Linear Arithmetic synthesis

Linear Arithmetic synthesis, or LA synthesis, is a term that was invented by the Roland Corporation when they released their ground-breaking D-50 synthesizer in 1987.

It was the first keyboard to combine a synthesizer with sampled waveforms that could be modified.

According to Roland literature, "LA synthesis involves a great many technological advances resulting not only in a superior sound quality but also an improved ease of programming."

Linear arithmetic makes one think of simple math such as addition, and indeed, the primary way that LA synthesis created sounds was by adding the attack portion of a sampled waveform to one or more internally generated 'synthesizer' waveforms.

In order to save memory, which was quite expensive in 1987, Roland used small PCM (Pulse-Code Modulation) sampled waveforms (which required memory) for the short attack of the sound, then sound wave generators (which required no memory) for the long sustain of the sound. Thus, LA synthesis offered the realistic sounds of a sampler with the control of a synthesizer, all at an affordable price.

Roland called the PCM samples and sound wave generators, "Partials". Each Partial was like an individual synthesizer, with its own pitch and time variant amplifier. Synthesizer waveforms from the sound wave generators, got additional time variant filters for cutoff frequency, and resonance. Two Partials grouped together created a Tone. Tones could be modified with up to three L.F.O. (Low Frequency Oscillators), a pitch envelope, chorus and a programmable equalizer, plus on-board effects such as reverb. All of these parameters could be stored in memory as a sound called a 'Patch'