In Reply to: Harmonic - Harvard Dictionary Of Music posted by Neward T on February 27, 2001 at 10:41:02:
regarding the earlier post about Harmonic Analysis as a mathematic field.Mathematicians often use big words which usually have deeper meanings. As I understand it, Hamonic Analysis is the study of "functions" that are invariant under a mathematical construct. For example, when the function is invariant under "traslation", we have so called periodic functions or "waves". The fact that most periodic functions can be expressed as a unique sum of sines (and or cosines) -- the Fourier series -- has nothing to do with musical waves; they simply happen to a be subset of periodic functions, which are a subclass of functions studied by Hamnonic Analysis.
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- Re: Harmonic - Harvard Dictionary Of Music - caa 19:46:35 03/03/01 (0)