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

Subject: Re: AUDITORY Digest - 24 Mar 2002 to 25 Mar 2002 (#2002-43)
From:    Jont Allen  <jba(at)auditorymodels.org>
Date:    Tue, 26 Mar 2002 20:46:35 -0500

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}
\be
\delta(f) = \sqrt{\eta/\rho 2 \pi f},
\ee
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
system.

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)
showed
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.}

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(at)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.
>
>________________________________
>
>Andrew Bell
>PO Box A348
>Australian National University
>Canberra, ACT 2601
>Australia
>Phone {61 2} 6258 7276
>Fax {61 2} 6258 0014
>Email bellring(at)smartchat.net.au
>________________________________
>
>
> |>-----Original Message-----
> |>From: AUDITORY Research in Auditory Perception
> |>[mailto:AUDITORY(at)LISTS.MCGILL.CA]On Behalf Of Fred Wightman
> |>Sent: Monday, 25 March 2002 12:02
> |>To: AUDITORY(at)LISTS.MCGILL.CA
> |>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(at)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
>
>
>------------------------------
>
>End of AUDITORY Digest - 24 Mar 2002 to 25 Mar 2002 (#2002-43)
>**************************************************************
>

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

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'
`

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