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Back in the day, a lot of (otherwise respectable) texts said "FM synthesis only started with digital synths because it was technologically not possible with analogue synths". Which is not true.
When you think "FM synth", you're immediately referred to Yamaha's DX7. Key ingredients: operators, made up of a sine osc, amp and envelope. Oscillator pitch was set relative to each other with a ratio, or could be set to a fixed value.
For some sounds (which usually are the "famous FM sounds"), having a pure sine wave and being able to set the frequency ratios precisely (and have them track) is important. The VCOs in most of the old analogue synths weren't good at this. But e.g. the Doepfer A-110-4 is.
Interestingly, it took until the SY generation that those oscillators could produce other things than sine waves. Yes, the TX81Z says it has new waveforms, but they aren't created by the oscillator itself, rather by wavemasking/multiplication (West-Coast)
