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Re: Subjective tones and TW?(Laws of physics and old history...
Dear List, Dick:
With Fletcher's auditory maps, Schouten's experiments with beats and
other historical references to the psycho-acoustic existence of harmonic
tones for pure tone stimuli, I think it is time that the term
"subjective tones" should be dropped and we accept that the auditory
system's method for frequency analyses actually provides for
determinable magnitudes of these subjective tones. I have described one
such method, though suspect that there could be others. If such a method
was deemed to be reasonable, than my suggestion that a pure tone could
be analyzed as a harmonic series should answer many psycho-acoustical
questions.
Now as far as to whether volume compliance is valid or whether the
results of experiments for stiffness as described by Dr. Mountain and
the papers he was kind enough to make available, if a TW were to exist,
and this TW does stretch towards the basal end for increasing signal
strength, then I would think that bumps too must exist on the BM. Of
course if we assume that it is so, than one has to describe how does the
extremely long stimulus wavelength shrinks to fit on to the BM. Various
wave propagation models have been proposed but I find them hard to
accept. On the other hand, if we assume that the TW is due to the
motility of the OHC's and is part of the "cochlear amplifier", the
wavelength shrinking could be explained. I personally don't think that
the cochlear amplifier (even if it does exist) is the reason for such a
need, a better answer maybe hidden in the needs of whichever new
frequency analyses method one comes up with.
In the end, it does seem that we are back to where this thread started
and that was the famous "missing fundamental" and till we recognize that
subjective tones are really not subjective, but have well defined
magnitudes, it is difficult to jump to the more detailed arguments about
what happens physiologically.
My best wishes for this holiday season, cheers,
Randy Randhawa
On 11/29/2011 10:53 PM, Richard F. Lyon wrote:
At 11:00 AM -0500 11/10/11, Ranjit Randhawa wrote:
Dear Dick,
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
these figures.
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 pressure.
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.
Dick