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Re: A new paradigm?(On pitch and periodicity (was "correction to post"))

Dear dr Heerens and list-members,
I hesitate to get involved in this discussion as I have tried to explain the hydrodynamics behind (transmission line) cochlea models before in another thread on this list and don't like repeating myself. But I feel I have to lend my support the comments made by Dick Lyon.
As I have stated before fluid physics states that a fluid domain (such as the cochlea or a pond) with a flexible boundary subject to a restoring force (such as the aochlear partition or the pond surface) MUST exhibit 'ripples' on the surface. In the cochlea these are refered to as traveling waves. The wave energy is not traveling in the boundary itself but in the fluid. Any attempts to prove that such waves do not exist, or are based on 'bad physics', are unfortunately based on a lack of understanding of the fluid mechanics.
Whether the traveling wave is the only mechanism responsible for transporting sound energy to the hair cells is still a valid question, but untill an alternative model produces similar or better results on modeling physiological, pshychophysical and OAE date, I'll stick with the transmission line. Things like pitch perception and the missing fundamental can perhaps not be explained purely by looking at the average excitation caused by the traveling wave, but I don't think anyone ever claimed they could. In my opinion it is good to develop new theories, but we should attempt to integrate them with existing ones instead of throwing away something that has proven to work.
Kind regards,
Peter van Hengel

2011/9/19 Willem Christiaan Heerens <heerens1@xxxxxxxxx>
Dear Dick Lyon,

Thank you for your substantial list of comments.  Of course I will reply.
With pleasure.

You wrote:
**Sometimes it's hard to get a reaction when you are trying to replace a
paradigm, as the silence here illustrates.  I didn't really get into the
new ideas of your book much, but I have some comments on the introductory
material about why you reject the current paradigm.**

Your reaction in the first sentence is pretty well familiar to me. It is
entirely in accordance with the procedure described by Thomas Kuhn in his
world famous 1962  essay:

“The Structure of Scientific Revolutions”

Besides that: a former colleague of mine, a highly skilled senior professor
in applied physics, who reviewed our booklet during a contribution
procedure for a scientific journal, quite recently gave us the verdict that
he fully agreed with our arguments and statements and he urged the editor
to make a full scientific discussion possible for our views. He also warned
me that to be in right is not the same as to be put in right. I myself
don’t see all this as a problematic issue. It’s part of the way messengers
or designers of new paradigms are encountered by the mayor supporters of
the competing one. Of course the scientific reputation rankings of so many
scientists are involved and in danger in case a paradigm shift is

The only issue that counts for me is that scientific arguments from both
sides brought in discussion, verified and weighted in a careful way must
turn the balance. Ignoring irrefutable arguments because they form a thread
for the ranking of a scientist has always been contra productive for the
progress in a field of science. History shows many of such examples. One of
the most salient among them certainly is the Copernican revolution.

The result of the second line of your comment I really regret, because in
the rest of your writings I clearly can see that you have apparently
missed, misread or misinterpreted a number of issues on cardinal points.

Let me discuss your next comment:

**You discuss and reject two wave concepts: first, the pressure sound wave
that travels so fast that wavelengths will always be long compared to the
size of the cochlea, and second, "capillary" or "interfacial" waves,
presumably meaning those water surface waves where gravity provides the
restoring force.  Of course, neither of these can be the explanation for
how the cochlea works.**

I don’t reject the pressure sound wave concept, at least not in general. It
is of course the vehicle of mechanical vibration energy and therefore also
acoustical vibration energy. How could an academic physics scientist reject
What I have argued is that for all the frequencies that can be sensed in
the cochlea even up to 20 kHz counts that the sound velocity in perilymph –
being 1500 m/s – in relation with these frequencies result in a wave length
always larger than 75 mm.
So therefore this mechanism cannot contribute to a discriminating mechanism
for frequency selectivity based on traveling waves.

And regarding the  "capillary" or "interfacial" waves I reject: yes indeed
in quite a number of textbooks I see the comparison of the propagation of
surface waves in a pond with the slow waves inside the cochlea. It simply
is an erroneous analogon. None of the parameters necessary for the
existence of capillary waves can be found inside the cochlea. So neither
they can play a role in evoking traveling waves that have short wavelengths.

You wrote:

**You also attribute to Lighthill some strange wrong ideas about
transmission lines only being able to transmit energy near their resonance.

Can you be more specific?  The only lines I describe are the lines in Fig.
1. That figure is a reproduction of the figure in Lighthill’s paper:

Lighthill MJ. (1981) Energy flow in the cochlea. J Fluid Mech 106: 149-213.

I haven’t attributed strange wrong ideas to Lighthill. I have studied
carefully all the 64 pages  of his paper.

He starts with a very informative series of premises and I cite this part:

*** With moderate acoustic stimuli, measurements of basilar-membrane
vibration (especially, those using a Mössbauer source attached to the
membrane) demonstrate:
(i) a high degree of asymmetry, in that the response to a pure tone falls
extremely sharply above the characteristic frequency, although much more
gradually below it;
(ii) a substantial phase-lag in that response, and one which increases
monotonically tip to the characteristic frequency;
(iii) a response to a 'click' in the form of a delayed 'ringing'
oscillation at the characteristic frequency, which persists for around 20
This paper uses energy-flow considerations to identify which features in a
mathe¬matical model of cochlear mechanics are necessary if it is to
reproduce these experi¬mental findings.
The response (iii) demands a travelling-wave model which incorporates an
only lightly damped resonance. Admittedly, waveguide systems including
resonance are described in classical applied physics. However, a classical
waveguide resonance reflects a travelling wave, thus converting it into a
standing wave devoid of the substantial phase-lag (ii); and produces a low-
frequency cut-off instead of the high –frequency cut-off (i).
By contrast, another general type of travelling-wave system with resonance
has become known more recently; initially, in a quite different context
(physics of the atmosphere). This is described as critical-layer resonance,
or else (because the reso¬nance  absorbs energy) critical-layer absorption.
It yields a high-frequency cut-off; but, above all, it is characterized by
the properties of the energy flow velocity. This falls to zero very steeply
as the point of resonance is approached; so that wave energy flow is
retarded drastically, giving any light damping which is present an
unlimited time in which to dissipate that energy.
Existing mathematical models of cochlear mechanics, whether using one-, two-
 or three-dimensional representations of cochlear geometry, are analysed
from this standpoint. All are found to have been successful (if only light
damping is incorporated, as (iii) requires) when and only when they
incorporate critical-layer absorption. This resolves the paradox of why
certain grossly unrealistic one-dimensional models can give a good
prediction of cochlear response; it is because they incorporate the one
dimensional feature of critical-layer absorption.***

Apparently Lighthill has never considered the possibility that the observed
movements of the basilar membrane could be caused by another phenomenon
than a sound energy transporting traveling wave.

Your next remark:

**Actually, he showed the opposite:  that a sinusoidal wave will propagate
until the point where the transmission line resonance gets low enough to
match the wave frequency, and at that point it will slow down to zero
velocity and die out.  This is not exactly how the cochlea works (the BM is
not very resonant), but not a bad concept from base to near the best

You say it clearly enough:   ‘It isn’t a bad concept from base to near the
best place.’
So not having an exact agreement between theory and practice makes the
underlying hypothesis directly vulnerable for falsification.

Indeed the cochlea cannot react like that. And I want to make this clear by
the following series of experiments:

Entirely based on the premises of the new paradigm I have described, I now
have calculated a number of predictable sound phenomena by using the
following frequencies together with prescribed phase relations in a
standard summation procedure to compose a Fourier series:

           10000 + 10004 + 10008 + 10012 + 10016 + 10020 + 10024 Hz
            Where all the contributions are sine functions.

Our paradigm predicts:  an undisputable beat of 4 Hz in a high beep tone.

           10000 + 10004 + 10008 + 10012 + 10016 + 10020 + 10024 Hz
           Where the contributions are successively alternating sine and
cosine functions.

Our paradigm now predicts:  an undisputable beat of 8 Hz in the same high
beep tone.

           10000 + 10004.0625 + 10008 + 10012.0625 + 10016 + 10020.0625 +
10024 Hz
           Where all the contributions are sine functions.

Our paradigm now predicts:  a  beep, in which an undisputable beat exists
that changes every 8 seconds from clearly 4 Hz to 8 Hz and then reverses
again to 4 Hz. So the beat pattern has a period of 8 seconds caused by the
systematic mistuning of 1/16 = 0.0625 Hz.

Additional changes in the mistuning, like for instance from 10004.0625 into
10003.9375 Hz, of either one, two or three of the mistuned frequencies are
predicted to give the same results in the beat pattern as experiment 3.

And actually I want to urge everybody to download the software program of
Yves Mangelinckx  with which these sound complexes can be properly
calculated in the form of wav files from the following site:


[ NOTE:    The standard setting in the 1/f mode in this software program
takes care that all the individually primary calculated frequencies
contribute equal energy to the resulting sound pressure signal. This
condition is very important for the influences on pitch calculations in
case higher values of the differences between contributing frequencies
exist. ]

This in order to give the interested reader the opportunity to falsify or –
in case our predictions are correct – to verify our findings.

And of course I wouldn’t have given these examples if I wasn’t sure of my
I can already inform you that verification will be the result.

If you carry out the same series of experiments with a start frequency of
1000 Hz instead of 10000 Hz, you will hear the same series of beat
phenomena, but now with the lower beep of the 1012 Hz instead of the 10012
Hz beep.
Even if you go down with the start frequency to 200 Hz or 400 Hz you will
still hear the same beat phenomena, but now with the low humming tone of
200 Hz respectively with the one octave higher humming tone of 400 Hz.

Hence it is a perception phenomenon that appears all over the entire
auditory frequency range.

And it must be remarked that according to the current hearing theory all
the used frequencies – especially in the higher frequencies like in the
10000 Hz experiments – according to auditory experts, and also supported by
Lighthill, will propagate by means of a traveling wave to one and the same
location on the basilar membrane.

If we then still follow the current hearing paradigm, we have to believe
that the medley of that seven totally unresolved frequencies will be
transferred via one and the same nerve fiber to a location in the auditory
cortex, where finally out of this ‘Gordian knot of stimuli’ a beep with the
described and also heard beat patterns will be reconstructed.

Once these beat phenomena are verified as really existing for every
listener with a reasonable normal hearing, do you agree with me that for
the current paradigm this is a very serious anomaly?
In my opinion forcing an explanation within the framework of the current
paradigm will result in such a complexity that the general rule in science,
known as  ‘Ockham’s Razor’, to strive to an optimum in simplicity will be
strongly violated.

Your next remark:

**You conclude that "the existence of two sound energy transport phenomena
with different transfer velocities within this tiny cochlear volume of
perilymph fluid as suggested by Lighthill is impossible."  Yet all
observations do see a slow wave, much slower than the speed of sound, and
basic mathematical physics of the same sort that has been working well for
over 100 years to describe waves in fluids predicts exactly that behavior.
Some may quibble that it has not been conclusively proved that the observed
slow wave carries energy; but no workable alternative has been put forward,
and no experiment convincingly contradicts this main hypothesis of the
current paradigm, as far as I know.  I know some on this list will probably
say I'm wrong, now that I've opened the door.**

Do you agree with me that the perilymph inside the cochlear duct, existing
of scala vestibuli and scala tympani, is just moving back and forth over
distances not exceeding a few micrometer?

If you admit this fact, you should also agree with me that all the known
and involved physical quantities and parameters indicate that we are
confronted here with the problem to find the hydrodynamic solution for the
non-stationary small movements of an incompressible non-viscous fluid in a
tiny narrow duct.
According to the rules of physics it is then permitted without any
additional constraints to use the non-stationary Bernoulli equation.

The exact and detailed solution of this equation I can – if you wish – send
you separately.

The result is exactly the mathematical _expression_ I have used in the
booklet:  the pressure decrease in the perilymph duct in front of the
basilar membrane is everywhere proportional to the perilymph velocity
What leads to the overall result that the pressure stimulus on the basilar
membrane is proportional to the sound energy stimulus offered to the ear.

You further wrote:

          **Yet all observations do see a slow wave, much slower than the
speed of sound.**

Indeed, an observation of a ‘slow wavy movement’ and the only place where
we can observe this is the basilar membrane.

It isn’t the occurrence of a wavy movement phenomenon that we have to
discuss. It is the origin of that ‘traveling wave’ that we have to
discover. Is it a vibration energy transporting wave or is it a phase wave,
originated out of the manner in which the resonators in the basilar
membrane are grouped?

By the way, that is also – but not in an extended way – explained in our
booklet. In that chapter of the booklet I describe why those ‘waves’ always
run from base to apex. It is conform to the peculiar mechanics of the
basilar membrane system that this phase wave behavior is prescribed as it
And that mathematical solution for this mechanics problem of resonators –
in case of the logarithmical frequency distribution, low near the apex to
high near the base – can be calculated, as I have done, analytically for a
pure sinusoidal tone, which exactly results in a tonotopical symmetrical
envelope of that running phase wave with center frequency equal to the
corresponding resonance frequency.
And the running direction of that phase wave is always from base to apex.
Exactly as Tianying Ren has reported in his then speech making paper that I
have cited:

Ren T. (2002) Longitudinal pattern of basilar membrane vibration in the
sensitive cochlea. Proc Nat Acad Sci USA 99: 17101-6.

The animation of such a phase wave can be seen in:


You wrote:

**It sounds like you're trying to get away from a Helmholtz-like conception
of resonators or places responding to frequencies, and replace it with a
more time-domain approach that works for a lot of pitch phenomena.  But it
will work better to put that time-domain mechanisms AFTER the what the
cochlea does.  Each hair cell is a "tap" on the BM, reporting a time-domain
waveform as filtered by the traveling-wave mechanism; that's where the
pitch-processing nonlinear time-domain operations start...**

As you already have indicated in the beginning, you haven’t studied the
booklet entirely. I know for sure that by not studying the booklet
entirely, you have drawn premature conclusions here.

It is quite on the contrary. I think that I have explained clearly enough
in the booklet that everywhere along the basilar membrane very local
resonance with a high quality factor takes place. However not on the
primary sound pressure signal, but on the sound energy signal. Next to that
the basilar membrane will react everywhere – but not in a resonance mode
and therefore with much smaller displacements – and will show a response on
other frequency components, including utmost low frequencies even until
stationary pressure signals.

And for the explanation of our hearing sense I don’t need a time domain
mechanism at all.
In the new paradigm, described by me, from all the distinguishable
frequencies next of course to their frequency also their individual
amplitude and phase are transmitted to the auditory cortex.

Our brain can directly compare the entire frequency selected sound energy
stimulus with patterns that are stored in our memory.

Actually I cannot imagine a much more simpler and faster way.

Finally about the definition of Ockham’s Razor – also spelled Occam – I
found on the Internet  the following physics educational website:


where among others a number of stronger but clear definitions are given,
and I cite:

*** If you have two theories that both explain the observed facts, then you
should use the simplest until more evidence comes along.

The simplest explanation for some phenomenon is more likely to be accurate
than more complicated explanations.

If you have two equally likely solutions to a problem, choose the simplest.

The explanation requiring the fewest assumptions is most likely to be

. . .or in the only form that takes its own advice. . .

Keep things simple! ***

Within this framework I am convinced that I have done my utmost best.

So I am awaiting for a much better explanation for the described beat
phenomena based on the current hearing paradigm.

Kind regards,

Pim Heerens