Linear Arithmetic synthesis
The term "linear arithmetic" is derived from the facts that the synthesis is all digital (linear) and a summing (arithmetic) of sounds. Roland were careful not to use the term "additive", as this is an entirely different method of synthesis.
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.
Yamaha's SY77, its rack-mounted equivalent TG77, and their successor SY99 introduced a PCM-playing technology termed Advanced Wave Memory (AWM), which enabled playback and filtering of samples. Notably, these workstations also allowed AWM samples to be used as transients to FM-synthesised sounds, as looped "oscillators" in their own right, or even as modulating waveforms of FM carriers. This, like LA synthesis, enabled even more realistic modeling of physical instruments, and in combination with FM, also enabled new possibilities for sculpting sounds. The SY99 was the last FM workstation by Yamaha, and the only later FM synthesiser Yamaha FS1r|FS1r did not feature AWM, so the SY99 was the last synthesiser in which the AWM and FM could be combined. However, AWM sampling on its own has gone on to be a mainstay of subsequent products by Yamaha, such as the Yamaha EX5 and Motif lines.