of Microprocessors

MUSIC SYNTHESIS PRINCIPLES 33
from zeto to the sustain is called the attack. The duration of the attack is of
primary importance, although its shape may also be important, particularly
if the attack is long. The transition from the sustain back to zero is the decay.
Again, time is the major variable. Some notes, such as a piano note, have no
real sustain and start to decay immediately after the attack. They may,
however, have two different rates ofdecay, a slow initial one, which could be
considered the sustain, even though it is decaying, and a faster final one.
Other envelope shapes are, of course, possible and quite useful in electronic
music.
As with frequency variation, an amplitude envelope may have a small
wavering superimposed on the otherwise steady-state portions. Such
amplitude wavering is called tremolo and, if small in amplitude, sounds much
like vibrato to the untrained ear. Actually, the physical manipulation required
to waver the tone of conventional instruments seldom results in pure
vibrato or tremolo; usually both are present to some degree. Large-amplitude
tremolo gives rise to an unmistakable throbbing sound. Generalized
amplitude modulation of one waveform by another is also possible, and in
many cases the effects are similar to frequency modulation. This will also be
examined more closely later.
Spectrum Variation
Finally, dynamic changes in the spectrum of a tone are the most interesting
and the most difficult to synthesize in general. The primary difference
between spectrum variation and frequency or amplitude variation is
that a spectrum shape is multidimensional and the other two parameters are
single-dimensional. Because of this multidimensional nature, standard electronic
synthesis techniques for dynamic spectrum changes generally utilize
schemes that attempt to cover a wide range of timbres by varying only one or
two parameters of a simplified spectrum shape.
One obvious way to control and vary the spectrum is to individually
control the amplitudes of the individual harmonics making up the tone. This
is a completely general technique applicable to any definitely pitched tone.
The problem with actually accomplishing this is twofold. The first is the
myriad ofparameters to control----dozens· of harmonic amplitudes for moderately
pitched tones. Involving a computer or microprocessor is the only
reasonable approach to such a control task. The other problem is deciding
how the harmonic amplitudes should vary to obtain the desired effect, if
indeed even that is known. There are methods such as analyzing natural
sounds, evaluating mathematical formulas, or choosing amplitude contours
at random and subjectively evaluating the results that work well in many
instances. In any case, a computer would probably be involved in generating
the data also.
As mentioned previously, common synthesis techniques aim at reducing
the dimensionality of the spectral variation problem. Consider for a