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


Subject: Re: A new paradigm?(On pitch and periodicity (was "correction to post"))
From:    Ranjit Randhawa  <rsran@xxxxxxxx>
Date:    Tue, 20 Sep 2011 12:46:20 -0400
List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>

Dear Pim, I have attempted to understand your booklet and the comments to Dick Lyon below, which I have to admit, I found more illuminating than the booklet. I can't claim that I understood all, mostly due to my poor background in mathematics, I think. But I do have some comments, these I hope the silent majority find interesting. The length of 75 mm, as calculated for 20 kHz, may not quite as important. My cursory search showed, and I don't remember where, that the high frequency response of elephants is limited to 12 kHz, and therefore the cochlear length must be longer, which is possible considering the size of its head. But the high frequency limit of a chicken is only 2 kHz, and therefore would imagine that the similarly calculated cochlear length to be totally out of proportion to head size. I also did come across some reading where it was shown the bees can distinguish tones, which are in our normal hearing range, though unfortunately the researchers did not indicate what the frequencies were of the tones they used. But, considering the size of the bees head, I have to conclude that stimulus pressure is not directly responsible for the BM movement. Bit of a jump there, but I do feel that cochlear dynamics do not follow directly the laws of physics. The quadratic expansion of summed sinusoid was, I believe, also proposed by Helmholtz to show how "combination tones" could be generated, though I don't believe he came upon this by the more logical approach you have taken. Some have also proposed the possibility of higher order non-linearity of the same sort. However, my own experiments do not bear out the results. For example, consider a complex tone of two frequencies with a ratio of 1:4, which by expansion should result in some level of intermediate tones, which I could not hear. A more definite existence or non-existence would require using beats as was done to show that a pure tone does have harmonics. I think Schouten did that and never quite explained this. By the way, I don't believe Helmholtz ever used this non-linearity to explain the "missing fundamental", at least I have not found a reference, though it must have been obvious to him. The possible existence of harmonics for a pure tone, does lead one to question the animation via the link provided by you in the response below. Furthermore, there are other animations that show the "traveling wave" in the more traditional sense, and also explained by the many experimentalists. I do have to admit that the animation was quite hypnotic but was troubled by the results described by others, and therefore am at a loss which is "correct". We do know (or do we?) that "phase locking" is lost at about 4 khz but starting earlier, and therefore have to assume that for experiments at 10 kHz would provide only localized excitation on the BM and therefore the beat phenomenon could be attributed to the waveform profile, but not necessarily a proof. For me, a sinusoidal harmonic series based on the fundamental root being in the non-hearing region could mean that a complete harmonic series is not formed and therefore the BM activity is localized and therefore we hear some kind of a beat. But if the root was in the range of hearing, a harmonic series is formed and therefore the sound tends to be much more pleasant and the beats vanish. At least I hope they do. Also, when one creates a harmonic series with alternating sinusoidal functions, there is an octave jump in pitch perception as indicated by you and also shown by others, but this is noticeable most when the base frequency of this series is in the high frequency range and a bit ambiguous when the root (the fundamental) of the harmonic series is in the hearing range. Mis-tuned harmonics have also been tested, Hartmann I think, and a perceived "pitch" reported, though no beats. Again, my caveat, this per my own tests and right away I have to say that I have been told that I am tone deaf! To shorten this email, there is one more point that I would like to add and that concerns the "bias" term that is created by the quadratic expansions, which as you imply cannot be heard but could be used to act as a feedback for reducing the gain for loud stimuli. I do have a problem with this as it then means that some part of the stimuli energy is lost and therefore some reduction of active stimuli energy takes place automatically. In other words, if two harmonic frequencies with a given amplitudes, are provided as a complex tone, would we hear a decrease in loudness as compared to the sum of energies of the two individually? I guess the same question would arise if one were to consider a single pure tone and add to it a constant bias. Would the loudness decrease or would it remain the same but the tone would change. Help! There are other issues that I could bring up, like pitch perception with dichotic hearing, the problems with pattern based recognition binaural hearing etc. But I have to admit that I am leaning towards joining the silent majority, which from one email to the list seems to be diminishing. But hope springs eternal and fully understand that trying to propose a new paradigm is difficult at best. Many regards, Randy Randhawa On 9/19/2011 6:07 AM, Willem Christiaan Heerens wrote: > 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 > happening. > > 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 > that? > 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 > cycles. > 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 > place.** > > 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: > > 1: > 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. > > 2: > 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. > > 3: > 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: > > http://www.a3ccm-apmas-eakoh.be/a3ccm-apmas-eakoh-index.htm > > [ 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 > statements. > 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 > squared. > 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 > is. > 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: > > http://www.a3ccm-apmas-eakoh.be/aobmm/bm-movement.htm > > 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: > > http://math.ucr.edu/home/baez/physics/General/occam.html > > 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 > correct. > > . . .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 >


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