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Appendix B Synthesizer Basics 475
Fourier theorem and harmonics
According to the Fourier theorem, 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—that is, ratios of small numbers. Translated into more musical terms, this means
that any tone with a certain pitch can be regarded as a mix of sine tones consisting of the
fundamental tone and its harmonics, or overtones. For example, the basic oscillation—the
fundamental tone or rst harmonic—is an “A” at 220 Hz, the second harmonic has double the
frequency (440 Hz), the third harmonic oscillates three times as fast (660 Hz), the next harmonics
four and ve times as fast, and so on.
Synthesizer fundamentals
Sound synthesis is the electronic production of sounds—starting from 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 barking
dog. 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. Such a synthesizer would not be able to synthesize anything except a sine
wave. Combining multiple sine generators with pitch control, however, can produce interesting
and useful tones.
In a synthesizer, the task of tone generation falls to a component known as an oscillator. Most
synthesizer oscillators generate harmonically rich waveforms such as sawtooth, triangle, square,
and pulse waves, in addition to sine waves. These waveform names are based on the resemblance
of their respective shapes to a tooth on the blade of a saw, to a triangle, to a square, and so on.
For information about the most common synthesizer waveforms, see Oscillators on page 479.
Sculpting the fundamental tone and related harmonics into another sound is achieved by
routing the signal from one component, also known as a module, to another in the synthesizer.
Each module performs a dierent job that aects the source signal.
In a modular synthesizer, signal routing is achieved by physically cabling modules to each other.
In most modern synthesizers the signal routing between modules is internally prewired and is
typically changed using switches, knobs, and other controls.
For a discussion of synthesizer components and their interaction with each other to control and
shape sound, see How subtractive synthesizers work on page 477.
Synthesizers have existed far longer than you might imagine. In the days that preceded the
use of digital technology, all electronic synthesizers were analog. Prior to the use of electricity,
synthesizers were mechanical. There are signicant dierences between analog and digital
synthesizers:
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Analog: An analog synthesizer combines voltage-controlled circuits—such as oscillators, lters,
and ampliers—to generate and shape sounds. The amount of voltage is typically related
directly to the waveform pitch, with higher voltages equaling higher pitches.
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Digital: In a digital synthesizer, the signal ow is digital. Binary descriptions of the signal—a
string of zeros and ones—are fed from one algorithm to another.