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Re: Laws of physics and old history...
At 11:00 AM -0500 11/10/11, Ranjit Randhawa wrote:
I came across these auditory patterns due to pure tones in a text
book on Physics where these figures have been attributed "courtesy
of Dr. Harvey Fletcher". Ref: Mechanics, Heat and Sound by Francis
Weston Sears, Library of Congress card No. 51-899, Addison-Wesley
Publishing Company, Inc., Second Edition, Seventh printing-June 1958
(pretty long ago!). I don't have the history on how Fletcher derived
I have over the years have thought about these figures with the
results of ISI statistics and came to the conclusion that the only
way a result such as shown in these figures could be explained is by
showing that it was possible to describe a frequency analysis method
that analyzes a pure tone as sum of a harmonic series in the energy
domain. But that is neither here or there, it was simply my approach.
Sorry for the delay. I got the Sears textbook so I could see what
you're referring to. The figures are from Fletcher's 1940 "Auditory
Patterns" paper (I can provide a copy on request). You're right that
Fletcher does show a cochlear response pattern that includes
responses at what he calls "subjective harmonics". He gets these by
measuring the masking effect of pure tones on other tone frequencies,
and assumes that masking is proportional to the response in the
cochlea at a place that responds to the fundamental of the probe
frequency. A slightly unusual idea, but not bad as a simplifying
assumption for its time.
No objective correlate in the form of a space pattern of mechanical
or neural response with harmonic bumps along the length of the
cochlea has ever been seen, as far as I know. If you want to
consider a time-domain mechanism to explain the masking patterns, you
can do that in the neural domain, based on the neural activity
patterns out of the quasi-linear cochlea. That's where the
inter-spike interval stuff can apply.
I don't quite understand the term "volume compliance", and am quite
happy to accept that not much of a change of BM geometry is required
to provide the required change of volume range for a TW, but was
more concerned with the restoring force available from the BM, and
hence "stiffness", I guess I could have called it "springiness?".
This does not vary as much as required, at least as reported.
Compliance is the inverse of stiffness; volume compliance, sometimes
written "(volume) compliance", is in the sort of dimensions that
works easily in a fluid problem: volume of fluid displaced per unit
In the case of the basilar membrane, it's the volume of fluid
displaced via membrane displacement, per unit length of cochlear
duct, per unit of pressure difference across the membrane; or the BM
is characterized by its local volume compliance per unit length.
Maybe with the "per unit length" in there it's not exactly the same
thing as used in characterizing blood vessels and lungs and such in
the medical field (see for example this book:
http://books.google.com/books?id=fqWIm8RmVYsC&pg=PA59 and this one
http://books.google.com/books?id=i5Y6vrWlnXkC&pg=PA31 ). But it's a
bit different from simple mechanical "compliance", which is just
displacement per force. In any case, I didn't really mean anything
significantly different from "stiffness" as usually interpreted in
the cochlea, but that term is too ambiguous as it might be that in
the factor-of-6 interpretation it was stiffness as resistance to
bending, without considering the membrane width.
Bottom line is that "springiness" does vary enough to explain the
wide range of traveling wave velocities.