Yamaha DX7 synth was released in 1983. Its technology is the Frequency Modulation (FM) synthesis, based on John Chowning research at Stanford University (California-USA). This synth was the first one which permitted to elaborate with precision very clear, bright metallic sounds; a sort of revolution comparing to analog synthesizers from the early 80's.

Basis of the sound is "the algorithm". An algorithm is a combination of six "sound operators" which are all pure sine waves that modulate each other in specific configurations . Each of these sound operators can be a carier or a modulator depending on how is configured the algorithm (there are a total of 32 available algorithms on the DX7). For example, algorithm n°32 is built with 6 cariers only (no modulators) and is very useful to emulate Hammond electric organ sounds. 
You can set the frequency of each sine wave independantly as a "keyboard mode" (common tempered scale on the whole keyboard) or as a "fixed frequence mode" (the same frequence on the whole keyboard). In the "keyboard mode", you can set the frequency coarse and fine. In both mode you can adjust detune on each sound operator to create subtle chorus or flange effect. One operator in each of the 32 algorithms has its output fed back to its input: this is the "feedback" operator. By increasing the feedback level the harmonics are increased, resulting in the generation of noise-like sounds.

Here is THE famous DX7 !!

Each sound operator has its own amplitude envelope controlled by eight different parameters ("rate" 1 through 4 and "level" 1 through 4). You can compare this envelope to a standard ADSR envelope that you commonly find on analog synthesizers. You can also adjust independantly output level, rate scaling and velocity amount for each sound operator. 
The keyboard scaling is very elaborated on the DX7: you can effectively assign a "breakpoint" key for each sound operator and then determine if the scaling will be increased or decreased linearly or exponantially for the left part and the right part of the keyboard (determined by the breakpoint).  This function is in fact used to create keyboard split sounds.
You also have a general pitch envelope (with the same parameters as the amplitude envelope) and a LFO (which produces low-frequency sine, saw-tooth or square waves, or a Sample&Hold waveform) that you can assign to modulate amplitude or pitch.

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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