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(see Huron, 1989). For the combined voices in the 48 fugues in Bach's Well ..... A sample isochronous passage from J. S. Bach's Partita. No .2 for solo violin is ...
What Is Melodic Accent? Converging Evidence from Musical Practice Author(s): David Huron and Matthew Royal Source: Music Perception: An Interdisciplinary Journal, Vol. 13, No. 4 (Summer, 1996), pp. 489-516 Published by: University of California Press Stable URL: http://www.jstor.org/stable/40285700 Accessed: 06/10/2010 18:18 Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/page/info/about/policies/terms.jsp. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, non-commercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at http://www.jstor.org/action/showPublisher?publisherCode=ucal. Each copy of any part of a JSTOR transmission must contain the same copyright notice that appears on the screen or printed page of such transmission. JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected].

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MusicPerception Summer1996, Vol. 13, No. 4, 489-516

© 1996 bythe regentsof the universityof California

What is Melodic Accent?ConvergingEvidencefrom Musical Practice DAVID HURON ConradGrebelCollege, Universityof Waterloo MATTHEW ROYAL Facultyof Music, Universityof WesternOntario The theoretical and experimental literatures pertaining to pitch-related accent are reviewed. From these literatures, eight competing notions of melodic accent are identified. All eight conceptions of melodic accent were investigated through correlational studies of three contrasting samples of music. Statistical correlations were calculated for each accent type with respect to the corresponding metric position or with respect to the syllabic/melismatic status of associated sung text. The results for all three studies are most consistent with a perceptual model of melodic accent developed by Joseph Thomassen (1982). The remaining conceptions of melodic accent receive little or no empirical support. In addition, this study reveals an endemic use of text-melody displacement in a sample of Gregorian chant- suggesting that the chant melodies were constructed so as to avoid strong rhythmic stresses.

accentmaybe definedas an increasedprominence,noticeability, or salienceascribedto a givensoundevent.CooperandMeyer(1960) characterizedaccent as "a stimuluswhich is markedfor consciousness" Suchacousticstimuliarepresumedto be markedthroughdynamic,agogic, harmonic,melodic,timbrai,or other formsof stress.Of the varioustypes of accent proposed by music theorists,one of the most contentioushas been the so-called"melodicaccent."In this paper,we reviewsome of the pertinenttheoreticaland perceptualliteraturesrelatedto melodic accent. Using a correlationalmethod,we then compareand evaluateeight different notions of melodicaccentby analyzingthreesamplesof music.To anticipateour results,the analyseswill show that the musicalpracticeis most Requests for reprints may be sent to David Huron, Conrad Grebel College, University of Waterloo, Waterloo, Ontario, Canada N2L 3G6. (e-mail: [email protected]) 489

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consistent with an experimentally derived perceptual model of melodic accent developed by Thomassen (1982).

Theoretical Notions of Melodic Accent By melodic accent, theorists mean accent arising from pitch-related manipulations such as changes of pitch height, pitch interval, or pitch contour. In the case of pitch height, two hypothetical types of elemental accents can be distinguished: treble accent - in which higher pitches are presumed to be more salient than lower pitches, and bass accent- in which lower pitches are presumed to be more salient. Benward and White (1989) for example, subscribe to the first view- namely, that higher pitches receive greater perceptual weight. This notion of accent is shared by linguists who have studied pitch contours in speech ('t Hart, Collier,& Cohen, 1990). Other theorists have suggested the reverse- that lower pitched sounds tend to be perceived as more stressed (e.g., Parncutt, 1989). A third possibility would regard both extremes of high and low pitch as more salient than mid-registerpitches. We might dub this third view of melodic accent, registrai extreme accent. This view is one of two implied in Lerdahland Jackendoff's (1983) notion of phenomenal accent: By phenomenalaccentwe mean any event at the musicalsurfacethat gives emphasisto a momentin the musicalflow. Includedin this categoryare . . . leapsto relativelyhigh or low notes. . . (p. 17) Also implied in Lerdahl and Jackendoff's definition is the notion that melodic accent is evoked by large pitch movements- what might be dubbed interval size accent. According to this notion, the degree of melodic accent is proportional to the size of the interval movement and is independent of the direction of pitch motion. Along these lines, Graybill (1989) proposed that "a leap to a note, either high or low, will tend to accentuate that note, especially if the immediatelysurroundingcontext is stepwise" (p. 22). Again, two variants of this view of melodic accent arise by introducing interval direction as an additional factor. In the first of these views, size-related accents are presumed to arise only for ascending pitch movements (interval ascent accent), whereas in the second view, size-related accents would arise only for descending pitch movements [interval descent accent). Graybill (1989) claimed that ascending leaps are more accented than descending leaps. Rothgeb (1990) has argued more pointedly that interval size accent arises only in the case of ascending motions. In all of the views that link melodic accent to pitch movement, the accent has been presumed to occur at the point of arrival on the second pitch forming the interval.

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Yet another view suggests that melodic accent arises from changes of direction in pitch contours. According to this view, it is the "pivot points" in melodic contours that generate the greatest salience. Lester (1986, p. 33) has espoused this view, claiming that pitches that stand at the top or bottom of a melodic segment are accented. Graybill has also espoused this notion - although he claims that changes of melodic direction evoke less strong accents than treble or bass accents. By way of summary, we can distinguish at least seven different conceptions of melodic accent that are either implied or explicit in the music theory literature: (1) treble accent, (2) bass accent, (3) registrai extreme accent, (4) interval size accent, (5) interval ascent accent, (6) interval descent accent, and (7) contour pivot accent. Other conceptions of pitch-related accent arise from tonality-related considerations (e.g., scale degree or harmonic implication). In addition, further types of pitch-related accents are thought to arise from recurring pitch patterns, such as found in sequential motivic writing (e.g., Graybill, 1989). However, these latter forms of accent will not be addressed in this paper. Finally,it should be noted that some theorists- notably William Caplinhave voiced skepticism regarding the existence of melodic accent. Caplin (1978) suggested that because of the way high pitches are performed, the presumed melodic accent is merely an artifact of increased intensity (i.e., dynamic accent): . . . however,pitch-heightaccentis perhapsquestionable.In fact, if one left all other variablesout of consideration,it would be difficultto assertthat the highestnote of a successionof notes was perceivedas accented. . . That does not mean, however,that the so-calledpitchheight accent is a mere fantasy since, in actual fact, singersshow a tendencyto give highernotesgreaterintensity,(pp. 18-19 [ourtranslation]) Caplin's view is consistent with physiological research in speech intonation, which has shown that the pitch of the speaking voice is correlated with gross respiratory energy- and hence with the loudness of the voice ('t Hart et al., 1990). It is possible that pitch-height related accent may be a learned association with dynamic accent. In reviewing the extant theoretical writings, there appears to be little agreement among music theorists regarding the nature of melodic accent. Note that this lack of consensus may itself be suggestive. If melodic accent exists, perhaps its effect is minor compared with dynamic and agogic accents. Alternatively, much of the apparent confusion may originate from the difficulty of discriminating between certain of the above conceptions of melodic accent. For example, if it were the case that all melodic accents

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Fig. 1. Two melodic intervals that illustrate diverging predictions for melodic accent. If melodic accent is attributable to pitch height ("treble accent"), then F5should be perceived as more accented than C5. Alternatively, if melodic accent arises because of large upward intervals ("interval ascent accent"), then C5 should be perceived as more accented than F5.

arise due to treble accent alone, then most observations would tend to be consistent with interval ascent accent as well. That is, if the higher of two pitches is always more salient, then the second pitch of an ascending interval would also always appear to be more salient. Similarly, other possible confounds could exist between registrai extreme accent and either of treble accent or bass accent- or between registrai extreme accent and contour pivot accent. For example, notes corresponding to changes of pitch direction are more likely to coincide with points of registrai extremes. At the same time, there are some subtle differences between these proposed notions of melodic accent that can lead to divergent predictions. Hence, it may be possible to establish which of two or more competing conceptions of melodic accent better accounts for listener experience and/ or compositional practice. For example, consider the pitch movements from C4 to C5, and from A4 to F5 (as shown in Figure 1). According to the interval ascent view of melodic accent, C5would receive a greater accent than F5 because the interval size is larger (P8 versus m6). However, according to the treble accent view, F5 would be predicted to be more salient than C5 because it is higher in absolute pitch. In summary, we might expect a considerable degree of predictive similarity between the various proposed accent types. In a correlational study, this will necessarily mean a degree of shared variance. Under these circumstances, a high correlation may be spurious if another proposed accent type accounts for the same variance. Perceptual Evidence for Melodic Accent Apart from the theoretical accounts of melodic accent, a handful of perceptual studies are also pertinent. Squire (1901) carried out early experiments concerning the influence of pitch height on perceived accent. Squire manipulated the pitches of a recurring two-tone pattern; she then determined whether her listeners tended to hear the two tones as forming an

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iambic (weak-strong)or trochaic(strong-weak)rhythm.Squire'slisteners showed considerablevariabilityin their responses,and Squireconcluded That is, her resultsdid not that these perceptionsare listener-dependent. or lower either that notion pitchestend to be perceived higher supportthe as havinggreaterstress. Woodrow(1911) carriedout moredetailedexperimentswhereintensity, duration,and pitch were pitted againsteach other in orderto determine whichparameteris mosteffectivein inducingsubjectivegrouping.Woodrow found that loudertones tend to be heardas initiatinga group (forminga trochaicrhythm),whereaslongertones tend to be heardas terminatinga group (formingan iambicrhythm).Woodrowfoundthat changesof pitch do not systematicallyinduceeithera group-initiatingor a group-terminating effect.More precisely,Woodrowfoundthat changesof pitch alone are unableto evokeconsistentlythe perceptionof an iambicor trochaicrhythm. Like Squire,Woodrow'sresultsare inconsistentwith the notions of treble or bassaccent.Indeed,Woodrowexplicitlycalledinto questionthe validity of pitch-heightaccent. Perceptualresearchpertainingto pitch-contourmelodicaccenthas been carriedout by JosephThomassen(1982, 1983). Thomassenundertooka set of experimentsin which sequencesof pitchesexhibitingvarious melodic contours were embedded in a standardized metrical context. Thomassencollected data pertainingto the perceivedrelativestress for threetargettoneswithina metricalpassage.Bothmusicianandnonmusician listeners participatedin the study. On the basis of the collected data, Thomassendevelopeda predictivemodelof melodicaccent.Figure2 summarizesthe relationshipbetweenmelodiccontourandmelodicaccentidentified in Thomassen'sstudy.The accent values shown in Figure2 range betweenzero(no accent)andone (maximumaccent).AsThomassen'smodel is deriveddirectlyfrom perceptualdata, the model is not easilycharacterized analytically.In the first instance,the model is sensitiveonly to the gross melodic contour and ignoresintervalsize. In general,Thomassen's modelassignsmorestressto contourpivot tones- that is, tones coinciding with changesof direction.Note, however,that ascending-descending pivots are more stressedthan descending-ascending pivots. In orderto test his modelof melodicaccent,Thomassenusedthe model to predictthe perceivedstressof eachnote in sequencesof fourtargettones within a metricalpassage.Thesepredictionswere then comparedwith the resultsof a secondexperimentalstudyin whichthe modelpredictionswere confirmed.The valuespredictedby Thomassen'smodel yieldeda correlation of +.90 with listener'sresponses. As in all experiments,variousassumptionsweremadeand possibleconfounds left uncontrolled.In Thomassen'swork, only three intervalsizes were usedin the melodiccontours(one,four,andeightsemitoneintervals).

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Fig. 2. Schematic representation of basic accent configurations in Thomassen's model of melodic accent. Accent values pertain to the second and third notes of three-note contours. Thomassen's algorithm uses a moving window containing three pitches. The accent value for any given note is determined by the interaction of three overlapping three-note contours associated with that note.

Of course,differentintervalsizesmayinfluencemelodicaccentby evoking differentharmonicimplications.As Thomassendidnot investigatea broader sampleof intervalsizes,possibleharmonicimplicationsare not addressed in his model. Indeed,Thomassenfound small but consistentdifferences betweencontoursusingdifferent-sizedintervals.Despitethesesmalldeviations, the principalexperimentalresults showed a robust effect of pitch contourthat is largelyindependentof the type or size of intervalsused. Anotherpossible confound in Thomassen'sresults is the influenceof overall pitch register.Thomassen'sexperimentsused pure tones centered around 1000 Hz (B5)- somewhat higher than the typical musical pitch tessitura.Thusit is possiblethatThomassen'sresultsareonly applicableto "soprano"linesandcannotbegeneralizedto pitchcontoursin the midrange or bass. Two experimentalpapersthat take Thomassen'swork as a springboard and examinethe interactionof melodicaccentwith otheraccenttypes are Monahan,Kendall,andCarterette(1987) andDrake,Dowling,andPalmer (1991). Monahanet al. playedthreedifferenttypes of speciallycomposed melodiesto listeners.One group of melodiesconsistedof tones in which agogic and melodicaccentscoincided.Agogicand melodicaccentin a second group of melodiesoccurredat regularintervalsbut nevercoincided with each other.A thirdgroupexhibitedagogicand melodicaccentsusing differentmetricalrates. Drake et al. played variousmelodiesto children

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and adult pianistsin which metric,agogic, and melodicaccentswere systematicallypositionedin and out of synchronywith each other.Both experimentsassumedthat melodicaccentis inducedby (1) a contourchange, and (2) a largepitch interval.Both Monahanet al. and Drakeet al. found that pianistsplayedbackthe melodiesmost accuratelywhen all the accent types coincidedand that there was a deteriorationin performancewhen agogicor melodicaccentswereout of synchronywith eachother.The deteriorationof pianists'performanceswhen both melodiccontourchangeand melodicleap were desynchronizedprovidesperceptualevidenceconsistent with the existenceof both of these types of melodicaccent. In summary,the extant perceptualresearchprovidesstrongevidencein supportof Thomassen'smodel,good evidencein supportof intervalascent and intervalsize accent,but calls into questionthe notions of bass accent and treble accent. However,given the avowedly simple stimuli/contexts used (especiallyin Thomassen'sexperiments),thereremainsa questionof how these findingsrelateto musicalpractice. Melodic Accent in Musical Contexts In light of the wide discrepancyof views concerningthe natureof melodic accent,it is appropriateto compareboth the perceptualand theoretical literatureswith actualmusicalpractice.That is, we would proposeto measurethe degreeto which the musicalrepertoireprovidesevidenceconsistentwith one or moreof the conceptionsof melodicaccentjustdescribed. At the outset,it is importantto recognizethat accentsmay be usedfor a varietyof musicalpurposes.One such goal may be the establishmentor preservationof meter.In othercases,the goal may be the exact oppositethat is, to preventor dismantleany senseof metricframework.In yet other circumstances,the compositionalgoal maybe to play off accentswithinan existing metricframeworkbut without actuallydismantlingthe metersuch as in the casesof syncopationand hemiola.In thesecases,accentsare purposelymiscoordinated(for a parallelin speechperception,see Handel, 1989, regardingthe structureof tongue-twisters).Accentsmayalso be used for nonmetricrhythmicpurposes,such as adding dramaticemphasisor highlightingthe naturalsyllablestressesin vocal text-setting. A usefulway of evaluatingany hypotheticalform of accentis to relate its presenceto the presenceof known or establishedformsof phenomenal accent (such as agogic or dynamicaccent).For example,in most musical passages,agogic accentsand dynamicaccentstend to coincidewith each other,and they also show strongpositivecorrelationswith metricposition (seeHuron, 1989). Forthe combinedvoicesin the 48 fuguesin Bach'sWell

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TemperedClavier,for example,the correlationbetweennote durationsand metric position is +.34. (That is, longer notes tend to begin on stronger metricpositions.)Wewould presumethatthis synchronizationof phenomenal accentwith metricpositionis intended,at least in part,to help establish or maintainthe meter. One can study hypotheticalnotions of melodicaccentin a similarway, by examiningthe coincidenceof proposedmelodicaccentswith points in the metric hierarchy.The possible relationshipsbetween metric position and melodic accentsmight be viewed as existing along a continuum.At one end of the continuum,melodic accentswould be perfectlysynchronizedwith highpointsin the metrichierarchy.In this case, the most prominentmelodicaccentswouldcoincidewith downbeats.At the otherextreme, one can imaginemelodic accentscompletelyout of synchronywith high points in the metric hierarchy.For any given piece, the relationshipbetween metricpositionand melodicaccentmightlie at any point along this correlationalcontinuum.That is, the correlationbetweenmetricposition and hypotheticalmelodicaccentmayrangebetween+1 and-1. In orderto understandour researchapproach,it is crucialto considerin some detail possible interpretationsof variouscorrelationaloutcomes. Below we describe interpretationsof three circumstances:(1) statisticallysignificant positive correlationalvalues, (2) statisticallysignificantnegativecorrelational values,and (3) statisticallynonsignificantcorrelationalvalues(near zero). If we observeda seriesof momentsin a scorewhere a largenumberof known and hypotheticalaccenttypescoincided,we mightinfer(1) that the composerintendedto place especiallygreat stressat these moments,and (2) that the hypotheticalaccenttype actuallycontributes,or is thoughtby the composerto contribute,to phenomenalaccent. If we observeda seriesof momentsin a scorewhere a largenumberof known accentscoincide,but a hypotheticalaccentis systematicallyabsent fromthose momentsand appearsinsteadat othermoments,thenwe might inferthat: (1) the composerintendedto avoid especiallystrongstressesat these moments,and (2) that the hypotheticalaccenttype actuallycontributes, or is thoughtby the composerto contribute,to phenomenalaccent. In the first of the above cases, we would expectto observea significant positivecorrelationbetweenthe known and hypotheticalaccenttypes. In the second of the above cases, we would expect to observea significant negativecorrelationbetweenthe known and hypotheticalaccenttypes. Of course, a composermay changemusicalgoals from passageto passage or from work to work. That is, at one point, the composermay wish to avoid undue phenomenalaccent, and at anotherpoint, the composer may wish to create an especiallystrong phenomenalaccent. Where the composerchangesstrategyin this way, if the data are analyzedin the aggregate,then the resultis likely to be a nonsignificantcorrelationcoeffi-

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cient nearzero. However,thereareotherways of interpretinga nonsignificant (near-zero)correlation.We can inferno less than four possibleinterpretations:(1) thecomposer'saccentgoalsmayhavechangedoverthecourse of the passage,or (2) the placementof these hypotheticalaccentsis of less or little concernto the composer,or (3) the known and hypotheticalaccents are being usedfor differentpurposesby the composerand so appear to be unrelated,(4) the hypotheticalaccentdoes not exist;that is, the feature in questiondoes not producea phenomenalaccent.In addition,any combinationof (l)-(3) may resultin a nonsignificantcorrelation. Study 1: Western Folk Melodies As in the case of agogic and dynamicaccents,we mightexpect melodic accent to assist in the maintenanceor preservationof the perceptionof meter(seeJones& Boltz,1989;Jones,Boltz& Kidd,1982;Jones& Ralston, 1991). If this hypothesisis true, then a positivecorrelationwould be predicted between melodic accent and metricposition- such as the positive correlationsthat havebeenobservedboth for agogicand dynamicaccents. Becausewe haveidentifiedeightcompetingnotionsof melodicaccent,eight independentcorrelationsmay be calculated.A notion of melodic accent that is spuriouswould be expectedto have little or no systematicrelationship with the metricalorganization,and so would exhibit a correlation near zero. (However,as noted above, thereare other possibleinterpretations of a nonsignificantcorrelation.)Conversely,a notion of melodicaccent that best capturesthe presumedperceptualphenomenonwould be expectedto exhibitthe highestcorrelationwith metricposition(eithernegative or positive). SAMPLE

As an initialsample,we assembleda randomselectionof 100 vocalmelodies from Westerncultures- principallyEuropeanfolk songs. The majority of works were randomlyselectedfrom the Essen FolksongCollection computerdatabase(Schaffrath,1995). This databasecontainsmore than 6,000 melodiesencodedfrom a largenumberof traditionaland scholarly sources. The encoded data include informationconsistentwith conventional Westernnotation- includingmetersignatures,keys, badines, durations, absolutepitch(equallytemperedapproximations),accidentals,rests, ties, and phraseindications. Sincethe Essencollectioncontainsveryfew works from Britainand the United States, additionalmaterialswere randomlyselectedfrom existing databasesof Britishfolk ballads (Bronson,1959) and Americanpopular melodies by StephenFoster.In total, the sampleincludedvocal melodies

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fromBelgium,England,Finland,Flanders,France,Germany,Italy,Netherlands, Norway, Poland,Romania,Switzerland,Ukraine,United Statesof America,the formerYugoslavia,and the formerUnion of SovietSocialist Republics.The sampleworks displayeda wide rangeof metersincluding changingmeters.In orderto avoidpossibleconfoundingeffects,the works were auditedto identifysyncopatedpassages.As a result,five works were eliminated(mostlypopularsongs), and were replacedby other randomly selectedmelodies.AppendixI identifiesthe 100 songs used in the sample; metersignaturesare also identified. PROCEDURE For each note in each melody,the metricpositionwithinthe measurewas determined accordingto the traditionalhierarchyproposedin musictheory.Thosenotesfallingon the initialbeatof eachmeasurearedeemedto rankfirstin the hierarchyandmaybe designated by the value 1. Notes rankedsecondin the hierarchycoincidewith the second strongest metricpositionswithinthe measure:namely,the secondbeatin duplemeters,the thirdbeat in quadruplemeters,and the second and third beats in triple meters.The third ranked metricpositionsincludeall half-beatpositionswhereasquarter-beat positionsrankfourth. By way of illustration,the followingsequencespecifiesthe metric-positionvaluesfor successiveeighthnotes withina 4 measure:1, 4, 3, 4, 2, 4, 3, 4. correlationassumesa linearrelationshipbetweentwo variPearson'sproduct-moment ables. Consequently,the choiceof numericalcodingfor metricpositionmightbe expected to influencethe correlationalresults.In orderto explorethe influenceof alternativecodings for metricposition,threemethodswereexamined.One methodusedthe rankvaluesthemselves, althoughnegativevalueswere used in orderto assurea positivecorrelationwith coincidentmelodicaccents(e.g.,-1, -4, -3, -4, -2, ...). A secondmethodassignedmetricpositionvaluesaccordingto the reciprocalof the rank (e.g., 1/1, 1/4, 1/3, 1/4, 1/2, ...). A third method assignedmetric-positionvalues accordingto the squareof the reciprocals (e.g., 1/1, 1/16, 1/9, 1/16, 1/4, ...). Havingcalculatedcorrelationsusingall threemethods,it was foundthat the correlationvaluesdifferedlittle.The simplereciprocalcodingfor metric-positionproducedmarginallylargervalues,and so this methodis usedin the following reportedresults. Havingassigneda metricpositionvaluefor eachnote, measureswerecalculatedfor the eighttypesof melodicaccentdescribedearlier:treble,bass,registraiextreme,intervalsize, intervalascent,intervaldescent,contourpivot,andThomassen'smodel.Fortrebleandbass to its semitonedistancefrommiddle accents,eachnote was assigneda valuecorresponding C (C4).Thusfor trebleaccent,A3would be -3, F4wouldbe +5, and so on. Forbassaccent, the opposite signs would apply,hence A3would be +3, F4would be -5, and so on. For registraiextremeaccent,eachpitchwas assigneda numericvalueaccordingto its absolute semitonedistancefromthe meanpitchfor thatpassage.Forintervalsizeaccent,eachpitch was assigneda numericvaluedependingon the absolutesemitonedistancefromthe previous pitch. For intervalascentand intervaldescentaccents,each pitch was assigneda numericvalue dependingon the relativesemitonedistancefromthe previouspitch.That is, pitch distanceretaineda positive or negativesign indicatingwhetherthe pitch was approachedfrom below or above, respectively.For intervaldescentaccent,the signs were simplyreversedwith respectto those usedto measureintervalascent.In all intervalmeasurements,the presenceof a rest was deemedto interruptthe pitch contour,and so no measureswere madeacrossrests. Forcontourpivot accent,the numericvalue0 was assignedto any note that maintained the existingpitch directionor repeatedthe previouspitch; the value 1 was assignedto pitchesthatmarkeda changein direction.Note thatthe conceptof "changeof direction"is

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subtle. For example, the pitch sequence A-B-A has a change of direction coinciding with the value B. Similarly,the sequence: A-B-C-A has a change of direction on C. But consider the following two cases, where repeated pitches are added. In the sequence: A-B-B-B-B-B-B-BB-B-B-B-B-Ait might be supposed that a change of direction occurs on the first B. However, the sequence A-B-B-B-B-B-B-B-B-B-B-B-B-Chas no change of direction at all. Any purported difference between these latter two sequences presupposes a form of backward listening wherein the listener retroactively either hears or does not hear an accent associated with a long-past note. As the notion of a retrospective accent is unproven, in our measurements, neither of the two repeated sequences just illustrated would be deemed to contain a pivot tone. In the case of Thomassen's contour accent, each pitch was assigned a value between 0 and 1 according to the algorithm described in Thomassen's model. Note that Thomassen's algorithm entails a moving window containing three pitches and that the accent value for each note is determined by the interaction of three overlapping three-note contours associated with that note. Refer to Thomassen (1982) for details. All of these accent measures were determined using the Humdrum Toolkit software (Huron, 1995). In total, 10 values were calculated for each note in the sample of works, including the eight measures of melodic accent as well as the metric position value; in order to permit comparisons with agogic accent, durations were also computed for each note. For all pairs of measured values, product-moment correlations were calculated in order to measure the linear relatedness of the variables. RESULTS

The results of this initial study are presented as a correlation matrix in Table 1. Because treble accent and bass accent are simply the reverse of each other, results are shown only for treble accent. Similarly, the results for interval descent accent are simply the negative of the values shown for interval ascent accent. Each value in the matrix represents the linear similarity between the factors identified in the corresponding row and column. Of principal interest are the correlations between each accent type and metric position. In the first instance, agogic (durational) accent shows the best correlation (+.50)- a finding consistent with earlier studies. Focusing on the different hypothetical types of melodic accent, the highest correlaTable 1 Melodic Accents in 100 Western Folk Melodies: Correlation Matrix Metric Treble Interval Registrai Interval Agogic Thomassen'sContour Pivot Model Ascent Extreme Size Position +0.078 0.000 Metric Position +1.000-0.021 +1.000 +0.355 -0.076 Treble +1.000 0.000 Interval Ascent +1.000 Registrai Extreme Interval Size Agogic Thomassen's Model Contour Pivot

+0.114 -0.034 +0.190 +0.219 +1.000

+0.503 -0.062 +0.016 +0.042 +0.079 +1.000

+0.204 +0.045 +0.129 +0.111 +0.373 +0.080 +1.000

+0.013 +0.026 +0.069 +0.243 +0.290 -0.017 +0.306 +1.000

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tion is exhibited by Thomassen's model (+.20), followed by interval size (+.11). Especially poor correlations are evident for registrai extreme, contour pivot, and treble (and bass) accents. As noted earlier,because of the strong relationship between various definitions of melodic accent, we would expect to see some significant intercorrelations. The correlation matrix in Table 1 shows some expected elevated correlations. Most notable are those correlations between treble accent and interval ascent, between interval size and registrai extreme, between contour pivot and registrai extreme, and between contour pivot and Thomassen's model (the latter, r = +.31). Given the logical overlap between these measures, none of these correlations is particularly noteworthy. Perhaps the most unexpected correlation is that between interval size and Thomassen's model (r = +.37). As Thomassen's model takes no account whatsoever of interval size, this correlation suggests that the variance shared by these factors arises through their relatively high mutual correlations with metric position. A useful way of measuring shared variance is provided by multiple regression analysis. To this end, a stepwise multiple regression analysis was carried out where the predicted variable was metric position. The musical sample provided 4,550 cases for analysis. The first factor to enter the model was agogic (durational) accent, followed by Thomassen's accent, followed by registrai extreme accent. Using an entry criterion of p = .05, no other factor reached statistical significance, and so no other factor entered into the multiple regression model. The adjusted R2 value using only agogic accent was .25. After Thomassen's accent was entered into the model, the adjusted R2 value rose to .28. With the addition of the registrai extreme factor, the adjusted R2value rose marginally to .283. By itself, Thomassen's model accounts for 4% of the variance in the relationship between pitches and their metric positions. Although this is a rather small affect, the majority of the variance accounted for by Thomassen's model is entirely independent of agogic accent. None of the other proposed accent types accounts for even 0.5% of the variance. As interval size accent had shown a positive correlation greater than registrai extreme accent, its absence from the multiple regression model indicates that most of the variance described by this variable must be accounted for by either agogic accent, Thomassen's accent, and/or registrai extreme accent. A partial correlation analysis confirmed that Thomassen's model alone accounted for a remarkable 96.5% of the variance attending the correlation between interval size accent and metric position. Once again, this is noteworthy because Thomassen's model does not consider interval size. Finally, a multiple regression analysis was carried out that excluded Thomassen's model. When all other notions of melodic accents are com-

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bined, they were found to account for just 1.3% of the variancewhen predictingmetricpositionvalues(i.e., an adjustedR2of .013). By contrast, Thomassen'smodel alone accountedfor more than three times as much variance(adjustedR2of .041). In general,the resultsof this initialstudy suggestthe following conclusions: (1) Of the proposedmelodic accentsstudied,Thomassen'sexperimentallyderivedperceptualmodel shows the strongestcorrelationwith metricpositionin a sampleof Westernvocal melodies.(2) Althoughinterval size showed a modestcorrelationwith metricposition, this factor did not account for any significantamount of variancethat was not already accountedfor by Thomassen'smodel.(3) Otherproposedaccenttypesshow little or no correlationwith metricposition. (4) Althoughthe correlation for Thomassen'smodel of melodicaccentis significant,the magnitudeof the effect is small when comparedwith the correspondingcorrelationfor agogic accent.Specifically,Thomassen'saccentis roughlyone tenth of the magnitudeof agogic accent. This implies that melodic accent may be a relativelyweak factorin rhythmicperceptionand musicalorganization. Study 2: Isochronous Passages Two plausibleobjectionsmightbe raisedconcerningthe precedingstudy: one possibleproblemrelatesto the natureof the musicalsample,whereasa secondpotentialproblemrelatesto the methodof analysis. Given the comparativeimportanceof agogic accent,we ought to considerthe possibilitythat the verypresenceof agogic accentsmighttend to obscure or mask the effect of melodic accents. It may be the case that, when notes of differentdurationsare used, the resultingagogic accents dominatethe rhythmiceffect.As a consequence,composersmighttend to ignoreor overlookpossiblepitch-relatedmanipulationsthat would otherwise contributeto particularrhythmicgoals. By way of analogy,although a flashlightmayprovidea usefulway of illuminatingan object,in the presence of sunlight,theremay be little meritto addingsuch a paltrylevel of illumination.In short, the presenceof agogic accentsmay be interfering with our abilityto measurethe effectof presumedmelodicaccents.A more sensitivesearchfor evidenceof pitch-relatedaccentmightcontrol for the presenceof otheraccenttypes.Accordingly,we carriedout a secondstudy in which we soughta musicalsamplein whichthe durationalaccentswere controlled. Anotherpossibleproblemwith the foregoingstudyarisesfrom assumptions entailed by the correlationalmeasures.In pooling the data, we assumedthat all of the musicalworks in the samplesharea common use of melodic accent.The phenomenonof syncopationought to alert us to the

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fact that differentworksmay deployaccenttypesin diametricallyopposed ways. Consequently,the musicaluse of a given accent type may become obscuredwhen calculatingstatisticsfor aggregatedata. Of course,we alreadynoted that the initial samplehad been screenedto eliminateovertly syncopatedpassages.However,there may exist other forms of rhythmically contradictorygoals of which we are unaware.Consequently,a more conservativestatisticalanalysiswould focus on the resultsfor individual works or passages.In our second study,we proposedto calculatecorrelational values independentlyfor each passageand to use a simplesign test on the correlationalvaluesas a way of testingthe importanceof the various proposedmelodicaccenttypes.This analyticapproachis conservative in that it assumesthat the mannerof pitch manipulationin each passage may be entirelyuniqueto that passage. SAMPLE

In orderto control for the possibleconfoundingaffectof agogic stress, we assembleda secondmusicalsampleof passagesconsistingof long segments of equal-durationnotes. Suitable"isochronous"passageswere unearthedthrougha manualsearchof materialsin a largemusiclibrary.Most passages consisting solely of isochronousnotes are quite brief. We presumedthat in the case of shortpassagesof isochronousnotes, the preceding musicalcontext would tend to be sufficientto ensurethat the existing meter perceptionwould be maintainedthroughoutthe passage. Only in longerpassagesmightit be necessaryfor the isochronouspassageitself to be structuredso as to maintainor sustainthe appropriatemeterperception- and so revealthe use of melodicaccents.Consequently,in our selection criterion,we sought musicalpassagescontaininga minimumof 100 contiguousisochronousnotes. AppendixII identifies50 passagesused in the sample.The sampleincludespassagesfrom works by Andersen,J. S. Bach,Bartók,Beethoven,Brahms,Bull,Byrd,Chopin,Franck,Furry,Gibbons, Mahler,Morley,Mozart,Munday,Ravel,Schumann,Shostakovich, and Tchaikovsky.A sampleisochronouspassagefromJ. S. Bach'sPartita No .2 for solo violin is shown in Figure3. In orderto avoid the possibleconfoundingaffect of vocal text, we limited our selectionto instrumentalpassagesfrom orchestral,chamber,and keyboardworks.The averagepassagelengthwas 145 notes- rangingfrom a minimumof 100 notes to a maximumof 316 notes. Only sevenof the 50 passagescontainedsuccessivelyrepeatedpitches, and for these passages, the total numberof repeatedpitch instancesaveragedjusteight. Although the numberof samplepassageswas smallerthan the sampleused in Study 1, the numberof notes involvedwas considerableincreased.Some 7,382 notes were included.

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Fig. 3. An excerpt from a sample passage of isochronous music used in Study 2. The excerpt is taken from the "monophonic-solo" subsample of melodic lines, and shows measures 710 of the Gigue from Violin Partita no. 2 in D minor, BWV 1013, by J. S. Bach. All sample passages used in Study 2 consisted of extracts containing a minimum of 100 successive notes of equal duration.

In assembling this sample, we also selected passages according to their placement in the musical texture: 16 passages occur in the highest voice of a texture ("treble"subsample), 14 passages occur in the lowest voice ("bass" subsample), 10 passages occur in a midvoice position ("inner" subsample), and 10 passages occur as monophonie solos- where no other parts are present ("solo" subsample). PROCEDURE Each of the sample passages was encoded in a computer database using the Humdrum music-encoding format (Huron, 1992). The encoded data were commensurate with that of the Essen Folksong Collection used in the first study. Once again, the encoded data included pitch, duration, barlines, meter signatures, and other information. As in Study 1, measurements were made for each of the proposed accent types: treble, bass, registrai extreme, interval ascent, interval descent, interval size, contour pivot, and Thomassen's model. Because note durations were fixed, no agogic values were calculated. RESULTS

Once again, correlations were calculated between the metric position and appropriate measurements for each of the eight proposed types of melodic accent. However, correlations were calculated separately for each sample passage. The correlational results are shown in Table 2 along with a sign test for the proportion of sample passages showing either positive or negative correlations. The first column identifies the eight types of hypothesized melodic accent studied. Note that treble accent and bass accent are simply the reverse of each other- as are interval-ascent and interval-descent accents. Columns 2 and 3 provide tallies of the number of sample passages exhibiting positive and negative correlations, respectively,for each accent type. The fourth column gives the value of chi-squared where the a priori ratio of positive to negative values is assumed to be 1:1. The fifth column indicates the corresponding probability (p) for the sign test. The

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Table 2 Melodic Accents in 50 Isochronous Passages AccentType Treble Bass Registrai Extreme Interval Size Interval Ascent Interval Descent Contour Pivot Thomassen

Correlationwith MetricPosition Positiver's Negativer's Chi-Squared p 21 29 35 20 18 32 31a 37

29 21 15 30 32 18 17a 13

L28 1.28 8.00 2.00 3.92 3.92 4.08 11.52

.258 n.s. .258 n.s. .005 .157 n.s. .048 .048 .043 .0007

Meanr ^08 +.08 +.05 +.00 -.07 +.07 +.11 +.12

Note. - n.s. = not significant aTwo correlation values were zero.

final column displaysthe averagecorrelation(r) for the 50 passagesthat were studied. Fiveof the eightaccentmeasureswerefoundto yieldstatisticallysignificant results.Once again,statisticalsignificancein itselfdoes not meanthat a particularform of accent holds merit, as many of the accent types are mutuallycorrelated.In the case of trebleaccent,bass accent,and interval size accent,no statisticallysignificantresultswereobtained.In general,the magnitudesof the correlationsare small- hoveringnearzero. The best resultsare evidentin the case of Thomassen'smodel, followed closely by contourpivot accent.Of the melodicaccenttypes examinedin this study,Thomassen'sexperimentally derivedmodelshowsboththe greatest averagecorrelation(r = +.12) and the greatestsignificancein a chisquaredtest of the positive/negativeratio for the individualsamplepassages (p = .0007). Table 3 providesa breakdownof the same data accordingto the four voice positions(solo, treble,inner,and bass voices).Eachcolumnin Table 3 tabulatesthe proportionof passagesthat show positivecorrelationsversus those that have negativecorrelations.Ratiosfor the totals are given at the bottom of each column.The most strikingresultevidentin Table3 is that the only significantratio is for the "solo" subsample.(This is especiallynoteworthyin lightof the fact that the trebleand bassconditionsare basedon largersamples.)In the firstinstance,this resultsuggeststhat melodic accentsmay be more important/evidentin solo passages.Of course solo passages bear the sole responsibilityfor maintainingthe meter.In nonsolo passages,it may be supposedthat otheraccompanimentpartscan be reliedon to maintainmetricperceptions. In general,the resultsof Study2 areconsistentwith the followinginterpretations.(1) Of themelodicaccenttypesexaminedin Study2, Thomassen's

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Table 3 Melodic Accents in Isochronous Passages: Results by Voice Position Accent Type Solo Passages (« = 10)

Treble Bass Registrai Extreme Interval Size Interval Ascent Interval Descent Contour Pivot Thomassen TOTALS Chi-squared Sign Test p

Ratios of Positive/Negative Correlations Treble Passages Inner-Voice Passages (« = 16) (« = 10)

Bass Passages (« = 14)

Ï/9

ÏÏ/5

6/4

3/ÎÏ

9/1 9/1 6/4 1/9 9/1 9/1 9/1 53/27 8.45 .004

5/11 8/8 9/7 10/6 6/10 8/7a 11/5 68/59 0.64 .42 n.s.

4/6 8/2 4/6 2/8 8/2 5/4a 6/4 43/36 0.62 .43 n.s.

11/3 10/4 3/11 5/9 9/5 9/5 11/3 61/51 0.89 .35 n.s.

Note. - n.s. = not significant. aExcludescorrelation values of zero.

model and contourpivot correlatemost stronglywith the notatedmetric hierarchy.(2) Evidenceof melodic accent appearsto be most easily detectedin unaccompaniedsolo passagesratherthanin otherpassages.(3) In general,the magnitudeof the correlationsis small,suggestingthat melodic accentmay be relativelyweak comparedwith otheraccenttypes. Study 3: Ametric Passages Althoughthe resultsof Studies1 and 2 arein broadagreement,a further possibleconfoundmightbe addressed.In contrastto the largecorrelations betweennote durationand metricposition, the correlationsbetweenmelodic accentand metricpositionremainquitelow. Again,it is possiblethat any purportedmelodic accentsmight be overwhelmedby other types of accent.WhereasStudy2 endeavoredto eliminatethe confoundingeffectof agogic accent,furtherattemptsto reducethe possibleconfoundingeffect of dynamicaccentsare warranted. Even if a solo isochronouspassageconsistedof a single repeatednote, performerscould still use dynamicaccentsto establishor maintaina sense of meter.Evidenceof the use of melodic acccentswould be easierto observeif performerswere unableto conveydynamicaccents.A betterrepertoire for the studyof melodicaccentwould have the followingproperties: (1) unaccompanied,single-linemelodies,(2) long passagesof isochronous note values, and (3) performanceresourcesthat do not permit dynamic differentiationbetween notes. A candidaterepertoiremight includepas-

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sages for harpsichordor organ that consist of isochronousnote values. However, keyboardworks rarely sustain long passages of isochronous monophony. Apartfromthe useof accentsto establishor maintainthe metricalframework, we notedearlierthat accentscan also havevaluein nonmetricrhythmicgoals suchas text setting.An appropriaterepertoirewouldentailmonophonicvocal musicin ametriccontextswith littledynamicor agogicstress. A suitablesamplemay be found in Gregorianchant. Of course,the chant repertoireraises other possibleconfounds.Clearly,performershave considerablelatitudeto introduceagogic and dynamicinterpretivenuances. Some scholarshave even suggestedthat Gregorianchant mighthave been originallyperformedin some type of metricalcontext. Thesecaveatsnotwithstanding,we choseto examinea selectionof Gregorianchantmelodies. Our hypothesiswas that the melodicaccentswill tend to coincidewith the syllableonsetsin the accompanyingLatintexts. In TheLiberUsualisthe standardrepositoryfor Gregorianchant- ligaturesin the squarenotation indicate the points of syllable onset, and clarify which tones form melismas(i.e., sustainedvowel continuations). SAMPLE

The sampleconsistedof 60 chantschosenrandomlyfrom the main section of The Liber Usualis(Benedictinesof Solesmes,1963). AppendixIII gives a completelist of the chants used. Randomselectionmeant that all typesof chant(in termsof liturgicalfunction,length,mode,periodof composition, and melodicstyle)were proportionallylikelyto be represented. PROCEDURE As with the two earliersamples,the chantswereencodedin a Humdrumdatabase.Both the text and pitcheswere encodedfor each chant.Pitchwas encodedusingan octaveand pitch-classdesignationfor eachnoteheadgivenin the original(square)chantnotation.The C- and F-clefsgivenin TheLiberUsualisweretakento correspondto the pitchesC4and F3, respectively.Althoughthese fixed pitch assignmentsare arbitrary,correlationalmeasures are insensitiveto absolutenumericalvalues,and so absolutepitch heighthas no effecton the analyticresults. The texts wereencodedsyllableby syllable.In addition,eachnote was assigneda stress levelaccordingto its relationshipwith the text- as illustratedin Figure4. A highstresslevel (1) was assignedto all notes coincidingwith syllableonsets. A low stress level (0) was assignedto all notes occurringin the middleor at the end of a melisma. As in the case of the two earliersamples,measureswerecalculatedfor eachof the eight typesof melodicaccentinvestigatedin this study. RESULTS

The resultsof Study 3 are summarizedin Table 4. As in Study2, the analysispresentedin Table4 uses the more conservativesign test of the

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Fig. 4. Incipit of Alma Redemptoris Mater showing the numerical coding used in Study 3. The values 1 and 0 are assigned to notes according to whether the associated sung text is syllabic or melismatic, respectively.

correlationvalues for individualworks. Seven of the eight hypothesized melodicaccenttypeswerefoundto be statisticallysignificant.(Onceagain, this does not mean that all seven forms of accent hold merit,because,as explainedearlier,some accenttypes overlapin theirpredictions.)The best resultsare evidentin the case of Thomassen'smodel. Of the sixty chants studied,only a singlework (Ego sum resurrectioet vita) failed to show a negative correlation.Of the melodic accent types examinedin Study 3, Thomassen'smodelshowedboth the greatestcorrelation(r = -.29) and the greatestsignificance(p « .000001). In contrastto Studies1 and 2, the most strikingresultin Study3 is that the correlationvalues are overwhelminglynegativeratherthan positive. The highly significantnegativecorrelationfor Thomassen'smodel of melodic accentcannot be dismissedlightly.If the chantmelodiesdid not conform to Thomassen'smodel of melodicaccent,then one would expect to see nonsignificantcorrelationsnearzero. The robustnegativecorrelations indicatethat the melodicaccentsare systematicallyout of synchronywith the notated syllableonsets in the correspondingLatin texts. That is, the resultsrevealan endemicuse of syllable/melody-accent displacementin the chants studied. Ratherthan using the melodic accents to emphasizethe syllableonsets, musically,the resultssuggestthat the chant melodieswere Table4 Melodic Accents in Gregorgian Chant: Analysis of Individual Correlations AccentType Treble Bass Registrai Extreme Interval Size Interval Ascent Interval Descent Contour Pivot Thomassen's Model

Positiver's 13 47 29 9 22 38 5 1

Note. - n.s. = not significant.

Correlationwith SyllableOnset p Negativer's Chi-Squared 47 13 31 51 38 22 55 59

19.27 19.27 0.07 29.40 4.27 4.27 41.67 56.07

.000011 .000011 .796 n.s.