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Path: utzoo!linus!philabs!seismo!hao!kpno!ut-sally!crandell
From: crandell@ut-sally.UUCP
Newsgroups: net.physics
Subject: Re: music harmony
Message-ID: <211@ut-sally.UUCP>
Date: Thu, 8-Sep-83 01:26:51 EDT
Article-I.D.: ut-sally.211
Posted: Thu Sep  8 01:26:51 1983
Date-Received: Fri, 2-Sep-83 17:53:43 EDT
References: <764@inuxc.UUCP>, <459@sbcs.UUCP>
Organization: U. Texas CS Dept., Austin, Texas
Lines: 34


     In continuous tones, the instantaneous phase relationships of the
harmonics do NOT affect the quality of the tone.  You can demonstrate
this to yourself with a relatively simple experiment.  Obtain four or
five sine-wave oscillators and mix their outputs through a resistor
network (or an audio mixer, if you happen to have one) feeding the output
to a speaker or headphones.  Then adjust the frequencies of the oscil-
lators to the first four or five (as appropriate) integer multiples of
some convenient frequency (e.g., 300, 600, 900, 1200, 1500).  Observe
the composite waveform on a 'scope; you'll have to, in order to get the
frequencies reasonably precise, and that's exactly the point!  As long as
even one of the components is even a fraction of a Hz off the exact
multiple, it seems to be a harmonic whose phase is continually shifting,
and the waveform as displayed by the 'scope will "roll" correspondingly.
In the middle range, a reasonably good ear has a pitch sensitivity in
the neighborhood of 0.25%; as long as the harmonic's frequency error
doesn't exceed that bound, the tone sounds uniform and stable.
     The explanation of this effect is not very obscure.  For about
20 years, hearing researchers have been reasonably confident that the
ear actually analyzes a continuous composite tone into its sinusoidal
components, and transmits some form of spectral plot to the brain.  The
information in this plot seems to consist of frequencies (well, pitches,
actually) and loudnesses.  The times at which the individual pitch re-
ceptors are stimulated are fairly precisely detected, however, so the
maintenance of phase IS important to accurate reproduction of transient
sounds.  For example, you can easily discern the difference between the
simple "click" of a step function and a bird-call-like "chirp", but trans-
mission through a dispersive medium is all it takes to transform one
into the other!

			      Jim (ihnp4!ut-sally!crandell)

P.S.  If you can't get a hold of enough oscillators, see if you can get
your hands on an old, electric Hammond.  The experiment is then trivial.