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[[File:Roland_D-50.jpg|thumb|right|The Roland D-50 uses LA synthesis]]
LA synthesis employed traditional [[subtractive synthesis]] combined with [[Pulse-code modulation|PCM
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 [[Yamaha DX7|DX7]] [[frequency modulation synthesis|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.)
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