of Microprocessors

70 MUSICAL ApPLICAnONS OF MICROPROCESSORS
resembles a large number of copies of the input signal. An obvious control
parameter for such a device is the multiplicity factor.
Looking more" closely at the physical chorus effect, it is seen that the
difference between two separate players and one player playing twice as loud
is that the two sounds being combined are not exactly alike. For example, the
fundamental sound frequencies will be slightly different, resulting in a slight
beating effect. Unlike beating sine waves, the resultant amplitude of two
beating complex waves remains relatively constant, but individual harmonics
may momentarily cancel. Also vibrato, which is not synchronized between
the players, may cause even greater momentary frequency differences. The
end result is a slight, random, spectrum modulation of the resulting sound.
As more players are added, changes in the amplitude and phase of the
component harmonics become more pronounced and random. A spectral plot
of 100 trumpets playing the same note would show broad peaks at each of the
harmonic frequencies rather than narrow lines. Note that the overall spectral
envelope is unchanged, which allows one 'to distinguish 100 trumpets from
100 violins.
Research into construction of the chorus box mentioned earlier has been
in two different directions. One attempts to directly simulate multiple sound
sources with a number of audio delay lines, whose delay is constantly changing
over a narrow range. The theory is that a second sound is exact!y like the
first except that the vibrations are occurring at different points in time. The
variation in delay times prevents a constant echo effect. Multiplicity can be
controlled fairly well with such a setup by changing the number of delay
lines. Digital signal processing techniques are well suited for implementation
of this scheme.
The other approach works on the basic parameters of the input sound
attempting to simulate the effect rather than the actual chorus itself. Accordingly,
it uses filters to separate the input spectrum into bands and amplitude
and phase modulators plus spectrum shifters to randomly manipulate the
individual bands. Finally, the sound is put back- together and sent out. Although
not particularly good for simulating a small group of players, the
technique is apparently very effective for simulating a large number. A taped
demonstration witnessed at the Spring 1977 Audio Engineering Society
convention made a cheap portable synthesizer sound like a whole auditorium
full of synthesizers.
Analysis-Synthesis Methods
It should now be well established that the synthesis of sound can be
controlled to the tiniest of details by appropriate manipulation of the fundamental
parameters. The basic problem, then, is in determining exactly
how these parameters should be varied to get the desired effect. One possibility,
of course, is experimentation so that the relation between parameter
change and audible effect becomes familiar. If this is adequately accom-