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Frequency modulation synthesis (or FM synthesis) is a form of sound synthesis whereby the frequency of a
waveform In electronics, acoustics, and related fields, the waveform of a signal is the shape of its graph as a function of time, independent of its time and magnitude scales and of any displacement in time.David Crecraft, David Gorham, ''Electro ...
is changed by modulating its frequency with a modulator. The frequency of an oscillator is altered "in accordance with the
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
of a modulating signal". FM synthesis can create both harmonic and inharmonic sounds. To synthesize harmonic sounds, the modulating signal must have a
harmonic A harmonic is a wave with a frequency that is a positive integer multiple of the ''fundamental frequency'', the frequency of the original periodic signal, such as a sinusoidal wave. The original signal is also called the ''1st harmonic'', t ...
relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. inharmonic), inharmonic bell-like and percussive spectra can be created. FM synthesis using analog
oscillator Oscillation is the repetitive or periodic variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples of oscillation include a swinging pendulum ...
s may result in pitch instability. However, FM synthesis can also be implemented digitally, which is more stable and became standard practice. Digital FM synthesis (implemented as phase modulation) was the basis of several musical instruments beginning as early as 1974. Yamaha built the first prototype
digital synthesizer A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. This in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digit ...
in 1974, based on FM synthesis, before commercially releasing the Yamaha GS-1 in 1980. The Synclavier I, manufactured by New England Digital Corporation beginning in 1978, included a digital FM synthesizer, using an FM synthesis algorithm licensed from Yamaha. Yamaha's groundbreaking
DX7 The Yamaha DX7 is a synthesizer manufactured by the Yamaha Corporation from 1983 to 1989. It was the first successful digital synthesizer and is one of the best-selling synthesizers in history, selling more than 200,000 units. In the early 1980 ...
synthesizer, released in 1983, brought FM to the forefront of synthesis in the mid-1980s. FM synthesis had also become the usual setting for games and software until the mid-nineties. Through sound cards like the AdLib and Sound Blaster,
IBM PC The IBM Personal Computer (model 5150, commonly known as the IBM PC) is the first microcomputer released in the IBM PC model line and the basis for the IBM PC compatible de facto standard. Released on August 12, 1981, it was created by a team ...
s popularized Yamaha chips like OPL2 and OPL3. OPNB was used as main basic sound generator board in SNK
Neo Geo Neo Geo is a family of video game hardware developed by SNK. On the market from 1990 to 2004, the brand originated with the release of an arcade system, the Neo Geo MVS and its home console counterpart, the Neo Geo AES. The Neo Geo MVS was ...
operated arcades (MVS) and home console (AES). Later variant in use for Taito Z System. The related OPN2 was used in the
Fujitsu is a Japanese multinational information and communications technology equipment and services corporation, established in 1935 and headquartered in Tokyo. Fujitsu is the world's sixth-largest IT services provider by annual revenue, and the la ...
FM Towns Marty and
Sega Genesis The Sega Genesis, known as the outside North America, is a 16-bit Fourth generation of video game consoles, fourth generation home video game console developed and sold by Sega. It was Sega's third console and the successor to the Master Syst ...
as one of its sound generator chips. Similarly, Sharp
X68000 The is a home computer created by Sharp Corporation. It was first released in 1987 and sold only in Japan. The initial model has a 10 MHz Motorola 68000 CPU, 1 MB of RAM, and lacks a hard drive. The final model was released in 1993 wi ...
and MSX ( Yamaha computer unit) also use FM-based soundchip, OPM. Throughout the 2000s, FM synthesis was also used on a wide range of phones to play ringtones and other sounds, typically in the Yamaha SMAF format.


History


1960s–1980s

By the mid-20th century,
frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog ...
(FM), a means of carrying sound, had been understood for decades and was being used to broadcast radio transmissions. FM synthesis was developed in the 1960s at
Stanford University Stanford University, officially Leland Stanford Junior University, is a private research university in Stanford, California. The campus occupies , among the largest in the United States, and enrolls over 17,000 students. Stanford is conside ...
, California, by John Chowning, who was trying to create sounds different from
analog synthesis An analog (or analogue) synthesizer is a synthesizer that uses analog circuits and analog signals to generate sound electronically. The earliest analog synthesizers in the 1920s and 1930s, such as the Trautonium, were built with a variety of ...
. His algorithm was licensed to Japanese company Yamaha in 1973. The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977 or U.S. Patent 4,018,121) is actually based on phase modulation, but the results end up being equivalent mathematically as both are essentially a special case of
quadrature amplitude modulation Quadrature amplitude modulation (QAM) is the name of a family of digital modulation methods and a related family of analog modulation methods widely used in modern telecommunications to transmit information. It conveys two analog message signa ...
. Yamaha's engineers began adapting Chowning's algorithm for use in a commercial digital synthesizer, adding improvements such as the "key scaling" method to avoid the introduction of distortion that normally occurred in analog systems during
frequency modulation Frequency modulation (FM) is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave. The technology is used in telecommunications, radio broadcasting, signal processing, and computing. In analog ...
, though it would take several years before Yamaha released their FM digital synthesizers. In the 1970s, Yamaha were granted a number of patents, under the company's former name "Nippon Gakki Seizo Kabushiki Kaisha", evolving Chowning's work. Yamaha built the first prototype FM
digital synthesizer A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. This in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digit ...
in 1974. Yamaha eventually commercialized FM synthesis technology with the Yamaha GS-1, the first FM digital synthesizer, released in 1980. FM synthesis was the basis of some of the early generations of
digital synthesizer A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. This in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digit ...
s, most notably those from Yamaha, as well as New England Digital Corporation under license from Yamaha. Yamaha's
DX7 The Yamaha DX7 is a synthesizer manufactured by the Yamaha Corporation from 1983 to 1989. It was the first successful digital synthesizer and is one of the best-selling synthesizers in history, selling more than 200,000 units. In the early 1980 ...
synthesizer, released in 1983, was ubiquitous throughout the 1980s. Several other models by Yamaha provided variations and evolutions of FM synthesis during that decade. Yamaha had patented its hardware implementation of FM in the 1970s, allowing it to nearly monopolize the market for FM technology until the mid-1990s.
Casio is a Japanese multinational electronics manufacturing corporation headquartered in Shibuya, Tokyo, Japan. Its products include calculators, mobile phones, digital cameras, electronic musical instruments, and analogue and digital watches. ...
developed a related form of synthesis called phase distortion synthesis, used in its CZ range of synthesizers. It had a similar (but slightly differently derived) sound quality to the DX series. Don Buchla implemented FM on his instruments in the mid-1960s, prior to Yamaha's patent. His 158, 258 and 259 dual oscillator modules had a specific FM control voltage input, and the model 208 (Music Easel) had a modulation oscillator hard-wired to allow FM as well as AM of the primary oscillator. These early applications used analog oscillators, and this capability was also followed by other modular synthesizers and portable synthesizers including
Minimoog The Minimoog is an analog synthesizer first manufactured by Moog Music between 1970 and 1981. Designed as a more affordable, portable version of the modular Moog synthesizer, it was the first synthesizer sold in retail stores. It was first pop ...
and
ARP Odyssey The ARP Odyssey is an analog synthesizer introduced by ARP Instruments in 1972. History ARP developed the Odyssey as a direct competitor to the Moog Minimoog and an answer to the demand for more affordable, portable, and less complicated "perf ...
.


1990s–present

With the expiration of the Stanford University FM patent in 1995, digital FM synthesis can now be implemented freely by other manufacturers. The FM synthesis patent brought Stanford $20 million before it expired, making it (in 1994) "the second most lucrative licensing agreement in Stanford's history". FM today is mostly found in software-based synths such as FM8 by Native Instruments or Sytrus by Image-Line, but it has also been incorporated into the synthesis repertoire of some modern digital synthesizers, usually coexisting as an option alongside other methods of synthesis such as subtractive,
sample-based synthesis Sample-based synthesis is a form of audio synthesis that can be contrasted to either subtractive synthesis or additive synthesis. The principal difference with sample-based synthesis is that the seed waveforms are sampled sounds or instruments ...
,
additive synthesis Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together. The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic '' partials'' ...
, and other techniques. The degree of complexity of the FM in such hardware synths may vary from simple 2-operator FM, to the highly flexible 6-operator engines of the Korg Kronos and Alesis Fusion, to creation of FM in extensively modular engines such as those in the latest synthesisers by
Kurzweil Music Systems Kurzweil Music Systems is an American company that produces electronic musical instruments. It was founded in 1982 by Stevie Wonder (musician), Ray Kurzweil (innovator) and Bruce Cichowlas (software developer). Kurzweil was a developer of rea ...
. New hardware synths specifically marketed for their FM capabilities disappeared from the market after the release of the
Yamaha SY99 The Yamaha SY99 is a synthesiser combining frequency modulation synthesis (branded as Advanced FM) and sample-based synthesis (branded as Advanced Wave Memory 2) and the direct successor to Yamaha's SY77/ TG77. Compared to the SY77, it has a larg ...
and FS1R, and even those marketed their highly powerful FM abilities as counterparts to
sample-based synthesis Sample-based synthesis is a form of audio synthesis that can be contrasted to either subtractive synthesis or additive synthesis. The principal difference with sample-based synthesis is that the seed waveforms are sampled sounds or instruments ...
and
formant synthesis Speech synthesis is the artificial production of human speech. A computer system used for this purpose is called a speech synthesizer, and can be implemented in software or hardware products. A text-to-speech (TTS) system converts normal langu ...
respectively. However, well-developed FM synthesis options are a feature of
Nord Lead The Nord Lead is a series of virtual analog subtractive synthesizers, manufactured by Clavia. Released in 1994, the original Nord Lead was the digital synthesizer that made the term ''virtual analog synthesis'' popular. The now widely accepted ...
synths manufactured by Clavia, the Alesis Fusion range, the Korg Oasys and Kronos and the Modor NF-1. Various other synthesizers offer limited FM abilities to supplement their main engines. In 2016,
Korg , founded as Keio Electronic Laboratories, is a Japanese multinational corporation that manufactures electronic musical instruments, audio processors and guitar pedals, recording equipment, and electronic tuners. Under the Vox brand name, th ...
released the Korg Volca FM, a, 3-voice, 6 operators FM iteration of the Korg Volca series of compact, affordable desktop modules, and Yamaha released the Montage, which combines a 128-voice sample-based engine with a 128-voice FM engine. This iteration of FM is called FM-X, and features 8 operators; each operator has a choice of several basic wave forms, but each wave form has several parameters to adjust its spectrum. The Yamaha Montage was followed by the more affordable Yamaha
MODX MODX (originally MODx) is an open source content management system and web application framework for publishing content on the World Wide Web and intranets. MODX is licensed under the GPL, is written in the PHP programming language, and supports ...
in 2018, with 64-voice, 8 operators FM-X architecture in addition to a 128-voice sample-based engine. Elektron in 2018 launched the Digitone, an 8-voice, 4 operators FM synth featuring Elektron's renowned sequence engine. FM-X synthesis was introduced with the Yamaha Montage synthesizers in 2016. FM-X uses 8 operators. Each FM-X operator has a set of multi-spectral wave forms to choose from, which means each FM-X operator can be equivalent to a stack of 3 or 4 DX7 FM operators. The list of selectable wave forms includes sine waves, the All1 and All2 wave forms, the Odd1 and Odd2 wave forms, and the Res1 and Res2 wave forms. The sine wave selection works the same as the DX7 wave forms. The All1 and All2 wave forms are a saw-tooth wave form. The Odd1 and Odd2 wave forms are pulse or square waves. These two types of wave forms can be used to model the basic harmonic peaks in the bottom of the harmonic spectrum of most instruments. The Res1 and Res2 wave forms move the spectral peak to a specific harmonic and can be used to model either triangular or rounded groups of harmonics further up in the spectrum of an instrument. Combining an All1 or Odd1 wave form with multiple Res1 (or Res2) wave forms (and adjusting their amplitudes) can model the harmonic spectrum of an instrument or sound. Combining sets of 8 FM operators with multi-spectral wave forms began in 1999 by Yamaha in the FS1R. The FS1R had 16 operators, 8 standard FM operators and 8 additional operators that used a noise source rather than an oscillator as its sound source. By adding in tuneable noise sources the FS1R could model the sounds produced in the human voice and in a wind instrument, along with making percussion instrument sounds. The FS1R also contained an additional wave form called the Formant wave form. Formants can be used to model resonating body instrument sounds like the cello, violin, acoustic guitar, bassoon, English horn, or human voice. Formants can even be found in the harmonic spectrum of several brass instruments.


Spectral analysis

The spectrum generated by FM synthesis with one modulator is expressed as follows: For modulation signal m(t) = B\,\sin(\omega_m t)\,, the carrier signal is: :\begin FM(t) & \ =\ A\,\sin\left(\,\int_0^t \left(\omega_c + B\,\sin(\omega_m\,\tau)\right)d\tau\right) \\ & \ =\ A\,\sin\left(\omega_c\,t - \frac\left(\cos(\omega_m\,t) - 1\right)\right) \\ & \ =\ A\,\sin\left(\omega_c\,t + \frac\left(\sin(\omega_m\,t - \pi/2) + 1\right)\right) \\ \end If we were to ignore the constant phase terms on the carrier \phi_c = B/\omega_m\, and the modulator \phi_m = - \pi/2\,, finally we would get the following expression, as seen on and : :\begin FM(t) & \ \approx\ A\,\sin\left(\omega_c\,t + \beta\,\sin(\omega_m\,t)\right) \\ & \ =\ A\left( J_0(\beta) \sin(\omega_c\,t) + \sum_^ J_n(\beta)\left ,\sin((\omega_c+n\,\omega_m)\,t)\ +\ (-1)^\sin((\omega_c-n\,\omega_m)\,t)\,\right\right) \\ & \ =\ A\sum_^ J_n(\beta)\,\sin((\omega_c+n\,\omega_m)\,t) \end where \omega_c\,,\,\omega_m\, are angular frequencies (\,\omega = 2\pi f\,) of carrier and modulator, \beta = B / \omega_m\, is frequency modulation index, and
amplitude The amplitude of a periodic variable is a measure of its change in a single period (such as time or spatial period). The amplitude of a non-periodic signal is its magnitude compared with a reference value. There are various definitions of am ...
s J_n(\beta)\, is n\,-th Bessel function of first kind, respectively.The above expression is transformed using trigonometric addition formulas : \begin \sin(x \pm y) &= \sin x \cos y \pm \cos x \sin y \end and a lemma of Bessel function : \begin \cos(\beta\sin \theta) & = J_0(\beta) + 2\sum_^J_(\beta)\cos(2n\theta) \\ \sin(\beta\sin \theta) & = 2\sum_^J_(\beta)\sin((2n+1)\theta) \end : (Source: ) as following: : \begin & \sin\left(\theta_c + \beta\,\sin(\theta_m)\right) \\ & \ =\ \sin(\theta_c)\cos(\beta\sin(\theta_m)) + \cos(\theta_c)\sin(\beta\sin(\theta_m)) \\ & \ =\ \sin(\theta_c)\left _0(\beta) + 2\sum_^J_(\beta)\cos(2n \theta_m)\right + \cos(\theta_c)\left \sum_^J_(\beta)\sin((2n+1)\theta_m)\right\\ & \ =\ J_0(\beta) \sin(\theta_c) + J_1(\beta) 2\cos(\theta_c)\sin(\theta_m) + J_2(\beta) 2\sin(\theta_c)\cos(2\theta_m) + J_3(\beta) 2\cos(\theta_c)\sin(3\theta_m) + ... \\ & \ =\ J_0(\beta) \sin(\theta_c) + \sum_^ J_n(\beta)\left ,\sin(\theta_c + n\theta_m)\ +\ (-1)^\sin(\theta_c - n\theta_m)\,\right\\ & \ =\ \sum_^ J_n(\beta)\,\sin(\theta_c + n\theta_m)\qquad(\because\ J_(x) = (-1)^n J_(x)) \end


See also

*
Additive synthesis Additive synthesis is a sound synthesis technique that creates timbre by adding sine waves together. The timbre of musical instruments can be considered in the light of Fourier theory to consist of multiple harmonic or inharmonic '' partials'' ...
*
Chiptune Chiptune, also known as chip music or 8-bit music, is a style of synthesized electronic music made using the programmable sound generator (PSG) sound chips or synthesizers in vintage arcade machines, computers and video game consoles. The ...
*
Digital synthesizer A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. This in contrast to older analog synthesizers, which produce music using analog electronics, and samplers, which play back digit ...
*
Electronic music Electronic music is a genre of music that employs electronic musical instruments, digital instruments, or circuitry-based music technology in its creation. It includes both music made using electronic and electromechanical means ( electro ...
*
Sound card A sound card (also known as an audio card) is an internal expansion card that provides input and output of audio signals to and from a computer under the control of computer programs. The term ''sound card'' is also applied to external audio ...
*
Sound chip A sound chip is an integrated circuit (chip) designed to produce audio signals through digital, analog or mixed-mode electronics. Sound chips are typically fabricated on metal–oxide–semiconductor (MOS) mixed-signal chips that process ...
*
Video game music Video game music (or VGM) is the soundtrack that accompanies video games. Early video game music was once limited to sounds of early sound chips, such as programmable sound generators (PSG) or FM synthesis chips. These limitations have led t ...


References


Footnotes


Citations


Bibliography

* * * * *


External links


An Introduction To FM
by Bill Schottstaedt



by Gordon Reid

by Gordon Reid


mirror site of F.M. Synthesis, 2019
{{Sound synthesis types Sound synthesis types