Audio Rate: When Modulation Becomes Sound
At 20 Hz, modulation crosses into hearing range and becomes sound. A cycling function generator at 200 Hz is an oscillator. When one oscillator modulates another's pitch, that's FM synthesis and now you understand why from first principles.
The 20 Hz Boundary
In Part 68, we stopped at 19 Hz. Push past 20 Hz and something fundamental changes. Your ears stop hearing the modulation as a wobble and start hearing it as a tone. The function generator hasn't changed; it's still cycling. But your perception of it has.
Below 20 Hz, a cycling function generator modulating a VCA produces tremolo, a rhythmic pulsing of volume. As the rate increases through 10, 15, 18 Hz, the pulses blur together. At 20 Hz they fuse into a continuous buzz. By 50 Hz you hear a distinct pitch. By 200 Hz it's unmistakably a musical tone. Watch the zone label in the demo change from "LFO" to "Audio" as you cross 20 Hz.
Your LFO Is Now an Oscillator
A function generator cycling at 200 Hz produces a tone at 200 Hz. Its Rise/Fall shape is its waveform. Equal rise and fall makes a triangle wave. The distinction between "modulation source" and "sound source" is just speed. An LFO at 0.5 Hz and an oscillator at 500 Hz are the same circuit doing the same thing at different rates.
This is why West Coast synthesizers don't draw a hard line between oscillators and LFOs. A function generator is both, depending on where you set the rate knob.
FM from First Principles
When a cycling function generator modulates a carrier oscillator's pitch, that's frequency modulation. In Parts 12–13, we introduced FM as a separate synthesis technique. Now you can see it's just a function generator cycling fast enough to hear. The carrier-to-modulator ratio determines whether the result sounds harmonic (2:1, 3:2) or metallic (irrational ratios like 1:1.414).
FM creates new frequency components called sidebands (we first met these in Part 12). Simple ratios produce tones with clear pitch because the sidebands land on harmonics of the carrier. Irrational ratios are ones that cannot be expressed as simple fractions, like 1:1.414 (the square root of 2). These scatter the sidebands across non-harmonic frequencies, producing bell-like, metallic, or noisy timbres. This is why FM synthesis can produce both lush electric pianos and clanging bells from the same basic mechanism.