A polyphonic synthesizer is one capable of sounding two or more notes at one time. Manufacturers learned long ago that a fully polyphonic synth, capable of sounding every note on the keyboard at once, is a bulky and expensive proposition, and that most performers don't really need that amount of polyphony. So, relatively few fully polyphonic synths with programmable patches have been produced; the two best known are the Korg PS-3100 series and the Polymoog. (And even the Polymoog was only paraphonic in certain modes.) Some of the string synthesizers of the 1970s were fully polyphonic, but these relied on stripped-down circuitry capable of reproducing only a few preset, non-editable sounds.
Rather, most polyphonic synths contain a certain number of voices, which are capable of playing a certain number of simultaneous notes depending on layering and voice allocation. In the simplest case of a synth which does not do layering internally, there is a 1-to-1 correspondence between voices and polyphony capability.
The polyphonic analog synthesizers of the 1980s relied heavily on specialized integrated circuits to keep the size and cost under control. Most of these were produced by Curtis Electromusic (CEM) or SSM. The former is now out of business, and the latter is now owned by Intersil, which has kept only a few of the SSM synthesizer parts in production. This unavailability of integrated circuits has mostly kept new analog polysynth designs from reaching production. (Alesis produced custom ICs for the Andromeda by way of a custom IC design division that it owned at the time the Andromeda was designed; Dave Smith Instruments has a source for some CEM ICs which it declines to disclose.) Most polysynths produced since 1990 have been digital designs. In these, the sound is usually produced using specialized digital signal processors, and the polyphony may depend on the complexity of the patch, according to how much DSP processing is required by the algorithms in use.
The first truly Polyphonic Keyboard for Analog Synthesizers was designed and built in 1969 and later patented (a part of the design was kept secret) in early 1970's. It boasted a full 61 key and multiple channels and keyboards (using early network innovations) were complimented with velocity and pressure sensing at a cost competitive with the existing one note keyboards (see Mark Vail's book second edition). This keyboard (the Ampoly - Polyphonopitch) and the lack of low cost Synthesizers prompted Jim Cooper of UCLA to develop the SEM-1 for Tom Oberhiem (after they both witnessed their first and second viewing). This keyboard started the realization that polyphony was finally viable. Lack of funding soon brought an end to the production of the Ampoly Keyboard which still has not been duplicated in the range and scope of features ti sported, to this day! Early album credits with Quincy Jones, Sergio Menendez, T.O.N.T.O. and others bare witness to how early this Polyphonic Keyboard System preceded everyone else by more than over a decade. If that technology was brought up to today's standards it would be one of the lowest cost systems created and be compatible not only with Analog and MIDI but also any digital format which someone might develop. While many attempts were made to circumvent the patent, the portion withheld from the patent was never fully discovered or understood even though it was such a simple concept. Allowing an unlimited number of notes to be played with very little total processing time expended at all using only the 1Mhz clocks of that day.