9

When you play two otherwise identical sounds out of phase, some frequency
components—harmonics—can cancel each other out, thereby producing silence in those
areas. This is known as phase cancellation, and it occurs where the same frequencies
intersect at the same level.
Phase: 180°
Phase: 0°
Fourier Theorem and Harmonics
“Every periodic wave can be seen as the sum of sine waves with certain wave lengths
and amplitudes, the wave lengths of which have harmonic relationships (ratios of small
numbers).” This is known as the Fourier theorem. Roughly translated into more musical
terms, this means that any tone with a certain pitch can be regarded as a mix of sine
tones. This is comprised of the fundamental tone and its harmonics (overtones). As an
example:The basic oscillation (the fundamental tone or first harmonic) is an “A” at 220 Hz.
The second harmonic has double the frequency (440 Hz), the third one oscillates three
times as fast (660 Hz), the next ones four and five times as fast, and so on.
What Is a Synthesizer?
Sound synthesis is the electronic production of sounds—starting from their basic
properties, such as sine tones and other simple waves.
Synthesizers are so named because they can emulate, or synthesize, a wide variety of
sounds—such as the sound of another instrument, a voice, a helicopter, a car, or a dog
bark. Synthesizers can also produce sounds that don’t occur in the natural world. The
ability to generate tones that cannot be created in any other way makes the synthesizer
a unique musical tool.
The simplest form of synthesizer would be a basic sine wave generator that provided
little or no control over pitch. Unfortunately, you could not use such a simple synthesizer
to synthesize anything except a sine wave.
Combining multiple sine generators with pitch control, however, can produce many
interesting and useful tones.
351Appendix Synthesizer Basics