A method of synthesis devised by Roland in the mid-1980s, and introduced to the market with the D-50 synth. Roland was looking for a digital synth product design that could compete with the Yamaha DX7, which was dominating the polyphonic synth market at the time and pushing older analog designs out of the market. Roland wanted to build a sampler, but at the time, building a straightforward sampler was expensive due to the cost of memory, which was about $1000 per megabyte in 1983. Roland had been canvassing psychoacoustic research and had noted some research results indicating that human sound recognition mostly occurs in the first 200 milliseconds or so of hearing a new sound. They reasoned that by sampling the initial portions of a variety of sounds, and then blending this to a simple waveform that could be computed on the fly by a microprocessor (and so didn't need to be stored in memory), they could achieve many of the desirable characteristics of a sampler without needing a lot of memory, therefore allowing the cost to be contained.
Roland termed the resulting method "Linear Arithmetic", or L/A, synthesis. As implemented on the D-50, the method allowed the user to graft a short sample of the attack portion of a sound onto a computed sine, triangle, or pulse waveform. The result was a variety of sounds which were novel at the time, compared to what analog polyphonic synths of the day were capable of. The D-50 and its follow-on models successfully competed with the DX7 in the marketplace and served as Roland's bridge into the digital era.
As the price of memory dropped rapidly, making a straight sampler more cost-effective, L/A synthesis was rendered obsolete by 1990. However, some of the D-50 sounds remained highly recognizable and desired by performers. Roland's later series of samplers and arranger workstations, including the current Fantom line, contain a number of samples of sounds which were originally produced using L/A synthesis.