Modulation at audio rate

The classic voice uses modulation slowly: an LFO at a few hertz and envelopes that take a fraction of a second. On a modular synthesiser, and on many others, a modulation source can also run much faster. Modulation at any rate adds new frequencies, called sidebands, either side of the frequency being modulated, spaced from it by the modulation rate. At a few hertz they are too close to the original to be heard separately, and the result is heard as vibrato, tremolo or a sweep. At audio rate they are far enough apart to be heard as separate frequencies, and the result is heard as a change in timbre.

The tool below modulates a 440 Hz sine wave, the carrier, with a second sine wave, the modulator. The modulator can move the carrier's pitch, move its level, or be multiplied with it, as in a ring modulator. The spectrum underneath is measured from the output, and the markers show where the sidebands are expected.

Sidebands

Moving the level of a 440 Hz tone up and down at 100 Hz is the same, as far as the spectrum is concerned, as adding two new tones at 340 Hz and 540 Hz. That is amplitude modulation, AM, and the two new frequencies are its sidebands: the carrier plus and minus the modulator. At a slow rate the sidebands are so close to the carrier that the ear hears them as one tone getting louder and quieter. Once they are more than a few tens of hertz away, the ear hears them as separate frequencies.

Ring modulation differs from amplitude modulation in one step. Amplitude modulation multiplies the carrier by the modulator plus a constant offset, so the level moves up and down around a fixed middle value. Ring modulation multiplies the carrier by the modulator alone. Without the offset the carrier frequency is absent from the output and only the two sidebands remain, so a 440 Hz tone ring-modulated at 100 Hz produces 340 Hz and 540 Hz and nothing at 440 Hz. Those two frequencies are not harmonics of any common fundamental that the ear readily hears, which is why ring modulation sounds bell-like or metallic. Ring modulators are named after the ring of four diodes in the original analogue circuit.

Frequency modulation

Moving the carrier's pitch at audio rate is frequency modulation, FM. Instead of one pair of sidebands it produces a series of them, at the carrier plus and minus one, two, three and more times the modulator's frequency. How many are strong depends on the modulation index: the frequency deviation, how far the modulator pushes the carrier, divided by the modulator's frequency. At a low index only the nearest sidebands are audible, and the tone changes slightly. At a high index the energy is spread across many sidebands, reaching roughly as far from the carrier as the deviation, and the sound is brighter.

When the modulator's frequency is a simple ratio of the carrier's, the sidebands fall on a harmonic series and the result has a clear pitch. The 110 Hz preset is a quarter of the carrier, so every sideband is a multiple of 110 Hz. The 311 Hz preset is about 0.71 of the carrier. The largest frequency that divides both 440 and 311 exactly is 1 Hz, so the sidebands at 129, 182, 751 and 1062 Hz are not harmonics of any fundamental in the audible range, and the result sounds clangorous. FM synthesis uses the ratio to choose which frequencies the sidebands fall on, and uses envelopes to change the index over the course of each note.

Between 15 and 40 Hz

Between about 15 and 40 Hz the sidebands are close enough to the carrier to beat against it, and the result is a rough, growling texture. The beats are too fast to hear as a wobble in level and the sidebands are too close to hear as separate pitches. An LFO that can run at these rates can produce this texture, and so can an audio oscillator set low enough.