JANUARY, 1940 REVIEWS OF MODERN PH YSI CS VOLUM E 12

Auc iI:Ory . . a1.1.ernSHARVEY FLETCHER

Bell Telephone I.aborafories, ¹m York, ¹m York

URING the last two decades considerableprogress has been made in understanding

the hearing processes taking place when we sensea sound. The application of the same instru-mentalities that have brought such a wonderfuldevelopment in the radio and sound pictures tothis problem is largely responsible for thisprogress. Such instrumentalities have made itpossible to make accurate measurements whichare the basis for understanding any physicalprocess.

To understand this problem then v e need toknow first how to describe and measure thesound reaching the ears; then we need to knowhow to describe and measure the sensations ofhearing produced by such a sound upon alistener. To do this quantitatively we must alsoknow the degree and kind of hearing abilitypossessed by the listener. It is with these threephases of the problem that this paper deals.

A pure tone can be defined physically bygiving the intensity, the frequency and the phaseof vibration at the position where the head ofthe listener is to be placed. To be precise, thisposition is taken as the middle of a line con-necting the two ears. The measurement of courseis made before the head is placed in this listeningposition. Then the listener faces the source ofsound. Any modifications of the sound waveproduced by introducing the head to this positionare considered as modifications produced by thehearing mechanism. The phase changes areusually unnoticed by the listener, so for mostwork only the intensity and the frequency aregiven. A pure tone then is specified by the twocoordinates, intensity I and frequency f. In mostexperimental work on pure tones an endeavor ismade to use a free progressive wave or itsequivalent, that is, one which is free from re-Hected waves. Under such circumstances, if I is

* From an address given before the joint dinner of theAmerican Physical Society and the American Associationof Physics Teachers held in Washington, D. C. , on Decem-ber 28, 1938.

measured in watts per square centimeter and thecorresponding pressure variation in the air wave,expressed in dynes per square centimeter, is p,then I and p are related by the equation'

I= (p'/4) X10 '.

The intensity I is usually determined from thisequation after making experimental measure-ments of p. To express the values for all puretones in the audible range requires a very largerange of values of I and p, so a new term calledthe intensity level and designated by the letter Phas been found useful. It is related to I and p bythe equation

p= 10 log (I/Io) = 20 log (p/po),

where the values

(2)

Io ——10 "watt per square centimeter,

po——0.0002 dyne per square centimeter,

have been adopted as international standards.The intensity level is expressed in decibels andvaries over a range of only about 130 db whendealing with acoustic problems.

In Fig. 1 is shown a chart on which may be

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FIG. 1.Auditory area. between threshold of feeling and thethreshold of hearing.

'This relation holds exactly for only one temperatureand pressure. The variations due to changes in pressureand temperature are small compared to the range in valuesused in acoustics ancl for most practical calculations canbe neglected.

H. FLETCHER

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FIG. 2. Auditory areas when hearing is impaired. Thecurves are indicated by the percent of a typical Americangroup who can hear sounds below the given leve].

represented all the pure tones which are audible.It will be noticed that there are three scales forthe ordinates and they correspond, respectively,to I, P and p. The values of the frequency f in

cycles per second are given by the abscissae.The upper and lower curves enclose the areacorresponding to tones which can be sensed assound. These results are for a young observerhaving acute hearing. The values of intensitylevel and pressure are the values obtained in afree air space before the head of the observer isintroduced to hear the sound and in a locationwhere the sound waves reAected from walls orother obstacles are negligible. The lower curvegives the faintest sound that such an observerlistening with both ears can hear and the uppercurve gives the loudest sound that a typical earcan tolerate.

It will be seen from this chart that the pitchrange is from 20 cycles per second to 20,000cycles per second, or a ratio of 1000 to one, andthat the intensity range is from 10 "watt persquare centimeter to 10 4 watt per square centi-meter, or a ratio of one thousand billion to one.It will also be seen that the pressure range isfrom 0.0002 dyne per square centimeter to 200dynes per square centimeter, or a ratio of onemillion to one. For a 60-cycle tone, at its maxi-mum tolerable intensity, the amplitude of theair particles is about —, millimeter. It will bereadily seen from these figures that the powernecessary to fill a hemisphere 15 meters from aloudspeaker with the maximum sound intensitywhich can be tolerated by the ear is about 1.5kilowatts. Of course the electrical power neces-

sary to drive a loudspeaker producing suchsounds may be three or four times this value,depending on the efficiency of the loudspeaker.So it is apparent that, although powers involvedin sounds are ordinarily very small, still toproduce in a large room the loudest sound thatthe ear can tolerate requires kilowatts of soundpower.

As stated before, this curve is for an individualhaving very acute hearing. As a matter of factabout only one in one hundred persons will haveas acute hearing as that shown. Recently theBell Telephone Laboratories cooperated with theU. S. Public Health Service in making a surveyof the hearing acuity of a typical American group.The results of this survey have been reportedrecently by the National Institute of Health in

a series of bulletins called the "Hearing StudySeries. " The results are given in relative in-tensity levels. Measurements made in our labora-tory by Mr. Munson made it possible to reducethese relative levels to absolute intensity levels.From these results the chart shown in Fig. 2 wasconstructed.

In a general audience, if no noise were present,one percent of the listeners could hear sounds assoft as indicated by the first curve; the nextcontour line is for 5 percent, and so on for theother curves as indicated. The important curveis the 50 percent curve which is shown by theheavy line. This means that half the people canhear tones at a level as low as indicated by thiscurve, but the other half must have higher in-tensities. However, in most auditoriums there isalways some background noise. Measurementshave shown that in such rooms the thresholdvalues even for acute ears are raised to some-where near the 50 percent line.

We have thus seen how we can represent apure tone by a point on the chart such as Fig. 2

by giving the frequency in cycles per second andthe intensity level in decibels. Most musicaltones have a fundamental and a series of har-monics, so to represent them quantitatively weneed to specify the intensity level and frequencyfor the fundamental and each harmonic. Thereis a 1arge class of sounds, however, that cannotbe specified in such a simple manner. Thesesounds have components scattered throughoutthe whole audible range of frequencies. Such

AUD ITO RY PATTERNS

sounds are represented physically by giving whatis called a spectrogram of the sound. For ex-ample, consider a noise like that arising in a busystreet. A spectrogram for such a noise is shownin Fig. 3. This spectrogram is determined experi-

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100 1000 10000 20000FREQUENCY IN CYCLES PER SECOND

FtG. 3. Spectrogram of street noise.

mentally as follows. The noise is picked up by amicrophone, amplified, and then sent through afilter which permits only a small band of fre-quencies to pass. The sound intensity of thissmall band is measured and divided by the widthof the band in cycles. This result is then reducedto decibels above 10 " watt per square centi-meter to obtain the ordinate in our spectrogram.Instruments are available which will read directlythe ordinates in such a spectrogram. The totalintensity level is given by the solid bar at the85-db level.

Similarly„ it has been found convenient to givea spectrogram for orchestral music. It is true, ofcourse, that such a spectrogram, to be a truerepresentation of the music, would be continuallyvarying. However, when the full orchestra is

playing the variations about the spectrogramcurve shown in Fig. 4 are only moderate.

Now we will ask ourselves the question, "Whatis going on in our ears as we sense such sounds&"

To understand more clearly what follows it isnecessary to give here a brief description of thehearing mechanism.

The main parts of the hearing mechanism areshown in Fig. 5, the inner ear being shown on avery much enlarged scale. As indicated in thisdiagram, it is usual to divide the mechanism intothree parts —the outer ear, the middle ear andthe inner ear. The outer ear consists of theexternal part, or pinna, and the ear canal whichleads into the drum. Beyond the drum is the

middle ear which contains three small bonescalled the hammer, the anvil and the stirrup. Thestirrup in turn is attached to a little membranecalled the oval window which separates themiddle ear from the inner ear. The inner ear isfilled with a fluid. As illustrated in the diagramthe inner ear is composed of two canals separatedby a membrane, all of which is wound into theform of a spiral. The nerve endings are scatteredalong the membrane separating the two canals.Very tiny nerve fibers coming from the mainauditory nerve are fanned out so as to reach eachof these nerve endings. The arrangement of thenerve fibers is similar to the arrangement ofwires in a telephone cable which are fanned outand connected to the jacks in a telephone switch-board. In such a switchboard, used to its full

capacity, there are 10,000 jacks and to each onethree wires are connected called the tip, ring andsleeve, making a total of 30,000 wire terminals.

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Fro. 4. Spectrogram of orchestral music.

There are approximately this number of nerveterminals along the basilar membrane and nervefibers leading from them to form a bundle calledthe auditory nerve. In telephone engineeringcircles it has been considered a real achievementto have developed a design which permits 30,000wire terminals to be within the reach of a singleoperator. The area of such a switchboard panelis about 10,000 square centimeters. Nature hasaccomplished a similar thing in the hearing mech-anizm occupying an area of only yo of a squarecentimeter, or only one hundred thousandths ofthe space in a telephone switchboard. The nerveterminals occupy a space only about —', millimeterwide and 30 millimeters long. Each one of thesetiny nerve endings acts like a telephone trans-

50 H. FLETCHER

mitter. %hen they are agitated by the soundwaves coming into the inner ear they transmitan electrical current along the nerve fiber. It isthese electrical currents which go to the brainand cause the sensation of hearing. The soundwave passes down the ear canal, strikes the drumof the ear at t, vibrates the drum, which in turnvibrates the anvil, which in turn vibrates thestirrup. The stirrup then vibrates the oval win-dow which transmits the vibrations to the fluidof the inner ear. This Quid transmits the vibra-tion to the nerve terminals, which in turn con-verts the vibration into an electrical disturbancewhich is sent to the brain.

In the following discussion it is not necessaryto know the details of this mechanism of hearing.It is important, however, to know that the nerveendings are scattered along a space which is onehundred times as long as it is wide. For thisreason we can designate the position of a small

group of nerves by a single coordinate. Also,since it is known that this long and narrow mem-brane containing the nerve endings is wound intoa spiral, I have chosen to represent the positionof the nerves on such a spiral diagram. A typicalform of this is shown in Fig. 6. The distancealong this spiral from one end to the other in atypical human cochlea is about 3 centimeters.The numbers along the outside run from zeroto 100. In talking about the positions in thiscochlear diagram I will refer to these small num-bers between zero and 100 as positions of nerve

Fro. 5. Semi-diagrammatic section through the right ear{Czermak}. G—external auditory meatus; T—membranatympani; P—tympanic cavity; 0—fenestra ovalis; r-fenestra rotunda; 8—semi-circular canal; 5—cochlea;Vt—scala vestibuli; Pt—scala tympani; 8—Eustachiantube; R—pinna.

100

80

FIG. 6. Typical auditory pattern.

endings, or more brieAy as nerve positions. Alsofor convenience I will speak of a group of nerveendings comprising one percent of the total as apatch of nerves. So the position of each patch isdesignated by one of the numbers between 0and 100.

On the chart of Fig, 6 we see a diagram whichI will call an auditory pattern. On this spiraldiagram representing the cochlea, the height ofthe dark portion is drawn proportional to theresponse of the nerves at that position. Thepattern shown is that produced in a typicalnormal ear when a 200-cycle tone is heard at anintensity level of 90 db. The response is measuredas the amount of loudness going from each nervepatch at the positions indicated. There is goodevidence, although not conclusive, that thisloudness is proportional to the number of nerveimpulses being sent to the brain per second byeach patch of nerves. For example, you see thatmost of the loudness comes from the regionaround position 5. However, there is considerablepart of the loudness coming from other partscorresponding to the subjective harmonics; forexample, at positions 10-'„17,23 and 28. Thesesubjective harmonics are introduced by themechanism of hearing. The total loudness corre-sponds to the total area of the darkened part andthis corresponds to the total number of nerveimpulses reaching the brain along the auditorynerve.

Later I will discuss methods of deducing suchauditory patterns from experimental measure-ments, but before doing this I wish to presentthe auditory patterns corresponding to the pure

AUDITORY PATTERNS

DeNIFIWO

oeAGNIFIEO

DBNIFIED

70 DeAGNIFIFD

Fio. 7. Auditory patterns for a 200-cycle tone at variousintensity levels.

tones. In Figs. 7 and 8 are shown such patternsfor a 200-cycle tone at the various intensity levelsshown. For intensity levels below 70 decibels theresponse is confined almost entirely to the posi-tions between 4 and 5. As the intensity level goesabove this value it will be seen that more andmore subjective harmonics begin to appear untilat an intensity level of 110 decibels there isresponse of the nerves all along the first turn anda half of the cochlea.

In Figs. 9, 10 and 11 are shown the auditorypatterns for tones having an intensity level of 90db but varying in frequency throughout theaudible range. It will be seen that the tones oflow pitch stimulate the nerves at positions corre-sponding to low numbers, that is, near the end ofthe inner spiral called the helicotrema. As thefrequency of the tone increases the position ofmaximum response gradually shifts to positionscorresponding to higher and higher numbers. Atthe same time the position of response due tothe harmonics continues to shift as the pitchincreases.

How do we know that these auditory patternscorrespond to what is taking place in our ears~To determine these patterns we need to know theamount of response as represented by the breadthof the dark portion in the auditory pattern andthe position along the spiral where the response isoccurring, that is, the nerve position. The funda-mental data from which such patterns are drawnare obtained from the masking eEect of suchsounds. For example, in Fig. 12 are shown suchdata on the masking produced by pure tones. Atthe top of this 6gure is shown the masking pro-

duced by a 200-cycle tone. The ordinates givethe masking or the number of decibels that theintensity level of a tone having the frequencyshown by the abscissa must be raised above itsquiet threshold in order to be heard in the pres-ence of this 200-cycle sound. The peaks' at 400,600, 800, 1000 are due to the subjective har-monics. For example, consider the point at 700.The masking here is seen to be 22, which meansthat a tone of 700 cycles must be raised 22 dbabove its quiet threshold to be heard in thepresence of a 200-cycle tone. Such a curve show-

ing the masking at each frequency is called anoise audiogram.

In the lower part of this figure the masking forseveral tones of di8'erent frequency is given. Onlythat part near the fundamental is shown. For thesake of clearness the peaks due to the harmonicsare omitted. I wish to call attention particularly

F.eEL eD DS

Fr@. 8. Auditory patterns for a 200-cycle tone at variousintensity levels.

~ There is an uncertainty of 4 or 5 db in determiningthese peak values, which is not due to observational errorbut due to interpretation. When testing the masking atfrequencies near the fundamental or any of its subjectiveharmonics, then beats occur. This new phenomenon makesit much easier to detect the masked tone. The points givenare for most distinct beats rather than where the beats justbecome audible. The points should be somewhere betweenthe best beat and minimum audible beat point. To enterinto the discussion here of the best point to take wouldtend to confuse the main argument of the paper. Changesdue to such uncertainty would not change the generalshape of the auditory patterns but only alter somewhat thesharpness of the peak.

H. F LETCH ER

to the fact that the breadth of these maskingcurves increases rapidly as the frequency of thetone doing the masking goes above 1000 cycles.Of course this must be related to how the earmechanism analyzes the sound. The bars at thetop of these curves are the minimum frequencyband widths of thermal noise for masking thesetones and will be discussed later.

In Fig. 13 is shown the masking effect of anoise whose importance will become evident as

TO

80

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100

YCLES90 DS

00

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390 DS

Frc. 11.Auditory patterns at 90 db for various frequencies.

100 the discussion proceeds. The curve at the bottomof the crosshatched area is the threshold ofhearing curve for a quiet place and is taken fromFig. 1. The curve at the top of the hatched areais the spectrogram for this noise. If If is the in-tensity per cycle of the noise for the frequencyregion f, then the ordinate for this spectrogramcurve is given by

Frc. 9. Auditory patterns at 90 db for various frequencies.y=10 log (Iq/Io)

and the total sound intensity I of the noise isgiven by

PITCH ISOO CYCLESNTEHSITY LEVEL 90 DS

100

390 DS

QO 2O, OOO

I= t Igdf = Io ~I 10'""df~o oo

(4)

and the intensity level P by

~0 PITCH 1960 CYCLES PITCH 2300 CYCLES

90 DS I 2Q, OOO

P=101og —= 101og t 10I" 'o df . (5)

100

80

—54 PIT

Flu. 10.Auditory patterns at 90 db for various frequencies.

This value calculated from the spectrogram isshown by the solid bar placed across the 1000-cycle ordinate.

The solid dots show the intensity levels of puretones which are just masked by this noise. Thenumber of decibels these dots are above thethreshold curve gives the masking. It will beseen that this is the same for each dot and isequal to 50 db. In other words, the masking for

AUDITORY PATTERNS

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0'200 400 800 800 1000

fREQUENCY

80.200 500 1000

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I I

0 500I I I

1000 1500 2000 2500 3000 3500 4000 4500 5000FREQUENCY

FIG. 12. Noise audiograms of pure tones.

120

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~ FEELING

this particular kind of noise is the same for allpure tones. The masking audiogram will then bevery simple, that is, a straight line at 50 db forall frequencies.

If we assume that constant masking indicatesconstant stimulation along the diferent patchesof nerves, then it is evident that the auditorypattern corresponding to this noise giving con-stant masking for all frequencies is similar tothat shown in Fig. 14. It is because such a noiseproduces a simple pattern that it becomes veryimportant in our discussion.

It is from masking curves like those shown inFig. 12 and the constancy of the masking byauditory nerves that the auditory patterns canbe drawn. To do this we must know how themasking in decibels, that is the ordinate in theseaudiograms, is related to loudness per patch ofnerves, and also how the frequency, that is theabscissae of these audiograms, is related to thenerve position.

First let us consider the data which enable usto determine the relation between the frequency

of the sound and the position of maximumstimulation in the cochlea. The nerve positionwill be designated by the coordinate x (see Fig. 6)going from 0 to 100, and the frequency of thesound will be designated by f Ou.r problem thenis to find the relation between x and f The. re arethree experiments dealing with quite differentphases of audition which give us data from whichthis relation can be calculated. The first set ofdata is obtained from experiments on the mini-mum perceptible diA'erences in pitch. In theseexperiments the frequency of the tone is varieduntil the observer perceives a change in pitch.The technique of doing such experiments is

-40100

80

FrG. 14. Auditory pattern stimulation uniform at allfrequencies.

described elsewhere. ' The results obtained byShomer and Biddulph are given in Fig. 15. Theordinate gives the value of the cycles change fora tone to be just audible and the abscissa givesthe frequency of the tone. As you will notice,tones whose frequencies are below 1000 cyclesrequire about the same number of cycles for aminimum perceptible change, namely, between2 and 3 cycles change, while for higher fre-quencies the fractional rather than the actualincrease of frequency is constant and equal toabout 0.3 percent. From these data we can derivethe desired relation' between x and f as follows.It was seen that the position of maximum stimu-lation shifted as the frequency changed. It seemsreasonable to assume that the amount of thisshift for a minimum perceptible change in fre-

20 100 1000 10000 20000FREQUENCY IN CYCLES PER SECOND

Fra, 13. Masking e8ect of a noise.

' Shower and Biddulph, J. Acous. Soc. 3, 275 (1931).4 This relation was first derived by Wegel and Lane of

the Bell Telephone Laboratories in )924,

H. FLETCHER

quency is the same for all positions. Therefore ifhx is this shift, then

dx = (dx/df)Df =A (6)

where A is a constant for all frequencies. Withthe scale we have chosen it is the percent of thetotal nerve endings passed over to make thechange noticeable. Then

pfx=A ' df. —

The condition x=100 when f= ~ determines theconstant A, or

x =100

From the curve of Fig. 15 the constant A isdetermined as 0.08 percent corresponding toabout 20 nerve endings.

A second set of data for obtaining this relationis obtained by 6nding the ratio of the intensityper cycle of the noise to the intensity of the puretone which is just masked by the noise. If wereturn again to Fig. 13 it will be noticed that in

the region below 1000 cycles the distances be-tween the dots and the spectrogram curve for thenoise are about the same and equal to 15 db. In

J /J. =C, (10)

where C is a constant independent of x and de-termined by condition x=0 when f= ~. There-fore

frequency positions in the ear are crowded to-gether in this higher pitch region. A wider bandof frequencies is going to each patch of nervescorresponding to these higher frequencies andconsequently produces a relatively greater stimu-lation, and consequently greater masking. Theseideas can be formulated into a mathematicalequation as follows:Let

sound intensity of noise in band between fand f+~f;

(AI/hf) =intensity per cycle of noise atfrequency f;

agitating power due to noise on cochlearnerve endings between x and x+Ax;

(6I/Dx) =agitating power due to noise uponone percent of nerves at position x. It maybe called agitation density;

sound intensity of tone of frequency fwhichis just perceptible in presence of noise;

total agitating power on nerve endings atposition x by this tone which is masked.

Then if the transmission system is linear (AI/I„)= (5//I„) or, substituting values for AI and 6L,we have

hx=(Ig/I )(I„/J,)hf

We will now make the following assumption'

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If we compare the relation given by Eq.(11) to that given by Eq. (8) we must concludethat, since these express the same relation be-tween x and f, the two integrands must beproportional, or

40 80 IOO 200 400 IOOO 2000 4000 IOOOO

FREQUENCY IN CYCLES PER SECONO

Frr. j.5. Minimum perceptible pitch change.

regions above 1000 cycles, however, the distancebecomes greater and greater until at 8000 cyclesit is 28 db. Now why is this? It is because the

6f= k(I /Ir), (12)

where k is a constant which has been found byexperiment to be equal to 20 when dealing withthermal noise.

~ For a more complete derivation of these relations seeProc. Nat. Acad. Sci. 24, 265-274 (1938).

PATTE R NS

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5 a —PITCH CHANGE DATA

Z 0 NOISE IAASKING DATA

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FIG. 16, Plot showing that the minimum perceptiblepitch change is proportional to the ratio of the intensity ofa tone having the same frequency to the intensity per cycleof the noise which just masks this tone.

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In obtaining these data the question which ledto the third type of experiment arose. It is: howdoes the ratio I /Ir vary as the width of thenoise band in the neighborhood of the frequencyof the masked tone becomes smaller and smaller.It would be expected that when this width be-came smaller than a certain limiting value, thenall of the acoustical intensity could be con-sidered as acting upon the same nerve endingsas those stimulated by the tone being masked.Consequently, for band widths smaller than thislimiting value, this ratio I /Ig becomes smallerand smaller as the band width becomes smallerand smaller. In fact it would be expected thatfor these smaller band widths the ratio of theintensity of the masked tone to the total in-tensity of the noise in the small band would be aconstant independent of both the band width

In other words, this analysis predicts that theminimum perceptible change in cycles for a toneof any frequency is equal to a constant times theratio of the intensity of a tone having the samefrequency to the intensity per cycle of the noisewhich just masks this tone. These two sets ofexperimental data are plotted in Fig. 16 and itwill be seen that they do determine the samecurve. The masking data were taken from theaverage of a large number of observations similarto those shown in Fig. 13. If X is the diA'erence

in decibels between the dots and the spectrogramcurve in this figure, then E is related to If/Ias follows:

%=10 log (I„/Ip)—10 log (Ig/Ip) (13)or

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8000 CYCLES

400020001000500250125

8000

4000

2000

1000—125"

500

1010 30 100 300 1000 3000 10000 30000

WIDTH OF NOISE 8AND IN CYCLES

FiG. 17. Ratio of the intensity of the mask tone to theintensity per cycle of the noise plotted against the widthof the noise band in cycles. The critical band width incycles is numerically equal to the ratio of the intensity ofthe tone masked to the intensity per cycle of the noiseproducing masking and always corresponds to —,

' mm oflength on the basilar membrane.

6 This work wi11 be presented in a future paper.

and the frequency region in which it is placed.Consequently, for these small band widths theratio I /Ir will be proportional to the width ofthe band. For all values of band widths largerthan this critical one this ratio will remainconstant.

Experimental tests were made to verify theserelations. I will not take the time to describe theapparatus and methods' for making this kind ofexperiment, but will be content however to showthe final results, which are given in Fig. 11.

The abscissae give the width of the noise bandand the ordinates the ratio of the intensity ofthe masked tone to the intensity per cycle of thenoise. The variable parameter which identifiesthe different curves is the frequency of themasked tone, which is also the frequency regionof the band of noise. It is evident from the resultsfor the 30-cycle band of noise that this ratio is thesame for all frequencies and is approximatelyequal to 30. This result makes the relations verysimple. For these smaller bands and for this typeof statistical noise, the intensity of the maskedtone must be adjusted to be equal to the averageintensity of the noise in the band in order for itto be perceived. It will be seen that as the bandwidths increase, this ratio also increases untilthe critical band widths are reached, which areindicated by the intersection of the horizontallines with the 45-degree line.

For example, consider the case for the 2000-cycle tone being masked by variously sized bands

H. FLETCHER

of noise, indicated by the squares on Fig. 17. Itwill be seen that the ratio increased until theband width of 100 cycles is reached. Increasingthe width beyond this value does not affect theratio. In other words, increasing the band width~

beyond 100 cycles does not change the maskingat all for hearing the 2000-cycle tone. The hori-zontal lines were determined from measurementson wide bands of thermal noise and are the samevalues as were given in Fig. 16. Since their inter-section of the 45-degree line determines thecritical values of band widths, this very impor-tant relation follows:

For this type of noise the critical band widthin cycles is numerically equal to the ratio of theintensity of the tone masked to the average in-tensity per cycle of the noise producing themasking. Regardless of where the band is located,we will see later that these critical widths alwayscorrespond to a single element of length on thebasilar membrane, namely -', mm. So we canreturn again to Fig. 16. The single curve showncan now be given three different interpretations:first, the ordinates can be interpreted as givingthe cycles change necessary to produce a per-ceptible change of pitch; second, when theordinates are multiplied by 20 they will then givethe critical band widths; third, when the ordi-nates are multiplied by 20 they will give the ratioof the intensity of the masked tone to theintensity per cycle at the frequency of the maskedtone of a statistical noise doing the masking. Forthese reasons we have considerable confidence inthe validity of the shape of this curve.

By means of this curve then and either of theformulae developed above, the relationship be-tween x and f can be obtained and is shown in

Fig. 18A on a rectangular plot and in Fig. 18B ona spiral diagram. This relation enables us to findthe position of maximum stimulation produced.by sounds whose power is confined in the regionnear the frequency f

Next we wi11 inquire as to what kind of data isused to determine the height of these stimulationpatterns. It will be remembered that the heightof these auditory patterns is proportional to theloudness being sent to the brain by 1 percent of

' It is realized that these critical band widths are notaccurately determined from these data. They may be~rong by a factor of 2, but that the bands are the rightorder there is no question.

IOO

tO„4Jxr eO—-0

I wa& 60ec n.'

~~4000I- ~N gL&20

4.0020 IOO IOOO

FREQUENCY IN CYCLES PER SECONO

I

I

I0000

FIG. j.8A. Position coordinate X of auditory nerve patchesfor various frequencies.

FIG. j.8B. Position in the cochlea for maximum responseto pure tones.

8 For this to be strictly true the patterns should beplotted in rectangular coordinates.

the nerves at each position. If this is true, thenof course the area' under the auditory patterncurve will give the total loudness. In order forthis to have any meaning we must have a quan-titative scale of loudness.

For purposes of making comparisons of loud-ness of various sounds, a reference sound has beenadopted by the American Standards Associationas a reference standard. This same standard hasrecently been recommended for adoption to theInternational Standards Association by an inter-national acoustical conference. This referencesound is a free progressive wave having a fre-quency of 1000 cycles per second to be receivedby the listener facing the source of this tone. Itsintensity could be defined by giving either I, p,or P, but it has been agreed internationally thatit shall be defined by giving the intensity levelin decibels. The loudness level of the referencetone expressed in phons is the intensity level ofthis tone expressed in decibels. The loudness levelof any other sound is determined by comparing

AUDITORY PATTERNS

it to the reference tone, adjusting the latter untilthe two sound equally loud. Then the loudnesslevel of the reference tone becomes also the loud-ness level of the sound being measured and isexpressed in phons.

Loudness is the magnitude of the auditorysensation produced by the sound. A scale forrepresenting loudness has been found such thatunits on this scale agree with common experiencein the estimates made of the sensation magni-tudes. This scale is de6nitely related to the loud-ness level scale. Units on the scale are calledloudness units, abbreviated LU.

A true loudness scale must be one such thatwhen the number of units on this scale is doubled,the magnitude of the sensation as experienced bytypical observers will be doubled, or whentrebled the loudness sensation is trebled, etc.The existence of such a scale is dependent uponthe supposition that consistent judgment testsof loudness can be obtained. Experimental testsindicate that such judgments are sufficientlyconsistent to warrant choosing such a scale. Tofind the relation between the loudness level andthe loudness on the proposed new scale, varioustypes of experiments were performed by in-vestigators in our laboratory and elsewhere.

The general scheme of these experiments is toAnd experimentally pairs of values of loudnesslevel Li and L2 phons, which correspond to pairsof values of the loudness ¹i and ¹2 LU. The first

type of experiment is concerned with a compari-son of the loudness experienced by a typical ob-server when listening first with one ear and thenwith both ears. Since we are dealing with thetypical observer, the two ears will be alike insensitivity. Consequently, if loudness is propor-tional to the total nerve energy sent to the brain,then it follows that the loudness experiencedwhen using two ears will be double that when

using one ear. To obtain such data the sound isfirst produced at any convenient intensity andlistened to with only one ear, and its loudnesslevel measured. Let us call this value Li. Withoutchanging the intensity of the sound the observerlistens with both ears and the loudness level ismeasured. Let us call its vaIue L2. If ¹ is thenumber of loudness units corresponding tolistening with one ear and ¹~ the number corre-sponding to listening with both ears, then it is

evident that ¹2 must be just double ¹~. We willagain listen with one ear, but increase the in-tensity of the sound until a loudness level of J2is obtained. If now again the intensity of thesound is held constant and we listen with bothears, we will find a loudness level L4. This mustcorrespond to a loudness ¹4 which is four times¹~. And so we might continue throughout theentire intensity range. If we now choosearbitrarily equal to some convenient number, wewill have a set of corresponding values of loudnessunits and loudness levels from which we candraw a curve giving the relation which we areseeking.

The experiments as outlined could not becarried out because our typical observer washypothetical. To obtain results corresponding tothat mhich mould be obtained by such a typicalobserver, one must deal with a large group ofobservers, taking the average value as thatcorresponding to a typical observer. For thisreason, pairs of loudness levels Li and L2 wereobtained starting with Li at various valuesthroughout the audible range. This experimentwas tried with pure tones having frequencies of100, 125, 500, 1000, 2000 and 4000 cycles persecond, respectively. The indicated points inFig. 19 show the observed values obtained. Asolid curve is drawn to give the best fit of theobserved points. From this curve the propervalues of Lj, L2, L4, L8, etc. , can be obtained tobuild the scale in the manner described above.

In the second type of experiment the followingprocedure is used. A 1000-cycle reference tone isbalanced against a pure tone having a frequencyfar removed from 1000 until they are equallyloud. Then the two tones are combined to forma complex tone having two components. Let L, ~

be the loudness level of each component alone,and L2 the loudness level of the combination.Since the components were adjusted to produceequal loudness, it is assumed that each is produc-ing the same nerve stimulation and that whenthey act together they will produce twice theloudness. This hypothesis is reasonable providedthat in the mechanism of hearing the two sets ofnerves do not interfere with each other. Theauditory patterns given for pure tones show thatsuch interference is negligibly small when theirfrequencies are widely separated. Consequently,

H. FLETCHER

120

110

100

80

O70

za 60

Lal

4LI~ 50

~ 40O

30

20

xf O

ij32,788

+0

16,384(t

&i~~/08192

QA

~f+'

pt 4096

A'2048

~ p4i 1024

+512g+ Iy

~ m m 256

BELI LABORATORIESI VS. 2 EARS

~-125~ ~-1000»-400%~-100& I-200& 0-500& &-1000% th 2000

x-2 COMPONFNT TONES

FIRESTONE 4 GEIGER&-HALF &-DOUBLE

GHURCHER. KING 3 PAYIES+-HALF

HAM 8 PARKINSON % CHANGE

i-350~, IOOO~ 8 2500~DAYIES I VS. 2 EARS

0[I 131,072

,536

r3218

40 10 20 30 40 50 80 70 80 90 100 IIO 120

LOUDNESS LEVEL, L2, IN PHONS

Fra. 19. Loudness determinations; various experimenters.

balancing such a two-component tone against

the reference tone should give pairs of values of

I & and I 2 which can be used in the same way as

indicated by the one-vs. -two-ear method de-

scribed above, that is, L,2 corresponds to a loud-

ness number which is just twice that correspond-

ing to I ~. Such observations are shown in Fig. 19

by the points indicated x.In the third type of experiment a typical

observer is asked to listen to a sound, first at aloudness level I.~ and then to the same sound

when its loudness level has been raised to avalue I.2 such that to him the loudness seems tohave doubled. The experiment is repeated,starting with another initial value of J1, and

thus a series of pairs of values of 1.1 and I.g areobtained which have the same relation to our

loudness scale as those obtained by the first two

methods. A much greater amount of data is

required by this method because the probable

error of a single judgment is very large. How-

ever, this method is related more directly to thescale we are seeking than the two preceding ones.Four different investigators' in different parts ofthis country and England have taken a verylarge number of observations by this method,not only on the 1000-cycle reference tone buton many types of tones. The data taken byLaird have been omitted since they were so farout of line from those obtained by the otherthree groups of investigators, namely, Ham andParkinson, Firestone and Geiger, and Churcher-

King-Davies. Their observations are given in

Fig. 19 by the points indicated.It will be seen that the observed points ob-

tained by these diverse methods fit consistentlyon one curve, particularly well in the range ofloudness usually experienced in everyday life;

9 In these experiments the loudness level was not meas-ured, but only the number of db above the threshold. Forthe 1000-cycle tone this was taken as the loudness level L.For other pure tones the loudness level was computedfrom our data on the loudness level of pure tones.

AUDITORY PATTE R NS

x~0

X

/'

X~ TEN TONE DATA

x TWO TONE DATA

0A

/!,i0

Z 1000

8N4JZ

1000

10 20 SO 40 50 BO 70 BO 90 '100 110 120LOUDNESS LEVEL, L, IN PHONS1'

Fro. 20. Loudness scale.

namely, from Lq=40 to L~=80 phons. It wassufFiciently consistent to justify choosing theresulting loudness scale as a true loudness scale.

F'rom this curve in Fig. 19, pairs of values of L&

and L~ were taken to construct the curve ofFig. 20 in the following way. It wi)1 be seen thata staircase has been erected upon the curve withthe corners of the steps lying on a 45-degreestraight line. The value of N for L =0 was takenas unity. If, then, the sound is adjusted so thatthe threshold is reached for either ear listeningalone, then when listening with both ears, theloudness level is between 2 and 3 phons and theloudness is doubled, or 2. This corresponds tothe bottom step. Now if the sound is adjusted sothat for each ear alone the loudness level is 2

phons, then if both ears are used the loudness israised to 4 LU. This corresponds to the secondstep. So it is seen that the width of the stepsshows the change in the loudness level necessaryto double the loudness. The values of the loud-ness X indicated on each step can now be plottedagainst the corresponding L to give the desiredrelation between I and E. This is shown bythe curve of Fig. 20.

This same scale can be developed from dataobtained by balancing a three-component toneagainst the reference tone or by judging when athreefold increase in loudness has been pro-duced. Or we could use any other number be-sides 2 or 3 and get the same scale if it is a realloudness scale. An extreme case would be to usea ten-component tone and use judgment tests

for one-tenth and ten times as loud. Tests ofthis kind have been made which I shall nowdescribe.

A complex tone" was generated having tenharmonics of a fundamental frequency of 530c.p.s. The components were each adjusted sothat when listened to separately they had thesame loudness leve1 L~ phons. They were thencombined into a complex tone, and it was foundthat the loudness level was raised to a value LiQ

phons. So in this way pairs of values of loudnesslevels Li and L~Q were obtained starting with Liat different intensities of sound. If the patchesof nerve stimulation corresponding to each com-ponent do not overlap, then the complex toneshould be ten times as loud as each component.Such pairs of intensities were obtained with agroup of observers, and are shown by the pointsin Fig. 21. Ham and Parkinson, and Firestoneand Geiger made judgment tests to find a pairof loudness levels L~ and L~Q such that the tonefor L~ was one-tenth the loudness of that for LgQ.

Their results are shown by the points indicated.The points are somewhat scattered but I thinkit is remarkable that the two sets of pointsdetermine the single curve within the observa-tional error, for such judgment tests are ex-tremely difficult to make. The three points for theten-tone data at the higher levels are definitelyoff the curve as drawn and should be, for atthese high levels the auditory patterns for thedifferent components overlap. The judgmenttests and the ten-tone balance tests were allmade in diAerent laboratories and before anyloudness scale of the type discussed here wasconstructed.

Now the curve of Fig. 21 can be used toconstruct a loudness scale. In this case thewidth of the steps of the staircase correspondsto the phons increase necessary to make thesound ten times as loud. The correspondingvalues of N and L can be used to determine thecurve of Fig. 20. The solid curve was drawn sothat points on it would yield the same loudnessscale as shown in Fig. 20. It is seen that such acurve does indeed fit the observed data. Thefollowing equation

' The description of this generator is given in the paperby Fletcher and Munson, J. Acous. Soc. Am. 5, 82-108(1933).

H. FLETCHER.

100

90

80

70Ox

60

504d

BELL LABORATORIES+-TEN TONES

FIRESTONE 8 GEIGERi- 1(10 r-10 X

HAM 8 PARKINSONi-I 0/o

40

O 30

20

k 0

~, 1000

10' 100

&oa0 10 20 30 40 50 60 70 80 90 100 110 120

LOUDNESS LEVEL, Le, IN PHONS

FIG. 2 i. Loudness determinations; various experimenters.

&05~3I 105/310 E /10

(&5)(g+ fo5/2) 2/3 (fOI/10+ $O5/2) 2/3

proposed by Knauss represents approximatelythe relation shown in the curve of Fig. 20.This reduces to

X=I= 10&»o

for values of I below 20; that is, at very low

levels the loudness numbers are equal to theintensity, where I is expressed in terms of thereference intensity Io.

2V 10 ' (f) ' —10 ' 10~/ao 46X10 '" (17)

for values of I, above 40. This last relation htsthe curve more accurately, the other two onlyapproximately. The last relation states, through-out most of the range ordinarily encountered in

practice the loudness numbers are proportionalto the cube root of the intensity.

It is important to remember that the valuesof the intensity I in the above equation referonly to the 1000-cycle reference tone but thevalues of I. are for any type of steady sound.

The curve of Fig. 20 has been taken as de6ningthe relation between the loudness N expressedin LU's and the loudness level I expressed in

phons. The loudness of any other tone, eithersimple or complex, can be determined by com-

paring it to this reference tone and adjustingthe intensity of the latter until the two sound

equally loud. The loudness of the reference tonethus adjusted is then the loudness of the un-

known sound being measured. Stevens" hasproposed using the word "sone" for a loudnessunit 1000 times that called the LU in this paper.Consequently the LU mould be the same as amillisone. Loudness levels below 40 db are veryfaint sounds. For example, the tick of a high

quality watch held close to the ear has a loudnesslevel between 40 and 50 phons. The curve in

Fig. 22 shows the relationship between the loud-ness in sones and the intensity level of thereference tone expressed in decibels, both plottedon a linear scale. If one were listening to a1000-cycle tone and increased the intensity leveluniformly by turning a dial of an attenuator

'1 Hearing, Its Psychology and Physiology, Stevens andDavis, p. 119.

AU D I TORY PATTE RNS

'ISO

140

'I20—V)4Jz0& looz

V)w 8020Q 60—

40

20

0—40

LOUDNESSREFERENCE

50 60 70 80 90INTENSITY LEVEL

100 110

Q 7Z0ZZO

5

A

u) 4

3 rr

0 10 20 30 40 50 60 70 80 gP 1PP

MASKING' M

FIG. 22. Loudness of reference tones in sones. FIG. 23. Relation between the masking, M, and the loudnessper patch in sones.

calibrated in decibels, then the loudness increaseas sensed by the ear would correspond to theincrease in height of this curve as sensed by theeye. One can easily perform this experiment andsatisfy himself that this is indeed true.

Ke now want to use these loudness relationsto determine the loudness of our important typeof noise, that corresponding to the spectrogramshown in Fig. 13. It will be remembered that sucha noise produces a uniform response of all thenerve patches. Consequently, measurements ofloudness and masking were made of this noise.The intensity of the noise was then changedwithout changing the shape of the spectrogram.It was found that within the observational errorthe masking was again the same for each fre-

quency. Another pair of values of loudness andmasking were measured. This was continueduntil such pairs of values were obtained through-out the entire audible range. Since all the nervepatches are responding equally, if the totalloudness is divided by 100 we obtain the loudnessper patch. The results of these measurements aregiven in Fig. 23. This curve then gives us thenecessary relation between the masking lYL andthe loudness per patch. In other words, it enablesus to know how high to draw the auditorypattern at each position corresponding to thefrequency of the tone being masked by theamount 3II.

Summarizing the procedure then, for anysound we 6rst determine experimentally the

eo

20 ~

I I I I I I

0 500

80-

o 60-z& 40-CX 20-

I I I I I I I I I I I

1000 15OO 2OOO 2500I I 1 I I I

3000 3500 4000

4000

80-

60.40-

I

4500I

5000 5500 6000 6500 &000 7500 8000

I

6500I

9000 9500 10000 10500FREQUENCY

11000 11500 12000

Frr. 24. Masking audiogram for steamboat whistle.

masking audiogram. This gives the mas ing Mfor each frequency. The frequency scale is trans-ferred to the nerve position scale by the relationof Fig. 18A, and the masking scale to a loudnessper patch scale by the relation of Fig. 23. Theresults are plotted on the spiral diagram to givethe auditory patterns corresponding to the noisemeasured. For example, in Fig. 24 is shown themasking audiogram for a steamboat whistle andin Fig. 25 is the corresponding auditory pattern.In Figs. 26 and 27 are similar diagrams for streetnoise. Notice that all of the nerve patches arebeing continually stimulated when one is in suc ha noise. In Fig. 28 are given the auditory pat-terns corresponding to the notes of a bugleplaying taps. Notice that the harmonics in the

H. FLETCHER

50

Io 40 .40

IOO

FIG. 25. Auditory pattern of steamboat whistle.80

FiG. 27. Auditory pattern of street noise.

positions between 40 and 60 carry most of theloudness. For example, in the first note the 6th,7th and 8th harmonics each carry about threetimes as much loudness as the fundamental.For each note the fundamental carries only asmall fraction of the total loudness. This isdue both to the mechanism of the cornet andalso to the mechanism of hearing.

So it is the interpretation of these continuallychanging auditory patterns in the ear whichbrings to us all of our information about theacoustic world about us. These patterns havebeen those experienced by a typical listener whohas normal hearing. The question now arises asto what patterns are experienced by a deafenedlistener. There are two kinds of deafness, whichare usually designated "nerve deafness" and"obstructive deafness. " In the former the nervetransmitters are defective, while in the latterthe mechanical transmitting mechanism fromthe outside air to the nerves of the inner earis defective. Of course, both types of deafnesscan occur in the same ear. It can be shown that

IOO

90n.

7C

~ 00(

~ 40

30

2C

00 1000 2000 3000 4000 5000 0000 7000 8000 9000 I0000

FREQUENCY IN CYCLES PER SECOND

FIG. 26. Masking audiogram for street noise.

nerve deafness is equivalent to having a noisecontinually present which produces a similarmasking of sounds, while obstructive deafness isequivalent to introducing attenuation betweenthe source of the sound and the listener. If weunroll one of these auditory patterns and makeit into an ordinary rectangular plot, for exampleone corresponding to pure tones of 200 cyclesand 2000 cycles, we wi11 get the curves shown atthe top of Fig. 29.

Now if we change the two scales, plottingmasking in decibels as ordinates instead ofloudness per patch and plotting frequency asabscissae instead of nerve position x, then thetop figure resolves itself into the one shown atthe bottom of Fig. 29. This plot as it now standsis called the noise audiogram and it gives theexperimental data as they are usually tabulated.It has been shown that it is such noise audio-grams which give the fundamental data fromwhich the auditory patterns can be drawn.This plot divers from those shown earlier inthat the frequency is plotted on a logarithmicrather than a linear frequency scale. This makesit possible to plot the audible range of frequenciesin a single diagram.

Similarly, when a person is deafened werepresent the amount of the deafness by thissame type of audiogram, but of course in thiscase there is no noise present and the ordinatesrepresent the decibels that tones of the fre-quencies indicated by the abscissae must beraised above that for normal hearing. So wecan say, that a person of normal hearing whois immersed in a noise which produces a given

AU DITOR Y PATTERNS

50 50

I00 I00

80

FUNDAMFNTAL = 3(i CYCLES PER SECOND

80

FUNDAMENTAL = 415 CYCLES PER SECOND

50

100

80

FUNDAMENTAL = 518 CYCLES PER SECOND

80

FUNDAMENTAL = 622 CYCLES PER SECOND

FIc*'. 28. Au~)itory patterns for four notes of bugle playing "taps."

audiogram will have only those capabilities forhearing desired sounds that a deafened personwould have with the same kind of a deafnessaudiogram. Because of this equivalence a personof normal hearing who is immersed in a noiseexperiences the same difhculties of hearing speechwhich are actually experienced by deafenedpersons.

Let us consider a moderate case of nervedeafness. The audiogram for such a case is shownin Fig. 30, curve A. If we use this audiogram andplot the corresponding auditory pattern, we getthe results shown in Fig. 31. The breadth of thecrosshatched portion now indicates the amountof damage to the nerve endings at the variouspositions along the basilar membrane. Insteadof an auditory pattern I will call this area adeafness pattern. The scale is so chosen that ifthis deafened person is to hear any sound the

pattern which would be plotted for a nortnalhearing person must project through the pattern

v) go~g iLL ~~ I L

& ~0 Io 20 30 gOX

100

60 &0 80 00 tQO

80—

7Q

~ 60Z& 50

& ~o

30—j

( A. '

00 6~ I26 256 S~2 ~02~ 20M 4096 eWZFREQVENC& IN C&CLOS PER SECOND

F&G. 29. Upper curve, auditory pattern on a rectangularplot. Lower curve, masking in decibels vs. frequency.

H. FLFTCHE1&

here shown. In other words, the normal auditorypattern must project through the deafness pat-tern, For exan&pie, in Fig. 30, curve 8, is shownthe audiogram for a case of nerve deafness whichis 30 db n&ore severe than the one in Fig. 30,curve A. The corresponding deafness pattern isshown by the crosshatched portions of Fig. 32. 100

cO 70

—60cfog

O~ 50

2 40a,'

~ 30x

0 64 128 256 512 1024 204d 40gd 61g2FREOUENCY tN CYCLES PER SECOND

Fr( . 30. e'en e deafness audio~~ran&s.

50lDC 40Z

10 30O~ 2oQz

10

4Jz 00

8'O

FIG. 32. Nerve deafness pattern.

128 258 512 1024 2048 4008 8192f'REQUENCY IN CYCLES PER SECOND

FIG. 33. Obstructive deafness audiogram.

FIG. 31. Nerve deafness pattern.

Also, on this deafness pattern are shown, by thewhite portions, the normal auditory patternsproduced by the pure tones having frequenciesof 2300 cycles and 6500 cycles. It will be seenthat the latter tone will not be heard becauseits normal auditory pattern does not projectthrough the crosshatched area corresponding tothe deafness pattern. However, a 2300-cycletone will be heard and the loudness with whichit will be heard is equal to the amount of whitenedarea projecting above the crosshatched area inthis figure. Indeed, loudness tests upon suchdeafened persons have verified that these resultsagree with such calculated values of loudness.So the auditory pattern for a person having

nerve deafness is that part of the normal auditorypattern which protrudes above the deafnesspattern. It has been shown that both the normalauditory pattern and also the deafness patterncan be obtained quantitatively from auditionmeasurements. Consequently the auditory pat-tern for the deafened person can also be drawnin a quantitative way. "

Obstructive deafness is equivalent to puttingattenuation in the transmission path betweenthe source of sound and the listener. In Fig. 33is shown the audiogram for a typical case ofobstructive deafness. Now we wish to knowwhat the auditory pattern is for such a deafenedperson when he listens to the steamboat whistlewhose audiogram was shown in Fig. 25. In Fig. 34the deafness audiogram is shown again by theline at the bottom and the noise audiogram forthe steamboat whistle is shown by the top heavyline. Since obstructive deafness is equivalent toattenuation between the source of sound andthe listener, then the effective noise audiogramfor this deafened person is just the differencebetween the ordinates of these curves, or that

"See paper by Steinberg and Gardner, J. Acous. Soc.Am. 9, 11 (1937).

AUDI TORY PATTERNS

given by the dotted line. This effective noiseaudiogram can now be used to plot the corre-sponding auditory pattern in the manner out-lined above and it will correspond to the patternof sensation experienced by such a deafenedperson. Such an auditory pattern for the steam-boat whistle listened to by a person deafened bythe amount shown in Fig. 33 is given in Fig. 35.The loudness experienced by such a deafenedperson is equal to the area of this auditorypattern. Loudness tests with persons havingsuch obstructive deafness agree with these ca1cu-lated results.

To treat the case of mixed deafness we mustseparate the deafness audiogram into two parts,one due to obstructive deafness and the otherdue to nerve deafness. This can be done byfinding by tests a deafness audiogram by airconduction (the audiograrn used above) and then

by bone conduction. In the bone conduction testthe testing instrument conducts the sounddirectly into the bones of the head. The vibrationthus produced by-passes the transmission mecha-nism of the middle ear and is transmitteddirectly to the Huid of the inner ear. Conse-quently, a bone conduction audiogram gives thehearing loss due to nerve deafness, or the nerve

IOO

70Ci

z-80II)

~50V2' 40

w 30

20

l~W' 1'~ii

r) ( ) ~p

00 84 I28 258 5 I2 1024 2048 4090FRKCIUKNCY IM CYCLKS PKR SKCONO

8I92

FrG. 34. Noise audiogram of steamboat whistle (topline) and the deafness audiogram (bottom solid line) for acase of obstructive deafness.

80

FIG. 35. Auditory pattern for steamboat whistle —fordeafened listener.

deafness audiogram. The difference of the ordi-nates in the bone conduction audiogram and theair conduction audiogram gives the amount ofobstructive deafness, or the obstructive deafnessaudiogram. Having these two audiograms, theprocedure is as follows. First apply the obstruc-tive deafness audiogram to the noise audiogram,subtracting the ordinates of the former from thelatter. Then use the difference audiogram toconstruct the auditory pattern of the noise.Next construct the nerve deafness pattern fromthe nerve deafness audiogram. The part of thediA'erence auditory pattern above the nervedeafness auditory pattern is the pattern whichwe are seeking and corresponds to that experi-enced by the person having the mixed deafness.

It has been shown that an auditory patternshows the amount and kind of sensation beingtransmitted from the inner ear to the brain.To determine it for any person A immersed ina sound 8, one needs to measure, first, the noiseaudiogram of the sound 8 for a typical normalear, and second, the obstructive and nervedeafness audiograms for the person A. Thenfrom the relations established in this paper, theauditory pattern can be drawn for the person Alistening to the sound B.