Frequency Modulation (FM) is where the output of one oscillator is used to modulate the pitch of another, the oscillators being called modulator and carrier respectively. “Modulate the pitch”…that’s the key phrase. The pitch of the carrier is being changed (modulated) in tandem (in sync/going up and down at the same time) by the modulator.
Think of it as one person singing and another person grabbing the throat of the first and shaking him in a rhythm manner; the singer being the carrier and the throttler being the modulator.
In analog synthesizers, you can use an LFO (Low Frequency Oscillator) to modulate a VCO (Voltage Controlled Oscillator). Let’s take a slow LFO and modulate VCO…what happens is that the slowly rising and falling LFO makes the pitch of the VCO rise and fall also, giving you a sort of wobbly sound (referred to as Vibrato). Increase the modulating LFO amount and there’s more wobbling. Increase the modulating LFO speed and the wobbling gets faster. This is commonly called “Pitch Modulation”.
On DX synthesizers (DX-FM), the only real difference is that the Modulator is a “musically-tuned frequency” (whose frequency is determined by the notes actually played on the keyboard). The other difference is that DX-FM oscillators are all Sine-waves.
Imagine an old analog synth with 2 VCOs. When you play the keyboard, both the VCOs will emit their respective waveforms, taking its pitch by reference of the notes played on the keyboard. Now imagine rerouting VCO1 into the modulation input for VCO2. Play the keyboard and both VCOs will play their respective notes but now the pitch of VCO2 is changing exactly in time with the frequency of VCO1. And there we have it - one FM synthesizer. (VCO1=Modulator; VCO2=Carrier).
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