2. Oscillator

In a classic Moog synthesizer of the 1970s, an oscillator produced a vibration with a sine-, square or saw-shape, 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 sine-wave 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 square-wave 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.