Yamaha DX7 synth was released in 1983. Its sound generating principle is called "algorithm synthesis" - it is a combination of Frequency Modulation (FM) synthesis, based on John Chowning research at Stanford University (California-USA) and additive synthesis. This synth was the first one which permitted to create very clear, bright metallic, plucked and percussive sounds; a sort of revolution comparing to analog synthesizers from the early 80's.

Basic architecture of the sound engine is the "algorithm" - a combination of six "operators" producing sine waves. Some operators can be used as a carrier or a modulator depending on their position in the structure of the algorithm (there are 32 algorithms on the DX7). For example, algorithm 5 combines additively three pairs of carrier/modulator, while algorithm 32 has 6 carriers only and is good for making organ sounds. 
You can set the frequency of each operator independently in tuned "keyboard mode" (common tempered scale on the whole keyboard) or in "fixed frequency mode" (the same pitch on all keys). Operator frequency can coarse and fine tuned - in the "keyboard mode" as a ratio, in fixed frequency mode in Hertz. In both modes you can detune each operator to get a subtle chorus or flange effect. One operator in each of the 32 algorithms has its output fed back to its input (or to the input of some lower operator in the operator stack). By increasing the "feedback" level, the level of harmonics is increased, resulting in the generation of sawtooth wave. It's also useful for generating the noise when modulation index is enough high (= high level of modulator).

Here is THE famous DX7 !!

Each sound operator has its own amplitude envelope generator with eight parameters ("rate" 1 through 4 and "level" 1 through 4) which allows to create 5-segment envelope (also inverted one). It can be considered as an improved ADSR envelope commonly found on analog synthesizers. It's also possible to adjust independently output level, rate scaling and amount of velocity control for each sound operator. 
The keyboard scaling is very elaborated on the DX7: you can assign a "breakpoint" key for each sound operator and determine if the operator level will be increased or decreased linearly or exponentially for the left side and the right side from the breakpoint. This function can be used to create crossfaded sounds or simulate split keyboard.
There's also a pitch envelope (with the same parameters as the amplitude envelope but with level offset of 50 to allow positive and negative pitch change) and a LFO (which produces low-frequency sine, saw-tooth or square waves, or a Sample&Hold waveform) that you can assign to modulate pitch, timbre or amplitude.

Algorithm, EG/Pitch  & Keyboard Level Scaling schema

You can control and modulate DX7 sounds with a breath controller

DX7 Soundbanks Listing

DX7 Famous Examples

DX7 All The Web Patches

DX7 Video Demos

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