Editing Frequency modulation synthesis (section)

=== John Chowning (late-1960s–1970s) ===
[[File:Chowning.jpg|thumb|Digital frequency modulation synthesis was developed by [[John Chowning]]]]

By the mid-20th century, [[frequency modulation]] (FM), a means of carrying sound, had been understood for decades and was being used to [[FM broadcasting|broadcast radio transmissions]]. FM synthesis was developed since 1967 at [[Stanford University]], California, by [[John Chowning]], {{citation needed span|through his exploration of digital synthesis and spatialization, inspired by the new possibilities of digital sound as described by [[Max Mathews]]|date=November 2024}}. His {{citation needed span|algorithm|date=March 2023|reason=next word "license" implies patent}}  was licensed to Japanese company [[Yamaha Corporation|Yamaha]] in 1973.<ref name="yamaha2014">{{cite web |ref={{sfnref|Yamaha|2014}} | title     = [Chapter 2] FM Tone Generators and the Dawn of Home Music Production | url       = http://usa.yamaha.com/products/music-production/synthesizers/synth_40th/history/chapter02/ | archive-url= https://web.archive.org/web/20170511080846/http://usa.yamaha.com/products/music-production/synthesizers/synth_40th/history/chapter02/ | archive-date=2017-05-11 | work      = Yamaha Synth 40th Anniversary - History | year      = 2014 | publisher = Yamaha Corporation}}</ref> The implementation commercialized by Yamaha (US Patent 4018121 Apr 1977<ref name="uspto">{{cite web|url=http://patft.uspto.gov/netacgi/nph-Parser?patentnumber=4018121|publisher=patft.uspto.gov|title=U.S. Patent 4018121 Apr 1977|access-date=2017-04-30}}</ref> or U.S. Patent 4,018,121<ref name="patent">{{cite web|url=https://patents.google.com/patent/US4018121A/en=|title=Patent US4018121 - Method of synthesizing a musical sound - Google Patents |access-date=2017-04-30}}</ref>) {{citation needed span|is actually based on [[phase modulation]]|date=February 2023|reason=Although Yamaha's multiple-operator extension (FM Algorithm derived from their PAMS in the 1970s) seems possibly lacking the time integration of instantaneous frequency, clear sources are needed yet.}}, {{citation needed span|but the results end up being equivalent mathematically as both are essentially a special case of [[quadrature amplitude modulation]]|date=February 2023|reason=The omit of time integration of instantaneous frequency is not the equivalence}}.<ref>
{{cite web
 |author       = Rob Hordijk
 |title        = FM synthesis on Modular
 |url          = http://www.clavia.se/nordmodular/Modularzone/FMsynthesis.html
 |work         = Nord Modular & Micro Modular V3.03 tips & tricks
 |publisher    = Clavia DMI AB
 |access-date  = 2013-03-23
 |archive-url  = https://web.archive.org/web/20070407072439/http://www.clavia.se/nordmodular/Modularzone/FMsynthesis.html
 |archive-date = 2007-04-07
 }}</ref>