of Microprocessors

528 MUSICAL ApPLICATIONS OF MICROPROCESSORS
tling, thus producing random noise directly. Synthesizing such sounds basically
amounts to determining the amplitude response of the filter and the
shape of the amplitude envelope. Cymbals, drums with snares, and sand
blocks produce sounds that are excellent examples of this type of percussion.
The last class most resembles the first but has great potential for a wide
variety of distinctive percussive sounds. These are sounds made by a nonlinear
vibrator such as a ruler held over the edge of a table. The difference is
that the basic parameters of the vibration such as frequency and waveform
change as the amplitude of the vibration changes. In the case of the ruler, the
nonlinearity arises from the fact that the effective vibrating length is less on
the downstroke, where it bears against the table edge, than on the upstroke,
where it is restrained by the player's hand. The relative time spent in each of
the two states varies with amplitude, until at low amplitude the table edge
becomes dominant and the vibration expires with a Type 1 characteristic.
Damped Sine Wave Generation
Most sounds in the first two categories can be quite adequately simulated
with one or more exponentially damped sine waves. Although a sine
wave tone generator can be given an amplitude envelope for this purpose, the
very fast attack characteristic of these sounds requires that the attack begin at
the zero crossing of the sine wave. Otherwise, audible dicks may be generated,
particularly when the wave being enveloped is of low frequency.
A convenient way of obtaining damped sine waves with the required
attack phase continuity is to ring a high Q filter! The center frequency
determines the wave frequency and the Q determines the decay rate. Because
of the precision and stability of digital filters, even very slow decay rates are
easily handled.
The filter-ringing technique is very common in the analog world for
simulating the sounds of all kinds of percussive instruments. Its use is most
popular in electronic organs, where up to a dozen different percussion "instruments"
are driven by digital logic to provide rhythm accompaniment to
the standard organ sound. For example, a fairly high-frequency (1-2 kHz),
high-Q (50) ringing filter is used to simulate daves. A lower-frequency (500
Hz), lower-Q (10-20) filter makes a convincing wood block sound. Even
lower frequencies (100-250 Hz) and moderate Qs do a surprisingly good job
of simulating tom-tam's even though a real tom-tom is a Type 2 percussive
sound. Much lower frequencies (50 Hz) have all of the oomph ofa bass drum
when played through a good speaker system.
To these rather common-sounding percussion "instruments," one may
add many others by manipulating the frequencies and Qs. In particular, if a
number of dave-like instruments with pitches on a musical scale are defined,
a tune can be played that the average person almost invariably associates with
falling raindrops. And who has not heard a melody "played" by a coffee