with cheap, mixed methods, and
allow programmers to re-write methods are likely
to be the most successful rather than any grand
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