In
a classic Moog synthesizer of the 1970s, an oscillator produced a
vibration with a sine, square or sawshape, because these
oscillations can easily be generated with electronic circuits.
The
waveform determines the sound color (timbre). You can imagine that
each waveform can be created by superimposing of a sinewave with an
appropriate collection of overtones (= tones with frequencies that
are a multiple integer of the root frequency). This is called a
Fourier synthesis. The more overtones a vibration has, that brighter
it sounds3. For example a squarewave is made up by all odd overtones
with decreasing amounts: square = sum( sine 1 + sine 3 +
sine 5 ...). A
sinus oscillation does not contain any overtones, but only the root
wave. For this reason it sounds very calm like a flute.
Wave
= Sin( 2 * Pi * F * t) = Sin(w*t) w = 2 * Pi * Frequency
A
square wave contains all odd numbered overtones with in decreasing
intensity. It sounds a little sharper like a clarinet.
Wave
= Sum( 1/i * Sin(w* i * t)) i = 1,3,5, 7 …
A
saw wave consist of all harmonic overtones in decreasing intensity.
It sounds shill and can be used to construct piano, violin or acid
synthesizer sounds.
Wave
= Sum( 1/i * Sin(w*i*t)) i = 1,2,3,4 …
Nowadays vibrations are no longer made by electronic circuits, but are calculated with the computer. This makes it possible to create an endless number of different waves with different symmetries. They all have their characteristic overtone spectrum and sound color.

Learning Synthesizer >