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1、Arch.Hist.ExactSci.(2007)61:343424DOI10.1007/s00407-007-0003-9TheacousticoriginsofharmonicanalysisOlivierDarrigolReceived:20December2006/Publishedonline:6April2007©Springer-Verlag2007Inmusic,harmonyreferstoapleasantcombinationofsounds.Inmathemat-ics,aharmonicfunctionisasinefunctionobtainedbyproj
2、ectingacircularmotiononadiameter,andharmonicanalysisisthetheoryofthedevelop-mentofperiodicfunctionsintoharmoniccomponents,orthetheoryofsimilardevelopments.Theoccurrenceofthesamewordinmusicalandmathematicalcontextsisneitheracoincidencenorapurelymetaphoricaleffect.Asiswellknown,inthemid-nineteenth
3、centuryHermannHelmholtzconnectedthetwomeaningsthroughtheideathattheearfunctionsasaharmonicanalyzerinaphysico-mathematicalsense.1ThisformulationofHelmholtzsachievementsuggeststhatharmonicanal-ysisprecededitsacousticandmusicalapplication.SodoestoothefactthatJosephFouriersfoundationofthiskindofanal
4、ysishadtodowithheatrather1Cf.StevenTurner,TheOhm-Seebeckdispute,HermannvonHelmholtz,andtheoriginsofphysiologicalacoustics,BJHS,10(1977),124.CommunicatedbyJ.Z.Buchwald.Thefollowingabbreviationsareused:AHES,Archiveforthehistoryofexactsciences;BJHS,Britishjournalforthehistoryofscience;CAP,AcademiaS
5、cientiarumImperialisPetropolitana,Commentarii;EOm:n,LeonhardEuler,Operaomnia(Leipzig,1911on),seriesm,vol.n;FOn,JosephFourier,Oeuvres,2vols.(18881890),vol.n;HAB,AcadémieRoyaledesSciencesetdesBelles-LettresdeBerlin,Histoire;HAS,AcadémieRoyaledesSciences,Histoire;JEP,JournaldelEcolePolytechnique;LO
6、n,JosephLouisLagrange,Oeuvres,14vols.(Paris,18671892),vol.n;MAS,Académie(Royale)desSciences,Mémoires;MT,MiscellaneaTaurinensia;NCAP,AcademiaScientiarumImperialisPetropolitana,Novicommentarii.Anachronisticnotationisusedforsumsandintegrals(Lagrangewasfirsttosystematicallyusethenotationsfordiscrete
7、sums,andFourierthefirsttoindicatethelimitsofsummationorintegrationinthemodernway).O.Darrigol(B)CNRS:Rehseis,83rueBroca,75013Paris,Francee-mail:darrigol@paris7.jussieu.fr344O.DarrigolthansoundandprecededOhmsandHelmholtzsacoust
