FM synthesis

FM stands for frequency modulation: one oscillator wobbles the pitch of another. At a few cycles a second that wobble is vibrato. Speed it up into the hundreds and you stop hearing movement and hear a new tone with extra overtones. The oscillator you hear is the carrier, and the one doing the wobbling is the modulator. Yamaha calls each sine oscillator, with its own envelope and level, an operator, and most FM synths use the same word.

Two settings do most of the work:

• Ratio is the modulator’s frequency compared with the carrier’s, written carrier first (C:M). Whole-number ratios such as 1:1, 1:2 or 1:3 put the new overtones on the note’s harmonic series, so you hear a pitched, instrument-like tone. In-between ratios such as 1:1.4 or 1:3.5 put overtones between the harmonics, which is where metallic bells and gongs come from.
• Amount (also called the index, or the modulator’s level) sets how many overtones appear. At zero you hear the carrier’s plain sine. Turn it up and the sound gets brighter, then harsh and noisy.

Put an envelope on the amount so it starts high and falls, and each note gets a bright strike that settles into a purer tone. That is the recipe behind FM electric pianos, mallets and bells. For a tubular bell on C5, try a 1:3.5 ratio, a volume decay of about 5 seconds with sustain at zero, and an FM amount that dies away over about a second. Making an FM bell gives the full settings.

John Chowning worked out the method at Stanford starting in 1967, and Yamaha licensed it in 1973. The Yamaha DX7 of 1983 made FM famous with six operators per voice and no filter at all, so every change in brightness came from the modulators.

In Gelato Synth, the Osc B page has a Ratio slider from x0.5 to x8, and the FM page has Amount and Envelope to FM, which gives a bright attack and a purer tail. FM synthesis explained simply walks through ratios and a first patch.