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| {|style="float:right;width:400px;text-align:center;" <!-- class="wikitable" -->
| | I'm Verna and I live in Geertruidenberg. <br>I'm interested in Economics, Insect collecting and Korean art. I like travelling and reading fantasy.<br><br>My web-site; [http://www.humitech.co.nz/images/beats-by-dre.asp beats music] |
| |+ '''FM synthesis using 2 operators'''
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| |style="line-height:1.8ex;text-align:left;"|<small>[[Image:2op FM.svg|left|200px]] A 220 Hz carrier tone ''f<sub>c</sub>'' modulated by a 440 Hz modulating tone ''f<sub>m</sub>'', with various choices of [[frequency modulation#Modulation index|modulation index]], ''β''. The time domain signals are illustrated above, and the corresponding spectra are shown below (spectrum amplitudes in [[decibel|dB]]).
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| ; Waveforms for each ''β'':
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| [[Image:frequencymodulationdemo-td.png]]
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| ; Spectra for each ''β'':
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| [[Image:frequencymodulationdemo-fd.png]]
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| |}
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| In [[Sound recording and reproduction|audio]] and [[music]], '''Frequency Modulation Synthesis''' (or '''FM synthesis''') is a form of [[sound synthesis|audio synthesis]] where the [[timbre]] of a simple waveform (such as a square, triangle, or sawtooth) is changed by [[Frequency modulation|modulating its frequency]] with a modulator frequency that is also in the audio range, resulting in a more complex waveform and a different-sounding tone that can also be described as "gritty" if it is a thick and dark timbre. The frequency of an oscillator is altered or [[distortion synthesis|distorted]], "in accordance with the [[amplitude]] of a modulating signal." {{harv|Dodge|Jerse|1997|p=115}}
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| FM synthesis can create both harmonic and [[Inharmonicity|inharmonic]] sounds. For synthesizing harmonic sounds, the modulating signal must have a [[harmonic]] relationship to the original carrier signal. As the amount of frequency modulation increases, the sound grows progressively more complex. Through the use of modulators with frequencies that are non-integer multiples of the carrier signal (i.e. non harmonic), [[Atonality|atonal]] and [[Tonality|tonal]] bell-like and percussive sounds can easily be created.
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| FM synthesis using analog [[oscillator]]s may result in pitch instability, but FM synthesis can be implemented digitally, and the latter proved so much more reliable that it became the standard. As a result, digital FM synthesis (using the more frequency-stable [[phase modulation]] variant) was the basis of Yamaha's groundbreaking [[Yamaha DX7|DX7]], which brought FM to the forefront of synthesis in the mid-1980s.
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| ==History==
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| The technique of the digital implementation of frequency modulation, which was developed by [[John Chowning]] ({{harvnb|Chowning|1973}}, cited in {{harvnb|Dodge|Jerse|1997|p=115}}) at [[Stanford University]] in 1967-68, was patented in 1975 and later licensed to [[Yamaha Corporation|Yamaha]].
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| The implementation commercialized by Yamaha ([http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=4018121 US Patent 4018121 Apr 1977] or [http://www.google.com/patents/about?id=GNEzAAAAEBAJ&dq= U.S. Patent 4,018,121]) is actually based on [[phase modulation]], but the results end up being equivalent mathematically, with phase modulation simply making the implementation resilient against undesirable drift in frequency of carrier waves due to self-modulation or due to DC bias in the modulating wave.<ref>
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| {{cite web
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| | author = Rob Hordijk
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| | title = FM synthesis on Modular
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| | url = http://www.clavia.se/nordmodular/Modularzone/FMsynthesis.html
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| | work = Nord Modular & Micro Modular V3.03 tips & tricks
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| | publisher = Clavia DMI AB
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| }}</ref>
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| As noted earlier, FM synthesis was the basis of some of the early generations of [[digital synthesizer]]s from Yamaha, with Yamaha's flagship [[Yamaha DX7|DX7]] synthesizer being ubiquitous throughout the 1980s and several other models by Yamaha providing variations of FM synthesis. The most advanced FM synths produced by Yamaha were the 6-operator keyboard [[Yamaha SY99|SY99]] and the 8-operator module [[Yamaha FS1R|FS1R]]: each features Yamaha's Advanced FM (AFM) alongside and able to be layered or interfaced with other synthesising technologies, respectively AWM2 (Advanced Wave Memory 2) [[sample-based synthesis]] in the SY99 and [[formant synthesis]] in the FS1R, neither of which combinations have ever been duplicated, as neither have some of the other advanced FM features of these Yamaha devices.
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| Yamaha had patented its hardware implementation of FM in the 1980s, allowing it to nearly monopolize the market for that technology until the mid-1990s. [[Casio]] developed a related form of synthesis called [[phase distortion synthesis]], used in its [[Casio CZ synthesizers|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.
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| 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".<ref>Stanford University News Service (06/07/94), [http://news.stanford.edu/pr/94/940607Arc4222.html Music synthesis approaches sound quality of real instruments]</ref> 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 synthesis|subtractive]], [[sample-based synthesis]], [[additive synthesis]], 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]].
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| However, new hardware synths that were specifically marketed for their FM capabilities have not been seen since the [[Yamaha SY99]], which itself was split evenly between this and [[sample-based synthesis]] in terms of marketing. Yamaha's later [[Yamaha FS1R|FS1R]] was marketed chiefly as a device for [[formant synthesis]], despite the fact that it was the only standalone 8-operator FM synth that they, or any other hardware manufacturer, had produced, and had other unique features in its FM engine. Yamaha also produced the FVX1, an 8-op FM expander for certain of their organs, but these are rare, and information on how to actually program them has never been released or derived. Yamaha re-released the engine of the DX7 II in the form of the PLG150DX and PLG100DX expansion cards for certain of their synths, including a standalone model enclosed in the table-top unit DX200, but this was simply a re-release of an existing platform. Thus, since the SY99 and FS1R by Yamaha, no manufacturer has released any new hardware synth dedicated solely/mainly to FM synthesis, though it is a main feature of [[Nord_Lead|Nord Lead]] synths manufactured by Clavia.
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| == Spectral analysis ==
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| The spectrum generated by FM synthesis with one modulator is expressed as following:<ref>{{harvnb|Chowning|1973|pp=1–2}}</ref><ref>
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| {{cite web
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| | last = Doering
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| | first = Ed
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| | authorlink =
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| | coauthors =
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| | title = Frequency Modulation Mathematics
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| | work =
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| | publisher =
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| | date =
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| | url = http://cnx.org/content/m15482/latest/
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| | format =
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| | doi =
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| | accessdate = 2013-04-11
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| | archiveurl =
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| | archivedate = }}</ref>
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| :<math>\begin{align}
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| &\sin(f_c\cdot t+I\cdot\sin(f_m\cdot t)) \\
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| &\quad = J_0(I)\sin(f_c\cdot t)
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| + \sum_{k=1}^{\infty} J_k(I)\left[\sin(f_c+k f_m)t+(-1)^{k}\sin(f_c-k f_m)t\right]
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| \end{align}</math>
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| :where <math>f_c\,,\,f_m\,</math> are frequencies of carrier and modulator, <math>I\,</math> is modulation index, and <math>J_k(I)\,</math> is <math>k\,</math>-th [[Bessel_function#Bessel_functions_of_the_first_kind_:_J.CE.B1|Bessel function of first kind]], respectively.
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| ==See also==
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| *[[Chiptune]]
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| *[[Digital synthesizer]]
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| *[[Electronic music]]
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| *[[Sound card]]
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| *[[Sound chip]]
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| *[[Video game music]]
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| ==References==
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| * {{cite journal
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| | last = Chowning | first = J.
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| | year = 1973
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| | title = The Synthesis of Complex Audio Spectra by Means of Frequency Modulation
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| | url = http://people.ece.cornell.edu/land/courses/ece4760/Math/GCC644/FM_synth/Chowning.pdf
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| | journal = Journal of the Audio Engineering Society
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| | volume = 21 | issue = 7
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| }} (also available in PDF as [https://ccrma.stanford.edu/sites/default/files/user/jc/fmsynthesispaperfinal_1.pdf digital version 2/13/2007])
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| * {{cite book
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| | last = Chowning | first = John
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| | coauthors = Bristow, David
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| | year = 1986
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| | title = FM Theory & Applications - By Musicians For Musicians
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| | publisher = Yamaha | location = Tokyo
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| | isbn = 4-636-17482-8
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| }}
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| * {{cite book
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| | last = Dodge | first = Charles
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| | coauthors = Jerse, Thomas A.
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| | year = 1997
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| | title = Computer Music: Synthesis, Composition and Performance
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| | publisher = Schirmer Books | location = New York
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| | isbn = 0-02-864682-7
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| }}
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| {{reflist}}
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| == External links ==
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| * [http://ccrma.stanford.edu/software/snd/snd/fm.html An Introduction To FM], by Bill Schottstaedt
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| * [http://www.sfu.ca/~truax/fmtut.html FM tutorial]
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| * [http://www.soundonsound.com/sos/apr00/articles/synthsecrets.htm Synth Secrets, Part 12: An Introduction To Frequency Modulation], by Gordon Reid
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| * [http://www.soundonsound.com/sos/may00/articles/synth.htm Synth Secrets, Part 13: More On Frequency Modulation], by Gordon Reid
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| * [http://www.soundonsound.com/sos/1997_articles/sep97/synthschool3.html Paul Wiffens Synth School: Part 3]
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| * [http://yala.freeservers.com/2fmsynth.htm#2Mod F.M. Synthesis including complex operator analysis]
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| * [http://www.youtube.com/watch?v=h3yrd2YvkUo Part 1 of a 2-part YouTube tutorial on FM synthesis with numerous audio examples]
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| {{Sound synthesis types}}
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| [[Category:Sound synthesis types]]
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I'm Verna and I live in Geertruidenberg.
I'm interested in Economics, Insect collecting and Korean art. I like travelling and reading fantasy.
My web-site; beats music