Linear Arithmetic synthesis

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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.

Linear arithmetic makes one think of simple math, such as addition, and indeed, the primary way that LA synthesis created sounds was by adding sampled waveforms to digitally-generated waveforms.

In order to save memory, which was quite expensive in 1987, the engineers at Roland recorded/sampled different instruments and sounds, then used the recordings/samples to make PCM (Pulse-Code Modulation) samples/waveforms which were stored in the unit's memory. These PCM waveforms (samples) used very little memory because they usually lasted less than one second. This brief period of time was enough, because the PCM waveforms were used only¹ for the short attack part of the sound, while the digital oscillators, which needed no memory, were used for the long lasting sustain part of the sound. Thus, LA synthesis offered the realistic sounds of a sampler with the control and creativity of a synthesizer, all at an affordable price.

The PCM samples/waveforms could be modified with a pitch envelope and a Time Variant Amplifier. Waveforms from the sound wave generators, could be further modified with Time Variant Filters for cutoff frequency, and resonance. These modified waveforms were called Partials.

Two Partials grouped together created a Tone. Tones could be modified using up to three Low Frequency Oscillators, a pitch envelope, a programmable equalizer, and on-board effects such as reverb and chorus. Two Tones grouped together created a patch.

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¹Some of the PCM waveforms in the D-50 could be played in a loop to create a sound that would last as long as a key was being pressed.