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.

LA synthesis employed traditional subtractive synthesis combined with PCM-based samples.

The term "linear arithmetic" refers to synthesis that is all digital (linear) and a summing (arithmetic) of sounds. Roland was careful not to use the term "additive", as this is an entirely different method of synthesis.

This technology was first seen in 1987 with the groundbreaking Roland D-50 synthesizer. At the time, resynthesizing samplers were very expensive, so Roland set out to present a machine to the general public that could be easy to program, sound realistic, and at the same time sound like a "synth". Also, Yamaha had previously gained world market lead with their DX7 FM synth, which excelled at metallic, percussive sounds, something that Roland's synths using subtractive synthesis were not good at.

Roland understood that their subtractive synthesis method needed to be changed. One of the more complex parts of a sound to program is the attack transient, so Roland added a suite of sampled attack transients to subtractive synthesis. As well as the attack transients, Roland added a suite of single-cycle sampled waveforms that could be continuously looped. Sounds could now have three components: An attack, a body made from a subtractive synth sound (saw or pulse wave through a filter) and an "embellishment" of one of many looped samples. (The looped samples also contained a collection of totally synthetic waves derived from additive synthesis, as well as sequences of inharmonic wave cycles. Thus, LA synthesis offered the realistic sounds of a sampler with the control and creativity of a synthesizer.)

The PCM 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 reverberation and chorus. Two tones grouped together created a patch.

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