Linear Arithmetic Synthesis, or LA synthesis, is a type of audio synthesis. In particular, this one is backed up by the theory that the attack transient of a sound is essential for human perception. It uses a combination of simple digital oscillators and sampled attack transients. The oscillators involve pulse and saw-tooth waveforms to produce a sustained sound. Both digital sampling and subtractive synthesis are types of linear arithmetic synthesis.
Linear Arithmetic Synthesis: the Origins
The first synthesizer that used this method was the Roland D-50. It was a digital device and emerged around 1980. The Roland D-50 creates sounds through a series of complex calculations. For example, it usedas addition and subtraction, as well as sum and difference. The sounds are the result of combining partials and tones, removing unwanted notes, and using ring modulation.
LA Synth and the Piano
The sounds produced by a piano are perfect examples of this synth. They can be classified into initial attack and decay. In turn, the initial attack subdivides into the high transient of a hammer hitting a string and the complex harmonics that represent the vibration of the string. After the initial attack, the decay tends to be longer, and the harmonics shift on the reverb of the soundboard. Some features vary from one point of the piano to another.
Traditional types of sound synthesis were unable to mimic the sounds produced by pianos. Firstly, it wasn’t easy for envelopes to generate the sharp initial transient followed by the proper decay. Secondly, adding to this difficulty, the harmonic content was extremely complex. It, too, was unable to manipulate the traditional waveforms that match the piano’s harmonic spectrum. Lastly, when the user was synthesizing at one range of the piano, the timbre was usually far away.
A case in point: the Roland D-50 included attack and decay, as well as a third component: a looped sample. Looped samples contained a series of synthetic waves as well as inharmonious wave cycles.
Final Thoughts on Linear Arithmetic Synthesis
Linear arithmetic synthesis allows the user to control individual sound components and produce sounds by combining them. Also, it mixes the creativity of a synthesizer with the realistic sounds of a sampler.
If you want to learn more about other types of synthesis, please consult our entries on subtractive, granular, wavetable, additive, and physical modeling synthesis.
