From: David Josephson <email@example.com>
Subject: Re: Helium & Sound
Date: 19 Dec 1995 20:12:38 GMT
Organization: Josephson Engineering
In <4b5jjtINNeee@HOBBES.NA.CS.YALE.EDU> firstname.lastname@example.org (Norman
>strange since the first stage of processing of sound (performed by the
>cochlea) produces a pretty good resemblance to a Fourier transform of
>the sound wave.
Yes, or so it seems -- and the information is on a frequency axis.
>To phrase things differently, I assume there is agreement that a tone
>of a single frequency (that is, a pure sine wave) has the same pitch as
>it has frequency.
>Then what are the circumstances under which a pitch
>is perceived which is lower than any of the frequency components of the
When several harmonics of a frequency are present, (i. e. sineaves
of 2f, 3f, 4f, etc) but the fundamental (f) is missing, the ear perceives
that to be the same pitch as the fundamental without the harmonics. This
effect has been used for artificial bass extension in radios, etc. whose
speakers can't reproduce low frequencies; for instance take the band
50-100 Hz, remove it from the signal, run it through some diodes to make
lots of harmonics and mix the harmonics with the signal -- sounds like
David Josephson / Josephson Engineering / San Jose CA / email@example.com
From: Mark Barton <firstname.lastname@example.org>
Subject: Re: Helium & Sound
X-Xxdate: Wed, 20 Dec 1995 06:41:46 GMT
Organization: Institute for Cosmic Ray Research, Tokyo Uni.
Date: Wed, 20 Dec 1995 06:40:02 GMT
>From: Matt McIrvin, email@example.com
>>Norman Yarvin <firstname.lastname@example.org> wrote:
>>To phrase things differently, I assume there is agreement that a tone
>>of a single frequency (that is, a pure sine wave) has the same pitch as
>>it has frequency.
Well the idea is there, but it's a sloppy way of putting it. Pitch is
not a simple linear (or log) scale - it's a complicated function with
multiple inputs and outputs and being completely subjective it doesn't
properly have units. The input with the most weight in most people is
actually differential - just about anybody can say very accurately (one
semitone = 5% is trivial) if one pitch is higher or lower than a
second. With a bit of training, most people can even identify the
ratio of the frequencies. (If you can sing the first few notes of
Twinkle Twinkle Little Star, you know what a 3:2 frequency ratio sounds
like, so you already have the skill - it just needs calibration.)
However if given a single frequency without a reference, even most
musicians will be lucky to get the octave right. Thus you _can_ say
that of two sine waves presented in rapid succession, the one with the
higher frequency will be judged to have the higher pitch. But most
people can't truthfully say that a single sine wave in isolation _has_
a pitch to better than an octave or so.
>Actually, I've heard that it's difficult to judge the pitch of a pure
>sine wave; we are used to hearing some overtones at integer multiples
>of the fundamental, and the overtones are used to reconstruct the
>pitch, as well as the fundamental. (Even tuning forks have
>significant overtones unless they are struck very lightly.)
In my experience, _under ideal listening conditions_, i.e. no
background noise, sine waves are very easy to compare. However if
there is broadband noise in the background, it very easily overwhelms a
sine wave at the sort of pitches used in music. A complex waveform has
more cutting power than a flutey tone, and this is certainly due to the
high frequency components and the way the ear matches up them up.
There is probably an evolutionary story to be told about why the ear
should have learnt to do this.
>>Then what are the circumstances under which a pitch
>>is perceived which is lower than any of the frequency components of the
>I'd *guess* that this could happen if the major frequency components of
>the sound wave were three or four successive small-integer multiples of
>a given frequency, say 2f, 3f, 4f, and 5f. But all of this information
>comes from my having read a Scientific American Library book called
>_The Science of Musical Sound_, and that was a long time ago, so my
>memory may be fuzzy.
This can happen. A standard application is in building organs - any
organist would love to have a 32 foot rank of pipes, i.e. a rank in
which the C pipe was (approximately) 32 feet long, but such big pipes
are expensive and bulky, so organ builders often cheat and use matched
pairs of pipes twice and three times the frequency of the note to be
faked. It's not as good as the real thing but it gives the idea.
>Unfortunately, the experts who know the answers to these questions
>have probably killfiled this whole thread, since this kind of
>discussion is probably as common on alt.sci.physics.acoustics as
>confusion over relativistic velocity addition on sci.physics.
>Unfortunately, it's not covered in the alt.sci.physics.acoustics FAQ.
On the contrary, this is the sort of thread kill-files are designed to
give one time to read. (I wish I had a kill-file.)