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((Short description|Frequency mixing function in signal processing))
((Use dmy dates|date=August 2019))
((Use American English|date=March 2020))

[[File:Ring Modulator.PNG|thumb|right|300px|Schematic diagram of a [[ring modulator]], showing ring of [[diode]]s]]
[[File:Ring modulation two forms Multiplilcation RM.svg|thumb|upright=1.1|An example of ring modulation on sine waves of frequency <math>f</math> (top) and <math>12f</math> (middle), producing a variation in amplitude of the sine wave-like frequency on <math>12f</math> (bottom)<ref name="Roads">[[Curtis Roads]] (1996). ''[https://books.google.com/books?id=nZ-TetwzVcIC&pg=PA220 The Computer Music Tutorial]'', pp. 220-221. MIT Press. ((ISBN|9780262680820)).</ref>]]

In [[electronics]], '''ring modulation''' is a [[signal processing]] function, an implementation of [[frequency mixer|frequency mixing]], in which two [[Signal|signals]] are combined to yield an output signal. One signal, called the carrier, is typically a [[sine wave]] or another simple [[waveform]]; the other signal is typically more complicated and is called the input or the [[Modulation|modulator]] signal.  A '''ring modulator''' is an electronic device for ring modulation. A ring modulator may be used in music [[synthesizer]]s and as an [[effects unit]].

The name derives from the fact that the [[analog circuit]] of [[diode]]s originally used to implement this technique takes the shape of a ring: a '''diode ring'''.<ref>Richard Orton, "Ring Modulator", ''The New Grove Dictionary of Music and Musicians'', page 429, volume 21, second edition, edited by [[Stanley Sadie]] and [[John Tyrrell (professor of music)|John Tyrrell]] (London: Macmillan Publishers, 2001): "the ring modulator takes its name from the characteristic ring formation of four diodes in its analog circuit."</ref> The circuit is similar to a [[bridge rectifier]], except that instead of the diodes facing left or right, they face clockwise or counterclockwise.

Ring modulation is quite similar to [[amplitude modulation]], with the difference that in the latter the modulator is shifted to be positive before being multiplied with the carrier, while in the former the unshifted modulator is multiplied with the carrier. This has the effect that ring modulation of two sine waves having frequencies of 1,500 Hz and 400 Hz will produce as output signal the sum of a sine wave with frequency 1,900 Hz and one with frequency 1,100 Hz. These two output frequencies are known as [[sideband]]s. If one of the input signals has significant [[overtones]] (which is the case for [[square waves]]), the output will sound quite different, since each [[harmonic]] will generate its own pair of sidebands that won't be harmonically-related.<ref>[[Allen Strange|Strange, Allen]] (1972). ''Electronic Music'', p. 11. Wm. C. Brown Co. Publishers. ((ISBN|0-697-03612-X)).</ref>

== Operation ==
Denoting the carrier signal by <math>c(t)</math>, the modulator signal by <math>x(t)</math> and the output signal by <math>y(t)</math> (where <math>t</math> denotes time), ring modulation is described by the formula

:<math>y(t)=x(t)\cdot c(t).</math>

[[File:Frequenzy Mixer Mini-Circuits SBL-1.png|thumb|Double balanced high level frequency mixer Mini-Circuits SBL-1 with four Schottky diodes. [[Local oscillator|LO]] level +7 dBm (1.41 V<sub>p-p</sub>) and RF 1–500 MHz (ADE-1: 0.5–500 MHz)]]
[[File:Frequency mixer Mini Circuits ADE-1 macro.png|thumb|Macro of the ADE-1]]
[[File:Ring modulation two forms Diode-clipping or 'chopper' RM.svg|thumb|upright=1.1|An example of ring modulation on a sine wave of frequency <math>f</math> and a square wave of frequency <math>12f</math>, resulting in a complex sound using analog FM known as ''diode-clipping'' or ''chopper'' RM, producing a variation in amplitude of the square wave-like frequency on <math>12f</math><ref name="Roads"/>]]

If <math>c(t)</math> and <math>x(t)</math> are sine waves with frequencies <math>f_c</math> and <math>f_x</math>, respectively, then <math>y(t)</math> will be the sum of two ([[Phase shift|phase-shifted]]) sine waves, one of frequency <math>f_c+f_x</math> and the other of frequency <math>f_c-f_x</math>. This is a consequence of the [[trigonometric identity]]

:<math>\sin(u)\cdot \sin(v)=\frac{1}{2}\left(\cos(u-v)-\cos(u+v)\right).</math>

Alternatively, one can use the fact that multiplication in the [[time domain]] is the same as [[convolution]] in the [[frequency domain]].

Ring modulators thus output the [[combination tone|sum and difference]] of the frequencies present in each waveform. This process of ring modulation produces a signal rich in [[Partial (music)|partials]]. As well, neither the carrier nor the incoming signal are prominent in the output, and ideally, not present at all.

Two oscillators, whose frequencies were harmonically related and ring modulated against each other, produce sounds that still adhere to the harmonic partials of the notes but contain a very different spectral makeup. When the oscillators' frequencies are ''not'' harmonically related, ring modulation creates [[inharmonic]]s, often producing bell-like or otherwise metallic sounds.

If the carrier signal is a [[square wave]] of frequency <math>f_c</math>, whose [[Fourier expansion]] contains the [[Fundamental frequency|fundamental]] and a series of reducing-amplitude odd [[harmonic]]s:

:<math>c(t) = \sin f_ct + \frac 1 3 \sin 3f_ct + \frac 1 5 \sin 5f_ct + \frac 1 7 \sin 7f_ct + \ldots</math>

and the carrier frequency <math>f_c</math> is at least twice the maximum frequency of the modulating signal ''<math>x(t)</math>'', then the resulting output is a series of duplicates of ''<math>x(t)</math>'' at increasing regions of the frequency spectrum.<ref name="analog.com" /> For example, let ''<math>x(t)</math>'' represent a sine wave at 100&nbsp;Hz, and the carrier ''<math>c(t)</math>'' be an ideal square wave at 300&nbsp;Hz. The output will then include sine waves at 100±300&nbsp;Hz, 100±900&nbsp;Hz, 100±1500&nbsp;Hz, 100±2100&nbsp;Hz, etc., at decreasing amplitudes according to the Fourier expansion of the carrier square wave. If the carrier frequency is less than twice the upper frequency of the signal then the resulting output signal contains spectral components from both the signal and the carrier that combine in the time domain. 

Because the output contains neither the individual modulator or carrier components, the ring modulator is said to be a ''double-balanced'' mixer,<ref>((cite web|url=https://www.electronics-notes.com/articles/radio/rf-mixer/double-balanced-mixer.php|title=Double Balanced Mixer – Theory; Circuit; Operation – Tutorial – Electronics Notes))</ref> where both input signals are suppressed (not present in the output)—the output is composed entirely of the sum of the products of the frequency components of the two inputs.

== History ==
The ring modulator was invented by Frank A. Cowan in 1934 and patented in 1935<ref>((US patent|src=uspto|2025158))</ref> as an improvement on the invention of Clyde R. Keith at [[Bell Labs]].<ref>((US patent|src=uspto|1855576))</ref> The original application was in the field of [[Telephone|analog telephony]] for [[frequency-division multiplexing]] for carrying multiple voice signals over telephone cables. It has since been applied to a wider range of uses, such as [[voice inversion]], radio [[transceiver]]s, and [[electronic music]].

While the original Cowan patent describes a circuit with a ring of four diodes, later implementations used [[field effect transistor|FET]]s as the switching elements.

== Circuit description ==
The ring modulator includes an input stage, a ring of four diodes excited by a carrier signal, and an output stage. The input and output stages typically include [[Transformer|transformers]] with center-taps towards the diode ring. It is important to note that while the diode ring has some similarities to a [[bridge rectifier]] the diodes in a ring modulator all point in the same clockwise or counterclockwise direction. (See the schematic of a ring modulator in the upper right.)

The carrier, which alternates between positive and negative current, at any given time makes one pair of diodes conduct, and [[P–n junction#Reverse bias|reverse-biases]] the other pair. The conducting pair carries the signal from the left transformer secondary to the primary of the transformer at the right. If the left carrier terminal is positive, the top and bottom diodes conduct. If that terminal is negative, then the side diodes conduct, but create a polarity inversion between the transformers. This action is much like that of a [[DPDT#Contact terminology|DPDT]] (''double pole, double throw'') switch wired for reversing connections.

A particular elegance of the ring modulator is that it is bidirectional: the signal flow can be reversed allowing the same circuit with the same carrier to be used either as a [[modulator]] or [[demodulator]], for example in low-cost radio transceivers.

==Integrated circuit methods of ring modulation==
((more citations needed section|date=February 2015))
Some modern ring modulators are implemented using [[digital signal processing]] techniques by simply multiplying the time domain signals, producing a nearly-perfect signal output. [[Intermodulation]] products can be generated by carefully selecting and changing the [[frequency]] of the two input waveforms. If the signals are processed digitally, the frequency-domain convolution becomes [[circular convolution]]. If the signals are [[wideband]], this will cause [[aliasing]] distortion, so it is common to [[oversampling|oversample]] the operation or low-pass filter the signals prior to ring modulation.

The [[MOS Technology SID|SID]] chip found in the [[Commodore 64]] allows for [[triangle wave]]s to be ring modulated. Oscillator 1 gets modulated by oscillator 3's frequency, oscillator 2 by oscillator 1's frequency, and oscillator 3 by oscillator 2's frequency. Ring modulation is disabled unless the carrier oscillator is set to produce a triangle wave, but the modulating oscillator can be set to generate any of its available waveforms. However, no matter what waveform you set the modulating oscillator to, the ring modulation will always have the effect of modulating a triangle wave with a square wave.<ref>Commodore Programmer's Reference Guide, page 463</ref>((not in ref|reason=Although the programming guide says that none of the parameters of the modulating oscillator affect the modulation, it does not state that a square wave is used|date=August 2021))

On an [[ARP Odyssey]] synthesizer (and a few others from that era as well) the ring modulator is an [[XOR gate|XOR function]] (formed from [[XOR gate#Alternatives|four]] [[NAND gate]]s) fed from the square wave outputs of the two oscillators. For the limited case of square or pulse wave signals, this is identical to true ring modulation.

Analog multiplier ICs (such as those made by Analog Devices) would work as ring modulators, of course with regard to such matters as their operating limits and scale factors. Use of multiplier ICs means that the modulation products are largely confined to sum and difference frequency of inputs (unless the circuit is overdriven), rather than the much more complicated products of the rectifier circuit.

== Limitations ==

Any DC component of the carrier will degrade the suppression of the carrier and thus in radio applications the carrier is typically transformer- or capacitor-coupled; in low frequency (e.g., audio) applications the carrier may or may not be desired in the output.<ref>((cite web|url=http://www.soundonsound.com/sos/mar00/articles/synthsecrets.htm|title=Synth Secrets, Part 11: Amplitude Modulation))</ref>

Imperfections in the diodes and transformers introduce artifacts of the two input signals. In practical ring modulators, this leakage can be reduced by introducing opposing imbalances (''e.g.'', variable resistors or capacitors).

== Applications ==
=== Radio communications ===
Ring modulation has also been extensively used in [[radio receiver]]s, for example, to [[demodulate]] an [[FM broadcasting|FM]] stereo signal, and to heterodyne microwave signals in mobile telephone and wireless networking systems. In this case, the circuit is sometimes called a ''ring demodulator'', one of many possible [[Chopper (electronics)|chopper circuits]].<ref name="Meikle 2008 336"/><ref name="Yadav 2008 83"/> A ring modulator can be used to generate a double-sideband suppressed-carrier (DSB-SC) wave used in radio transmission.<ref name="T G Thomas S Chandra Sekhar 2005 37"/>

=== Music and sound effects ===
((listen
 | header       = Audio samples of the ring modulation effect:
 | filename     = Ring_Modulation-Original_sample.ogg
 | title        = Unprocessed original sample
 | description  =
 | format       =
 | filename2    = Ring_Modulation-with_2500Hz.ogg
 | title2       = Ring modulation with a 2500 Hz sound
 | description2 = Notice the bell-like sound.
 | format2      =
 | filename3    = Ring_Modulation-with_sweep_to_9kHz.ogg
 | title3       = Ring modulation with an exponential sweep from 0 Hz to 9 kHz
 | description3 = On lower modulation frequencies, the ring modulation is perceived as a tremolo effect (as in the first part of the sound)
 | format3      =
))

One of the earliest musical instruments utilizing a ring modulator was the ''Melochord'' (1947) built by [[Harald Bode]]. It was a two-tone melody keyboard instrument with foot controllers and later added a second keyboard for timbre control, featuring a white-noise generator, envelope controller, formant filters and ring modulators for harmonics.<ref name="palov"/> The early Melochord was extensively used by [[Werner Meyer-Eppler]] in the early days of the electronic music studio at [[Bonn University]].<ref name="melo"/> Meyer-Eppler mentioned the musical application of ring modulator in his book ''Elektrische Klangerzeugung'', published in 1949.<ref name="meyer-eppler1949"/>

Meyer-Eppler's student [[Karlheinz Stockhausen]] used ring modulation in 1956 for some sounds in ''[[Gesang der Jünglinge]]'' and his realization score for ''[[Telemusik]]'' (1966<ref name="Collins">[[Nick Collins (composer)|Collins, Nick]] (2010). ''[https://books.google.com/books?id=mCpqmESEOEcC&pg=PA124 Introduction to Computer Music]'', pp. 124-125. John Wiley & Sons. ((ISBN|9780470714553)).</ref>) also calls for it. Indeed, several entire compositions by Stockhausen are based around it, such as ''[[Mixtur]]'' (1964), one of the first compositions for orchestra and live electronics; ''[[Mikrophonie (Stockhausen)|Mikrophonie II]]'' (1965), where the sounds of choral voices are modulated with a [[Hammond organ]]; ''[[Mantra (Stockhausen)|Mantra]]'' (1970),<ref name="Collins"/> where the sounds from two pianos are routed through ring modulators; and ''Licht-Bilder'' (2002) from ''[[Sonntag aus Licht]]'' (2003),<ref name="Roads"/> which ring-modulates flute and trumpet.<ref name="Brümmer 2008"/><ref name="Stockhausen 1996"/><ref name="Stockhausen 2005"/> Other Stockhausen pieces employing ring modulation include ''[[Kontakte]]'' (1960),<ref name="Roads"/> ''Mikrophonie I'' (1964),<ref name="Roads"/> ''[[Hymnen]]'' (1969),<ref name="Roads"/> ''[[Prozession]]'' (1967),<ref name="Roads"/> and ''[[Kurzwellen]]'' (1968).<ref name="Roads"/>

A ring-modulator was the major component used in [[Louis and Bebe Barron]]'s music for the film ''[[Forbidden Planet]]'' (1956). One of the best-known applications of the ring modulator may be its use by [[Brian Hodgson]] of the [[BBC Radiophonic Workshop]] to produce the distinctive voice of the [[Dalek]]s in the [[television series]] ''[[Doctor Who]]'', starting in 1963.<ref name="Jeremy Bentham"/>

One of the first products dedicated for music was the ''Bode Ring Modulator'' developed in 1961 by [[Harald Bode]]. Also in 1964 he developed the ''Bode Frequency Shifter,'' which produced a clearer sound by eliminating a side band.<ref name="HaraldBodeLifetime"/> These devices were designed to be controlled by voltage, compatible with modular synthesizer architecture also advocated by him,<ref name="bode1961"/> and these modules were licensed to [[Moog Music|R.A. Moog]] for their [[Moog modular synthesizer]]s started in 1963–1964.<ref name="TomRhea2004"/> In 1963, [[Don Buchla]] included an optional ring modulator in his first modular synthesizer, the [[Buchla|Model 100]].<ref name="Buchla"/> Also [[Tom Oberheim]] built a ring modulator unit for [[The United States of America (band)|his musician friend]] in the late 1960s,<ref name="oberheim1970"/><ref name="oberheim2008"/> and it became an origin of [[Oberheim Electronics]] ''Music Modulator''<ref name="Oberheim Music Modulator"/> and ''[[Gibson Guitar Corporation#Brand names|Maestro]] Ring Modulator'',<ref name="maestroRM1A"/> one of the earliest ring modulator [[Effects unit|effect]] products for guitarists. The [[Electronic Music Studios|EMS]] [[VCS3]], [[Synthi A]], [[ARP 2600]], [[ARP Odyssey|Odyssey]], [[Rhodes Chroma]] and [[Yamaha CS-80]] synthesizers also featured built-in ring modulators.

[[John McLaughlin (musician)|John McLaughlin]] employs the ring modulator heavily in the 1974 [[Mahavishnu Orchestra]] album ''[[Visions of the Emerald Beyond]]'', especially on the track "On the Way Home to Earth". On [[Miles Davis]]' 1975 live album ''[[Agharta (album)|Agharta]]'', guitarist [[Pete Cosey]] ran the sounds he played through a ring modulator.<ref name="Trzaskowski"/> [[Deep Purple]]'s [[Jon Lord]] fed the signal from his Hammond through a Gibson Ring Modulator unit live on stage, which he described in 1989.<ref name="Lord Almighty"/><ref name="Jon Lord"/> Founding member of [[Hawkwind]], Dik Mik, a self-confessed non-musician, used a ring modulator as his main instrument during his time with the band (1969-1973).<ref name="Hawkwind"/>

[[Vangelis]] used a ring modulator with his [[Yamaha CS-80]] to improvise his 1978 avant-garde-experimental album ''[[Beaubourg (album)|Beaubourg]]''. The music on the album is often atonal, with the ring modulator converting the synthesizer's sound into complex metallic timbres.<ref name="BeaubourgReviewSynthopia"/> It remains the most experimental released work by the artist, with reviewers calling it "difficult listening at best".<ref name="BeaubourgReviewAllmusic"/>

Ring modulation is used in the piece ''Ofanim'' (1988/<!--revised-->1997) by [[Luciano Berio]], and in the first section is applied to a child's voice and a [[clarinet]]: "The transformation of the child voice into a clarinet was desired. For this purpose, a pitch detector computes the instantaneous frequency <math>f_0 (n)</math> of the voice. Then the child voice passes through a ring modulator, where the frequency of the carrier <math>f_c</math> is set to <math>f_0 (n)/2</math>. In this case odd harmonics prevail which is similar to the sound of a clarinet in the low register."<ref name="DAFX">Zölzer, Udo; ed. (2002). ''[https://books.google.com/books?id=h90HIV0uwVsC&pg=PA75 DAFX - Digital Audio Effects]'', p.76-7. John Wiley & Sons. ((ISBN|9780471490784)).</ref>((failed verification|reason=may verify the math but does not verify the quote|date=March 2020))

=== Analogue telephone systems ===
An early application of the ring modulator was for combining multiple analog telephone voice channels into a single wideband signal to be carried on a single cable using [[frequency-division multiplexing]]. A ring modulator in combination with [[carrier wave]] and filter was used to assign channels to different frequencies.

Early attempts at [[Privacy|securing]] analog telephone channels used ring modulators to modify the spectrum of the audio speech signals. One application is spectral inversion, typically of speech; a carrier frequency is chosen to be above the highest speech frequencies (which are low-pass filtered at, say, 3&nbsp;kHz, for a carrier of perhaps 3.3&nbsp;kHz), and the sum frequencies from the modulator are removed by more low-pass filtering. The remaining difference frequencies have an inverted spectrum: high frequencies become low, and vice versa.

== See also ==
* [[Theremin]]

==References==
((Reflist|refs=
<ref name="HaraldBodeLifetime">
((citation
 | title     = Harald Bode—A Lifetime for Sound
 | url       = http://rebekkahpalov.us/HBodeProgram.pdf
 | publisher = Harald Bode News
 | access-date= 2011-01-27
))</ref>
<ref name="bode1961">Harald Bode, "European Electronic Music Instrument Design", ''Journal of the [[Audio Engineering Society]]'' 9 (1961): 267.</ref>
<ref name="TomRhea2004">
((citation
 | author    = Tom Rhea
 | url       = https://www.experimentaltvcenter.org/harald-bode
 | title     = Harald Bode Biography
 |date = 21 March 2011| location  = (New York
 | publisher = Experimental Television Center Ltd, 2004)
 | url-status = live
 | archive-url  = https://web.archive.org/web/20110719162439/http://www.experimentaltvcenter.org/history/people/bio.php3?id=83
 | archive-date = 2011-07-19
)) </ref>
<ref name="analog.com">((cite web|url=http://www.analog.com/library/analogdialogue/archives/47-06/multipliers_modulators.html|title=Multipliers vs. Modulators))</ref>
<ref name="Meikle 2008 336">((cite book| author = Hamish Meikle| title = Modern Radar Systems| url = https://books.google.com/books?id=mGSE_tmA_HQC&pg=PA336| year = 2008| publisher = Artech House| isbn = 978-1-59693-243-2| page = 336 ))</ref>
<ref name="Yadav 2008 83">((cite book| author = Abhishek Yadav| title = Analog Communication System| url = https://books.google.com/books?id=FoSyJcvPPUwC&pg=PA83| year = 2008| publisher = Firewall Media| isbn = 978-81-318-0319-6| page = 83 ))</ref>
<ref name="T G Thomas S Chandra Sekhar 2005 37">((cite book| author = T G Thomas S Chandra Sekhar| title = Communication Theory| url = https://books.google.com/books?id=C1C6IBiCoXsC&pg=PA37| year = 2005| publisher = Tata McGraw-Hill Education| isbn = 978-0-07-059091-5| page = 37 ))</ref>
<ref name="palov">
((citation
 | author     = Rebekkah Palov
 | title      = Harald Bode—A Short Biography
 | journal    = EContact!
 | volume     = 13 | issue = 4
 | date       = July 2011
 | url        = http://cec.sonus.ca/econtact/13_4/palov_bode_biography.html
 | publisher  = Canadian Electroacoustic Community
))</ref>
<ref name="melo">
((citation
 | title      = The "Melochord" (1947–9)
 | url        = http://www.keyboardmuseum.org/pre60/1940/melochord.html
 | archive-url = https://web.archive.org/web/20071114183540/http://www.keyboardmuseum.org/pre60/1940/melochord.html
 | archive-date= 2007-11-14
 | work       = The Keyboardmuseum Online
)) (description and history)
</ref>
<ref name="meyer-eppler1949">
((citation
 | author    = Werner Meyer-Eppler
 | title     = Elektronische Klangerzeugung: Elektronische Musik und synthetische Sprache
 | language  = <!-- Germany -->
 | location  = (Bonn
 | publisher = Ferdinand Dümmlers, 1949)
))</ref>
<ref name="Brümmer 2008">Ludger Brümmer, "Stockhausen on Electronics, 2004", ''[[Computer Music Journal]]'' 32, no. 4 (2008):10–16.</ref>
<ref name="Stockhausen 1996">Karlheinz Stockhausen, "Electroacoustic Performance Practice", translated by [[Jerome Kohl]], ''[[Perspectives of New Music]]'' 34, no. 1 (Winter, 1996): 74–105. Citation on 89.</ref>
<ref name="Stockhausen 2005">Karlheinz Stockhausen, "Einführung"/"Introduction", English translation by [[Suzanne Stephens]], in booklet accompanying Karlheinz Stockhausen, ''Licht-Bilder (3. Szene vom SONNTAG aus LICHT)'', 2-CD set, Stockhausen Gesamtausgabe/Complete Edition 68A–B (Kürten: Stockhausen-Verlag, 2005): 10 & 51</ref>
<ref name="Buchla">
((citation
 | title     = Buchla Electronic Musical Instruments—Historical Overview
 | url       = http://www.buchla.com/historical/
 | publisher = Buchla & Associates
 | access-date= 2011-01-27
))</ref>
<ref name="oberheim1970">
((citation
 | author    = Thomas E. Oberheim
 | title     = A Ring Modulator Device for the Performing Musician
 | url       = https://secure.aes.org/forum/pubs/conventions/?elib=1304
 | work      = [[AES Convention]] 38 (May 1970)
)), No. 708 (G-4). <!-- not the page number but the paper number -->
</ref>
<ref name="oberheim2008">
((citation
 | title     = Session Transcript: Tom Oberheim
 | url       = http://www.redbullmusicacademy.com/lectures/tom-oberheim-polyphonic-one-love?template=RBMA_Lecture%2Ftranscript
 | work      = [[Red Bull Music Academy]] Barcelona 2008
))</ref>
<ref name="Oberheim Music Modulator">
((cite AV media
 | title     = Oberheim Music Modulator
 | url       = http://www.myspace.com/edisonmusiccorp/photos/4125267
 | medium    = photo
 | publisher = Edison Music Corporation
))
</ref>
<ref name="maestroRM1A">
((citation
 | title     = Maestro RM-1A Ring Modulator
 | url       = http://www.effectsdatabase.com/model/maestro/rm1/a
 | publisher = DiscoFreq's Effects Database
))</ref>
<ref name="Trzaskowski">((cite journal|last=Trzaskowski|first=Andrzej|author-link=Andrzej Trzaskowski|year=1976|journal=Jazz Forum: The Magazine of the International Jazz Federation|page=74|quote=Most of the selections are kept in the rock-jazz climate with the rhythm course being interrupted now and again by an overflowing patch of accumulated layers of electronic and percussive effects (Theme from Jack Johnson, Prelude). In fact, electronic effects appear repeatedly in the form of 'bruitistic' whizzes and grinds of the synthi resembling a buzz saw and of the guitar steered through a ring modulator.))</ref>
<ref name="Lord Almighty">((cite journal|url=https://books.google.com/books?id=-2IJAQAAMAAJ&q=%22jon+lord%22+%22ring+modulator%22|title=Lord Almighty|journal=[[Keyboard (magazine)|Keyboard]]|volume=24|year=1998|access-date=21 January 2016))</ref>
<ref name="Jon Lord">((cite web|url=http://www.thehighwaystar.com/interviews/lord/jl19890100.html|title=Interview with Jon Lord|work=Modern Keyboard|date=January 1989|access-date=21 January 2015))</ref>
<ref name="Hawkwind">((cite book|title=Hawkwind: Sonic Assassins|page=20|author=Ian Abrahams|publisher=SAF Publishing|year=2004|isbn=9780946719693))</ref>
<ref name="Jeremy Bentham">
((citation
 | author    = Jeremy Bentham
 | year      =1986
 | title     = Doctor Who: The Early Years
 | location  = (London
 | publisher = [[W. H. Allen & Co.]], 1986)
 | page      = 127
 | isbn      = 0-491-03612-4
))</ref>
<ref name="BeaubourgReviewSynthopia">
((cite web
|url=https://www.synthtopia.com/content/2003/12/07/vangelis-beaubourg/
|title=Vangelis - Beaubourg
|work=Synthtopia
|date=7 December 2003
|access-date=26 August 2022
))</ref>
<ref name="BeaubourgReviewAllmusic">
((cite web
|url=((AllMusic|class=album|id=r108871|pure_url=yes))
|title=Vangelis - Beaubourg
|publisher=AllMusic
|first=Steven
|last=McDonald
|access-date=26 August 2022
))</ref>
))

==External links==
* ((cite web |url=http://www.harmony-central.com/Effects/Articles/Ring_Modulation/ |publisher=Harmony Central |title=Effects Explained: Ring Modulation |author=Scott Lehman |archive-url=https://web.archive.org/web/20051201090154/http://www.harmony-central.com/Effects/Articles/Ring_Modulation/ |archive-date=2005-12-01))

((music technology))

[[Category:Audio effects]]
[[Category:Electronic musical instruments]]
[[Category:Frequency mixers]]
[[Category:Radio modulation modes]]

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