source file: m1483.txt Date: Fri, 24 Jul 1998 08:52:51 -0500 (CDT) Subject: Re: TUNING digest 1481 From: Paul Hahn On Wed, 22 Jul 1998, John Starrett wrote: > It is not so much that rich tones are composed of a fundamental > frequency and its overtones as that they can be decomposed this way. [snip] > Joseph Fourier figured out how to add up cosine and sine > waves, which are mathematical representations of the the simplest kinds of > sounds, to obtain any type of periodic function whatsoever, [snip] > Describing a complex waveform in terms of its decomposition into a > sum of sine and cosine waves whose frequencies are simple multiples of > the fundamental (such as A 440) is useful, but not necessary, for > describing a tone and understanding why a waveform looks and sounds as it > does. There's been much excellent discussion on this topic already; I'd just like to interject that the reason Fourier-type decomposition of periodic waveforms is useful is because we believe that the inner ear does something very similar, therefore it tells us something significant (_pace_ Brian, not _everything_) about how we would hear such a sound. --pH http://library.wustl.edu/~manynote O /\ "Churchill? Can he run a hundred balls?" -\-\-- o NOTE: dehyphenate node to remove spamblock. <*>