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

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