10.6

704Logic Pro Instruments
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 cancelation, and it occurs where the same
frequencies intersect at the same level.
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 first 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 five 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.
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 different job that affects the source signal.