Dichotic fusionof two tonesone octaveapart: Evidence for internal octave templatesa) Laurent Demany
Laboratoire dePsychologie Expbrimentale, •tssocib auC.N.R.S.,Universitb Renb Descartes, 28rueSerpente, 75006Paris, France
Catherine
Semal
Laboratoire dePsychoacoustique, U.E. R. desSciences Sociales etPsychologiques, Universit• deBordeaux II, 33405Talence, France andLaboratoire dePsychologie Expbrimentale, Associb auC.N. R.S., Universitb Renb Descartes, 28 rueSerpente,75006Paris,France
(Received 16July1987;accepted forpublication 30October1987).
Stimuli consisting oftwosimultaneous andsinusoidally frequency-modulated puretones were dichotically presented to fourlisteners. Thetwocomponent tonesof eachstimulus were approximately anoctave apart.Theywerebothmodulated at 2 Hz, andthefrequency swing resulting fromeachmodulation corresponded to onetenthofthecarrierfrequency. The listeners' taskwasto detectphasedifferences betweenthemodulation waveforms of thetwo
simultaneous tones: Withanadaptive 2IFCprocedure, just-noticeable values of•, thephase angleofthemodulation waveforms, weremeasured asa function oftheinterval formed bythe carrierfrequencies (oneoctave,i.e., 1200cents,ñ 0, 25, 50,or 100cents).Whenthecarrier
frequencies werenottoohigh,just-noticeable values ofß oftenvariednonmonotonically with theinterval, showing a minimum atornear1200cents. An additional experiment indicated that most,if not all, of theseoctaveeffectswere not due to someform of beat detection.As a
whole,theresults reported hereprovide evidence fortheexistence ofinternal octave templates. Suchtemplates mightplayanimportant rolein theperceptual segregation ofsimultaneous harmonic signals, aswellasin pitchperception. PACSnumbers: 43.66.Hg,43.66.Rq,43.66.Lj[NFV]
intervalscorresponding to thesehypothesized templates are the frequency ratios of the partials of harmonic signals, Any complexand periodicsoundsignal,with periodp, an intercanbedescribed asa sumof sinusoidal toneswith frequen- whichimpliesthat humanlistenerswouldpossess nal octave,an internalfifth (or twelfth), etc.It canbeargued ciesequalto nk/p, wherenk isan integer.The signalissaid that thesinetonescontainedin steadyharmonicsignalsfuse to be"harmonic"whennk isalwaysequalto nk_ • + I, or in the intervalstheyform match otherwords,whenthefrequency ratioof twoadjacentpar- intoonesoundimagebecause internally defined templates (see MeAdams, 1984). tialsisalwaystheratioof twosuccessive integers(2/1, 3/2, But do such internal templates really exist?This reetc.). This conditionis not satisfiedfor "inharmonic"sigmains, in fact, to be demonstrated objectively. Psyehophysnals.Generallyspeaking, harmonicsignalsarenot perceived ical evidence for the existence of internal octave templates in the sameway asinharmonicsignals.Harmonicsignals was looked for in the present research. tend to evokea single,clearly definedlow-pitch sensation; Evidence for the existence of internal harmonic temtheirpartialsfuseintoa coherent soundimage.By contrast, inharmonic signalsdo not,in general,evokea singlepitch, platescan be soughtin the followingway. Assumethat a andtheirpartialstendto bemoreeasilyheardindividually humanlisteneris requiredto detectsmallchangesin the intervalformed by two simultaneoussinetones,that is, to (Bregmanand Doehring, 1984;Grandori, 1984;Martens, discriminate betweenslightlydifferentfrequency ratios.As1984;MeAdams, 1982;Moore etal., 1985, 1986). sume, in addition, that the listener possesses, for instance, an Thisperceptualdifference betweenharmonicandinharinternal octave template but no internal template corremoniesignalscanbe accountedfor in the frameworkof the to a seventhor a ninth.It mightthenbeexpected "patternrecognition" theoriesof low-pitchperception, espe- sponding that the listener's performance in thetaskwill bebetterif the ciallyTerhardt'sand Goldstein'stheories(Terhardt, 1974; standard frequency ratio corresponds to an octavethanif it Terhardtetal., 1982;Goldstein,1973;Duifhuiset al., 1982; INTRODUCTION
Scheffers, 1983). Both of these theories assumethe exis-
correspondsto a seventhor a ninth.
tence,in the central auditory system,of "internal templates"representing specific intervalsbetweenpartials.The
beenstudiedby Viemeisterand Fantini (1987). Their data
The discriminability of frequencyratioshasrecently indeed show that deviations from an octave interval are easi-
er to detectthandeviations froma somewhatsmalleror larger interval. In their experiments, however,the two tones Partofthisarticlewaspresented at thel 12thMeeting oftheAcoustical formingeachstimuluswerepresented monaurallyand at a Society ofAmerica, Anaheim, CA [J.Acoust. Soc.Am.Suppl.I g0,S91 (1986)]. rather high level (67.5 dB SPL). In suchconditions,the 687
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observed octaveeffectmightoriginatefromperipheralinteractions between the tones and not from the existence of inter-
nal octavetemplates.When two puretonesof moderateor high level and about one octaveapart are simultaneously presented to thesamehumanear,somecochlearfibersof the listenercertainlyrespondto bothof thesetones[seethedata obtainedin thesquirrelmonkeyby Roseetal. ( 1971), andin the cat by Greenberg(submittedfor publication)]. If the two tonesare separatedby exactlyoneoctave,the effective waveformdriving thesefiberswill havea very shortperiod (the periodof the lowerfrequencytone). But the waveform periodwill be muchlongerif the two tonesform a slightly differentinterval,andthismaybesignaledperceptually by a beatsensation(cf. Plomp, 1976,Chap.3). In orderto provideevidencefor theexistenceof internal harmonic templatesby means of discriminationexperiments,it is, therefore,necessary to preventperipheralinteractionsbetweenpartials.In the presentresearch,which attemptedto demonstratethe existenceof octavetemplates, peripheralinteractionswere preventedby presentingpartials dichoticallyand at low level. I. EXPERIMENT
Ear 1
............................
FH (a•
Ear 2
Ear
............................
FL
1
1
A. Method I. Stimuli
and rationale
In thisfirst,mainexperiment,eachstimulusconsisted of two simultaneous, dichoticallypresented, andslowlyfrequency-modulated pure tones.The two toneshad different carrier frequencies; the lower carrier frequencywill be labeledFL andthehigheroneF,. For eachtone,the instantaneousfrequencyvariedsinusoidallyat a rate of 2 Hz, and the total frequencyswingwas 10% of the carrierfrequency. Two successive stimuliwerepresented oneachtrial. For one of the two stimuli (stimulus a; seeFig. 1, upper part), the modulationwaveformsof the two toneswerein phase;thus, while eachtonevariedin frequency,the frequencyratio of the two toneshad a steadyvalue,equalto the ratio of their carrier frequencies(Fn/FL). The two tonesforming the otherstimulus(stimulusb; Fig. 1, lower part) had the same carrierfrequencies, FL andFn, but their modulationwaveformswerenot in phase;thustheir frequencyratio wasnot steady,but variedin a quasisinusoidal way arounda central valuecorresponding to Fn/F L .1On eachthai, the listener had to decidewhetherstimulusb hadbeenpresentedin the firstor secondposition.Note that for everystimuluspresentation, the initial phasesof the two modulationfunctions wererandomvariables.Thispreventedthe subjects from usingmonauralpitchcuesto performthetask.2 Within trial blocks,the phasedifferenceq>betweenthe two modulations contained in stimulus b was varied, and
just-noticeablevaluesof ß weremeasured.The logicof this measureliesin the fact that, in stimulusb, the amplitudeof the frequency ratio fluctuation (expressedin cents) increasesquasilinearlywith ß when q• goesfrom 0øto about 70'. Thusmeasuring ajust-noticeable valueof• was,in fact, equivalentto measuringa just-noticeablefrequencyratio fluctuation.Figure2 showstheexactrelationbetween• and the frequencyratio fluctuation.It mustbe emphasized that 688
J. Acoust.Soc.Am.,Vol. 83, No. 2, February1988
'•.
FH/ FL
FIG. I. The two typesof stimulususedin experiment1. The two tones formingeach stimuluswere frequencymodulatedin phase(a) or not in phase(b). Also,FL andFn arethe carrierfrequencies of the tones;fLand f. are their instantaneous frequencies. In the experiment,the frequency swingoff• andf. corresponded to an intervalof 173cents,whiletheinterval formedby FL and Fn wascloseto 1200cents;thusthesetwo intervals
weremuchmoredifferentthan the figuresuggests. In addition,only two modulationcyclesarerepresented here,whereassixmodulationcycleswere actuallyheard.
thisrelationdoesnot dependon the standardfrequencyratio, i.e., Our main independentvariablewas,of course,F•/FL. This ratio took sevenpossiblevalues:one octave (1200 cents) _+0, 25, 50, and 100 cents.In addition, the absolute
valuesofFL andF, werevariedovera widerange.Generally, thetonewiththelowercarrierfrequency(FL ) washeard throughthe right ear, but we lookedfor possibleear asymmetriesby reversing,in someexperimentalconditions,the positionof the earphones. All tonesbut onewerepresented at 45 dB SPL. The exceptionwasthe tonewith the lowestof the carrier frequenciesused,180 Hz; it waspresentedat 50 dB $PL.
Each stimulushad a steady-stateportion of 3 s and 200ms rise/fall times,which wereshapedwith a raised-cosine function.The twostimulipresented in everytrial wereseparated by a 200-ms silent interval. Stimuli were heard in an IAC soundproofroom through TDH 49 earphones.They L. Domanyand C. Semal:Dichoticfusionof twotones
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aftereachresponse, if the response wascorrector not. In eachexperimentalsession, Ft. wasfixedand seven thresholdswere measured,one for eachpossiblevalueof FH/FL. Theseseventhresholds weremeasured in a random order,varyingfrom session to session and unknownto the subjectthroughout eachsession. For a givenvalueof FL (and a givenpositionof the earphones), eachsubjectwas
lOO
90
8O
tested for at least six successive sessions:a variable number ß
70
of trainingsessions plussixdatacollection sessions. All sessionswere run on differentdays.For eachsubject,at least
threevaluesof FL wereused.Theywereextractedfromthe followingset of frequencies: 180, 270, 400, 600, 900, and 1350 Hz.
5o 0
3. Subjects '•
40
Four subjects, aged22 to 32, participated in theexperiment.All had a normalaudiogram(thresholdsbetterthan 15dB HL) from 250 to 4000 Hz. SubjectsI and4, the authors,had participatedassubjectsin previouspsycheacoustic experiments; thiswasnot the casefor subjects 2 and 3. Subjeers 1 and 3 were amateurmusicians,but subjects2 and 4 were relativelynaivemusically.
3o
e
2o e
lO
B. Results 10
20
30
40
50
60
70
• (degrees) FIG. 2. Excursion off./f• asa functionof•. Eachclosedcirclerepresents an "upper"excursion,i.e., the intervalspannedfrom the centralvalueof fu/fc upto its maximumvalue.Eachopencirclerepresents a "lower"excursion,i.e.,the intervalspannedfrom the centralvalueoff,/fL downto its minimumvalue.For smallvaluesof •), both of the excursions are approximately equalto 1.51•.
The resultsare displayedin Figs.3-6. Eachpanelof thesefiguresshowsthemeanthresholds obtainedin a given fL at right ear
fL at left ear
3O
3O
900
Hz
:30
600
Hz
10
were generatedin real time by a two-channelDMX 1000 digital synthesizer,underthe controlof a microcomputer (Northstar Horizon). Each tone was sampledat a rate of 27.9 kHz andwith a precisionof at least14 bits ( 16bitsfor the tone with carrier frequencyFL ). Two low-passfilters with a cutofffrequencyof 9.6 kHz wereusedto eliminate foldover.The absence of significant distortionwaschecked by measuringthe spectrumof a nominallypuretoneof 400 Hz (sampledat 27.9 kHz and with a precisionof 16 bits) at the input of the earphones.It was found that the first six
2Q 1(3
3O
400
Hz
270
Hz
harmonics of the tone were each at least 75 dB below the fundamental.
30
-
20
-
2. Procedure
Thresholds for ß weremeasured with an adaptiveproeedurecontrolledby the microcomputer.A thresholdwas measuredin a trial blockwhereß wasinitially setwell above 180 Hz FH/F L(cents) the expectedthreshold,dividedby 1.5aftereachsuccession of threecorrectresponses, and multipliedby 1.5after each incorrectresponse? Eve• trial blockendedaftertheoccuro o g• o reneeof 16reversal pointsin thevariationof•. Thegeometric meanof these16 reversalpoints,estimatingthe 79.4%FIG. 3. Meanthresholds ofsubjectI in experiment 1.Eachdatapointreprecorrectpoint,wastakenasthethreshold(of. Levitt, 1971). sents the mean of six thresholds. Vertical bars are two standard deviations A terminalof the microcomputerindicatedto the subject, (fir_ 1 weighting)in total length. 689
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fL at right ear
fL. at right ear
50• I I FL = 600
FL=
Hz
3O
-
270
1350
Hz
600
Hz
270
Hz
10 I
Hz
I I I I I
I
40
30
10
I
I I I I I
I
FH/F L(cents) 180
Hz
FIG. 5. Mean thresholdsof subject3 in experiment1.
1L at right ear
1350
Hz
FIG. 4. Mean thresholds of subject2 in experiment1.
•o
subjectfor a givenvalueof F•: and a givenpositionof the earphones. We wantedto know, mainly, if thresholdswould be a nonmonotonic functionof Fn/FL, with a minimumat or
900
Hz
600
Hz
400
Hz
180
Hz
20 lO
neartheoctave( 1200cents).To answerthisquestion, the •o
datapresentedin eachpanelweresubmittedto an analysisof variancewhereFH/FL, thesinglefactor,wasconsidered asa "treatment" factor (cf. Winer, 1971, Chap. 4). The useof analyses of variancewasjustifiedsincetherewasnoevidence that the measures wereseriallydependent(ShineandBow-
2• lO
I
er, 1971). In eachanalysis,an overallF statistic,testingthe existence of differences between the mean thresholds, was
firstcomputed.If the computedF allowedfor a rejectionof the null hypothesis[F(6,30)>2.87; p<0.025], the existenceof a significantquadratictrend wasthen testedusing
the appropriate contrastbetweenmeans. 4 In addition,the existenceof a significantlinear trend was also testedby meansof the appropriatecontrast. Table I presentsthe resultsof theseanalyses.Clearly, the resultsdependon both F• and the subject.For each subject,the overall F test was significantfor at least one value of F•: and at least one reliablequadratictrend was 890
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•o 20
10
I
I
I I
I
I
FH/F L{cents) 10
FIG. 6. Meanthresholds of subject4 in experiment1. L. Demany and C. Semah Dichoticfusionof two tones
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TABLE I. F statistics computed fromthedataobtained in experiment 1.Earphoneposition a: lowerfrequency toneat therightear;earphone positionb: lowerfrequency toneat theleftear.** *: p < 0.001;**: p < 0.01;*: p < 0.025;ns:p > 0.025. Degrees of
Earphone
S•bject
position
I
a
b
F test
FL (Hz)
freedom
Overall
6,30
Quadratic trend
1,5
Linear trend
1,$
Overall
6,30
Quadratictrend
1,5
Linear trend
1,5
180 6.1 (***) 5.8 (ns) 14.2 (*)
270
400
600
900
22.9 (***) I 11.5 (***) O.1 (ns) 11.3 (***)
33.5 (***) 57.5 (***) 87.7 (***)
!.3 (ns)
0.7 (ns)
1350
0.9 (ns)
24.0 (**) 0.0 (as)
2
a
3
a
4
a
Overall
6,30
Quadratic trend
1,5
Linear trend
1,5
Overall
6,30
Quadratictrend
1,5
122.4
Linear trend
1,5
(***) 11.0 (*)
Overall
6,30
Quadratictrend Linear Trend Overall
Quadratictrend Linear trend
found.On the whole,more than half of the analysesdemon-
7.5 {***) 49.8 (***) 0.0 (ns)
7. i (***) 9.8 (ns) 133.0 (***)
2.0 (ns)
11.9 (***)
20.5 (***)
2.5 (ns)
9.3
24.8 (***)
(***)
5.6
(***)
1,5
38.4
150.0
13.9
32.6
(***) 1.0 (ns) 33.9 (***)
(*)
(**)
1,5
(**) 1.3 (ns)
6,30
1,5
234.8
1,5
(***) 27.2 (**)
0.5
0.2
(ns)
(ns)
2.4
(ns)
1.4
(ns)
'
stratedtheexistence of a significant quadratictrend.How-
I
ever, theoverall F testwasnotalways significant, andthe sub,.c,, subjects oftendidnotbehavein oneandthesamewayat the samevalueof FL . Note that significantlinear trendswere foundin fivecases; theseunexpected trends,eachreflecting a thresholddecrease whenFH/FL increases, are difficultto
9.6 (***) 37.7 (**) 1.0 (ns)
............................
I
--
I !
?
2 3
interpret.
Withrespect to thesignificance oftheoverallF testand the presence or absence of a reliablequadratictrend,the position oftheearphones appeared tohavenoinfluence. Figures3-6 andTableI suggest that,foreachsubject, quadratic
4 :•o
3O0
•00
10100
20100 30;O0
variationsof the thresholdwith FH/FL occurif andonly if F,_ and/or F, are locatedwithinsomelimitedfrequency domain.The probablelimitsof the individualdomainsare
FIG. 7. Frequency domainswithinwhichstatistically significant octaveef-
shownin Fig. 7. A lower limit could not be estimatedfor
fects(i.e., quadraticthresholdvariations)werefoundin experiment1. The
subjects 2 and4, butan upperlimit seems to existfor each subject.Whenexpressed as a functionof 2FL, this upper limit seems to varyfromabout1000Hz in subject1 to about
domainsarerepresented bydottedlines.Horizontaldashes indicatetheex-
2000 Hz in subject4.
ear presentationof this tone.
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J. Acoust. Soc.Am.,Vol.83, No.2, February 1988
2 . Ft ½Hz, log scale)
istence of an octave effect and vertical dashes indicate the absence of an
octaveeffect.For subjectsI and 4, the upperdashesreferto a right-ear presentation of thelowerfrequencytoneandthelowerdashes referto a left-
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Thefunctionobtainedby averagingthe20 functionsdisplayedin Figs.3-6 hasa minimumforFn/F L = 1200cents andisnearlysymmetrical. However,whenthresholds varied nonmonotonicallywith Fn/FL, the minimum threshold was sometimesobtainednot for Fn/F• = 1200 cents,but rather25 or 50 centsloweror higher.Consider,in this respect,thecircleddatapointsin Figs.3 and6. Eachof these threepointsrepresents a meanthresholdthatissignificantly smaller(p < 0.025ona Studentt test)thanthemeanthreshold obtained•during the same sessions!--forFH/FL = 1200cents.Admittedly,it isdifficultto draw firm conclusionsfrom post-hoestatisticalcomparisons. Nevertheless, the small "mistunings"just noted might be meaningful: Sinceeachstimuluswasdichotic,theymightoriginatefrom binauraldiplacusis andreflectsmalldeviations of thesubjective octavefrom the physicaloctave (see, e.g., van den Brink, 1974). C. Discussion
Experiment1wasperformed to provideevidence forthe existence of internaloctavetemplates, andtheresultsindeed suggest thatsuchinternaltemplates exist.However,another possible interpretation of the octaveeffectsfoundmustbe consideredimmediately.Although the two tonesforming eachstimulushad low SPLsand werepresenteddichotically, it mightstillbeimaginedthat the octaveeffectsstemfrom some form of beat detection. Assume, for instance,that in
the experimentalsituation,significantaural harmonicsare producedat the earreceivingthe lowerfrequencytone (carder frequencyF• ). For Fs/Fr = 1200cents(oneoctave), oneof thesepotentialauralharmonics hasthesameinstantaneousfrequencyasthe contralateraltoneaslongasß = 0ø, and thisis no longertrue whenß %0ø.Thus ordinarylateralizationcuescan,in principle,beusedto detectsmallphase differences between the modulation
functions of the two
tones.
With regardto this hypothesis, it shouldbe notedfirst that the subjects,in fact, never reportedhearing beatsor "rotating"soundimages whenthefrequency ratioofthetwo toneswasfluctuating,i.e., whenß differedfrom 0ø.For all the conditionsin which octaveeffectson performancewere observed,theseeffectsseemedto be, introspectively,the direct consequence of spectralfusionphenomenaand not the by-productof someform of beat detection.Especiallyfor barelydetectable valuesof •, subjects basedtheirresponses on the amountof fusionof the two tones:On eachtrial, they voted for the stimulusin which the two tonesappearedto fuselessor, in other words, were more difficult to hear as a singlesoundentity. Even whenF•/FL wasequalto 1100or 1300 cents,the two tonesfusedbetter for ß = 0ø than for ß %0ø;fusionwaspromotedwhenthetwomodulations were coherent,as could be anticipatedfrom previousresearch (Bregman and Doehring, 1984; MeAdams, 1984). But whenF•/FL wasequalor verycloseto 1200cents,ß hada morepronounced effecton perceptualfusionbecausethe
twotonesfusedparticularly wellforß = 0ø. 5 In additionto the fact that no subjectreportedhearing beatsor rotatingtones,a secondargumentagainsttheaural harmonics hypothesis canbeadvanced. It restson thesmall 692
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"mistunings" pointedoutin thepreceding section: If aural harmonicswerereallyresponsible for the observedoctave effects,then thresholdsshouldhave alwaysbeenminimum for F•/FL ----1200cents.Actually,the tipsof the U-shaped functionsobtainedwere sometimeslocateda bit higher or lower. This seemsto rule out not only the aural harmonics hypothesis, but alsothe possible interventionof artifactual monaural interactions due to interaural cross talk.
It may be considered, however,that the smallmistuningsjust mentioned,as well as phenomenological arguments,do not rule out convincinglyenoughuninteresting explanations for the octaveeffectsfoundin experiment1, i.e.,thepossibility of someformof beatdetection.In orderto providemore supportfor the "interesting"explanation-the octavetemplatehypothesis--asecondexperimentwas performed.Its logicwasasfollows.Assumethat, in experiment1, a givensubjectdetectssomeformof beatwhenFL hasa certainvalue(f), F• = 2f, andß 20 ø.Thedetectionof thebeatimpliesa sensitivity to therelationbetween thetemporal fine structuresof the two monauralwaveforms:No beatcouldbedetectedif onlyspectralinformation(i.e., fluctuatingpitches)wasextractedfrom the waveformof each tone. Assume, therefore, that the two modulated tones are
replacedby two steadypuretoneswith frequencies respectivelycorresponding tof( = Ft ) and2f. The beatdetection hypothesisimplies that the subjectwill be able to detect changesin the interauralphaserelationof thesetwo steady tones.The aim of experiment2 was to determineif such changeswereindeeddetectable. II. EXPERIMENT
2
A. Method
This experimentwasconducted on the four subjetsalreadyusedin experiment1. Each stimulus consisted of two simultaneous and di-
choticallypresentedpure tones,with frequencies f (at the rightear) and2f(at theleft ear). For eachsubject,thevalue takenbyfwas alwaysa valueof F• for whicha quadratic thresholdvariation (i.e., an octaveeffect) had beenobtained
in experiment1. The two tonesformingeachstimulushad the sameSPL as the corresponding tonesin experiment1. Theyweregenerated at a samplingrateof 43.8kHz, with the sameequipmentandthe sameprecisionasin experiment1. Eachstimulushad a steady-state portionof 1 s and 200-ms rise/fall times,shapedwith a raised-cosine function. On eachtrial, four successive stimuli were presented. They were arrangedin two successive pairs:200-mssilent intervalsseparated thetwostimuliof eachpair,anda 600-ms silent interval separatedthe two pairs. Three of the four
stimuliwereidentical;their two componenttoneswerein sinephaseat theinputof theearphones. The remainingstimulushadthe samecomponenttones,but in a differentphase relation:In sometrial blocks,therelativephaseof thehigher frequencytone was shiftedby + 90ø;in other trial blocks, the phaseshift was + 180ø.The "different"stimuluswas alwaysthesecondof a pair, andthe subjecthad to decide,on eachtrial, if it occurredin thefirstor secondpair.Feedback wasprovidedexactlyasin experiment1. In eachsession, fwas fixedandeightblocksof 50 trials L. DemanyandC. Semal:Dichoticfusionof twotones
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wererun (four blockswith eachof the two phaseshifts). Twoor threesuccessive sessions wererun,ondifferentdays, for a givenvalueoff
all--of the octaveeffectsfoundin experiment1 do not stem
B. Results and discussion
III. GENERAL
Table II showsthe percentages of correctresponses obtainedin eachsubjectfor eachvalueoff andeachphaseshift.
The presentfindingstally very well with the idea that octavetemplatesexistin the centralauditorysystemof man.
Randomresponses would,of course,yield50%-correctperformance.It canbe seenthat performance is at the chance levelin subjets2 and 3, but oftenexceedsthe chancelevelin subjects1 and4. Evenin subjects1 and4, however,performanceis generallyquitepoor:Exceptfor subject4 when f= 180Hz, the percentages of correctresponses neverexceed65%. Subjects1 and4 felt that thephaseshiftswere,at times,detectable on the basisof an extremelysubtlechange in the "timbre" of the standardstimulus;but they alsofelt thatphaseshiftswerecompletelyimpossible to detecton the
Strongsupportforthatideawasprovidedin sofar as (i) our dataconsistof discrimination performances, andarethusas "objective"aspsychophysical datacanbe,and (ii) results supportingthe octavetemplatehypothesis were obtained fromeachof thefoursubjects testedin themainexperiment (experiment1). In connectionwith the latter point, it is worthy to notethat in experiment1, the mostpronounced octaveeffectswerefoundin theleast"musical"subject(sub-
basis of lateralization
criteria.
The authorsof twoprevious studies(Craigand$effress, 1962;AyresandClack, 1984) reportedthat at low sensation levels,humanlistenerscannotreliablydiscriminatebetween dichoticoctavecomplexes thatdifferonlyby thephaserelationshipof their two componenttones.As a whole,the resuitsof experiment2 confirmthesefindings.Conflicting claimshave beenmade by Thurlow and Bernstein(1957) andTobias(1964): Accordingto theseauthors,a beatsensation can be evokedin at leastsomesubjectsby a low-level dichotic stimulus that consistsof two steady pure tones forminga mistuned Octave(e.g.,2f + l/f). Butit mightbe that the tonesusedin thesetwo studiessuffered,in fact, from harmonic distortion.In an informal experiment,we produceddichoticmistunedoctaveswith two steadypure tones at the sameSPLs as in experimentsI and 2. No beat was audibleto us, althoughwe were,in experiment2, the two subjectsperformingabovethe chancelevel.
We thusconcludefromexperiment2 that most--if not
TABLE II. Subjects' performances in experiment2. Starsand"ns" referto the probabilityof reachingor exceeding the indicatedpercentage if responscs arerandom.***:p <0.001; **:p <0.01; ns:p> 0.025.
Subject I
3
4
DISCUSSION
ject 4); this can be taken as evidencethat the octaveeffects foundare truly sensoryeffectsand shouldnot be attributed
to a musicalacculturationprocess. The existenceof internal templatesfor harmonicfrequencyratiosisa centralassumption of Goldstein'sandTerhardt's"patternrecognition"theoriesof pitchperception. In sofar asour resultsdirectlysupportthiscentralassumption, they indirectlysupportbothof the theories.However, the presentstudywasconcernedonly with the existenceof octavetemplates, whileGoldstein's andTerhardt'stheories assumethe existenceof other harmonictemplates.Among all the harmonicfrequencyratios,the octavemay be "special" (Bachem,1950;Demany and Armand, 1984). We are presentlydeterminingif, with the methodusedin experiment 1, evidencefor the existence of internaltemplatescorresponding to frequencyratiossuchas 3/1, 3/2, or 4/1 can be provided. Our resultsindirectlysupportpatternrecognition modelsof pitchperception, but it mustbe acknowledged that they are alsocompatiblewith a pitch theorythat doesnot assumethat the extractionof pitch from complextonesis basedon a patternrecognitionprocess(Moore, 1982,Sec. 4.4.; van Noorden, 1982). FollowingMoore and van Noorden, it may be speculated that the centralauditorysystem detectsharmonicrelationshipsbetweentwo simultaneous pure tonesby comparingneuraltiminginformationsconveyedby remotecochlearfibers.The neuralspikesproduced in cochlearfibersby a puretonewith periodpareseparated by time intervalsapproximatelycorresponding top, 2p, 3p, etc. Thus a pure tone with periodp and a pure tone with period2p produceneuralspikesthat are separatedby common time intervals.The centralauditory systemmight detecttheharmonicrelationshipof the twotoneson thisbasis.
Phase
Number
shift (deg}
of trials
Percentage correct
90 180 90
400 400 600
63.2 (***) 64.7 (***) 52.7 (ns)
180
600
46.0
90
6O0
49.0
Since Moore (1982) and van Noorden (1982) admit that
180
600
49.8
90
600
48.5
the harmonicrelationshipof two simultaneouspure tones can be recognizedin the absenceof peripheralinteractions
180
600
51.2 (ns)
between these tones, our resultsdo not conflict with their
90
4430
66.5 (***)
180
0d}O
75.2 (***)
600
90
600
56.8 (***)
900
180 90 180
600 600 600
62.0 (***) 53.8 (ns) 55.7 (**)
speculations. In Sec.I C, we statedthat throughoutexperiment1, the responsecriterionusedby the subjectswas the amount of fusionof the two tonesformingeachstimulus.It is interesting to considerhere an alternativehypothesisbasedon the
f(Hz) 270 400
2
from some form of beat detection.
180
600
180
well-known results of Houtsma and Goldstein (1972). 693
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Houtsma and Goldstein demonstrated that two simulta-
neousand diehoticallypresentedpure tonesthat are succes-
sive harmonicsof somemissingfundamentalare able to evokea "central"pitchcorresponding to themissing fundamental.With regardto experiment1,it mightthusbeimaginedthat: (i) thetwo tonesformingthestimulialwaysfused, and the amountof fusiondid not dependon the stimulus; (ii) eachstimulusevokeda fluctuatingcentralpitch,determinedat any momentby the instantaneous frequencies of the two tones;and (iii) on eachtrial, subjectsbasedtheir response onthemagnitude of thefluctuationof centralpitch for each of the two stimuli. We applied Goldstein'stheory (Goldstein, 1973) to simulate the fluctuation of central
pitchfor variousvaluesofFn/F r and•: For twoinstantaneousfrequeneiesfL andfn (fL
•fL (instantaneous frequency ofthelowerfrequency tone)andfn (instantaneousfrequencyof the higherfrequencytone) variedwith time according to
fL =fL [ 1 + (0.05 sin4•) ], and
( 1)
fn =f•{1 + [O.05sin (4qrt+
(2)
sincethe amplitudesof the frequencyvariationsweresmall,we had
X {1 4- [0.05sin(4•rtq-•) ] -- (0.05sin4•rt)).
(3)
This can be rewritten as
f•
F•t
Thus fu/fL varied in a quasisinusoidal way between (F•r/F•) X[1 -- (0.1 sinqV2)] and (F./F•) [1 +0.1 sin•/2)].
21ftheinitialphase ofthemodulation ofoneofthetwotones hadbeenfined, subjects couldhaveperformedthe taskby detectingchangesin the initial
pitchof theothertone.Randomizing theinitialphases prevented thispossibility.For clarity,the randomization of the initial phaseshasbeenignoredin theequationsof footnote1. •However,themaximum valuethatß couldtakewas180';thustbwassetto 18if'when,accordingto thevariationrule,it shouldhaveexceeded180'.In fact,• veryrarelyreached! 80' duringtheexperiment.
valueof FH/FL, the amplitudeof the fluctuationof central pitch (expressedas a frequencyratio) decreases when ß deviatesfrom 0'; second,the rate of this decreaseis a monoconsisted of thefoBowing weighting coefficients: 10for 1100 tonicfunctionof F•t /F L , and is largestfor Fn/FL = 1100 ßThecontrast and 1300cents, -- 2 for 1150and 1250cents, -- 5 for 1175and 1225cents, cents.Thustheoctaveeffectsfoundin experiment1werenot and -- 6 for 1200cents.This wasthe appropriatecontrastto testthe hypredictablefrom the resultsof the simulation;theseresults pothesis thatthevariationof thresholds withF.r/F• wasa quadraticfuncpredictedthatthresholds for ß wouldalwaysdecrease regution with an extremumfor F./FL ----1200cents.SeeWiner (1971) for explanations on the rationaleof statisticaltestsfor trendß larly with Fn/FL. We believethat the simulationfailedto thatwhenthecomponent tones ofa stimulus fused very predictoctaveeffectsbecause it wasbasedontheassumption •$ubjectI reported well,thesetonesweresometimes heardascomingbothfromthesameplace that the fusionof the two tonesmakingthe stimulidid not withinthe head.But accordingto the subject's report,thisphenomenon dependonFn/F L or •: In fact,the fusionof thetwo tones, wasgenerallyproducedb• eachof thetwostimulipresentedin a giventrial. Thusthephenomenon couldnotus•ffully serveasa response cue.Another andthusthesaliencyof centralpitch,depended onthesetwo variables.
Finally, onemust ask why, in experiment1, octaveeffectsappearedto occuronly for a limitedrangeof F•_values, varying from subjectto subject.There may be somelink
subject(subject4) reportedthatwhenthetonesfusedverywell,thehigher frequencytonesometimes disappeared duringthe stimuluspresentation. This phenomenon,which resemblesthe illusion describedby Deutsch (1974), wasexploitedby the subjectbecauseshefelt that it occurredmostly for • = (Y'and couldserveas an efficientcue.
betweenthisphenomenon andtheso•called"spectraldominance" phenomenonin pitch perception(Plomp, 1976, Chap.7; Mooreetal., 1985).However,thefrequency limits of the observedoctaveeffectsmay be principallydueto the
eq'he centralpitchwascomputed fromEq.(12) ofGoldstein's article.Ac-
useof diehotic,and thus "abnormal," stimuli (seeHall and Soderquist,1975;RaatgeverandBakkum,1986).Oneof our projectsis to replicateexperiment1 with monauralrather thandiehoticstimuli.In experiment1, the two tonesform. ing the stimuliwerepresenteddichoticallyin orderto preventperipheralinteractions. But peripheralinteractions can alsobepreventedin a monaurallisteningsituationbyadding to the tonesa narrow-bandnoisespectrallycenteredhalfwaybetweentheir frequencies. It will beinterestingto determinewhether,in thissituation,octaveeffectsoccurfor larger rangesof FL valuesthan in a dichoticlisteningsituation.
where• represents theestimated harmonicrankof thetonewithfrequency fL, Xr andx. arethetwoaurallymeasured instantaneous frequencies, and 5L andbn canbeconsidered aserrorestimates for theauralmeasurement offL andf•. For realisticvaluesofxr andxn, i.eß,valuesveryclosetofL andfn, thepitchprocessor will alwaysset• to 1.Then,if oneassumes that bn =2.b•, the central pitch can be numerically computed as (J'L+ 0.Sfn)/2ßIt issomewhat arbitrarytoassume that•.-- 2.&L.HOW-
ACKNOWLEDGMENTS
cording to that equation, the central pitch correspondsto
•x•/• + (•+ l)x./6•. •2/• + (• + l)•/b•.'
(5)
ever,the qualitativeconclusions we draw from the simulationdo not de-
pendonthisparticularassumption: For anyvalueoftru/&r, thesameconclusionsare reached.It shouldbe notedthat Goldstein's(1973) pitch processor alwaysinterpretsthespectralcomponents of a complextoneas successive harmonics.Gemon and Goldstein (1978) modifiedGoldstein's
originalmodel,andthepitchprocessor thattheyproposecanalsoconsider spectralcomponents as nonzucceasive harmonics.But in the presentcase, usingGoldstein's originalmodelto computecentralpitchwasjustifiedbecausethe subjectsneverheardcentralpitchescorresponding to frequencies distantfromf L, whichimpliesthatf6 andf. wereneverinWxpreted as nonsuccessive harmoniesof somemissingfundamental.
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