Two sine waves and a handful of numbers can sound like a brass section, a bell or a slap bass. That is the trick of FM (frequency modulation) synthesis: instead of adding up dozens of pure tones, let one oscillator wobble the pitch of another so fast that the wobble becomes part of the sound. John Chowning worked out how to make music with it at Stanford, Stanford licensed it to Yamaha, and Yamaha shrank it onto chips cheap enough for a games console. Those chips are the sound of Sega’s and Capcom’s arcade boards, Sharp’s X68000, the Ad Lib and Sound Blaster cards in DOS PCs, MSX-MUSIC and the Sega Mega Drive.
Fast facts
- The principle: “the variation of the frequency of one repeating waveform, the carrier, by an amount proportional to the instantaneous amplitude of a second waveform, the modulating wave” (Robert Moog, BYTE, 1986).
- Inventor: John Chowning, Stanford University; his centre dates the discovery to 1967. US patent 4,018,121, “Method of synthesizing a musical sound”, filed 1975 and granted in April 1977, was assigned to Stanford.
- Licensee: Yamaha, from 1973 by Stanford’s account; Yamaha’s DX and TX synthesisers followed.
- Game chips: YM2151 (OPM, eight voices of four operators), YM3526 and YM3812 (OPL and OPL2, nine voices of two operators), YMF262 (OPL3, up to 18 voices), YM2413 (OPLL, nine voices with built-in instruments), YM2612 (OPN2, six voices of four operators).
- The cost: tones that move and shine from very little data, in exchange for patches that are hard to design by ear.
Chowning and Yamaha
Moog’s account in BYTE puts Chowning at a Stanford research computer “in the early seventies”, where “he systematically explored the relationships between the values of the coefficients of the FM algorithm … and the resultant tone colors”. Stanford’s Center for Computer Research in Music and Acoustics, which Chowning co-founded in 1974, dates his discovery of the FM synthesis algorithm to 1967, and says Stanford licensed the patent to Yamaha in 1973. The US patent, applied for in 1975 on the basis of a filing in March 1974, describes “frequency modulation with the carrier and modulating frequencies being in the audio range and the modulating index being related to a function to control the bandwidth and evolution in time of the partial frequencies”: an index that changes over the length of a note.
Amiga Format told the story in 1989 as one of American indifference. Chowning, it said, “had tried to sell the concept to several leading US electronic instrument makers who stared at him blankly”; meeting Yamaha’s engineers, “he found that they were some way down the paths he had already trodden”. Hobbyists could read the method for themselves. In January 1981 Creative Computing, reviewing an S-100 synthesiser board that could modulate one channel with another, sent readers to “‘The Synthesis of Complex Audio Spectra by Means of Frequency Modulation’ by John M. Chowning” for “‘real’ FM music synthesis”. By 1986 Moog could describe Yamaha’s DX and TX instruments as the latest in “a series of commercial keyboard instruments” that Chowning’s work had led to.
How it works
Moog’s description is the plainest. Take a carrier sine wave at frequency A and modulate its frequency with a second sine wave at frequency B, with a depth I, the modulation index:
W(t) = P sin(At + I sin Bt)
The output contains the carrier plus sidebands at A±B, A±2B, A±3B and so on. Yamaha’s application manual for the YM2413 gives the rule for how loud each one is: “The amplitude of each harmonic component is expressed as a Bessel function of the modulation index.” With I at zero there is only the sine wave; as I rises, energy spreads into more and more sidebands and the sound grows brighter, though not smoothly, because each Bessel function rises and falls in its own way.
The ratio of the two frequencies decides whether the result sounds like a note. “If you set the modulating frequency B equal to the carrier frequency A, the sideband frequencies are then whole-number multiples, or harmonics” of the carrier, Moog wrote. Simple whole-number ratios give pitched tones; ratios that are not whole numbers put the sidebands between the harmonics, which is where FM’s bells, gongs and metallic clangs come from.
Yamaha’s YM2151 manual writes the same equation as a chip uses it, with the two numbers that matter made into envelopes: E(t) = A(t)·sin[(Nc+Dc)·ωt + B(t)·sin(Nm+Dm)·ωt], with “A(t): Volume envelope, B(t): Timbre envelope”. “When B(t) = 0, you get a sine wave”; raise it and “the output will not be a sine wave but a wave form including a high harmonic component”. Because B(t) is an envelope, “the timbre can be altered and output by temporal adjustment of B(t)”. A brass patch gets brighter as the modulator’s envelope rises; a plucked bass starts bright and dulls as it decays. That moving tone colour, from a few numbers per operator, is what made FM worth putting on a chip.
Plain FM has a gap. Its harmonics do not fall away evenly, so it cannot easily make the smooth, bright spectrum of a bowed string. Yamaha’s answer was feedback: an operator fed with its own output. The YM2413 manual explains that “String sounds, however, cannot be obtained as the distribution of harmonics is not uniform. A method called ‘Feedback FM’ has been incorporated to solve the problem”, and that feedback FM’s spectrum is that of “a saw-tooth waveform and therefore it can be used to synthesize string sounds”. The YM2151 manual makes the same claim for its feedback circuit, with which “virtually any type of wave form can be obtained”.
Operators and algorithms
An operator is one sine oscillator with its own frequency multiple and its own envelope. An algorithm is the wiring: which operators modulate which, and which are heard. Moog’s account of the DX keyboards has “one of 32 preprogrammed algorithms, which are configurations of operators”. The game chips have fewer operators and fewer choices.
On the YM2151 each of the eight voices has four operators, and a three-bit connection register (CON) picks one of eight wirings, from four operators in a single chain, the brightest and most complex, to four sine waves side by side. The first operator can feed back into itself, set by a three-bit feedback level. On the two-operator OPL chips the choice is down to two: the YM3812 datasheet gives one formula for “the production of a tone by sine waves addition” and one for “a sine wave modulating another sine wave, i.e. frequency modulation”, selected by a single bit per channel, with a feedback factor for the modulator.
| Chip | Family | Operators per voice | Voices | What the datasheet stresses |
|---|---|---|---|---|
| YM2151 | OPM | 4 | 8 | Stereo through the separate YM3012 DAC; noise, vibrato, amplitude modulation, timers |
| YM3526 | OPL | 2 | 9, or 6 + 5 rhythm | Designed for CAPTAIN videotex and teletext terminals; needs a YM3014 DAC |
| YM3812 | OPL2 | 2 | 9, or 6 + 5 rhythm | Adds a choice of four waveforms; sine mode is YM3526-compatible; needs a YM3014 DAC |
| YMF262 | OPL3 | 2 or 4 | 18 two-operator, or up to six four-operator | Register-compatible with OPL2; eight waveforms; four outputs |
| YM2413 | OPLL | 2 | 9, or 6 + 5 rhythm | 15 built-in instruments plus one programmable tone; 9-bit DAC on the chip |
| YM2612 | OPN2 | 4 | 6 | Channel 6 can be swapped for an 8-bit sample channel; DAC on the chip |
The five rhythm sounds on the OPL chips are a bass drum, snare, tom, top cymbal and hi-hat, made from mixed waveforms and the chip’s noise generator. The YM2151’s noise works differently: switching it on turns the last of the chip’s 32 operator slots into a noise source.
Where it turned up
Arcades and the X68000. Sega’s own developer manual describes the YM2151 as the chip “used in SEGA’s coin-operated machines”. On Capcom’s CP System it sits beside a Z80 that drives it and an OKI chip for sampled effects; Fabien Sanglard’s book on the board describes its “8 channels … Each channel consists of four operators (a.k.a. slots) which can be setup to produce either percussion or instrument sounds”. Sharp’s X68000 home computer used the same chip for its music.
Mega Drive. The YM2612, Sega’s manual says, “resembles the Yamaha 2151 (used in SEGA’s coin-operated machines) and the chips used in Yamaha’s synthesizers”: six four-operator channels, with the sixth replaceable by an 8-bit digitised-audio channel, which is how the console plays samples, at the cost of one FM voice and the processor time needed to feed it.
PC. The Ad Lib Music Synthesizer Card, from the Canadian company Ad Lib Inc., put Yamaha’s OPL2 on an ISA card. PC Review reported in 1992 that the chip was “produced, many suspected, by Yamaha (although Ad Lib always scratched the name off the chip for some reason)”. COMPUTE! described it in 1990 as “a half-size FM synthesizer card” that “can play up to nine different melodic instruments or six melodic and five percussion instruments”, the OPL2’s two modes. Ad Lib’s own 1989 advert, pricing the card at $195, claimed it had “set the home computer music world on its ear just a year ago” and listed Sierra’s King’s Quest IV, Space Quest III and Police Quest II among the games that used it. When Creative Labs announced the card that became the Sound Blaster that autumn, the news was that it was “fully Ad Lib-compatible”, with “the 11 voices available on the popular Ad Lib card” alongside the Game Blaster’s 12, for the same $195. By 1993 PC Player in Germany could say that almost every game still supported “the good old OPL2 chip from Yamaha”, known as the AdLib sound because the AdLib was the first card to use it. The OPL3 that followed doubled the voices and added four-operator modes while staying register-compatible.
MSX. MSX-MUSIC is the YM2413, at I/O ports 7CH and 7DH, either built into the machine or added as a cartridge. ASCII’s MSX Datapack warns that fitting a cartridge to a machine that already has one puts two chips at the same address, so “the volume becomes twice as large as normal”, and tells programmers to go through the FM BIOS rather than write to the chip directly. The OPLL’s instrument ROM held fifteen fixed tones (violin, guitar, piano, flute, clarinet, oboe, trumpet, organ, horn, synthesizer, harpsichord, vibraphone, synthesizer bass, acoustic bass and electric guitar) and left room for one tone the program could define, so a cheap add-on could play a usable band without the programmer designing a single patch. Yamaha’s datasheet put the point plainly: “Unlike conventional FM sound generators, this OPLL has a built-in Instruments ROM, permitting a substantial simplification of sound generation commands from the processor.”
The sound, and the price
FM’s signature is moving harmonic content: a note’s colour changes as it plays, from one tiny set of numbers. Whole-number ratios with a modest index give electric pianos, organs and brass; higher indices give the buzz and bite of an arcade lead line; ratios that are not whole numbers give bells and metallic percussion. The weakness comes from the same mechanism. Because the sidebands follow Bessel functions, a small change to the index or ratio reshapes the whole spectrum, so patches are hard to design by ear, and a programmer who wanted good sounds had to learn the chip as an instrument. The YM2413’s preset instruments were one answer to that; the composers who wrote for the Mega Drive, the X68000 and the CP System boards, building their own patches, were the other.
Sources
- Robert A. Moog, “Digital Music Synthesis”, BYTE, June 1986, p. 155: the definition of FM, the formula and its sidebands, harmonic ratios, Chowning at Stanford, the DX and TX series, 16 voices and 32 algorithms.
- US Patent 4,018,121, John M. Chowning, “Method of synthesizing a musical sound”, assigned to Leland Stanford Junior University; priority 26 March 1974, filed 2 May 1975, granted 19 April 1977 (web, Google Patents). https://patents.google.com/patent/US4018121A/en
- Stanford University, Center for Computer Research in Music and Acoustics, “John Chowning” (web, secondary): the 1967 discovery, the 1973 licence to Yamaha, the founding of CCRMA in 1974. https://ccrma.stanford.edu/people/john-chowning
- Amiga Format issue 4, November 1989: music feature (Chowning, the US instrument makers and Yamaha).
- Creative Computing, January 1981: Jon Bondy, “The Casheab Music Synthesizer” (Chowning’s paper).
- Yamaha, YM2151 (OPM) application manual, chapters 1 and 2: the FM equation and envelopes, the connection and feedback registers, the noise generator, the YM3012 DAC. YM2151 datasheet: features and pins.
- Yamaha, YM3526 (OPL) datasheet: CAPTAIN and teletext, the voice modes, the YM3014 DAC. YM3812 (OPL2) datasheet: two operators, the two algorithms, rhythm sounds, feedback, waveform selection, the YM3014 DAC. YMF262 (OPL3) datasheet: register compatibility, voices, waveforms, outputs.
- Yamaha, YM2413 (OPLL) datasheet: modes, built-in instruments and their names, the 9-bit DAC, the instrument ROM. YM2413 application manual, section 1-3: Bessel functions and feedback FM.
- Sega, Genesis Software Manual (1989, revised 1992), sound manual overview, p. 3: the YM2612 and its resemblance to the YM2151; channel 6 and the DAC.
- Fabien Sanglard, The Book of CP-System (self-published, May 2026 edition): the CPS-1 audio section and the YM2151; the X68000’s music chip.
- COMPUTE!, January 1989: Ad Lib advertisement, “Hear This!”. October 1989: news item on Creative Labs’ “Killer Kard”. March 1990: reply to a reader, “The Killer Kard was renamed Sound Blaster shortly before its release”. April 1990, pp. 22–23: Joey Latimer, “The latest sound hardware will have your PC singing”.
- PC Review issue 7, May 1992: Paul Rigby on the Ad Lib Gold Card (Ad Lib Inc. and the unnamed Yamaha chip).
- PC Player (Germany), November 1993: sound card group test (the OPL2 as “AdLib-Sound”).
- ASCII Corporation, MSX Datapack volume 2, §3, MSX-MUSIC: the OPLL ports, the doubled volume, the FM BIOS.