9

To model a drum sound, for example, the following aspects would need to be taken into
account. Of primary importance would be the actual drum strike—how hard it is and
whether the drumhead is struck with a wooden stick, a mallet, a beater, and so on. The
properties of the drumhead (the skin or membrane) would include the kind of material,
its degree of stiffness, its density, its diameter, and the way it is attached to the shell of
the drum. The volume of the drum cylinder itself, its material, and the resonance
characteristics of all of the above would need to be mathematically described.
To model a violin, you’d need to take into account the bow against the string, the
bow-width and material, the bow tension, the string material, the string density, the string
tension, the resonance and damping behavior of the strings, the transfer of string
vibrations through the bridge (materials, size, and shape of the bridge), and the materials,
size and resonance characteristics of the violin body. Further considerations would include
the environment that your modeled violin is played in, and the playing style-“hammering”
or tapping with the bow as opposed to drawing it across the strings.
Logic Express includes Ultrabeat, a drum synthesizer that incorporates physical modelling
components.
Wavetable, Vector, and Linear Arithmetic (LA) Synthesis
Wavetable synthesis uses a number of different single-cycle waveforms, laid out in what
is known as a wavetable.
Playing a note on the keyboard triggers a predetermined sequence of waves. In general,
this is not a stepped transition but rather a smooth blend from one waveform into another,
resulting in a constantly evolving waveform. Multiple wavetables can also be used
simultaneously—either played one after the other, or blended together—resulting in
more harmonically complex waveforms.
A single wavetable can emulate filter cutoff with a series of bright, less bright, then
dull-sounding waveforms played in sequence—which resembles a reduction of the filter
cutoff frequency in a subtractive synthesizer.
Wavetable synthesis isn’t particularly successful at emulating acoustic instruments. It is,
however, extremely successful at producing constantly evolving sounds; harsh and
metallic, or bell-like sounds; punchy basses; and other digital tones.
Wavetable synthesis was championed by the PPG and Waldorf instruments. The ES2 also
includes wavetable facilities.
Roland LA (Linear Arithmetic) synthesizers such as the D-50 work on a similar principle.
In these synthesizers, however, complex sampled attack phases are combined with simple
sustain or decay phases to create a sound. In essence, this is a simple wavetable that
consists of two samples.
369Appendix Synthesizer Basics