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Re: AUDITORY Digest - 24 Mar 2002 to 25 Mar 2002 (#2002-43)

Dear Aud list,

Here are some comments I recently wrote re P&G and their ideas of a high
loss cochlea
hopefully to be published soon (but so far not reviewed! Also, please
excuse the Latex
word processing math symbols, delimited by $$):

In 1948 Gold \cite{Gold48a} proposed that the cochlea must be a
"regenerative receiver." This thought was based on early electronic
theory of feedback amplifiers and electronic circuits.  Gold assumed
that the cochlea must have high viscous losses, and this has resulted
in scores of researchers believing today that the cochlea was a high
loss device. In fact the losses in the cochlea are close to zero. Wave
propagation is very low loss, with viscosity being important only at
low frequencies, in the scalae, and in the sub-tectorial space (between
the TM and the RL) where the proximity of two moving surfaces are large,
with fluid in between.

In fluid mechanics there is an approximation technique called
``Boundary layer theory'' that allows one to model losses accurately,
with a trick of mathematics. The way it works is that the solid side of
every solid-liquid surface interface is made thicker by the boundary layer
thickness \cite{Freeman85}
\delta(f) = \sqrt{\eta/\rho 2 \pi f},
where $\eta$ is the viscosity, $\rho$ is the density and $f$ is
frequency. Once each solid surface has been increased by $\delta(f)$, the
viscosity of the new geometry may be taken as zero. This modified structure,
having no viscosity, is a good approximation to the original physical

Since $\delta$ is on the order of 10 $\mu m$ at 1 kHz, and the scala of
the cochlea are on the order of 100-300 $\mu m$, this boundary layer
shrinks the scala by less than 10\%. At low frequencies the scalae
narrows sufficiently (making the boundary layer increase) so viscosity
has an
effect at low frequencies, and thus must be included in the calculation
(i.e., the boundary layer approximation fails) \cite{Puria91}.

The distance between the tectorial membrane and the reticular
lamina, where the cilia of the inner and outer hair cells live, is less
than $\delta$, so this region must be modeled as having damping, at all
frequencies \cite{Allen80a}. However this resistance appears at the
characteristic place of the transmission line for each frequency,
because the motion of the tectorial
membrane relative to the reticular lamina is significant only near the
characteristic place.

Thus over most of the frequency range Gold was solving a problem
that did not exist since his assumption that the damping seen by the
propagated wave was large, was incorrect.
Scores of researchers accepted his view that the cochlea was
a high-loss device, that needed a power source (the regenerative receiver
concept) to reduce the high damping. Gold had a nice idea, but the argument
was wrong. The cochlear amplifier is still an appealing, but unproven,
concept in cochlear mechanics.  There is also strong support from
experiment that
cochlea is relatively lossless at all levels.  Recio {\it et al.} (1990)
basilar membrane responses to clicks that ring for more than a dozen
cycles ,
even at levels greater than 104 dB SPL.
\cite{Recio, A., Rich, N.C., Narayan, S. and Ruggero, M.A. (1998).
``Basilar-membrane responses to clicks at the base of the chincilla
cochlea," J. Acoust. Soc. Am., {\bf 103}, 1972-1989.}

I hope this helps. Comments?

Jont Allen

Automatic digest processor wrote:

There are 2 messages totalling 165 lines in this issue.

Topics of the day:

 1. paper on human cochlear tuning
 2. Gold & Pumphrey


Date:    Mon, 25 Mar 2002 20:42:46 +1100
From:    Andrew Bell <bellring@SMARTCHAT.NET.AU>
Subject: Re: paper on human cochlear tuning

From the parenthetical part of Fred Wightman's comment, it seems he
may now have some doubts about how effective his refutation of
Pumphrey and Gold was. Perhaps he could elaborate on those doubts?

Notwithstanding Green et al.'s 1975 JASA, I would maintain that
Pumphrey and Gold's interpretation is fundamentally correct. No
matter whether you invoke pitch or any other effect, and whether one
considers the time domain or frequency domain, the stimuli are such
that at the end of the day Pumphrey and Gold's statement remains
irrefutable: "No frequency analyser [biological or physical, natural
or man-made] could distinguish between the two stimuli unless its
oscillatory time constants were so large that phase was 'remembered'
across the silent interval."

The 1975 JASA paper of Green et al. misses the point by looking at
the two compound stimuli (A and B) in the frequency domain. Whether
one chooses to examine the stimuli in the time or frequency domain
is immaterial: there is nothing in one domain that is not implicit
in the other. The fact remains that an inverted signal can only be
distinguished, after a silent interval, from its antiphase
counterpart if the phase is remembered across the interval. Moving
the analysis from the time domain to the frequency domain does not
change the truth of the statement that _no_ frequency analyser can
distinguish the two stimuli unless phase is remembered.

Pumphrey and Gold would not dispute that there is a (spectral)
difference between the two wavetrains A and B. Indeed, if there were
absolutely no difference, then no frequency analyser on earth would
be able to tell the difference between them. What Pumphrey and Gold
are simply saying is that any difference between A and B can only be
perceived if the analyser has a sufficiently high Q. Green et al.
attribute that difference to a pitch mechanism; that may be so --
the difference may manifest as pitch or timbre or any other
psychophysical percept (clearly, there has to be some psychophysical
difference if we can consciously distinguish the stimuli) -- but the
pitch differences concerned are only detectable if the detector has
a suitably high Q.

This is because the magnitude of the spectral components of n wave
periods is _precisely_the_same_ as the n periods of its antiphase
version (note once again that this is _not_ saying that the spectral
components of the compound waveforms A and B are identical).

The only exception to the detectability criterion would be if the
ear were sensitive to absolute phase, and Pumphrey and Gold exclude
this by noting that, if this were true, then a person's ability to
distinguish between the two stimuli would be independent of the
length of the silent interval -- and this is clearly not so, with
the length of the silent interval having a large effect on
discriminability. A 10-cycle silent interval gives an obvious
difference, whereas with 30 cycles it is hard.

Green et al. repeat the Pumphrey and Gold experiments, and it should
be noted that their results more or less confirm the earlier ones
(confirmed also by Hiesey and Schubert, JASA 51, 1972, 518, who also
make the same epistemological error as Green et al. in thinking that
because there is a pitch difference this explains away the
difference, a position implicit in Fred Wightman's comment to which
I am replying). The result remains that since the ear can detect the
difference between the A and B waveforms, it must be using a high Q
analyser. That it appears as if the pitch of the two waveforms
differs is an interesting psychophysical observation, but it does
not change the conclusion as to the necessarily high Q of the
detector that perceives the pitch difference. To reiterate the
statement I made above, whether the difference manifests as pitch or
any other psychophysical parameter is beside the point -- the brute
fact is that there is a difference, despite identical spectral
energy in the n waves and in its delayed antiphasic counterpart.

In an interesting modification of the Pumphrey and Gold experiments,
Green et al. embed the signals in broad-band noise to produce
"[p]robably the most direct test of Gold and Pumphrey's narrow-band
estimate of the bandwidth". They looked for a difference in
threshold between the A and B waveforms, since the ear should be
more able to detect the former because the supposed resonant element
could accumulate in-phase energy. Indeed, A was more easily
detected, albeit with just a 1 dB advantage. This is said to
correspond to a Q value of about 10. The authors note that this is
much smaller than the Q values found by Pumphrey and Gold. Although
this is true, it is not unexpected, in that the added broad-band
noise means the ear is operating at much higher intensities (perhaps
40 or 60 dB SPL? -- the paper does not give us that important
information). As we now know, the selectivity of the ear at moderate
intensities is much broader than it is at threshold.

Now that we have the SFOAE results of Shera et al., does Fred
Wightman not believe that the Q of the ear can be as high as 30 (at
10 kHz and 40 dB SPL) or as high as 1000 (based on an SOAE of 1 kHz,
0 dB SPL, with 1-Hz bandwidth)?



Andrew Bell
PO Box A348
Australian National University
Canberra, ACT 2601
Phone {61 2} 6258 7276
Fax {61 2} 6258 0014
Email bellring@smartchat.net.au

|>-----Original Message-----
|>From: AUDITORY Research in Auditory Perception
|>[mailto:AUDITORY@LISTS.MCGILL.CA]On Behalf Of Fred Wightman
|>Sent: Monday, 25 March 2002 12:02
|>Subject: Re: paper on human cochlear tuning
|>What Andrew Bell might have mentioned is that in an
|>article that Dave Green, Craig Wier and I published
|>in JASA (1975, vol 57, p 935) we argued (convincingly,
|>we thought at the time at least) that Pumphrey and
|>Gold's result could more parsimoniously be explained
|>as a product of simple pitch judgement. In the
|>classical tradition of psychoacoustics, we would argue
|>that one should look at the stimulus first.


Date:    Mon, 25 Mar 2002 09:24:34 -0500
From:    Christopher Shera <shera@EPL.MEEI.HARVARD.EDU>
Subject: Re: Gold & Pumphrey

Andrew Bell wrote:

Pumphrey and Gold would not dispute that there is a (spectral)
difference between the two wavetrains A and B. Indeed, if there were
absolutely no difference, then no frequency analyser on earth would
be able to tell the difference between them. What Pumphrey and Gold
are simply saying is that any difference between A and B can only be
perceived if the analyser has a sufficiently high Q.

The point missed here (and the point missed by G&P) is that
G&P's analysis--and hence their derived numerical values of Q---only
applies if the frequency analyzer in question is a single harmonic
oscillator (2nd-order resonator) tuned to the sine-tone frequency.
Of course, the ear (even the cochlear part) is more complicated than
that. For a nice discussion see Hartmann's "Signals, Sound, and
Sensation." pg. 310ff.

Christopher Shera                               617-573-4235 voice
Eaton-Peabody Laboratory                        617-720-4408 fax
243 Charles Street, Boston, MA 02114-3096       http://epl.harvard.edu

"Sadism and farce are always inexplicably linked." -- Alexander Theroux


End of AUDITORY Digest - 24 Mar 2002 to 25 Mar 2002 (#2002-43)

Jont B. Allen,     jba@auditorymodels.org;   908/654-1274voice; 908/789-9575 fax
382 Forest Hill Way
Mountainside NJ 0709

``It is hard to abandon the feeling that the unfamiliar is absurd and illogical.''
       --G.A. Miller, p. 5 of his book `Language and communication'