Sound waves are made up of various elements which can be analysed and then synthesised electronically. Those elements are:
In addition, various filters can be applied to emphasis or reduce various harmonics and effects such as echo, phasing or ring modulation (whose best known use is to imitate Daleks). More than one synthesised sound may be produced and mixed together to form a final sound.
Synthesisers normally generate waveforms which are the basis of the sound. A sinusoidal waveform will give a pure sound while a square wave has a more complex sound because it contains many harmonics. Other waveforms include saw-tooth and triangular which many think of as 'brassy'.
Stands for Attack - Decay - Sustain - Release and describes the overall shape of an actual instrument note. A plucked instrument will have a fast attack and a rapid decay, poor sustain and rapid release while a wind instrument will have a slower attack and a longer sustain and release. A synthesiser can manipulate all these parameters to mimic an instrument or create something entirely artificial.
Possibly the best known synthesiser is the Moog, named after Robert Moog its inventor who started out making Theramins. The synthesiser is usually a Keyboard instrument, the keys controlling the frequency and amplitude of the note, while a control panel allows manipulation of filters, effects and the adsr to affect the quality of the notes.