Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Posting-Version: version B 2.10.1 6/24/83; site rand-unix.UUCP Path: utzoo!watmath!clyde!burl!ulysses!mhuxl!ihnp4!zehntel!hplabs!sdcrdcf!rand-unix!edhall 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