Tool · 2026-08-17
FM, two operators.
One sine wave drives the frequency of another. That is the whole of two-operator frequency modulation. The ratio between the two frequencies decides which harmonics fall out; the modulation index decides how many. From those two numbers you can pull a bell, a brass horn, a wood block or a bass note.
What you are hearing
Two sine oscillators. The first, the modulator, runs at some multiple of the second, the carrier. The modulator's output is fed into the frequency input of the carrier, so the carrier's pitch wobbles above and below its centre in time with the modulator. When that wobble happens hundreds of times per second the ear stops hearing a wobble and starts hearing a new set of frequencies: the carrier itself, plus sidebands spaced by the modulator frequency on either side.
The ratio
An integer ratio puts every sideband on an exact harmonic of the carrier, so the tone reads as pitched: ratio 1 is a stack of every harmonic, close to a sawtooth; ratio 2 keeps only odd harmonics, close to a square. Non-integer ratios put the sidebands off the harmonic grid. The ear gives up on a single pitch and hears the sum as an inharmonic clang. That is where bells, wood and metal all live.
The index
The modulation index controls how many sidebands are audible. At index 0 the modulator has no effect and you hear a pure sine on the carrier. As the index climbs, the energy flows outward from the carrier into more and more sidebands, following the Bessel functions of the first kind. High indices are bright and complex; low indices are dim and close to a single sine. If the index moves over the length of a note, the timbre changes with it — which is exactly what the decay slider does here for both operators at once.
The presets
Bell sits at ratio 3.5 with a long decay: the fractional ratio scatters the sidebands off the harmonic grid, the slow fade lets them ring. Brass keeps ratio 1 with a steady index around 4, which gives the growing brightness of a horn attack. Bass uses ratio 1 with a small index, producing a fat harmonic tone. Wood at ratio 6 with a very short decay and a large index gives the click of a struck block. Drift uses the square root of 2 as the ratio: the tone never resolves to a pitch, just floats.