Harmonic and Melodic Octave Templates - Google Sites

Harmonic and melodic octave templates Laurent Demany Laboratoire dePsychoacoustique, Universit• deBordeaux II, 146rueLbo-Saignat, F-33076Bordeaux, France andLaboratoire d•4udiologie Exl•rimentale, INSERM U.229,HbpitalPellegrin, F-33076Bordeau•France Catherine $emal

Laboratoire dePsychoacoustique, Universit• deBordeaux II, 146rueL•o-$aignat, F-33076Bordeaux, France

( Received 27January1989;revised 9 July1990;accepted 16July1990) For normal-hearing adultlisteners, twosimultaneous puretoneswitha frequency ratiocloseto 2/1 mayperceptually fuseinto a singlesound,whichshowsthat suchlistenersaresensitive to "octaveharmony."Manyadultlisteners arealsoableto consistently adjusttwosuccessive puretones"oneoctaveapart,"whichshowsthattheypossess melodicoctavetemplates.

According to Terhardt[J.Acoust.Sec.Am. 55, 1061-1069(1974)], melodic octavetemplates andtheperception of octaveharmony originate froma common learning process takingplace in earlylife.In thetwoexperiments reported here,subjects performed repeated octave adjustments forpairsof simultaneous andsuccessive tonebursts. Bothtoneswerepresented monaurally, at 45 or 65dBSPL.Thefrequency of thelowertone(fref)wasanindependent variable, whilethefrequency ofthehighertonewasadjustable withina 500-cent range.In someconditions, whenthetwotoneswerepresented simultaneously, theyweresinusoidally frequency modulated in a coherent manner, at a rateof 2 or4 Hz;theaimofthisfrequency modulation wasto forcethesubjects to adopta synthetic listening strategy, i.e.,to basetheir adjustments onperceived harmony.Forf•,f valuesrangingfrom270-2000Hz, subjects performed consistent adjustments whenthetoneswerepresented successively:f•f hadlittle effectontheadjustments' variability. However, in thesamefrequency range,thevariability of theharmonic adjustments markedly increased withf•,f;forthehighestf• values, it wasmuch greaterthanthevariabilityof themelodicadjustments. Theresults suggest that,in adult listeners, theperception of octaveharmonydisappears at frequencies for whichmelodic octavesare still accuratelyperceived.

PACS numbers:43.66.Ba,43.66.Hg,43.66.Lj,43.75.Cd[NFV]

INTRODUCTION

A long-durationsoundsignalmadeup of two simultaneousandsteadypuretoneswith frequenciesf andabout2.f canbelistenedto either"analytically"or "synthetically."In the analytic mode,the listenerdirectshis attentionto only onecomponenttoneat a time and the pitch of a givencomponenttoneisheardseparately; thepitchintervalformedby the two componentscan be assessed by attentionswitching, asif thecomponentswerepresentedsuccessively; a musician requiredto saywhetherthepitchintervalis,or isnot, a welltunedmelodicoctavewill beableto provideconsistent judgments(but hisjudgmentsmayshowthat a well-tunedmelodicoctavedoesnotalwayscorrespond to a frequencyratioof exactly 2/1, as we shall seebelow). In the syntheticmode, the complex signal is heard as a whole; dependingon the

frequencyratioof itstwo components, it maythenbejudged as more or less consonant or dissonant, i.e., harmonic or

inharmonic;this doesnot requirea consciousknowledgeof musicalpitch intervals,sinceevenmusicallyilliterate personswill provideconsistent judgments;they will tendto say

that whenthe frequencyratio of the two components is exactly 2.0, the signalis more "fused,"i.e., easierto hear as a singlesoundwith onlyonepitch,thanwhenthe frequency

ratiois,e.g.,1.8or 2.2 (seeBregman andDoehring,1984)? Thus, octaverelationscorrespondto perceptualsingu-

2126

larities in two phenomenologically differentdomains,the domainof melodyand the domainof harmony.On the one hand,musicians(as well asotherlisteners,of course)possess"melodicoctavetemplates,"corresponding to internal representations of the octaveasa musicalpitchinterval.On the other hand, the perceptualintegrationof two simultaneouspuretonesoneoctaveapartinto a singlesoundimage with onlyonepitchreflectsa sensitivityto whatcanbecalled "octave harmony."

The melodicoctavetemplatesof musicianshave been investigatedin a classicwork by Ward ( 1953,1954). In most of his experiments,subjectswerepresentedwith sequences of puretonesin whicha referencetonewith a fixedfrequency alternatedwith a testtonewhosefrequencywasadjustable; the test tone had to be adjustedone octave above the referencetone. Ward found that the meanadjustmentsof the test tone were generallynot locatedat the physicaloctave ( 1200 cents} of the referencetone, but 20-I00 centshigher, a result that hasbeenconfirmedby subsequent investigations(Waliser, 1969; Terhardt, 1970, 1971a, 1971b; van den Brink,

1977;DobbinsandCuddy,1982;Ohgushi,1983;Rakowski, 1988}. In addition, Ward found that the standard deviation

of a givensubject'sadjustmentsfor a givenreferencetone wasabout 10 centsand did not vary markedlyfor reference tones between 250 and 2225 Hz. This indicates that musi-

J.Acoust. Soc.Am.88(5),November 1990 0001-4966/90/112126-10500.80 ¸ 1990Acoustical Society ofAmerica 2126

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cians'melodic octavetemplates areaccurately defined upto

Our main aim wasto determineif this precisionis or is not

at least 4000 Hz.

the samefunctionof frequencyregisterin the domainsof harmonyand melody.Previousstudiescited abovesuggest that suchis not the caseand that the perceptionof octave harmonydisappearsabove2000 Hz, whereasmelodicoctavesremainaccurately definedupto at least4000Hz. However,thisdivergence hadto beconfirmedby meansof within-subject comparisons in directlycomparable experimental

Ward (1953, 1954) alsoperformedan adjustmentexperimentin which the referenceand test toneswere not successive but presentedsimultaneously and continuously throughouteachtrial. This experimentalconditionwasambiguousin sofar assubjects could,in principle,performthe task usingboth melodicand harmoniccues.The adjustmentsagaintendedto exceedone physicaloctave,but less

conditions.

than in the former condition;their standarddeviationswere

Relating the harmonic and melodic modesof octave

slightlylargerthanin theformercondition,butagaindidnot vary markedlyfor referencetonesrangingfrom 250-2225

perception seemed especially interesting in thelightof ideas

Hz.

ingto Terhardt,thereisa closelinkbetweenoctaveharmony andmelodicoctavetemplatessincebothwouldderivefroma commonlearningprocesstaking place in early life. More precisely,Terhardthypothesized that: ( 1) in earlylife, the spectral components of periodicsoundsignals, suchasvowels,arenotfusedintounifiedsoundentities,butalwaysper-

A study on the perceptionof octaveharmonywas recentlyreportedbyDemanyandSemal(1988). In thatstudy,

we investigated the sensitivityof four subjects --including nonmusicians--to variationsin the frequencyratio of two simultaneous and dichoticallypresentedpure tones.The standardfrequency ratiosrangedfrom 1100cents(1.888) to 1300cents(2.119). Eachtonewasfrequency modulated at a rate of 2 Hz and with a peak-to-peakwidth of 173 cents ( 10.5%). Sincethepitchof eachtonecontinuouslyvariedin time,andattentionswitchingtakestime, it wasverydifficult for the subjectsto perform the task by making sequential comparisonsof momentarypitch valuestaken by the two simultaneous tones;in other words,subjectswere forcedto listento the stimuli synthetically.In addition,the dichotic presentation of the stimuliensuredthat subjectscouldnot detectbeatsofmistunedconsonances resultingfrominteractionsof the tonesin the sameperipheralauditoryfilter (see Plomp, 1976, Chap. 3). It was found in eachsubjectthat, whenthetwo toneswerelocatedwithin somefrequencydo-

expressedby Terhardt (1970, 1971b, 1974, 1980). Accord-

ceivedasseparate toneswithdistinct"spectral pitches; "2 (2) followingrepeatedexposure to suchperiodicsignals, associative linksare createdbetweenthe spectralpitches evokedbytheirFouriercomponents, whichformsimplefrequencyratios;(3) as a resultOf this learningprocess,the spectralpitchesof simultaneous puretoneswith simplefrequencyratioscanfinallygiveriseto a single"virtual" pitch, andthisis the basisof harmonysensations; (4) throughthe

same learning process,the distancesbetweenspectral pitchesevokedby components in a givenfrequencyratio (for instance 2/1 ) becometheinternaltemplates of a given melodicinterval (for instance,the melodicoctave).

Thus, in Te?hardt'stheory,the melodicoctavetemplatesof a givensubject correspond exactlyto thepitchintervalsformedby simultaneous puretonesinducing,in the main, deviationsfrom an octave ratio (2/1 ) were easier to samesubject, anoptimalsensation of octaveharmony. The detectthandeviations froma slightlysmaller(e.g., 1.888) or well-tuned melodic octave isgenlarger (e.g., 2.119) ratio. This providedobjectiveevidence factthattheperceptually erallyobtained for a frequency ratioslightlylargerthan2/1 that humanlistenersare sensitiveto octaveharmony.Howis explained by perceptual interactions betweensimultaever,theoctaveeffectdisappeared whenthe highertoneexspectral components onephysical octaveapart:such ceededsomefrequencylimit, varyingbetweenabout 1000 neous wouldresultin smallpitchshiftsof theindividand2000Hz fromsubjectto subject.Onepossible explana- interactions ual components (seeTerhardt,1970,1971b). tionof thelatterresultisthatoctaveharmonydisappears for tonesexceeding2000 Hz. This hypothesisis consistentwith informal observationsbriefly reported by Hall and Hess ( 1984, p. 170). On the other hand, the frequencylimits observedmighthavebeenlargelydueto the dichotic,and thus abnormal,listeningsituation.

We wishedto clarify this point in the presentstudy, wherethe perceptionof both the harmonicand the melodic octaveby subjectswith somemusicaleducationwasinvestigatedwith monaurallypresentedtones.The studyconsisted of two adjustmentexperimentsin which octavematches wereperformedfor pairsof eithersimultaneous or successivepuretones.In someconditionsassessing the perception of the harmonic octave, the reference and test tones were

both simultaneousand frequencymodulatedin a coherent (i.e., parallel) manner in order to preventthe perceptualuse of melodic cues.

The variabilityof a givensubject'sadjustmentsin a given conditionwas taken as an index of the precisionwith whichoctaverelationscouldbe perceivedin that condition. 2127

J, Acoust.Soc. Am., Vol, 88, No. 5, November 1990

We shalldiscuss Terhardt'sconjectureconcerning the originof melodicoctavetemplates in thefinalsection of this article.

I. EXPERIMENT

1

A. Method

1. Subjects

Threenormal-hearinglisteners,LD, MG, andOL, aged 23-35, servedassubjects in theexperiment.Subjects LD and MG were the first author and a psychologystudent;they practicemusicoccasionally but are not expertmusicians. SubjectOL wasan advancedpianostudentwho hadshown remarkablepitch perceptionabilitiesin a previouspsychoacousticexperiment;he waspaid for his services. L. Demany and C. Semah Octave templates

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2. Experimental condit

DMX-1000 digitalsynthesizer includingantialiasing filters Each subjectwas testedin three experimentalcondi- with a cutofffrequencyof 9.6 kHz. tions,whichwill belabeledasM, H,, andHvu. 3. Procedure In eachtrial of conditionM, subjectswerepresented with a sequence of steadypure tonesin which a reference The subject,sittingin a soundproof booth,had at his tonewithfixedfrequency alternated witha frequency-adjus- disposala box with six pushbuttons. He starteda trial by table test tone. Both tones had a total duration of 800 ms and pressing button1 and thenusedbuttons2-5 to adjustthe 100-msrise/fall times,shapedwith a raised-cosine function. frequencyof the test tone, whoseinitial value was deterThe reference andtesttoneswere,respectively, followedby minedat random.Pressingbuttons2 or 3 decreasedthe test 200-msand 650-mspausesin the sequence. Subjects were tonefrequency,by 40-centstepsfor button2, and 5-cent requiredto adjustthe testtoneonemelodicoctaveabovethe stepsfor button3; pressing buttons4 or 5 increased thetest referencetone,asaccuratelyaspossible. tonefrequency, by 5-centand 40-centsteps,respectively. In conditionH,, thesoundsequence heardoneachtrial Froma giventonepairto thenextonein thesequence, only wasmadeup of two-component complexes. The two pure one-stepchangescouldbe produced;no changeoccurredff tonesformingeachcomplexweresteadyand gatedon and no buttonwaspressed. Whensatisfied with the adjustment, off simultaneously, with the samerampsas in conditionM. thesubjectpressed button6 andthefinalsettingwasrecordEach tone had a total duration of 1700 ms and the inter-tone ed.Throughouteachexperimental session, subjects werenot pauseslasted650 ms. The lower frequencytone (reference informedof the valuesof theiradjustments. Each sessionconsisted of 30 trials run in the same conditone) was fixed,while the frequencyof the other tone (test tone) wasadjustable.Subjectswererequiredto adjustthe tion (M, H•, or HvM), andcomprised 5 trialsfor eachof the testtone,asaccuratelyaspossible, at thefrequencyproduc- 6 referencefrequencies. During a session, the referencefreingthemaximum"fusion,"or "harmony,"of thetwosimul- quencywasvariedin a sawtoothmanner(270 Hz, 400 Hz, taneoustones.Sincethe rangeof possible adjustments was 600 Hz,...,2000 Hz, 270 Hz,...), so that adjustments were restricted(seebelow),it wasunnecessary to tellthesubjects neverrepeated immediately for thesamereference frequenthat their perceptualtargethad to be an octaoeharmony. cy.4Foreachsubject, thewholeexperiment consisted of 15 Noneof thesubjects reportedperceptualcriterionproblems daily sessions, i.e., 5 sessions for eachof the threeconditions. and/or askedfor additionalinstructions duringthe experi- The meanrankorderof thefivesessions runin a givencondiment. It must be stressedthat, in this condition, the test tone tion wasapproximatelythe samefor the threeconditions. frequencyneverchangedwhilea stimuluswasbeingpresented. Suchwas also the easein condition M. JrIowever,in con-

ditionH,, this methodological detailwasespeciallyimportant becauseit stronglypromoteda syntheticlistening attitude.In Ward's(1954) experiment onoctaveperception with simultaneoustones, subjectsadjustedthe test tone whileit waspresented; thispromoted,conversely, an analytic listeningattitude (see Rasch, 1978; MeAdams, 1984; Hartmann, 1988).

The thirdcondition,HFs•,wasidenticalto condition exceptfor onepoint:In conditionHvs•,thetonesusedwere not steadybut sinusoidally frequencymodulatedat a rateof 4 Hz. The adjusted frequency wasthenthecarrierfrequency ofthehighertone.Thetwotonesformingeachcomplex were modulatedwith in-phasewaveforms, startingat a positivegoingzerocrossing, andthecarrier-to-peak frequency swing

B. Results

L Mean values of the adjustments

The meanvaluesof the 25 adjustments performedby eachsubjectfor eachconditionandreferencefrequencyare givenin TableI, togetherwith thestandarddeviationsacross sessionsof the within-sessionmeans. (All the standard de-

viationsreferredto in this article are N -- 1 weighted.) In condition M, where the referenceand test toneswere

presentedsuccessively, most of the adjustedoctavesare

stretched with respect to thephysicaloctave,in agreement withprevious results. Theamountof stretching, whichhasa maximummeanvalueof 76 cents(subjectLD, 2000Hz), is not the samefunctionof reference frequencyfor the three subjects.

resultingfrom eachmodulation wasa fixedproportion, In theothertwoconditions, wherethetoneswerepre1/20, of thecarrierfrequency. Thus,duringeachcomplex, sentedsimultaneously, it appearsthat manyof themeanadthe ratioof the two instantaneous frequencies did not vary justments arealsosignificantly differentfroma physical ocwith time and remainedequalto the ratio of the two carrier frequencies.

In eachcondition,thefrequency(or carrierfrequency) of thereferencetonetooksixpossible values:270,400, 600, 900, 1350,and2000Hz. The frequencyratioswhichcouldbe adjustedby the subjectrangedfrom 900-1400 centson some of thetrials,andfrom 1000-1500centson theothers;oneof thesetwo possiblerangeswasrandomlyselectedat the beginningof eachtrial. The reference andtesttoneswerepresentedto thesubject's rightear,eachat 45 dB SPL, through a TDH-49 earphone? Theyweregenerated, witha precision of at least 14 bits and a sampling rate of 36.2 kHz, by a

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J.Acoust. Sec.Am.,Vol.88,No.5,November 1990

tave,andgenerallyexceedthisinterval.Thisimplies,at least, that beatcueswerenot usedto performthe task.In conditionHvM aswell asin conditionH•, subjectLD couldhear beats,but onlyfor the lowestreference frequency, 270 Hz. The othertwosubjectneverreportedhearingbeats. Ward ( 1953,1954) founda strongcorrelationbetween a givensubject'sadjustmentsof successive andsimultaneous

octavesfor variousreferencefrequencies. In the present study, there is a rather strong correlation (r=0.84) betweenthe meanadjustments of subjectMG in conditions M andH•. However,the corresponding correlationis only 0.51for subjectOL andbecomes negative( -- 0.43) for sub-

L.Domany andC.Semal: Octave templates 2128


TABLE I. Differences in centsbetween themeanvaluesof theadjusted intervalsandonephysical octave( 1200cents).Negativenumbers indicateadjustmentssmallerthan 1200cents.Standarddeviationsacrosssessions of the within-session meansare in parentheses.

Subject

Condition

LD

M

Hs

HFM MG

M

OL

61.0

27.4

50.0

(3.3)

(6.9)

(7.0)

1.2

14.8

50.6

(1.3)

(8.6)

(12.4)

2000

33.2

15.6

75.8

(10.5)

(11.3)

(5.8)

-- 4.8

1.2

-- 54.6

(6.8}

(18.8)

(37.4)

1.4

42.6

63.6

23.4

18.0

42.0

(3.0)

( I 1.3)

(21.6)

(32.9)

(33.3)

(30.2)

8.6

38.8

44.2

(9.1)

(5.1)

(9.6)

(9.4)

(10.2)

3.2 (9.4)

21.8 (19.6)

- 9.2 (18.8)

18.8 (11.8)

24.2 (8.9)

37.4 (35.6)

-- 10.6

40.2

-- 28.2

3.6

0.0

-- 21.8

-- 74.0

27.2

(35.0)

(6.1)

(20.0)

(25.6)

(42.0)

(66.3)

Hs

4.2

33.4

33.6

29.0

(9.5)

(6.8)

(4.9)

(11.2)

(12.5)

(4.6)

5.4 (9.1)

31.2 (6.1)

37.8 (10.7)

19.6 (5.4)

20.6 (11.5)

55.4 (31.1)

5.4

21.0

-- 14.4

16.8

18.4

15.6

5.2

-- 33.6

(14.0)

(19.0)

(35.3)

(35.3)

(29.7)

(26.0)

ject LD. Generally,eachof the threeconditionsis poorly correlatedwith the other two. This might be partly due to the poor accuracyof the adjustments for someconditions and referencefrequencies, aswe shallseeimmediately. ,2.Accuracy of the adjustments

Sincetheneuralencodingof puretones,andalsoadjustmentcriteria,may showslightday-to-dayfluctuations,the

7140

1350

(14.8)

M

HF•4

400

-- 3.2

H,

HFs•

Referencefrequency(Hz) 600 900

270

accuracyofa subject'sadjustments for a givenconditionand referencefrequencyis best describedby the adjustments' averagestandarddeviationwithina session. The corresponding data are displayedin Figs. 1-3. For clarity, we did not plot error barsin thesefigures;on the average,the standard error of a data point amountsto 18.3% of its value.

Figures1-3 firstindicatethatthesubjects differedfrom eachotherwithrespect to theiroverallaccuracy. OL wasthe mostaccuratesubject;this is not surprisingin sofar as he was the most "musical"subject(Elliot et al., 1987). But moreimportant,the patternsof data displayedin the figures

Subject LD

,.•120 lOO

.............

......................................................... •'200-

Subject MG

17.5............................................................................................... &Hfm •H s

60 40

eM

150 ........................................................................ • ............................

125 ...............................................................................

.................................... ......................... 100-

20

............................ ,[• ................ •:•.•v.•.....: •.•......•.:.:. • ............

ß

......

....

0 270

400

600

•00

1350

2000

Referencefrequency(Hz, log scale) FIG. I. Mean variabilityof the adjustments performedby subjectLD, asa functionof theexperimental condition(M, H•, or Hrs• ) andthereference frequency. Eachdatapointrepresents themeanof fivestandarddeviations, that wereeachcomputedfrom the fivesettingsobtainedin a givenexperimental session.

2129

J. Acoust. Sec. Am., Vol. 88, No. 5, November 1990

75-

5025o 270

4-00

600

900

1350

2000

Reference frequency (Hz, log scale) FIG. 2. Sameas Fig. 1, but for subjectMO. L. Domany and C. Somal: Octave templates

2129


080' c

Subject OL

andHvu. However,conditionHru wasomittedfor subject LD.

On each trial, the referencefrequency(or carrier frequency) was randomly selectedwithin a logarithmic frequency range extendingfrom 300-400 Hz or from 15002000 Hz. In all sessions,thesetwo rangeswere usedalternately from trial to trial. The total duration of eachtonewas 500 msin conditionM, 800 msin conditionH,, and 1050ms in condition Hrt •. All tones had 50-ms rise/fall times,

'- 60o

._u 50-

u 30-

g 20c10 270

400

600

900

1,350

2000

Referencefrequency (Hz, log scale) FIG. 3. SameasFig. 1, but for subjectOL.

areaboutthesamefor thethreesubjects. In conditionM, the standarddeviationsaresmallanddo not vary markedlywith referencefrequency;their averagevalueis 14.6centsfor subject LD, 15.3 centsfor MG, and 6.3 centsfor OL. In conditions H s and Hvt•, by contrast, the standard deviations stronglydependon referencefrequency;they are almostalwayshigherthanin conditionM, but thedifferenceincreases with referencefrequency.The data obtainedfor condition Hs are roughlyintermediatebetweenthe data for the other two conditions,but when the referencefrequencyreaches 2000 Hz, accuracyis aboutequallypoor in conditionsH• andH•vt. For thisreference frequency, thesubjects' accuracy is, on the average,7.2 timespoorerin conditionsH• and HrM than in conditionM. Note that, sincetherangesof possibleadjustments were restrictedto 500 cents,a standarddeviationapproachingor exceeding100 centsmay reflectessentiallyrandom adjustments.Indeed, subjectsreportedthat for the highestreferencefrequency,it wasvery difficultto adjustthe testtonein conditionsH, and H•vt: There was no narrow rangeof test tone frequenciesinducinga distinctivesensationof harmony. By contrast,in the same register,melodic octaves wereheardaswell-tunedonly for a narrow rangeof testtone frequencies. II. EXPERIMENT

2

shapedwith a raised-cosine function.In conditionM, the referenceand testtoneswere,respectively, followedby 200msand600-mspauses.In conditionsH, andHrta, the interstimuluspauseslasted600 ms. In conditionHvs•, the sinusoidalfrequencymodulationof each tone had a 2-Hz rate andthecarrier-to-peakfrequencyswingresultingfrom each modulationamountedto 10% of the carrierfrequency. For subjectLD, the SPL of the referenceand testtones took two possiblevaluesin conditionM 45 and 65 dB• and three possiblevaluesin conditionH• •45, 55, and 65 dB.5Thus,thereweretensubconditions, i.e.,fivesubconditionsfor eachof the two rangesof referencefrequencies. In a givendaily session, four adjustmentsweremadein eachsubcondition.Ten sessions were run, which provideda total of 40 data points in each subcondition. For subjectCL, the experimentwas run in two parts.

The firstpart includedeightsubconditions, i.e., four subconditionsfor eachfrequencyrange:conditionM at 45 and 65 dB, and conditionH, at the sametwo levels.For eachsubcondition,3 adjustments weremadein a daily session and a

total of 36 adjustments wereperformedduring 12 sessions. In thesecond partof theexperiment, consisting of 5 sessions, theonlyconditioninvolvedwasHv•, at 45 and65 dB;again, a total of 36 adjustmentswasobtainedfor eachsubcondition. Subjectswere testedin a double-walledsoundproof booth and performedtheir adjustmentsusinga computer keyboard,with thesameproceduralrulesasin experiment1. The tones,deliveredto the subjects'right ear via a TDH-39 earphone,weregenerated bymeansof a digitalsignalprocessor (Oros AU22, basedon a TMS 320C25 chip), with a precisionof at least12bits,at a rate of 40 kHz for conditions M andH,, and28 kHz for conditionHv•; the outputof the digital-to-analog converterwaslow-pass-filtered at 20 kHz for conditionsM andH,, and 8 kHz for conditionHr•. B. Results

Experiment2 wasbasicallysimilarto experiment1, but differedfrom it in two majorrespects. First, the SPL of the

Figure4 shows theadjustments madebysubject LD for tonesat 45 and55dB.In condition M (upperpanels),sysreferenceand testtoneswas not fixedat 45 dB, but took two tematicoctavestretchings areapparent, andtheyarequite . mainvalues: 45 and65dB.Second, thereference frequencies largein thehigherfrequency range.However, theadjustdid not form a finite set, but varied randomlywithin two separateranges:300400 Hz and 1500-2000 Hz. A. Method

Two subjectswereused:the first author (LD) and a 20-

year-oldharpist(CL). SubjectCL hada normalaudiogram and was paid for her services.The subjectswere testedin three conditions,similar to thoseof experiment1: M, H•, 2130

J.Acoust. Sec.Am.,Vol.88,No.5, November 1990

mentshaverelativelysmallstandarddeviationsand are thus consistent. In conditionH•, at 45 aswellas55 dB, themean valuesof the adjustments neverdiffermarkedlyfrom one physical octave,butthestandard deviations arecompletely

differentfor thetwofrequency ranges. In thehigherrange (right-handpanels),thesubject wasunableto performaccurate adjustmentsby any criterion; variationsin the fre-

quency ofthetesttoneproduced noticeable pitchchanges in the stimulusasa whole,but the two tonescouldnot be clear-

b Demany andC.Semal: Octave templates

2130


3OO LD:

LD:

M 45 dB

200

M 45 dB

200 a

1 oo

0ooo oo o•oaoo•c• o o ø•o8• c• •

•

116.8

s.d.:

o

0 -100

-lOO

-200

-200

mean:

32_5

s.d.:

14.5

mean:

03

30.1

- 300 400 1500

- 3O0

•

o øø%

o %,o •oom ø % ooø

100

o

o

300

300

2000

3OO

LD: Hs 45 dB

LD: Hs 45 dB 2O0

2OO

o

o

o

o

100

1 oo

o

FIG. 4. Adjustmentsperformedfor 45-

o

o

o

o

•Po•o •o

o•

•øoO•

8 o Oo•

øo

0

0

o o •-

-lOO

--1OO

•

0

o

o o

oo

0

0

0

d•ø

and 55-dB tonesby subjectLD in experiment2. Eachdatapointrepresents a single adjustment.In eachpanel,corresponding to a givensu•ondition, the overallmean and standarddeviation of the adjustments

• -200 .9

mean:O.9

sd

' 66

12 5

mean

-3oo

>

are indicated in cents.

-200

s.d.:

107.2

-300

300

400

3OO

1500

20O0

3OO

LD: Hs 55 dB

LD: Hs 55 dB

200

200

o

o o

o o

o

o

1 oo

lOO øo o

o

oø ooo

o

0

OoO•%8•,oO6• ooo o m o øo oO

oo

o

o

-lOO

øo

o o

o

o

o

o

o

-lOO o

-2oo

o

o

oo

o o

-200

mean:

2.9

sd..

13.2

meon:41.1

-3OO

s.d_:

1159

-300

300

400

Reference

1500

2000

frequency (Hz, log scale)

In conditionHs, it wasalmostimpossible for subjectLD ly heardoutandnoqualitativesingularitycouldbedetected, to adopt an analytic listening strategy. The (spectral) so that all possible adjustments wereperceptually equivapitches of the two simultaneous tones were difficult to hear lent.In thelowerrange,by contrast,a distinctive sensation ofharmony,fusion,singleness of pitch,emerged in thevicin- out,exceptfor markedlymistuned octaves in thelowerfre-

range.On thecontrary,subject CL reported thatit ity of thephysical octave. In addition,withinthefrequency quency regionwherethissensation ofharmony wasmaximum, beats wasveryeasyfor herto adoptan analyticlisteningstrategy of mistuned consonancescould be heard with some atten-

tionaleffort.Smallfrequencyvariationsproduceddetectablechanges in theirrate whiletherewasno perceptible changein theamountof harmony.The subjectdid notattemptto ignorethesebeats;onthecontrary,hedeliberately tried to cancelthem in order to improvethe adjustments' reliability.Sincethebeatsmayhavearisenfrominteractions of thetonesin the sameperipheralauditoryfilter, the subject'sdatafor the lowerfrequency rangemaynot givean adequate imageof hisperception of octaveharmony. For 65-dBtones,the subject'sdataare quitesimilar,as shownby Fig.5. Thislouderleveldid notenablethesubject to performreliableadjustments in the higherregisterfor condition H,. On the otherhand,the octavesadjustedin conditionM and the higherregisterstill havea relatively smallvariability, although theyareevenmorestretched than for 45-rib tones.

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J. Acoust. Sec.Am.,VoL88,No.5, November 1990

in conditionH•: Shecouldeasilyhearoutthetwotones.She feltthatsettingthetwotonesa melodicoctaveapartwasthe strategy leadingto themostaccurate adjustments. For this condition,shewasinstructedto beasaccurateaspossibleby any method.

Figures6 and7 showthatwhateverthefrequency range, CL performedrelativelyconsistent adjustments in conditionsM and H,. In conditionH•, the adjustedfrequency ratiosaresignificantly smallerthanonephysicaloctavefor thehigherregister, buttheadjustments' variabilitydoesnot increasemuchfrom the lowerregisterto the higherone.In conditionM, CL did not adjuststretchedoctaves;for 45-dB tonesin the higherregister,the standarddeviationof her adjustments islarge(36.1cents),butit canbeseenthatthis isdueto onlyoneadjustment ( + 155cents)outof 36;if this atypicaladjustment is left out, the standarddeviationbecomes 21.8 cents.

L.Demany andC. SomakOctavetemplates

2131


300

3O0

LD:

M

65 dB

LD:

M 65dB o

200

200

1 O0

•øo o oo o OoO ooø•oø• o ooo oo

1 O0 o

o

ooo%••

0

0

-100

-100

-200

-200

mean:

35,5

s.d.:

15,9

mean:

-300

175.4

s,d.

: 21.2

-500 400

3oo 300

1500

2000

LD: Hs 65 dB

LD: Hs 65 dB

200

200

o

o o

o o

o

100

100 o½

o

o

ß

o

o

o

o

Oo

9oo•ø0%øoo • oooo •o •%o 0%0•

o o

0

o o

-lOO

100 'o

-200

2O0

o%

o

o

o

o

o

o

mean

: 0.9

s.d.:

FIG. 5. Same as Fig. 4, but for 65-dB tones.

30O

mean:

6.9

-300 300

400

9.4

oo

s.d.:

114.4

3OO 1500

2000

Reference frequency (Hz, log scole)

III. DISCUSSION

In conditionH•, CL was able to hear out the two tones and to setthem a melodicoctaveapart as if they werepresentedsuccessively'. However,thiswasno longerpossiblein conditionH?st.Figure 8 showsthat in thiscondition,for 45dB as well as 65-dB tones,the adjustmentswere relatively accuratein the lower registerbut essentiallyrandomin the higher register.CL reportedthat in the higherregister,she couldnot find any perceptualcueallowingfor accurateand reliableadjustments.

300

Our mainresultsmaybesummarized asfollows.When

musically educated adultlisteners are presented with two successive toneburstsandrequiredtoadjustoneofthetones a melodic octave abovetheothertone(withfrequencyf•c ),

theycanmakeconsistent adjustments forf•ervalues ranging from 270-2000Hz. On theotherhand,if the two tonebursts

arepresented simultaneously andthetaskisto adjusta harmonicoctavecomplex, by anyperceptual mean,theconsis-

300 CL:

M

45 dB

CL:

200

200

100

100

M 45 dB

o

0

•,o•

o o

-100

o

o

%o oO

oO•&

%% ood

-10o

-200

-200

mean

: 0.0

s.d. : 16.4-

mean

-300

: --11.9

s.d. : 36.1

-300

300

400

300

1500

2OO0

300

CL: Hs 45 dB

CL: H• 45 dB

200

FIG. 6. Adjustmentsperformedby subject CL, for 45-dB tonesandconditionsM and H•.

200 100 o

o

0 DaD øo oo o½o oø o o øoøq•

o

o o

o o o•OO

Oo o o ooo o ø

o o

-lOO

- 1O0

-2O0

o o

oo

o

% oaoø%

o o

-200 mean:

-3.9

s.d.:

25.7

-300

mean:

-52.4

- 300 400 1500

300

Reference

2132

o

0

o

s.d.:

36.0 2000

frequency (Hz, log scale)

J.Acoust. Soc.Am.,Vol.88,No.5, November 1990

L.Domany andC.Semal: Octavo templates

2132


3OO

30C

CL:

M 65 dB

CL:

200

2OO

tO0

100

0

o %•% oO•%%omOo•o % øo

-100

0

-200

o•mo o %ooooo ø•øø%o o o

-lOO

M 65 dB

o

o

o

ooo

o

•

-200

mean

: 0.7

s.d. : 14.7

mean:

-300

-22.9

s.d. : 17.9

-300 400

300 300

1500

2O00

FIG. 7. SameFig. 6, but for 65-dB tones.

30O

CL: Hs 65 dB

CL: Hs 65 d8

200

2OO

1oo

1 oo o

o©

0

o

o

o

o

o

-lOO

o o

oo•O oøø

8øøo m o o øøo

-100

o

o

o

o

o

o

-200

-200

mean:

-13.1

s.d.:

17.7

meon:

-3OO

-52.9

s.d.:

38.6

-300 4-O0 1500

3OO

2000

Reference frequency (Hz, log scale)

consistentadjustmentsfor lowf•,r values.However,consistent adjustments will be impossible forf,,r valuesexceeding 1000or 1500Hz. Usingsimultaneous frequencymodulated

tencyof the adjustments depends on two factors:the subject'sabilitytohearoutthetwotones, andthevalueof f•er.If thesubject caneasilyhearoutthetwotones,thenhewill be ableto adjustmelodicoctaves, asif thetoneswerepresented successively, andhewill berelativelyconsistent for a wide rangeoffset values, upto2000Hz. Butthesubject mayhave difficulties hearingoutthetwotones,evenwhentheyhave

tonesin orderto studytheperception of octaveharmonyper se,we foundin four subjectsout of four that consistent octaveadjustments couldbeperformedfor lowliervalues,but not forf•,r > 1000-1500Hz. Let us try to understandthe subjects'difficultieswith harmonicadjustments at highfrequencies. In thisrespect, it is usefulto considerthat, whenmakingharmonicadjust-

the sameSPL and are well abovetheir detectionthreshold.

He canthenadopta synthetic listening strategy andbasehis adjustments onconsonance, i.e.,harmony. Thiswillleadto

300

Hfm 45 dB

CL: Hfm 45 dB 200

200

o oo

o

lOO

1 oo

o

o

•

o

0

o

oo

•

o

o

•

•

o

o

o

o o

o

o o

o

-100 - 200

-200 mean:

0.6

mean:

s.d. : 35.6

31.7

s.d.:

[56.5

-300

-300

•

o

oo

oø© o o

c-•

E

o o

oo o o 0

o

o

c -100 •

o

400

300

300

2OOO

1500

300

CL: Hfm 65 dB

c o

Hfm 65 dB

200

200

•oo

1 O0

o

o

o

'5

o

o

0

o%•8C•ooO o %•7Oo o Oo

•

oøoo•

0

Do o

o

o oø

o

o

o

•z•

FIG. 8. Adjustmentsperformedby subjectCL in condition Hru.

o

o

o o

oo

o o

-100

-100

o

o

o

-200

-200 mean:

-0.6

s.d.:

mean:

16.7

13.2

o

s.d.:

97.8

-300

-300 300

400

1500

2000

Reference frequency (Hz, log scale) 2133

J. Acoust.Sec. Am., Vol. 88, No. 5, November1990

L. Demanyand C, Semal:Octave templates

2133


ments,the subjectswereattemptingto matchthe stimulito "harmonicoctavetemplates,"corresponding to internal representations of the harmonicoctave(no assumption being made,actually,aboutthe physiological basisof octave harmonyasa perceptual phenomenon). The inconsistency of thehigh-frequency harmonicadjustments canthenbeascribedto: ( 1) anabsence (or aninaccuracy ) ofthenecessary harmonicoctavetemplates; or (2) an inaccuracy of thesensoryinformationwhichwasmatchedto the templates. Let us first considerthe secondpossibility.Of course, harmonicoctaveadjustmentswill be inconsistent if, for instance,theSPLof thetonesissolowthatthetonesarebarely detectable. Thiswasnotthecasein ourexperiments. Yet, the subjects' inconsistency canbe ascribedto a specialform of interactionbetweenthetwocomponent tonesof thestimuli: At somelevelof the auditorysystem,whenpresented simultaneouslyand listenedto synthetically, the high-frequency toneswouldnot beencodedwith the sameaccuracyaswhen presentedsuccessively. This explanationmay seemunlikely since,accordingto Nelsonand Bilger (1974), a pure toneof 2000 Hz and 45 dB SPL does not raise at all the detection

threshold of a simultaneous 4000-Hz tone. However, it has

beenpreviouslyshownthat auditoryinteractionscanoccur in casesfor which simplemaskingis not observed(Wake-

compatible with Terhardt'sviewon the originof melodic octavetemplates.

In any case,our resultsconcerning the perceptionof octaveharmonyare basicallycongruentwith thoseof Demany and Semal (1988), describedin the Introduction; thus,in thisprevious study,thedichoticpresentation of the stimuliwasprobablynot an importantfactor.At low fre-

quencies, the standarddeviations of our subjects' adjustmentsin conditionsH s and HFst amountto 7-40 cents, whichcorresponds to frequencyvariationsof 0.4%-2.3%.

Mooreetal. (1986)measured thresholds forinharmonicity perception in periodic complex sounds witha richspectrum, a fundamentalfrequencyof 100-400Hz, andoneharmonic mistuned. Theyfoundthresholdmistunings of 1%-2% for thefirstandsecond harmonic(onephysical octaveapart); thesethresholds are roughlysimilarto our standarddeviations.

With respectto theperceptionof the melodicoctave,we did not find,in thesubconditions Mofexperiment 2, systematic andclear-cutfluctuationsof the frequencyratiosadjusted by a givensubjectwithin a given rangeof referencefrequencies.Yet, eachrangecorresponded to a musicalfourth and within suchranges,idiosyncraticmicrofluctuations of adjustedmelodic octaveswere reported by, e.g., Ward

field and Viemeister, 1985).

(1954) and van den Brink (1977). Ward (1954) showed

The alternative--and more likely-- possibilityis that the high-frequencyharmonicadjustmentswere not impairedby suchinteractions,andthat thetoneswereencoded with aboutthesameaccuracywhenpresented simultaneously and when presentedsuccessively.(This doesnot mean that the encodedfrequenciesof the toneswere exactly the samein conditionsof simultaneous and successive presentation, but only that the encodedfrequencies wereequallywell defined in the two conditions.) The inconsistencyof the high-frequencyharmonicadjustmentswouldthen resultentirely from deficiencies in the subjects'harmonicoctavetemplatesthemselves. The latter interpretationis difficultto conciliatewith a conjecture of Terhardt (1970, 1971b, 1974, 1980)mentionedin the Introduction.Terhardt hypothesizedthat melodicoctavetemplates andtheperception of octaveharmony originatefrom one and the samelearningprocess, taking placein early life and basedon the perceptualanalysisof complexperiodicsoundssuchas vowels.This hypothesis seemsto imply that the accuracyof harmonicand melodic octavetemplates shoulddependin thesamewayonfrequency register.The problemmaybemoreexplicitlyphrasedas follows. Accordingto Terhardt, the pitch interval corresponding to a melodicoctaveislearnedby listeningto physically harmoniccomplextones.This impliesthat a subject who is ableto adjustmelodicoctavesin a givenfrequency registermust know, or have known, what is a harmonic octave in the samefrequencyregister.If one assumesthat the twospectralcomponents of ourcomplexstimuliwereencoded with the sameaccuracyaswhenpresented successively,

thatthesemicrofluctuations changefromdayto day.It may bethattheydonotclearlyappearin Figs.4-7 partlybecause we pooleddata collectedon differentdays.Their existence and their variabilityfrom day to day wouldimply that the standarddeviations displayed in theupperpanelsof Figs.47 underestimate the accuracyof the subjects'melodicoctave templates. Someresultsobtainedby Attneave and Olson (1971)

indicatethat theconsistency of melodicoctaveadjustments shoulddrop rathersharplynot far abovethe highestreferencefrequencywe used,2000 Hz. Yet, the precisionwith which,in a verywiderangeof frequencies, manyadultlisteners are able to set two successive pure tones "one octave apart" is amazing.In this respect,the octaveseemsto beat any other interval of the musical scale (Burns and Ward,

1982;Rakowski,1988).We mentioned aboveTerhardt'shypothesis concerning the originof melodicoctavetemplates. Let us point out here that other hypotheses havebeenadvanced.In particular,someauthors (van Noorden, 1982; Ohgushi,1983) arguedthat thesetemplatesoriginatefrom innatepropertiesof the auditorysystemratherthan from a learningprocess. Sucha viewis congruent with experimental data showingthat 3-month-oldinfantsalreadypossess melodicoctavetemplates in sofar as,at leastat lowfrequencies,they perceivetwo pure tonesan octaveapart as more similarthan two pure tonesa seventhor a ninth apart (Demany and Armand, 1984). ACKNOWLEDGMENTS

thenour resultsindicatethat, at highfrequencies, people actuallydo not knowwhat is a harmonicoctavecomplex sincethey are unableto recognize sucha stimulusamong

This work wassupportedby the ConseilR•gionald'Aquitaineanda grantfromtheInstitutNationaldela Sant6et de la RechercheMrdicale (CRE No. 886014). Experiment 1wasrun at the Laboratoirede Psychologie Exprrimentale,

other, inharmonicdyadsof pure tones;this doesnot seem

Universit6 Ren6 Descartes, Paris. The first author is affiliat-

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L.Domany andC.Semal: Octave templates

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ed with the CentreNationalde la RechercheScientifique. Elliott, J., Platt, 1. R., andRacine,R. 1. (1987). "Adjustmentof successive and simultaneous intervalsby musicallyexperienced and inexperienced We thankErnstTerhardt,DixonWard, StephenMeAdams, subjects," Percept.Psychephys. 42, 594-598. and BertramScharffor their comments on a previousver- Hall,D. E.,andHess,J.T. (1984)."Perception ofmusical intervaltuning," sionof the manuscript. Music Percept.2, 166-195. Hartmann,W. M (1988). "Pitchperception andthesegregation andintegrationofauditoryentities," in•4uditory Function, editedbyG. M. Edelman,W. E. Gall, andW. M. Cowan(Wiley,NewYork), pp.623-645. Kameoka,A., and Kuriyagawa,M. (1969). "Consonance theoryPart I:

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in theexperiments justmentioned, thesubjects ignoredharmonyanddirectedtheir attentionon sensoryconsonance only.

2Wearereferring heretospectral components thatareresolved intheauditory periphery.

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