Hearing colophone (44K)


Measured values for in vivo humans


Last Update: July 2009             Activa™: See Citation Page

The elements of the human ear are designed to collect acoustic energy over a broad spectrum and convert that energy to a set of neurological signals that the brain can interpret.

The human ear can be described most effectively by dividing it into a series of functional elements.

The initial elements operate in the physical domain while the later elements operate in the neurological (electrolytic) domain. The following tabulation conforms to these elements.

The Outer Ear acts as an energy collector

The primary purpose of each outer ear is to simultaneously collect acoustic energy arriving from any direction within a wide field of acceptance and funnel that energy so that the wavefronts representing that energy arrive at the eardrum parallel to the surface of the eardrum.

EAch outer ear consists of a cylindrical tube of rigid material (at acoustic frequencies) and decreasing diameter (a horn) ending at the eardrum. The external portion of the outer ear, the pinna, acts as the bell of the above horn. The bell acts as an acoustic impedance matching device because the impedance of the horn is different from the impedance of the free-space beyond the bell.

The horn of the outer ear terminates functionally at the outer surface of the eardrum.

The first order frequency response of the outer ear is flat (doesn't vary with frequency).

There is a second order frequency response that exhibits peaks and valleys due to interference resulting from the geometric acoustics of the folds of the pinna. The center frequency of these peaks and valleys varies between individuals.

The nominal velocity of acoustic propogation in air is 345 meters/second @ 23C to 353 meters/second at 37C.

The Middle Ear acts as an impedance transformer

The primary purpose of the middle ear is to act as an impedance matching device for terrestrial animals. It is vestigial or non-existant in aquatic animals (frequently represented by a piece of straight bone).

The middle ear begins functionally at the outer surface of the eardrum and ends at the fluid surface of the oval window of the vestibule of the labyrinth. Its purpose is to transform the acoustic energy applied to the eardrum by the low-impedance gaseous external environment into a similar signal in the much higher impedance of the fluid and tissue environment of the inner ear.

The energy applied to the eardrum is the product of the effective displacement of the eardrum times the effective area of the eardrum.

The energy delivered to the fluid environment of the inner ear is the product of the effective displacement of the oval window times the effective area of the oval window.

Merely describing the relative lengths of the small bones of the middle ear (as done in most introductory material) does not adequately describe the effective acoustic pressure and displacement amplification achieved by the middle ear.

The small bones of the middle ear are not attached to each other rigidly and their pivot points are established by ligaments, not bones. As a result, the middle ear exhibits a bandpass characteristic under nominal excitation conditions (a range of at least 100 dB. In the presence of excessive excitation, the flexibility of the mounting arrangement provides a degree of overload protection.

The Vestibule of the Labyrinth acts as a sound velocity reducer

The primary purpose of the vestibule of the labyrinth associated with hearing is to accept acoustic energy traveling as a compression wave within a fluid and convert it to a surface acoustic wave (or Rayleigh wave) traveling along the liquid crystalline surface of the Tectorial Membrane extending into the cochlear partition of the cochlea.

The nominal velocity of the initial acoustic energy propogating as a compression wave in the fluids of the labyrinth is 1500 meters/second regardless of the frequency of the energy.

The nominal velocity of acoustic energy propogating along the liquid crystalline surface of the tectorial membrane leaving the middle ear as a Rayleigh wave is six (6+) meters/second regardless of the frequency of the energy.

The frequency response of the gel surface of the Tectorial Membrane, and the uncoiled Hensen's stripe, is basically flat from a frequency below that associated with human hearing to beyond 150 kHz (based on the performance of the same material in the dolphins and bats).

The coiled Hensen's Stripe acts as a sound frequency dispersing device

The gel surface of the Tectorial Membrane curves in two different planes from its point of origin to its termination near the Helicotrema of the cochlea.

During the initial curvature between its creation in the Caecum of the Vestibule and the beginning of the Organ of Corti, the curvature of the gel surface is in a plane perpendicular to the surface of the gel. This curvature is provided primarily for physical positioning. It is not frequency selective. The energy propagating along the gel surface is concentrated in Hensen's stripe in this region.

Beginning at the start of the Organ of Corti, the curvature of the gel surface of the tectorial membrane and particularly the curvature of Hensen's stripe, is in the plane containing the gel surface. This curvature introduces a frequency selective dispersion of energy from Hensen's stripe onto the surface of the gel. This is the primary frequency selective mechanism of hearing.

The curvature of Hensen's stripe in the plane of the gel surface is described mathematically by a modified Hankel Function. This function completely describes the frequency dispersion properties of the Organ of Corti as a function of distance from the beginning of this curvature.

The same Hankel Function defines the remarkable attenuation of Hensen's stripe. Integration of the dispersion characteristic associated with the Hankel Function results in an attenuation function that is described by "an exponential of an exponential." The extreme attenuation above best frequency achieved by this function appears to be unique to hearing and has not been found elsewhere in science.

The gel-surface of the Tectorial Membrane acts as a narrowband frequency selector

As the energy propagating along Hensen's stripe is dispersed onto the gel surface of the tectorial membrane, the energy approaches and is absorbed by groups of outer hair cells. It is the physical positions and dimensions of the outer hair cells relative to Hensen's stripe and the laws of geometrical acoustics that describe the narrowband of acoustic energy that is captured by eack group of outer hair cells.

The IHC & OHC Neurons act as energy sensors and converters

The cilia associated with the inner and outer hair cells of the Organ of Corti operate analogously to the stylus of a phonograph player. They sense the movement of the gel surface of the tectorial membrane as the Rayleigh waves move along or across the gel surface.

The inner hair cells are mounted along the top of Hensen's stripe so as to sense the modified Rayleigh wave propagating along the top of Hensen's stripe. These IHC sense the cumulative energy of that wave. This energy is truncated at a frequency determined by the local curvature of Hensen's stripe at their location.

The outer hair cells are mounted along the gel surface at a nominally fixed distance from Hensen's stripe. They are typically arranged in groups of three cells arranged in echelon formation at an angle defined by the angle at which the acoustic energy is shed by Hensen's stripe. As a result, each group of OHC only intercept acoustic energy at a specific frequency determined by their location relative to the length of Hensen's stripe.

The energy sensed by the cilia of the hair cells is transferred to the piezoelectric proteins within the cilia and the nearby region of the body of the hair cells. These proteins create an electrical potential between the two surfaces of the proteins perpendicular to the direction of the applied energy. It is this initial electrical potential that is amplified and processed by the neural circuits within the body of the sensory neurons.

The piezoelectric proteins of the sensory neurons are continually removed and replaced by new proteins. The rate of protein replacement, relative to the rate of acoustic energy application to the sensory neurons, plays a major role in determining the short-term sensitivity of both the IHC and OHC sensory neurons.

The remainder of the Neurological System

The organization of the neurological system of hearing is different from that associated with vision.

The limited space within the cochlear partition allows only the most critical neural signal processing to be carried out within the confines of the cochlea. This processing is carried out in a series of spiral ganglia associated with each incremetal length of the Organ of Corti. The remaining signal processing dedicated to hearing is carried out in the cochlear nuclei located close by but external to the cochlea. The cochlear nuclei create a set of functionally separate signals that can diverge in proceeding to various higher neurological centers.

A small amount of the most time critical signal processing associated with external source location determination occurs within the cochlear nuclei. However, most of this signal processing is accomplished in the elements of the central nervous system.


Energy Threshold of Adaptation Amplifier

Nominal energy threshold of first Activa in photoreceptor adaptation amplifiers >2.0 Electron-volts equiv. to 600 nm. Not over 2.34 EV based on Sliney data

Time Constants

Iris-- closing 1.2 sec
        opening 6.0 sec

Photoexcitation/De-excitation process

Intrinsic t 0.5(25) ms dominant during falling edge in P/D equation
Dynamic,       s*F*t s*F*0.525 sec. dominant during rising edge of P/D equation. Where F = radiant flux in photons/sec micron2; s = absorption coefficient in electrons-microns2/photon; product usually much less than t
absorption coefficient, s 0.76 (From file, Fulton_Rushton79 fg 3.ai for the scotopic region)

Adaptation amplifier

Attack < 0.1 sec dominant during increase in illumination
The attack characteristic is due to a "charging" circuit and depends on the illumination level.
Recovery   dominant during decrease in illumination
1st 3 seconds electronic
2nd (1st vascular) 2 minutes vascular, est. from Spillmann
3rd (2nd vascular) 10 minutes vascular    "      "      "    "

The recovery time constants vary dramatically with position in the retina mosaic. They are a function of the impedance of the cell wall, the vascular supply and the capacitance shunting the collector of the Activa. The first time constant, interpreted from the recording of the Class C waveform by Baylor (1984), is electronic and has a value of three seconds.

Nominal pass band of signaling channels

Low frequency (RC type) pole XXX  Due to adaptation amplifier collector circuit
High frequency pole XXX   

Nominal transmission velocity of signaling channels

Phase velocity of signals within the electrolytic medium 4,400 m/sec. at 37C
Group velocity of action potential signals between regenerative nodes 44 m/sec. at 37C

Nominal spectrum of P/D equation (& generator potentials)

Low frequency pole none
High frequency poles at  
1/t = 2p x f = 1.9 0.3 Hz from LaPlace of P/D equation
s x F = 2 p x f = XXX  

Nominal action potential parameters

Nominal action potential pulse shape @ 37 C
Time constant of pulse rise, tR 0.012 msec
Time constant of pulse fall,tF 0.25 msec
Switching time, tS 0.075 msec

[For VQ = zero; VM = -95 mV, VS = -94 mV, tR = 0.012 msec, tS = 0.075 msec & tF = 0.25, Temp. 37 Celsius. Parameters from Schwarz & Eikhof]

Nominal action potential frequency

dark adapted luminance channels zero no pulses are generated absent illumination
dark adapted chrominance channels 30  Hz 33 ms.between pulse peaks
dark adapted polarization channels 30  Hz assumed, lacking data

Maximum action potential frequency

all signal projection channels 100 Hz nominal value, may be exceeded

Perceived Spectral Response Characteristics

There are four distinctly different regions of the luminosity function; the hyperopic, photopic, mesopic and scotopic. Each exhibits different absolute maxima and various relative maxima depending on the state of adaptation of the three individual chromophores. Confirmation experiments must use narrow band filters, express the state of adaptation of each chromophoric channel individually and specify the color temperature of the source. The nominal peaks in each are:

Name Absolute maximum Type Relative maxima or inflection point
Hyperopic 580 nm. Perceived 437, 494, 523, 625
Photopic 523 nm. Chromophoric 437, 494, 580, 625
Mesopic 523 nm. Chromophoric details change significantly with intensity
Scotopic 494 nm. Perceived 437,494

Note that none of these absolute maxima are related directly to a chromophoric peak. Additional selective adaptation must be employed to observe the other chromophoric peaks. The above peaks are obtained with instrumentation of less than five nanometers spectral bandwidth. The following values were defined based on averaging, and smoothing, of wideband filter data collected at relatively uncontrolled color temperatures.

CIE Photopic 555 nm. Smoothed
CIE Scotopic 507 nm. Smoothed

V Optic Nerve Parameters

(Includes vascular support to the ocular globe and retina)
optic nerve artery divides into choroid and retinal portion.

Total number of neurons 106
Efferent few dozen
     non-signal few dozen
     signal to LGN 106
     signal to Pretectum 2 x 104

Important features;
    Transposition, and first bifurcation at the optic chiasm to support binocular vision
    Second bifurcation to support both the LGN and Pretectum


Spatial Pointing



Spatial Resolution

Temporal Resolution

The temporal performance of the human eye is a function of which signal path is involved and the irradiance level. The following selected values have been gleaned from the literature.

Electrical Passband

The values in this compendium are for the human at 37 Centigrade. Temperature plays a major role in the biology of hearing. However, it does not follow the Arrhenius Rule. Biological activity essentially stops at zero Centigrade and fails due to denaturing near 50 Centigrade.

Other recent sources providing parameters related to the Human Hearing are;
An introductory text
A general text, with a good glossary

Many of the values in these texts were drawn from disparate sources without attempting to correlate the values within a consistent framework. One of the authors actually solicited individual parametric values over the INTERNET. Some of the values in these texts are not supported here and must be interpreted in the light of the Theory of this work. Example, the terms

Copyright © 2008 James T. Fulton