Prologue: Bone conducted signals are considered to be evoked by the perilymph fluid moving back and forth out of the cerebrospinal cavity, via the cochlear aqueduct, towards the scala tympani. And not by mechanical deformation of the cochlea. “the fact that the bone conduction phenomenon is actually the result of the push-pull movement of the perilymph fluid instead of the presumed deformation of the bony structures.”
by Willem Christiaan Heerens
‘Hydrodynamic Cross Talk’.
I have had contact with Willem Heerens.
Based on the new cochlear model that is described by Heerens in his booklet: “Applying Physics Makes Auditory Sense”, he explained to me that two sine tones played to the individual ears of a listener — a dichotic stimulation experiment — is just one of the following series of experiments which can be extremely well explained by what he names: “hydro dynamical cross talk between both ears”.
He explained to me that it works as follows:
Under normal conditions every stimulus of the one ear — i.e. perilymph push-pull inside the cochlea — will be transferred for a small part via the two cochlear aqueducts and the cerebrospinal cavity of the skull to the other ear [most of the push-pull occurs between the oval window and the round window].
Due to the place where the entrance of the cochlear aqueduct in the scala tympani is situated this dichotic transfer is mainly in opposite phase [based on the time delay due to the travel time of the signal from ear to ear the signal’s phase delay increases linearly with increasing frequency].
And after arriving from the one ear in the other ear the stimulus will become a contribution to the perilymph push-pull and hence will be part of differentiating and squaring process.
The mathematical differentiating and squaring process in the cochlea is explained in the “booklet Applying physics makes auditory sense”.
Year Article Author(s) Source 2010 1 Applying physics makes auditory sense : a new paradigm in hearing Abstract | Full-text Heerens, W.C., Ru, J.A. de Medicine (2010), pp: 1-74
Mathematically, this signifies that the mammalian cochlea differentiates and squares the incoming sound pressure signal.
In terms of physics, it means that a sound energy signal is offered to the organ of Corti. Functioning as a Fourier analyzer, the organ of Corti subsequently converts these incoming signals into the sound energy frequency spectrum that is transferred to the auditory cortex in a frequency selective way.
Salient experimental results so far:
For residual tone complexes — harmonic series where the first harmonic or fundamental is missing — the differentiating and squaring process in the cochlea reconstructs perfectly the corresponding but missing fundamental.
Contrary to the conclusion that an early neural mechanism is responsible for the mystery of the inferential pitch, strong evidence exists that the cause for this reconstruction of the virtual or fundamental pitch is hydrodynamic in origin.
Automatically the sound energy stimulus of the basilar membrane will be generated by the non-stationary Bernoulli Effect and the sum and difference frequencies of the two primary stimuli will be evoked as well, next to the two doubled frequencies.
And now we can look at a number of experiments:
The Huggins pitch.
If we give the one ear a stimulus of white or pink noise and the other ear the same stimulus except for a 180° phase shift in a small frequency domain around approx. 600 Hz, the listener will hear a faint tone of 600 Hz.
Explanation: All the frequencies — both lower and higher than the small 600 Hz domain — that arrive from the one ear via the cerebrospinal cavity into the other are almost in opposite phase. Hence they will reduce the summated stimulus in each ear.
However the mutual frequency contributions close to 600 Hz are pretty well in phase. And they will increase the summated stimulus around 600 Hz in each ear. The result is that above the noise signal in each ear a faint but hearable 600 Hz tone is evoked.
The Binaural Masking Level Difference.
See for instance: Brian C.J. Moore: “An Introduction to the Psychology of Hearing”.
The following happens:
A pure tone — low frequency and not higher than 1500 Hz — in combination with white noise is fed identical to both ears.
The loudness of the tone is reduced to the level of “just masked by the noise” stimulus.
a. Changing the phase with 180° of one of the two tones while the noise stimuli remain unchanged makes the tone hearable again in both ears. The tone rises above the noise level in both ears.
b. Changing the phase of the noise stimulus in one ear with 180° while the two tone contributions remain in identical phase makes that the tone will be heard again in both ears. Because the noise level is lowering.
If we stimulate only one ear with the tone masked by the noise, the following happens:
c. The tone won’t be heard in both ears of course.
d. However if we stimulate the other ear with the same noise stimulus as the firstly stimulated ear the tone will be heard again in that ear. The noise masking level is lowered and the tone is heard again — but in one ear.
Also here the explanation is found in the either in of off phase effects in the transferred stimuli via the cerebrospinal cavity.
Binaural Beat Phenomena.
The same hydro-dynamic behavior exists for binaural beat stimuli. The only difference with the experiments — actually the so called Diana Deutsch illusions — described is that the two frequencies applied have a low (approx. 10 Hz) frequency difference.
And again: No mixing in the brain, but pure ‘hydro dynamical cross talk’.
It is simply a matter of observing the cochlear functioning in a completely different but realistic way.
by Willem Christiaan Heerens
Of course the dichotic phenomena [Huggins pitch and Binaural Masking Level Difference] are simple additions caused by a hydrodynamic process, where the two signals have either equal or [partly] opposite phase.
The two dichotic phenomena [Binaural Beat and Diana Deutsch illusions] are the result of addition of signals, resulting for each ear in a total velocity signal, which is the result of differentiation of the added sound pressure stimuli.
The non-stationary Bernoulli effect will evoke by squaring the quadratic Fourier series as a pressure distribution on the basilar membrane.
Therefore the 400 Hz stimulus in the one ear and the 410 Hz stimulus in the other ear in the binaural beat experiment create the following sound energy spectra:
In the one ear the tones 800 Hz [strong]; 810 [weak]; 820 Hz [extreme weak] and the beat of 10 Hz [weak], which isn’t heard as a tone.
In the other ear the tones 800 Hz [extreme weak]; 810 Hz [weak]; 820 Hz [strong] and the beat of 10 Hz [weak], which isn’t heard as a tone.
In literature the 10 Hz beat is always observed in an objective way by means of an EEG and interpreted as alpha brainwaves.
In the Diana Deutsch illusion experiment you can use 400 Hz in the one ear and 800 Hz in the other ear.
This results in:
In the one ear the tones 800 Hz [strong]; 1200 Hz [weak]; 1600 Hz [extreme weak] and the fundamental of 400 Hz [weak], heard as the difference frequency or pitch of the combination.
In the other ear the tones 800 Hz [extreme weak]; 1200 Hz [weak]; 1600 Hz [strong] and the beat of 400 Hz [weak], heard as the difference frequency or pitch of the combination.
What you can comment is that these processes don’t belong to the category of sophisticated mathematical processes.
by Willem Christiaan Heerens & Experiments
The following experiment with a Fourier series with missing fundamental exists of:
All sine contributions with frequencies: 800 – 1000 – 1200 – 1400 – 1600 – 1800 – 2000 Hz.
And relative amplitudes reciprocal with the frequency.
The pitch that is observed is equal to 200 Hz and is the first harmonic in the series which is missed. But also the 400 and 600 Hz, which are absent in the stimulus can be detected in the sound energy signal.
If we change the 1000 – 1400 – 1800 Hz contributions from sine to cosine, while the other contributions remain sine functions, the pitch that is heard equals 400 Hz.
Among auditory pitch experts this is mentioned as very remarkable while the explanation of this phenomenon does not exists.
Even much stranger for the common hearing theory is the following effect:
If we create the composition of the following ‘modified Fourier series’
2000 – 2003.0334 – 2006 – 2009.0334 – 2012 – 2015.0334 – 2018 Hz
And we listen to this composition during 30 seconds we hear a high tone [the approx. 2009 Hz tone] with the following beat pattern:
This tone starts with a 3 Hz beat that changes at first slowly but while it is approaching the 7.5 seconds it changes more rapidly into a 6 Hz beat, which in the next 7.5 seconds changes at first rapidly and later on more slowly again into a 3 Hz beat at 15 seconds.
While for the next 15 seconds this entire beat pattern is repeated.
If you calculate the sound energy spectrum out of the above ‘modified Fourier series’ you clearly see that at the start [t = 0] all the lower frequencies of 3 – 6 – 9 – 12 – 15 – 18 Hz are present.
At t = 7.5 seconds the 3 – 9 – 15 Hz contributions are disappeared.
At t = 15 seconds these contributions are present again, at t = 22.5 seconds they are disappeared again and at t = 30 seconds they are present again.
Mathematically we can observe the above frequency composition as a ‘modified Fourier series’ with frequencies:
2000 – 2003 – 2006 – 2009 – 2012 – 2015 – 2018 Hz
in which the 2003 – 2009 – 2015 Hz contributions have an additional time dependent phase shift equal to: