FM synthesis: recipes from two sine waves
A carrier you hear, a modulator you don't. Ratio picks the harmonic recipe; modulation amount sets how bright.
Lesson 2 taught you that timbre is a recipe of harmonics, and lesson 4 taught you to carve a rich wave down. FM synthesis builds the recipe from nothing — out of two sine waves, the emptiest sound there is. One sine, the carrier, is the note you hear. The other, the modulator, never reaches the speaker: it wiggles the carrier's frequency, thousands of times a second. Wiggle a frequency that fast and it stops sounding like vibrato — new frequencies appear around the carrier, called sidebands. Those sidebands are the harmonics of your new sound.
Ratio picks the recipe
Sidebands land at the carrier plus and minus whole multiples of the modulator's frequency — an evenly spaced comb. So the ratio between the two frequencies decides which recipe you get, and the families are ones you already know: 1:1 lays sidebands on every harmonic — the sawtooth family. 2:1 hits only the odd ones — the hollow square/clarinet family. Higher whole numbers give sparser, brassier, more nasal sets. And a ratio that is not a whole-number relationship scatters the sidebands off the harmonic ladder entirely — which is precisely why FM is the king of bells and metallic sounds.
Modulation amount is brightness
The second knob is how hard the modulator wiggles — the modulation index. At zero, nothing: a pure sine. As it rises, energy is taken from the carrier and dealt outward into more and more sidebands: the sound brightens, hardens, eventually snarls. Where a subtractive patch would sweep a filter, an FM patch rides the modulator's level — same musical gesture, opposite mechanism: the filter removes what exists, the index creates what doesn't.
Two sine waves, nothing else. The amber ticks are the predicted sideband positions — carrier ± multiples of the modulator — and the green bars are what actually comes out; drag ratio and watch prediction and reality move together. Try the three presets, then set index to zero and raise it slowly: you can hear the energy leave the carrier for the sidebands. Nudge fine off zero and hear the bell appear.
This is the Digitone II's home game: four operators (C, A, B1, B2), an ALGO knob choosing who modulates whom, per-operator RATIOs, and each operator's LEV as its modulation index — plus DTUN for exactly the fine-detune bells you just made. The FM DRUM machine is the same engine tuned for percussion: