Acoustics psychoacoustics and sp ectral music

Daniel Pressnitzer

Institut de Recherche et de Co ordination AcoustiqueMusique IRCAM

Paris France

Stephen McAdams

Lab oratoire de Psychologie Experimentale CNRS Universite Rene

Descartes EPHE Paris France and IRCAM Paris France

Running Head Acoustics psychoacoustics and sp ectral music

Acoustics psychoacoustics and sp ectral music

Intro duction

The aim of this article is to examine the p oints at which acoustics

psychoacoustics and what has b een called spectral musicmeet The

motivations b ehind this bringing together of three more or less barbarous

words are to b e found in the principle of the sp ectral approach itself

The tonal system is governed by a set of harmonic rules that embody a

compromise b etween the will to mo dulate among keys the system of

symb olically notating music the available set of instruments certain laws of

acoustics as well as many other concerns This imp osing edice was patiently

constructed by an accumulation of exp erience and b eneted from a slow

cultural maturation But the bases of this edice were shaken in the evolution

of contemp orary music by recentdevelopments in our relation to sound

previously of a eeting and evanescent ungraspable nature sound has b een

captured and manipulated byway of recording technology The theory of

signals asso ciated with the computational p ower of mo dern computers has

made it p ossible to analyze sound to understand its ne structure and to

fashion it at will The p otential musical universe has thus explo ded in a

certain sense Sound synthesis op ens truly unheard p ersp ectives extending

the act of comp osition to the sound material itself The distinctions b etween

note frequencytimbre and harmony b ecome fuzzyoreven irrelevant and

accumulated traditional exp erience nds itself imp otent to organize the

emerging sound world

After suchashock new means of formalizing and structuring needed to

b e dened Rather than establish a series of arbitrary rules the sp ectral

intuition consisted in founding comp ositional systems on the structure of

Acoustics psychoacoustics and sp ectral music

sound and thus in deriving elds of musical relations from sound itself The

wager of such an approachistogive to a listener reference p oints that are

naturally understandable while allowing the use of the new p otential oered

by microcomp ositional work at the level of sound In other words the

structures sought should b e latently intelligible since the elements necessary

for their comprehension are contained in the materials If the work of the

forerunners of this approach could b e founded only on intuition and

exp erimentation the will to go further to not let oneself b e enclosed bya

limited numb er of eects or gestures requires a more rigorous

conceptualization and formalization of the fundamental ideas A p erfect

understanding of acoustic phenomena is thus necessary and we will address

this domain by insisting on the imp ortance of dierent representations of

sound Though it is necessary this comprehension is not sucient what

counts in the end is certainly at least in the logic of the sp ectral approach

what is p erceived and understo o d by the listener It is at this level that

psychoacoustics which extends and validates the reection on purely physical

structures enters the picture

As such it is not by a will to scientism at any cost that the sp ectral

comp osers were undoubtedly drawn to interest themselves in these disciplines

but simply b ecause of a necessity that pro ceeds from their approach

Numerous questions thus naturally come to the fore What in fact is a sound

What are its p ossible representations What are the interpretations made by

p erception to extract from a sound what is relevant for the listener Can we

exploit them musically Can we sp eak of sound ob jects in our psychological

representations Howdowe think music Doubts can also app ear notably

with resp ect to a fundamental asp ect of music if tonal harmony is considered

as a sort of syntax allowing expression bychanges in tension that o ccur as

Acoustics psychoacoustics and sp ectral music

one deviates from certain rules it relies undoubtedly on a strong even

implicit cultural learning Is it p ossible in no longer using this solid

conventional prop to nd a base contained in the material of sound for the

expression of tension In an attempt to resp ond to these questions and

esp ecially to incite new ones we will present a set of facts concerning sound

and its p erception starting with its birth in the acoustic world

The acoustic world

Representations

A vibrating b o dy creates in the surrounding air the propagation of a

pressure wave in the same manner that to agitate an ob ject on a surface of

water provokes the propagation of wavelets This is the physical realityof

sound the variation of acoustic pressure over time and this realityisunique

It can nevertheless b e represented in dierentways according to the

information that one wishes to emphasize Take theexampleofachord from

the piece Streamlines byJoshua Fineb erg Its classic musical

representation is the score Fig Centuries of exp erience allow the use of

this symb olic representation for comp ositional purp oses but it constitutes in

fact more instructions to the p erformers than a description of the sound

actually pro duced For example if the instrumentation changes the music

transcrib ed in the score is transformed In Baro que music where exact

instrumentation is often not sp ecied and in some pieces of contemp orary

music where the instrumentation is sp ecied vaguely as in the p ercussion

piece Ionisation by Edgar Varese the sound structure itself maybe

completely dierent from one rendering to the next

Acoustics psychoacoustics and sp ectral music

Insert Figure ab out here

To obtain a trace of a sp ecic sound it is p ossible to capture it through

a recording device that will convert the pressure variations in something that

can b e visualized Fig This representation of the pressure wave reects all

of the negrained temp oral evolution within the resolution limits of the

visual representation It is therefore particularly welladapted to

manipulations of sound such as cutting and splicing reversal in time or

rep etition In its early days musique concrete b ecause of the available

technologyworked with razor blades on tap es containing the exact magnetic

retranscription of this temp oral waveandthus used a lot of these kinds of

transformations However this temp oral image do es not translate in an

obvious fashion the dierentpitches that it is p ossible to distinguish in

listening attentively to sucha chord

Insert Figure ab out here

A representation that allows this is the one based on Fouriers theory

This theory states that any complex signal can b e decomp osed into a sum of

sinusoidal waves over an innite time frame by sp ecifying precisely their

relative amplitudes and phases It is thus p ossible to decomp ose a complex

sound into a sum of sine tones which are called the partials of the sound the

set of which form its sp ectrum Fig This Fourier transform represents well

the same chord but in a dierent form unveiling its frequency content This

knowledge of frequency comp onents present in the sound whichmay under

Acoustics psychoacoustics and sp ectral music

certain conditions b e heard as sp ectral pitches Terhardt is at the

origin of the emblematic idea of the music that is appropriately called

sp ectral As an example among others J Harveys piece Mortuos plango

vivos vo co uses the sp ectrum of a b ell sound and its transformations

as a foundation for the harmony If such a representation is a source of fertile

inspiration it makes the temp oral information ab out the sound no longer

explicit in the transform as the analysis is theoretically over an innite

duration

Insert Figure ab out here

The true nature of a sound phenomenon as we p erceive it is double it

evolves over time which is represented by the temp oral wave and it also has

a certain frequency content visible in the sp ectrum The shortterm Fourier

transform reconciles these twotyp es of informations It is thus called a

timefrequency representation The sound is sliced up by an analysis time

window into successive instants The Fourier transform is then computed for

successive instants by sliding the windowover the temp oral waveform bit by

bit In this way the evolution of the frequency content of the sound is

represented over time The result of this analysis can b e presented either in

the form of a sp ectrogram Fig having graphical similarities to a musical

score or in the form of a threedimensional p ersp ective plot that expresses the



acoustic variations in terms of frequency amplitude and time This typ e of

analysis is essential for p erforming additivesynthesis or its orchestral

derivations In Partiels for example Gerard Grisey explores the sound

of a tromb one by assigning to dierent instruments the pro duction of a given

partial of the tromb one sp ectrum analyzed with its dynamic temp oral

Acoustics psychoacoustics and sp ectral music

evolution The representation as a shortterm Fourier transform is quite

general but it should b e noted that there is an inevitable compromise

between the temp oral resolution the duration analyzed and the frequency

resolution the analysis precision For a high frequency precision a long

analysis duration is needed and so there is a loss of temp oral precision

Insert Figure ab out here

There are other representations that allow an optimization of this

compromise Loughlin Atlas and Pitton some such as the wavelet

transform adapting it to the frequencies analyzed Comb es Grossman and

Thamitchian This pro duces for a given sound various equivalent

representations

The idea of continuum

In the physical world frequency time and intensity are considered as

continuous dimensions Music on the other hand has b een built on discrete

scales of pitch and duration made necessary among many other reasons by

the desire to notate events and by instrumental playing constraints The

dierent representations we just presented asso ciated with sound synthesis

give us access to the physical continua This allows as Varese noted to catch



a glimpse of an alternativetothela coup er lo ctave From this p oint

onward b etween each degree of the scale there can b e a continuous thus

innite world to b e discovered and organized

Another continuum is revealed by these mathematical representations

What dierence is there b etween the sp ectrum of a note asso ciated with a

timbre and the sp ectrum of a chord considered as an element of harmony

Acoustics psychoacoustics and sp ectral music

The answer is to b e found on the computer screen at rst sight there isnt

any A simple note is a collection of sp ectral comp onents thus an chord and

achord is a collection of partials thus a timbre Sound synthesis allows the

organization of the note itself intro ducing harmonyinto timbre and

recipro cally sound analysis can intro duce timbre as a generator of harmony

This ambiguity is strikingly demonstrated in JeanClaude Rissets piece

Mutations where the same material is treated alternately as a

harmonic chord or a gongliketimbre If harmonyandtimbre are so

intimately linked the clearcut traditional classication of chords b etween

p erfect consonances imp erfect consonances and dissonances may b ecome

irrelevant Timbre manipulations op ens up the p ossibility to lo ok for a

continuous scale that could repro duce in some resp ects the expressivemeans



asso ciated with the tonal notions of consonance and dissonance

Insert Figure ab out here

Insert Figure ab out here

The exploration of such a dimension has b een undertaken bymany

comp osers essentially in an intuitive fashion Tristan Murail for example has

ordered timbres and aggregates thanks to a measure of inharmonicity

Desintegrations Kaija Saariaho has dened a soundnoise axis

intended to repro duce the harmonic capacity to create tension and relaxation

Verblendungen Joshua Fineb erg has adopted a hierarchy founded

on the pitch of virtual fundamentals Streamlines Is it p ossible that a

Acoustics psychoacoustics and sp ectral music

single phenomenon is hidden b ehind these dierentintuitive criteria

Hermann von Helmholtz prop osed an axis of reection in drawing our

attention to the attribute of sound that he called roughness Helmholtz

Two pure tones pro duced simultaneously and having closely related

frequencies create amplitude uctuations in the waveform that are called

b eats Fig These uctuations according to their rate of b eating can

giverisetoagrainy quality in the sound An example of this rough quality

can b e heard emerging from silence at the b eginning of Jour ContreJour

Grisey Helmholtz thoughthesaw in roughness the acoustic basis for

the dissonance of musical intervals Western music employs principally

instruments with harmonic sp ectra The partials of their complex sp ectra are

sup erimp osed when an interval is played resulting in b eats if their frequencies

do not coincide p erfectly Intervals with simple frequency ratios suchasthe

o ctave or the fth do haveasignicant degree of harmonic coincidence and

thus less b eating However intervals such as the tritone create a situation

where harmonics of one note b eat with those of the other note Fig

Coming back to the previous examples an inharmonic sound can b e a source

of roughness when sup erimp osed on harmonic sounds sounds describ ed as

noisy can often b e rough a sound with a very low fundamental frequency has

partials that are quite close to one another which creates b eating As such it

may b e that the same acoustic feature guided the comp osers mentioned ab ove

in the elab oration of their harmonic criteria If this was to b e the case such

a feature could b e used to dene a new continuum related to the vast and

complex notion of musical dissonance as some kind of an acoustic nucleus

to it Mathews and Pierce

One mightbeoverwhelmed b efore the immense eld of p ossibilities that

is thus op ened The mass of data available to the comp oser that are derived

Acoustics psychoacoustics and sp ectral music

from progressively more precise and sophisticated acoustic analyses the

abundance of at times redundant or p erceptually irrelevant masses of

numerical data coming out of analysis programs can mask the salient features

of musical sound For example when the interval b etween two pure tones is

large enough they are heard separately and without b eats resulting in no

roughness whatever even though the b eats still exist in the acoustic world as

can b e seen on an oscilloscop e So what happ ened to them

Perception

The ear from without to within

The notion of p erception is implicitly contained in the word sound A

sound is not just anykindofvariation in acoustic pressure but a pressure

variation that can generally b e heard our ears must b e able to co de its

features This co ding is conditioned bythephysiology of the p eripheral

auditory system Thus the very rst given of psychoacoustics is the denition

of the realm of validity of the word sound in other words the audible eld

Fig An audiogram traces the average hearing threshold that is the

intensity necessary to just detect a pure tone of a particular frequency This

curve simply translates our capacity to detect a sound signal and is a p o or

waytocharacterize the auditory system The relation b etween the pressure

wave and what we hear of it can only b e understo o d by studying certain

physiological mechanisms of p erception

Insert Figure ab out here

The air vibrations of a sound wave are transmitted and amplied bythe

external and middle ears the pinna the ear canal the eardrum the middle

Acoustics psychoacoustics and sp ectral music

ear ossicles up to the co chlea These vibrations are communicated in the

inner ear to the basilar membrane and the waves propagate and are damp ed

along this membrane The stiness of the membrane varies along its length

Thanks to this prop erty the higher frequencies create a maximal displacement

at its base while lower frequencies maximally stimulate the apical end These

deformations then result in electro chemical changes in the hair cells that are

arranged along the length of the membrane These cells in turn stimulate the

b ers of the auditory nerve along which electro chemical impulses are sent

toward the brain

The essential p oint to understand here is that the rst thing that

happ ens to an acoustic signal in the inner ear is some kind of a sp ectral

analysis In fact starting from the temp oral wave the basilar membrane

spatially decomp oses the signal into frequency bands The second imp ortant

point is that the hair cells in addition to co ding the frequency p osition of the

signal comp onents also preserve to a certain degree their temp oral

information by pro ducing neural rings at precise moments of the stimulating

wave they are resp onding to This phenomenon called phaselo cking

decreases with increasing frequency and eventually disapp ears b etween ab out

to Hz near the upp er end of the range of musical pitch The

auditory system thus p erforms a double co ding of the sound b oth sp ectral

and temp oral in sucha way as all the cues present in b oth kinds of

representation maybeavailable simultaneously

More than just a transmission

The co ding mechanisms intro duce certain phenomena that generate

paradoxes and ambiguities Sound comp onents called dierence tones or

combination tones are a rst example of the necessity to b ecome interested in

Acoustics psychoacoustics and sp ectral music

p erception in addition to physical representations Two pure tones presented

simultaneously to the auditory system stimulate the basilar membrane at

p ositions that are asso ciated with their resp ective frequencies but also at

p ositions corresp onding to frequencies that are the completion toward lower

frequencies of the harmonic series The causes and b ehavior of all these

distortion pro ducts are not fully understo o d However it is easy to hear the

dierence tone that corresp onds to the simple dierence b etween the

frequencies physically presented to the ear This tone is all the more audible

at higher levels It has even b een used comp ositionally for example in

Gyorgy Ligetis Zehn Stucke fur Blaserquinttet The phenomenon can

b e heard at the end of the rst piece for instance The dierence tone b elongs

to the world of physiology and p erception even if it is not presentinthe

stimulating waveform it is created physically in the inner ear It can also

create auditory b eats in the same way as a real sound since it is

mechanically present on the basilar membrane

The frequency decomp osition realized by the basilar membrane is

mechanical the displacements of the membrane are not limited to sp ecic

points but are spread out over a p ortion of it If two comp onents of a complex

signal are close in frequency these displacements will overlap There is thus a

minimal resolution called the critical band Greenwo o d inside of

which the ear cannot separate twosimultaneous frequencies The width of this

band varies as a function of the center frequency considered Fig The

mechanisms underlying the critical band playanessential role two

comp onents will not at all have the same p erceptual eect if they are resolved

thus heard separately or if they fall within a single critical band Let us just

make clear that the width of the critical band do es not at all representa

frequency band within which all sounds are p erceived to have the same pitch

Acoustics psychoacoustics and sp ectral music

Due to the temp oral co ding the ear is sensitive to dierences in frequency

that are less than The critical band is not a limit in precision but a limit

in selectivity

Insert Figure ab out here

This selectivity limit is obvious in the masking phenomenon

Simultaneous masking is related to the overlap of excitation patterns on the

basilar membrane and to the amount of activity present in the auditory nerve

that represents each sound comp onent present Simultaneous masking can b e

conceived as a kind of swamping of the neural activity due to one sound by

that of another usually more intense sound For example highlevel

comp onents noise partial create a level of activitythatoverwhelms that

created bylowerlevel comp onents which are subsequently not p erceived at all

or are p erceived as b eing of lower level than they would if presented alone

The dierent comp onents of a complex sound can also interact mutually

masking one another some having a sensation level that is lower than their

actual physical level would lead one to exp ect Masking relations are

determined largely by the excitation pattern on the basilar membrane This

pattern is actually asymmetrical extending more to the highfrequency side

than to the lowfrequency side and all the more so as the level of the sound

increases Therefore the frequency and amplitude relations b etween sounds

will aect their masking relations in a nontrivial way Fig The knowledge

of these relations is nevertheless essential to understand whichpartofa

musical message will actually b e p erceived

Acoustics psychoacoustics and sp ectral music

Insert Figure ab out here

The critical band also inuences the p erception of b eats b etween two

tones Acoustically the rate of the b eats increases with their frequency

dierence As such as the two pure tones are mistuned from unison we

should hear b eats that result from their interaction b ecoming progressively

more rapid This is in fact what happ ens at the b eginning of the separation

But very so on after approximately b eats p er second or a Hz frequency

dierence our p erception changes from a slow uctuation in amplitude

toward an exp erience of more and more rapid uctuations that pro duce

roughness Finally if the separation b ecomes large with resp ect to the critical

band the strength of the sensation of b eating diminishes leaving us with the

p erception of tworesolved pure tones Three very dierent p erceptual regions

can therefore arise from the same acoustical stimulus Let us come backfora

minute to our ongoing roughness example The roughness of b eating tone

pairs measured thanks to exp eriments involving judgments byhuman

listeners has b een found to dep end not on the absolute frequency dierence

but rather on the frequency dierence related to the width of the critical band

for a given center frequency Fig Roughness can therefore not b e

thought as an acoustic feature of sound it denitely b elongs to the world of

p erception This has several consequences As the width of the band varies

Fig a same interval wont have the same roughness according to the

register The thirds for example are free of roughness in the upp er register

but can b e rough in the lower one To b e able to predict that one needs some

kind of mo del that could extract and combine from the acoustic signal the

relevant features

Acoustics psychoacoustics and sp ectral music

Insert Figure ab out here

Mo deling

Wehaveseenthatallwe can hear in a sound is not obvious in anyofits

physical representations In the case of roughness these representation can

even b e seriously misleading Shouldnt it b e p ossible to prop ose mo dels that

allow to predict on the basis of data obtained from psychoacoustics which

p ercepts would b e induced bya physical stimulus It is necessary to take

certain precautions a classic psychoacoustic study precisely characterizes a

particular phenomenon by creating articial stimuli and by analyzing the

judgments of listeners within a controled lab oratory situation Quantitative

data are thus carefully obtained for each of the phenomena mentioned ab ove

and for many others as well The relations obtained can serve as the basis for

mo dels but in general each mo del describ es a particular mechanism within

the constraints we just mentioned In using these mo dels for musical purp oses

it is necessary to takeinto account a large numb er of phenomena whichof

course interact in a complex way It is extremely complicated not to say

imp ossible to establish a coherent ensemble from all of these sundry parts

However some of these phenomena are b eginning to b e understo o d in

physiological terms from which derives the idea of mo deling the causes rather

than repro ducing the eects In mo deling the b ehavior of the human ear all

of the interactions and distortions are taken into account in an implicit

manner to the extent that the mo del captures well the prop erties of the

auditory system In suchphysiological mo dels Patterson Allerhand and

Giguere Sene a new representation of the sound signal is in

Acoustics psychoacoustics and sp ectral music

fact prop osed This representation provides an image of what is eectively

heard within the limits of our ability to learn to read it The previous

representations were entirely oriented toward the mathematical description of

the signal Physiological mo dels are to the contrary adapted to our

p erception The sound synthesis pro cess could b e oriented by such

representations recentering the work on the relevant p erceptual parameters

Cosi De Poli and Lauzzana The analysis can b enet as well for

example roughness hidden in the other representations since it b elongs

intrinsically to the worldofsensationishererevealed by the uctuations

within each critical band Fig These uctuations are a reection of the

p erceived grainy quality The images pro duced bysuch mo dels thus

p otentially carry characterization of the evoked sensations The sensations are

however only very basic bricks up on whichthemental representation of the

acoustic world that surrounds us is organized

Insert Figure ab out here

Auditory scene organization

Auditory representations

When listening to a noisy environment or to a piece of music our

auditory exp erience is usually quite dierent from the collection of interleaved

sinusoids with frequencies and amplitudes varying over time that nonetheless

constitute the only available informations that reach the ears Quite to the

contrarywe structure the acoustic world in terms of coherent entities that we

can generally detect separate lo calize and identify For example in a concert

hall we hear separately the melo dy played by a ute soloist the cello

Acoustics psychoacoustics and sp ectral music

ensemble a sudden p ercussion entry and our neighb or sighing in certain

concerts This capacity is quite impressive The chaotic form of the

timefrequency representations of the sup erp osition of all these vibrating

sources that resemble the p eripheral analysis we just describ ed is totally

unintelligible to the human eyeandeven to the most p owerful computers

Auditory organization is nonetheless of vital imp ortance for the survival of the

sp ecies if only to b e able to distinguish the ute solo from a re alarm This

imp ortance allows us to state that a listener will always trywhatever the

situation or listening strategyvoluntary or musical to structure the acoustic

world that confronts his or her ears The creation of a structured

representation is what allows music to b e more than a simple succession of

p ercepts

The metaphor of the auditory image intuitively incorp orates the mo de

of structuring that is used An auditory image can b e dened as a

psychological representation of a sound entity that reveals a certain coherence

in its acoustic b ehavior McAdams This denition is broad enough to

allowittobeemployed at several levels a single p ercussion sound is one

auditory image the collection of events comp osing the rapid melo dy played by

the ute is another all those emitted by the cello section playing in harmony

a third From research attempting to make sense of all the p ossible sound cues

that the brain uses to organize the sound world appropriately it seems that

there are two principal mo des involved in auditory image formation

p erceptual fusion of simultaneously present acoustic comp onents and the

grouping of successiveevents into streams

Acoustics psychoacoustics and sp ectral music

Vertical organization p erceptual fusion

One of the rst immediate eect of vertical organization is the grouping

together in a same image of the multiple partials of a complex sound

sp ectrum as analyzed by the ear into coherent parts This kind of

organization allows us to hear a note played by a violin as a single note rather

than a collection of harmonic partials The main ob ject of vertical

organization is therefore at each and every instant to group what is likely to

come from the same acoustic source and to separate it from what is coming

from dierent acoustic sources One of music characteristics as we shall see is

to constantly try to break down this simple rule However the cues used by

the auditory system to form vertical images remain the same in musical and

nonmusical contexts Understanding them is of course the key to b e able to

go b eyond the simple equivalence b etween a vertical image and an acoustic

source

The p osition of a source in space intro duces dierences b etween the

waves received byeach ear time delays intensity dierences that allowto

lo calize it A rst cue of grouping is thus made available one image for each

spatial source Lo calization can playa musical role as in the religious

antiphonal music of Gabrieli as early as Comp ositional writing for the

classical orchestra with its co died disp osition of the instruments integrates

more or less consciously the cues of lo calization in its form It is thus

undoubtedly to favor the formation of vertical auditory images that some

comp osers using tap e or live electronics music do not hesitate to spatialize

their scores Nevertheless when one listens to sound emitted by a single

loudsp eaker and thus originating from a single physical source it is p ossible

to have a more or less clear representation of dierent auditory images

Imagine for a moment listening to a monophonic recording of a wind quintet

Acoustics psychoacoustics and sp ectral music

played over a loudsp eaker in general you should have no trouble p erceptually

segregating the ve sources Other strategies are thus available to the ear

based on regularities in the environment that would have b een learned

through an evolutionary pro cess Bregman It is highly unlikelyfor

example that dierent partials start and stop at exactly the same time if they

do not come from the same source The ear tends to group together partials

that start together If several partials evolveover time in similar fashion this

is called the common fate regularity they will have a high probabilityof

coming from the same source as a matter of fact a mo dulation of the

amplitude or of the fundamental frequency of a natural sound do es aect all

of its partials in a similar way And nally a harmonic series will probably

come from the same sound source due to the physics of sound pro duction and

sustain All these cues can b e used together to form vertical images

Horizontal organization streams

The second level of the auditory image metaphor enters the realm of

temp oral evolution and studies the formation of auditory streams A stream is

a sequence of events that can b e considered to come from a same source A

stream constitutes a single auditory image that is distributed over time For

example the voice of someone sp eaking or a melo dy played a musical

instrument p ossess a certain p erceptual unityandthus forms coherent images

The general lawgoverning the formation of streams app ears to b e based

on sp ectral continuity McAdams and Bregman This law also reects

some kind of regularityintheenvironment as a sound source tend to change

its parameters progressively over time Continuityisevaluated according to

several cues The most studied ones were frequency and time proximityvan

No orden Events that are close according to these dimensions will tend

Acoustics psychoacoustics and sp ectral music

to form a separate stream just as melo dies having a small range and rapid

tempi in dierent registers from one another will b e segregated into dierent

voices There is a tradeo b etween time and frequency proximity for stream

formation Actually most combinations of these two parameters giverisetwo

an ambiguous p erception where streams can b e voluntarily built or mo died

Timbral similarity is another grouping cue broughtinto playbyorchestration

The formation of auditory streams has dramatic eects on the

p erception of the acoustic events Judging the timing b etween two successive

events is usually a trivial task however if the events are part of two dierent

streams the judgments b ecome imp ossible Bregman and Campb ell

Melo dies recognition is also aected by the grouping of all the correct notes in

a same stream Dowling and Harwo o d

Emergent attributes

Vertical and horizontal grouping mechanisms can interact in a complex

manner It is more than likely that at some momentofanevolving auditory

scene energy in a certain frequency region could b e attributed to several

dierentvertical images or to an ongoing stream In this case choices are

made and once this energy has b een attributed to an auditory image it is

taken out from the others This stealing of energy b etween images can lead

to the consequence that attributes such as pitch and brightness Bregman and

Pinker or loudness McAdams Botte and Drake in press or roughness

Wright and Bregman can b e altered by auditory organization The

expression sound ob ject if used regardless of its original historical context

of musique concrete can therefore b e misleading A sound ob ject implies a

sound event p ossessing a basic unity dened by some characterizable features

It is in fact the case that all sound prop erties are dep endent on dynamic

Acoustics psychoacoustics and sp ectral music

relations with the context within which attributes as imp ortantaspitch

loudness roughness and other dimensions of timbre can nd themselves

signicantly changed as streams and vertical images are formed and

reorganized There exists no indivisible stable sound ob ject but rather

auditory images that p ossess more or less coherence in a dynamic relation

Eachvertical auditory image once it is formed and only then p ossesses

emergent attributes These emergent attributes are b orn of the fusion of its

comp onents An emergent attribute is dierent from the sum of elementary

attributes of the comp onents contributing to the image The addition to

sp ectral comp onents higher in frequency to a pure tone can lead to the

p erception of a pitchlower than the original pure tone one as in the case of

the missing fundamental Schouten Terhardt The recognition of

a certain sound source emerges from the fusion of many comp onents into a

global timbre each of them taken alone often b eing unable to unveil the sound

origin McAdams and Bigand Correct auditory grouping is therefore

essential to build these emergent attributes and grasp a representation of a

natural environment

Auditory images and musical structures

The usual result of auditory organization is to build stable auditory

images each corresp onding to a sound source to b e able to recognize them

In a musical context the emergent attributes often come from chimeric

sound sources If each instrument of the symphonic orchestra was to b e heard

as a single source the p erception of the musical structures imagined b e the

comp oser would certainly b e quite dicult just as dicult as if all the

instruments were fused into a single auditory image Auditory organization

has therefore b een explored by comp osers for a long time

Acoustics psychoacoustics and sp ectral music

Deceiving horizontal organization allowed the writing of virtual or

implied p olyphonywere a monophonic instrument expresses more than one

voice at the same time Fo oling vertical organization is the key to

orchestration were unheard and augmented timbre can b e created by fusing

dierent instruments It can also have radical structural consequences In his

piece Lontano Ligeti creates dense structures within which b ecause of

vertical fusion cues the instruments cannot b e distinguished He then

remarks that p olyphony is written but one hears harmony A few years

latter organization cues that induce the exact opp osite consequences were to

b e used by the same comp oser to write the San Francisco polyphony

this time clearly heard as p olyphony

The organization of the auditory scene can even b e an argumentfor

musical structure A rst example of this is Mutations by Risset were the

transformation of a chord into timbre that wementionned earlier is done

thanks to auditory organization cues The inharmonic structure of the chord

requires the convergence of other cues suchassynchrony to b e heard as a

fused timbre Another even more extreme example is the piece Desintegrations

byTristan Murail In this work a set of intervals is rst heard fused in

a section with a rapid temp o comprising a complex melo dic line though it

will b e heard in a disintegrated version in a nearly static section This

structure is expressed by using dierent organizational cues see Fig Insert Figure ab out here

Acoustics psychoacoustics and sp ectral music

Listening and cognition

Memory

Of course the b ottomup pro cesses that wehave describ ed so far that

to ok us from acoustic vibrations to auditory images are not the only ones to

intervene in musical listening nor even in the formation of auditory images A

complex set of highlevel cognitive pro cesses also come into play Without

pretending to describ e exhaustively and precisely these pro cesses insofar as

this is p ossible wewould like in concluding to address certain cognitive

asp ects of listening stressing the ones that are asso ciated more notably with

memory

Various notions are implicated in music cognition we might cite

attention cultural knowledge and temp oral organization in p erception A

common characteristic seems to tie together these kinds of pro cesses as they

play a role in listening memory Memory is linked to attending in the sense

that attention seems to b e predisp osed to fo cus on events that are exp ected

on the basis of cultural knowledge abstracted from past exp erience Jones and

Yee Memory allows listeners to implicitly learn the basic rules of the

musical culture they b elong to Krumhansl Bigand Finally the

very notion of time so essential to music derives from our abilityto mentally

establish event sequences through the use of memory Damasio et al

The auditory mo de of recall is remarkably p owerful Crowder and

Morton haveshown in a task requiring listeners to recall a list

presented either visually or auditorially that the auditory mo dality has a net

advantage over the visual mo dality for the later elements in the list The

hyp othesis advanced to explain this sup eriority is the existence of a sensory

storage asortofechoic memory sp ecic to hearing that conserves the

Acoustics psychoacoustics and sp ectral music

stimulus trace for a brief instant of time This hyp othesis has since b een

rened and there are most likely several dierent retention intervals Cowan

One of these intervals would b e on the order of several hundreds of

milliseconds and another one on the order of several seconds The rst storage

would b e related to sensation constituting a sort of p erceptual present

while the second one would serve as a basis for what is called working

memory These fairly short durations raise all kinds of questions concerning

the p ossibility of apprehending structures extended through time and carried

by sound The stimulus trace vanishes within a few milliseconds of the echoic

memory and the working memory cannot hold more than a few items

Still we can exp erience a p erception of form and meaning over time

with sp oken language for instance which is also carried by sound So is there

a long term storage of the facsimile of the acoustic stimuli we receive In

fact there are a great deal of b oth b ehavioral and neurophysiological data

that lead us to b elieve that there is not a memory center where this kind of

storage takes place in the brain Rosenfeld Memory would more likely

b e distributed as a bypro duct of cognitive pro cessing in the form of

potential representations In other words in the presence of a stimulus the

brain activity results in the extraction of the relevant features making

generalizations and forming categories This theory has some physiological

basis Perception activates the primary sensory cortices in the brain who

through their activity in time detect and enco de dierent features of sound

These activity patterns are then pro jected onto asso ciation cortex Each

neuron in asso ciation cortex receives a large numb er of connections from

various areas of the brain which allows for generalization stimuli sharing

similar features will activate the same groups of neurons reinforcing the

connections b etween the concerned sensory cortices and these neurons When

Acoustics psychoacoustics and sp ectral music

anewstimulus is p erceived if it is similar enough to a p otential

representation already memorized it will b e categorized as a memb er of the

same family In recall or in imagination or dreaming or also in forming

categories it would b e the convergence zones that then activate the sensory

cortices in the reverse direction Damasio

The transformation of stimuli into p otential representations whichare

not repro ductions but rather abstractions of features of a stimulus can help

to interpret a study on the memory for melo dies byCrowder The

recall of melo dies seems rst of all to b e based on the pitchcontour if recall

follows shortly after learning has taken place However if recall is delayed in

time the inuence of contour decreases to the b enet of pitch relations an

abstraction has b een p erformed from absolute pitch an early level of

p erception to relativepitchintervals and relations within a tonal framework

It is this kind of abstraction that seems to b e stored in longterm memory

This leads us back to what is implied in the p ossible use of dierent

continua for only discrete scales allow a classication of p erceptual values

that is apt to b e co ded in the brain in terms of abstract relations In fact the

existence of discrete degrees dividing the o ctave is one of the rare constants

that can b e found throughout nearly all cultures Dowling and Harwood

Further numerous studies on musical cognition seem to converge

toward the imp ortance of metric and rhythmic hierarchies and thus of the

discretization of time Lerdahl and Jackendo Clarke The

question is also raised for the use of timbre seen as a p otential carrier of

structure and its various apparently continuous dimensions McAdams

These considerations on memory thus have a direct inuence on

musical structures if one wants them to b e intelligible

Acoustics psychoacoustics and sp ectral music

Arousal

After all these considerations ab out acoustics psychoacoustics and

cognition a text ab out music would seem to p olitely avoid an uneasy p ointif

it did not address even sup ercially the question of arousal or emotion in

music This issue that may b e considered at rst glimpse b eyond the eld of

scientic investigation or with one fo ot in the aesthetics domain is in fact the

sub ject of numerous psychological studies that could nd an application in the

musical domain So what is arousal for the cognitivepsychologist

An interesting answer is prop osed by Mandler Human b eings

have a certain number of schemas some innate and directly linked to survival

others acquired and eventually mo diable that are linked to past exp erience

Perceptions are thus evaluated in terms of exp ectancies Inthecaseofa

p erception that conforms to our exp ectancies one might exp ect that little

cognitive activity is necessary On the other hand a p erception that go es

against exp ectancy triggers b oth an emotional reaction and cognitive

pro cessing the latter in order to adapt our representation of the external

world to what has b een p erceived Damasio go es even further in showing by

wayofnumerous examples from neuropathology that preceding arousal is not

only sucient but also absolutely necessary for the correct op eration of many

cognitive pro cesses such as so cially relevant decisionmaking and p ersonal

planning for the future Damasio If arousal o ccupies such an imp ortant

place in our cognitive pro cessing usually asso ciated with pure reason the

question of the relation b etween emotion and music takes on a new dimension

Let us try to make a parallel b etween what we learned from cognitive

psychology and what happ ens in music listening Bregman clearly

states that schemas inuence the waywe organize the auditory scene by

providing us with a mechanism to extract certain things that we are seeking

Acoustics psychoacoustics and sp ectral music

within that scene Another wellestablished schema is our knowledge of

tonality These schemas and esp ecially the latter will giveriseto

exp ectancies which b eing violated or not will evoke arousal In the domain

of musical tension the work of Bigand has demonstrated the inuence

that implicit knowledge of tonality has on music p erception in b oth

professional musicians and nonmusician listeners Asked to judge the degree

of tension of an interrupted melo dy the listeners clearly expressed

exp ectancies linked to tonality Bharucha has simulated with neural

nets the exp ectancies of Western and Indian listeners presented with their

resp ectivemusics and their erroneous comprehension faced with the music of

the other culture The arousal the feeling of tension can here b e seen as

the result of an enforcement of cultural rules that give rise to exp ectancies

These rules assumed to b e shared by listeners could b e called external

referents Sounds charged with an extramusical meaning can also b e

considered as playing with external referents On the other hand there are

also reactions to music that originate in the musical material based on its

immediate qualities and which generate exp ectancies over time The auditory

equivalent of Gestalt go o dcontinuation laws Koka havebeen

prop osed to generate exp ectancies that can give birth to arousal if they are

violated Meyer Another immediate sound quality roughness has

b een shown to play a part in tension p erception in the tonal context along to

these other factors The selfgenerated exp ectancies acquire even greater

imp ortance if external referents are kept in the background Pressnitzer

McAdams Winsb erg and Fineb erg In this case the emb edded

structure is revealed by cognitivemechanisms and thus dep ends to a great

extent on the organization into auditory images and thus on p erception

which in turn dep ends on the physical phenomena

Acoustics psychoacoustics and sp ectral music

To nish with our roughness example it is clear that in tonal music the

inuence of roughness is altered by the deep implicit or explicit acculturation



that wehave of basic harmonic rules However when the comp oser leaves

the welltro dden path of convention the mastery of a cue allowing the

expression of a simple and immediate tension can b ecome primordial again

For example the piece La tempesta dapres Giorgione by Hugues Dufourt

is constructed as a movement of latent tension going nearly all the

waytoitsown paroxysm This piece employs wind instruments in a very low

register In the low register the spacing b etween the partials of the instrument

sounds are very small compared to the critical band Dierent partials thus

fall into the same critical band this induces a p erception of roughness The

same material transp osed to a medium or high register would lose its meaning

to a large extent As such acoustics the b eats and psychoacoustics

p erception of these b eats contribute to the structure of the piece Work on

the meaning contained in the material op ens the waytoasearchona

structure p otentially submitted as a whole to the work of comp osition Gerard

Grisey can at last exclaim we are musicians and our mo del is sound not

literature sound not mathematics sound not theater plastic arts quantum

theory geology astrology or acupuncture As such sp ectral music in its

search for expression through the material itself without hidden or

conventional reference makes p ossible the recourse to certain data from

acoustics and psychoacoustics not only to justify certain choices a p osteriori

but also as a means of formalization of musical pro cesses

Conclusion

Throughout this article wehave attempted to evoke a set of facts

derived from acoustics psychoacoustics and cognitive psychology and which

Acoustics psychoacoustics and sp ectral music

have a certain resonance with the sp ectral approach Through the example of

roughness weshowed how a part of an essential musical feature suchas

dissonance could b e emb edded in the material itself involving the knowledge

of its acoustic ground the study of its transformation through p erception and

how it is put to p ersp ective through the inuence of cognitive pro cesses

involved in listening The mutual curiosity of scientists and musicians is not

recent but it has often had dierentmotivations Concerning our example

the question of why certain intervals are consonanthave sparked interest

throughout history When Pythagoras was interested in intervals it to ok the

form of a new manifestation of the omnipresence of numb ers Later with

Kircher divine intervention was sought in harmonic ratios Kepler Galileo

Leibniz Euler Helmholtz among others had an attempt to prop ose an

explanation of their own Assayag and Cholleton

The goal here is much more mo dest To bring this goal to lightwe

would liketociteamusical custom in New Guinea that is practiced bythe

Kaluli of Papua A ceremonytakes place in a hut where the memb ers of a

clan are gathered Passing visitors enter the hut at dusk singing the names of

places they crossed within the territory of their hosts This song pro duces

particular reactions among the listeners Schieelin quoted in Dowling

and Harwo o d tells the story as follows

After a while the audience the hosts b ecomes very deeply

moved Some of them burst into tears Then in reaction to the

sorrowtheyhave b een made to feel they jump angrily and burn

the dancers on the shoulders with the torches used to lightthe

ceremony The dancers continue their p erformance without

showing any sign of pain The dancing and singing with the

concomitantweeping and burning continue all night with brief rest

Acoustics psychoacoustics and sp ectral music

periods between songs p

Evoking the name of a place to which a tragic memory is p erhaps

attached the death of family or friends for example has triggered such

reactions in the listeners Obviously the singer is not interested in acoustics

nor even in psychoacoustics and whywould he b e so as he is leaning on

external referents to trigger arousals The p oint is here that he knows very

little ab out the referents he is using b eing a stranger to the territory of his

hosts If only the small amount of data concerning music p erception that have

b een presented here could b e used to avoid suchembarrassing situations

Acoustics psychoacoustics and sp ectral music

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Recherche

Bharucha J J and OlneyKL Tonal cognition articial

intelligence and neural nets In S McAdams and I Deliege Eds Music and

the cognitive sciences London Harwo o d Academic

Bigand E The inuence of implicit harmonyrhythm and

musical training on the abstraction of tensionrelaxation schemas in tonal

music phrases Contemp orary Music Review

Bregman A S Auditory Scene Analysis the p erceptual

organisation of sound Cambridge MA MIT Press

Bregman A S and Campb ell J Primary auditory stream

segregation and p erception of order in rapid sequences of tones Journal of

Exp erimental Psychology

Bregman A S and Pinker S Auditory streaming and the

building of timbre Canadian Journal of Psychology

Clarke E F Levels of structure in the organisation of musical

Contemp orary Music Review time

Comb es J M Grossman A and Thamitchian P Wavelets

Berlin Springer Verlag

Acoustics psychoacoustics and sp ectral music

Cosi P De Poli G and Lauzzana G Auditory mo delling and

Journal of New Music selforganizing neural network for timbre classication

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Cowan N On short and long auditory stores Psychological

Bulletin

Crowder R G Auditory memory In S McAdams and

E Bigand Eds Thinking in Sound pp Oxford Clarendon Press

Crowder R G and Morton J Precategorical acoustic storage

p erception and psychophysics Perception and Psychophysics

Damasio A R Descartes error Emotion Reason and the

Human Brain New York GrossetPutnam

Damasio A R Eslinger P J Damasio H Van Ho esen G and

Cornell S Multimo dal amnesic syndrome following bilateral temp oral

and basal forebrain damage Archives of Neurology

Dowling W J and Harwo o d D L Music Cognition London

Academic Press

Greenwo o d D D Critical bandwidth and the frequency

J Acoust So c Am co ordinates of basilar membrane

Helmholtz H L F v On the Sensations of Tone as the

Physiological Basis for the Theory of Music nd ed trans A J Ellis

from German th ed Reprinted Dover New York

JonesMRandYee W Attending to auditory events the role

Thinking in of temp oral organisation In S McAdams and E Bigand Eds

Soundpp Oxford Clarendon Press

Acoustics psychoacoustics and sp ectral music

Koka K Principles of Gestalt psychology New York

Harcourt Brace World

Krumhansl C L Cognitive foundations of musical pitch

Oxford Oxford University Press

Lerdahl F and Jackendo R A Generative Theory of Tonal

Music Cambridge MA MIT Press

Loughlin P J Atlas L E and Pitton J W Advanced

timefrequency representations for sp eech pro cessing In M Co oke S Beet

and M Crawford Eds Visual representations of sp eech signals pp

John Wiley and Sons

Mandler G Mind and Bo dy New York Norton

Mathews M V and Pierce J R Harmony and nonharmonic

J Acoust So c Am partials

McAdams S Sp ectral fusion sp ectral parsing and the formation

of auditory images PhD thesis Stanford University Stanford California

McAdams S Psychological constraints on form b earing

dimensions in music Contemp orary Music Review

McAdams S and Bigand E Thinking in Sound Oxford

Clarendon Press

McAdams S Botte M C and Drake C in press Auditory

continuity and loudness computation J Acoust So c Am

McAdams S and Bregman A Hearing musical streams

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Acoustics psychoacoustics and sp ectral music

eds The Foundations of Computer Music Cambridge MA MIT

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Meyer L B Emotion and Meaning in Music Toronto Chicago

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Mo ore B C J and Glasb erg B R Suggested formulae for

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Patterson R D Allerhand M H and Giguere C

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Plomp R and Levelt W Tonal consonance and critical

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Pressnitzer D McAdams S Winsb erg S and Fineb erg J

Roughness and musical tension of orchestral timbres In Pro ceedings of the

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Schouten J F The residue and the mechanism of hearing

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Acoustics psychoacoustics and sp ectral music

Author Note

The authors would like to thank Joshua Fineb erg for providing musical

material as well as useful comments on earlier versions of the manuscript

Corresp ondence should b e addressed to either Daniel Pressnitzer or Stephen

McAdams IRCAM place Igor Stravinsky F Paris France email pressnitzerircamfr smcircamfr

Acoustics psychoacoustics and sp ectral music

Fo otnotes

Classic up to a certain point considering the presence here of quarter

tones

One should note in passing the inuence of the to ols used on the end

result



It should be noted that it is p ossible to obtain sp ectrograms in an

analogous fashion with a bank of lters From a theoretical point of view

the two descriptions of the shortterm transform running window and lter

bank are equivalent Allen and Rabiner



Literally a slicing up of the o ctave ie the equaltemp ered scale



Let us remind that in the Western early p olyphonic p erio d the scale of

consonance and dissonance contained up to six dierent degrees The latter

simplication of this scale can b e paralleled with the progressive armation of

syntactic tonal rules Tenney



We might however ask ourselves if these rules that actually mo dulate

the p erceived roughness do not in fact have an unconscious foundation based on roughness

Acoustics psychoacoustics and sp ectral music

Figure Captions

Figure Excerpt from the score of Streamlines byJoshua Fineb erg The

excerpt was reorchestrated by the comp oser for the purp oses of

psychoacoustic exp erimentation The aggregate analyzed in subsequent gures

is the second one at the end of measure one

Figure Waveform of the second aggregate indicated in Fig

Figure Fourier transform frequency sp ectrum of the second aggregate in

Fig The partials of the harmonic tones pro duced by the dierent

instruments can b e seen emerging from the noise as thin vertical p eaks

Figure Shortterm Fourier transforms displayed as sp ectrograms The

amplitude of the comp onents is indicated through their darkness The

timefrequency tradeo chosen in a uses a long analysis window The

frequencies of the dierent partials can thus b e seen very accurately as

horizontal strip es but the ne evolution of their amplitudes is lost On the

other hand the short windowchosen in b b etter preserves the temp oral

evolution but blurs the frequency representation Dierent parameters such

as the overlap factor b etween windows or the display formatting can b e

adjusted to get a b etter picture But which is the b est picture of what we

hear

Beats b etween pure tones In the temp oral domain the addition of Figure

two sine waves with slightly dierent frequencies pro duces slow amplitude

variations in the amplitude envelop e a In the sp ectral domain the b eating

tone pair is seen as two adjacent comp onents b

Figure Sup erp osition of two complex harmonic tones separated by a small

Acoustics psychoacoustics and sp ectral music

interval With slightly dierent fundamental frequencies b eats o ccur b etween

adjacent partials If the frequency ratio was a simple one such as o ctave

or fth the coincidence of many of the partials would minimize these

b eats

Figure The audible eld This diagram represents the regions of frequency

and acoustic pressure in which vibrations are heard as sound

Figure The critical band The width of the critical band dep ends on the

center frequency b eing considered After Mo ore and Glasb erg

Figure Simultaneous masking Asinewave and a narrow band of noise are

presented simultaneously The sine wave is at a frequency just b elow a or

ab ove c that of the noise band In the rst case b although the frequency

dierence is the same b etween the two the sine tone is heard In the other

case d the noises excitation pattern swamps the sine waves and the latter

is not heard even though their frequency separation remained the same

compared to a

Perceived roughness of a b eating tone pair Roughness is plotted Figure

as a function of the frequency dierence b etween the two tones expressed as a

percentage of a critical bandwidth When the tones are wider apart than

critical band they cannot interact and no roughness is heard any more

Maximum roughness is p erceived when the two tones are separated by

approximately of the critical band After Plomp and Levelt

Figure Output of a mo del of auditory pro cessing derived from that of

Patterson The three adjacent lines around Hz visible in the

sp ectrogram of Fig a are revealed as pro ducing audible b eats variations in

Acoustics psychoacoustics and sp ectral music

level across frequency regions causing roughness The timefrequency

tradeo is here adapted to p erception in each critical band Ideallywhatwe

seeiswhatwewould hear

Figure Two excerpts from the score of Desintegrations by T Murail

Pages and by courtesy of Salab ert publishing Paris Atthe

b eginning of section VI I page the notes have simultaneous attacks the

evolution of the dierentvoices is rapid and follow the common fate

regularity sixteenth notes following a same melo dic contour It gives rise to

a feeling of fusion a unique orchestral mass in motion On the other hand in

section X page the attacks are asynchronous the register is widely spread

ute the timbres are varied It pro duces a p erception of the shattered parts

of the aggregate of section VI I and a feeling of disintegration +œ œ 3 #œ œ 3 +œ œ 4 +œœ #œ œ œ 7 œ. 3 Flute 1 & 4 J 4 8 4 π π p π F π P 1 n P π f F

3 ¿˙. 4 ¿œ œ œ œ 7 +œ. 3 Flute 2 & 4 4 8 Ó 4 p n P π f π F π π F n œ œ 3 ˜œ œ . 3 4 œ œ ˜œ œ œ 7 +œ ¿œ œ 3 Clarinette Sib& 4 J 4 8 4 p n P π f π F π π F π P

bœ œ 3 ¿œ œ œ œ +bœ œ œ 3 J 4 7 +œ œ œ œ 3 Violon & 4 4 8 J 4 p n P π f π F π π F π P

B 3 Œ Œ 3¿¿œ· œ· 4 ¿¿œ· œ· ++œ· œ· œ· 7 ##œ·. ¿¿œ· œ· 3 Alto 4 J 4 8 4 π π p π F π P 1 n f F 1

0.8

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f0 f0 Amplitude Amplitude

3/2f0 Frequency45/32f0 Frequency 140 Pain threshold 120

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60 Music Sound Pressure Level (dB) 40

20 Hearing threshold

0

10 100 1000 2000 5000 10000 Frequency (Hz) 1000

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10 10000 100 1000 Frequency (Hz) Stimulus Auditory representation

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Amplitude noise noise Excitation pattern

tone tone

Frequency Distance along the basilar membrane

(c) (d) Amplitude noise noise Excitation pattern

tone tone

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