vgmrips

1.8.2 FM
FM as a means of producing audio sounds was first comprehensively described
by John Chowning, in a paper entitled The Synthesis of Complex Audio
Spectra by Mean of Frequency Modulation, published in 1973. At the time, the
only way that this type of FM could be realized was by using digital computers,
which were expensive and not widely available to the general public.
As digital technology advanced, some synthesizer manufacturers began to
look into ways of producing sounds digitally, and Yamaha bought the rights
to use Chowning’s 1977-patented FM ideas. Early prototypes used large numbers
of simple transistor–transistor logic (TTL) chips, but these were quickly
replaced by custom-designed chips which compressed these onto just a few
more complex chips. The first functional all-digital FM synthesizer designed for
consumer use was the Yamaha GS1, which was a pathfinder product designed
to show expertise and competence, as well as test the market. Simple preset
machines designed for the home market followed. Although the implementation
of FM was very simple, the response from musicians and players was very
favorable.
The DX1, DX7 and DX9 were released in late 1982, with the DX1 apparently
intended as the professional player’s instrument, the DX7 a mid-range,
cut-down DX1, and the DX9 as the low-cost, large-volume ‘best seller ’. What
actually happened is very interesting. The DX9 was so restricted in terms of
functionality and sound that it did not sell at all, whereas the DX7 was hugely
in demand amongst both professional and semiprofessional musicians, and
the DX1 was interpreted as being a ‘super ’ DX7 for a huge increase in price.
Inevitably, it took Yamaha some time to increase the production of the DX7 to
meet the demand, and this scarcity only served to make it all the more soughtafter!
By the time that the mark II DX7 was released, about a quarter of a million
DX7s had been sold, which at the time was a record for a synthesizer.

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Here are some Yamaha patents for FM-related stuff:

US5033352 - Electronic musical instrument with frequency modulation
US5861568 - Generation of wave functions by storage of parameters for piecewise linear approximations
US4249447 - Tone production method for an electronic musical instrument
US4554857 - Electronic musical instrument capable of varying a tone synthesis operation algorithm

In the first one, it gives the example of 6 operators, which is what the Yamaha DX7 had, and in the last one, on sheet 3 of 8, Fig 5, you can see a chart with algorithms that are very similar to the DX7 algorithms.

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