Subtractive synthesis is a sound design approach, often associated with Robert Moog, that starts with a harmonically rich waveform, such as a sawtooth or square wave, and removes harmonics with filters and other processing. It is what people usually mean by east coast synthesis.
The east coast and west coast labels come from the locations of Moog (New York) and Don Buchla (California), who were both building synthesizers in the 1960s. West coast synthesis takes the opposite route, starting with simple waveforms and building harmonics with tools like wavefolders.
