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From: edhall@rand-unix.UUCP (Ed Hall)
Newsgroups: net.audio
Subject: Re: Re CDs and square waves
Message-ID: <1822@rand-unix.UUCP>
Date: Wed, 20-Jun-84 23:19:55 EDT
Article-I.D.: rand-uni.1822
Posted: Wed Jun 20 23:19:55 1984
Date-Received: Sat, 23-Jun-84 04:12:26 EDT
References: <3979@mordor.UUCP>
Organization: Rand Corp., Santa Monica
Lines: 50

+
One thing first: since square waves (and indeed all waveforms with
symmetrical peaks, like triangle waves and so forth) contain only
odd harmonics, the lowest non-fundamental harmonic in a 20KHz
square wave is 60KHz, not 40KHz.  Anyone here who can hear up
to 60KHz?  :-)

Human ears (and probably all biological ears) seem to respond
to frequency spectra, not waveform.  This is quite fortunate,
as small movements of sound source or sound receiver cause
huge changes in waveshape, and (usually) little change in
the frequency spectrum.  (Standing-wave effects are the exception,
but aren't very signifigant except in extremely reverberant
environments or other artificial conditions.  Our perceptual
system seems to ignore them unless they are very obvious.)

It appears that the ear does the biological equivalent of a continuous
fourier transform on the sound it receives, and responds to the
relative amplitudes of the various frequencies.

It is quite possible (by introducing phase shifts) to create
waveforms that look completely different, yet are essentially
indistiguishable by ear.  And it is quite possible (by introducing
low levels of higher harmonics) to produce waveforms that look
essentually identical to the eye but sound quite different.

The bottom line is that waveform purity of square-waves (or
any other specific waveform) is a poor measure of sound fidelity.

(And before someone starts arguing about the ability to perceive
phase, let me remind you that introduction of any non-linearity
into the reproduction chain, and I'm thinking specifically of
speakers or headphones, can create a phase-dependent change in
the frequency spectra.  This can easily explain the differences
heard by those who claim a need to preserve ``absolute phase'',
i.e. whether polarity is preserved from microphone to speaker,
since differences between tops and bottoms of the recorded
waveshapes would cause different spectra if passed through
a device with non-linearities.  And differences between the
top and bottom waveshape halves are quite the norm for natural
sound.

Note that I've said nothing about relative phase between ears
or between stereo channels.  This type of phase difference
is quite audible.  Also, there may be a certain amount of
ability to hear phase shifts at low (<500Hz) frequencies, but
it is a fairly subtle effect.)

		-Ed Hall
		decvax!randvax!edhall