Almost all synths let you layer sounds, be they oscilators or voices. But it rare to find a true additive synth, that is additive in the Fourier sense. The problem is that when you use only sine wave partials to create a complex waveform, you usually have to use quite a few. Since since waves are simple, it's not really a computational issue as a human one. Imagine having 64 partials, each with it's own ADSR envelope, and you can imagine how slow and time consuming it could be to program (and that's only one oscilator.)
Well that's what the Kawai K5000, sucessor to the K5, does, and does very well. It can be tedious to program at time, but the Kawai engineers did a very good job of creating shortcuts, like editing multiple partials at once. The result is a fascinating, though tricky, synth that has a totally unique pallette.
The K5000 line had 3 machinesS, R, and W. The S (for "synth" presumably) had the additive synth engine, a very nice 61 key synth action keyboard, an arpeggiator, and a 4x4 grid of knobs for fiddling. The R (for "rack") dropped the keyboard, arpeggiator, and extra knobs. Finally the W (for "workstation") was a keyboard version without arpeggiator or knobs, but with a PCM synth engine and sequencer.
These instruments were pretty shortlived in the market, though they were suprisingly well supported by Kawai, who released four major revisions of the OS before dropping support.
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