Linear Arithmetic synthesis
Encyclopedia
Linear Arithmetic synthesis, or LA synthesis, is a term that was invented by the Roland Corporation
Roland Corporation
is a Japanese manufacturer of electronic musical instruments, electronic equipment and software. It was founded by Ikutaro Kakehashi in Osaka on April 18, 1972, with ¥33 million in capital. In 2005 Roland's headquarters relocated to Hamamatsu in Shizuoka Prefecture. Today it has factories in Japan,...

when they released their ground-breaking D-50
Roland D-50
The Roland D-50 is a polyphonic 61-key synthesizer produced by Roland. It was released in 1987. Its features include Linear Arithmetic synthesis, on-board effects, a joystick for data manipulation, and an analog synthesis-styled layout design. The external Roland PG-1000 Programmer could also be...

 synthesizer in 1987.

Overview

LA Synthesis employed traditional subtractive synthesis combined with PCM-based
Pulse-code modulation
Pulse-code modulation is a method used to digitally represent sampled analog signals. It is the standard form for digital audio in computers and various Blu-ray, Compact Disc and DVD formats, as well as other uses such as digital telephone systems...

 samples.

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 yet sound realistic and at the same time sound like a 'synth'. Also, Yamaha had previously gained world market lead with their DX7 FM synth
Yamaha DX7
The Yamaha DX7 is an FM Digital Synthesizer manufactured by the Yamaha Corporation from 1983 to 1986. It was the first commercially successful digital synthesizer. Its distinctive sound can be heard on many recordings, especially Pop music from the 1980s...

, 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. As the most complex and so difficult to program part of a sound is the attack transient, Roland had the innovative idea to add a suite of sampled attack transients to their tried, tested and loved 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: A lifelike 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. Note: 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, 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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