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
2128
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-
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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
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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
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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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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
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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
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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
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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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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:
•Some previous experiments ontheperception of consonance (Plompand Levelt,1965;Levelteta!., 1966;KameokaandKuriyagawa,1969)suggest that dyadsof puretonesformingsimplefrequencyratiosare actuallynot perceived asmoreconsonant thanphysicallyinharmonicdyads.Terhardt ( 1984,p. 282) providesa convincing explanationof thesenegativeresults. In his view, consonance hastwo distinctcomponents, "sensoryconsonance"(which dependson roughness and sharpness of timbre) and "harmony"(whichisrelatedto virtualpitchperception). Terhardtarguesthat,
in theexperiments justmentioned, thesubjects ignoredharmonyanddirectedtheir attentionon sensoryconsonance only.
2Wearereferring heretospectral components thatareresolved intheauditory periphery.
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mal-hearing listeners," 1. SpeechHear. Res.17,223-251. 3Inexperiment I, a levelcalibration of thetesttonewasdoneonlyforthe in Music,Mind frequencies corresponding to the physicaloctaves of the six reference Neetden,L. van (1982). "Two channelpitchperception," andBrain,editedbyM. Clynes(Plenum,NewYork), pp.251-269. tones.Thus, irregularitiesin the earphoneresponse(especiallyaround 4000Hz) mayhaveproduced slightvariationsin thelevelof thetesttone whenits frequencywasvariedby the subject. 4When,in anadjustment task,theadjusted variablehasa largeeffectonthe perceptinducedby thestimulusbut thetaskis difficultbecause no clear perceptual singularity canbe found(i.e., theperceptual targetis fuzzy), subjects mayadoptanartifactual mnemonic strategy inordertoreducethe adjustments' variability: Oneachtrial,theymaytry toreproduce thestimulusadjustedon theprevioustrial insteadof makingan independent adjustment.Of course,thisispossible onlyif anaccuratemnemonic imageof thepreviously adjusted stimulus isavailable. Ourtemporal organization of thetrialsminimized thispotential memorybiassinceit wasdifficultforthe subjects to keepan accurate memorytraceof thestimulusadjusted on a giventrial untilthenexttrial involvingthesamereference frequency. •Levelcalibrations weredoneonlyfor the centerfrequencies of the two referencerangesandtheir physicaloctaves. Attneave,F., andOlson,R. K. ( 1971). "Pitchasa medium:a newapproach to psychephysical scaling,"Am. 1. Psychoi.84, 147-166.
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