Holleran, S., Jones, M. R., & Butler, D. (1995). Perceiving Implied Harmony- The Influence of...

7/27/2019 Holleran, S., Jones, M. R., & Butler, D. (1995). Perceiving Implied Harmony- The Influence of Melodic and Harmoni

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Journal of Experimental Psychology:Learning. Memory, and CognitionIWS.Vol . 21. Nn. '3 , 7.17-751Copyrisht 1995 by the American Psychological Association. Inc.0278-7393/95/S3.00

Perceiving Implied Harmony:The Influence of Melodic and Harmonic ContextSusan Holleran, M ari Riess Jones, and David Butler

Ohio State UniversityTwo experiments investigated th e influence of m elodic and harmonic context on the obviousness ofpitch changes in 3 Western tonal melodies. In Experiment 1, listeners with different levels ofmusical skill heard standard melodies followed by comparison melodies in which single pitchchanges could occur. In-key pitch changes that were not implied by the local harmony were judgedmore obvious than in-key pitch changes that were so implied. This effect was influenced by thesurrounding context of melodic line and chords and was absent when the context contained chordsthat were not consistent with the harmony implied by the melodic line. In Experiment 2, withsimilar listeners, implied harmony effects were eliminated by removing parts of the melodic line,indicating the relative importance of melodic context as a determinant of implied harmony.Questionnaire data suggested that knowledge of tonal relationships was tacit, even in many trainedlisteners.

The influence of context on linguistic inference and its rolein resolving phonological, syntactic, and lexical ambiguity havebeen extensively explored in research on language comprehen-sion. Although the mechanics and time course of contexteffects remain controversial, their existence and strength arewell established (see, for example, Gorfein, 1989; Graesser &Bower, 1990). Less is known about the influence of context onmusical inference. This is surprising because, at any level ofanalysis (e.g., note, chord, and key), the interpretation of amusical event seems eminently context dependent. For ex-ample, in music the individual sound unit (which might parallela speech phoneme), namely a tone, takes on different mean-ings in different contexts. An elementary example of a musicalcontext, one often termed a tonal context, is found in theordered subset of pitches known as a musical scale.1 Typically,the first note of a scale is its keynote, meaning that it functionsfor a listener as a cognitive anchor with respect to otherpitches. Among other things, identification of a keynotedefines for the listener a particular tonal context (or key). Forexample, the familiar C major scale has ordered pitches C, D,E, F, G, A, B, C, with a keynote pitch of C. The contextdependency of music quickly becomes apparent, however, withanother common scale, the F major scale (F, G, A, Bb, C, D, E,

Susan Holleran and Mari Riess Jones, Department of Psychology,Ohio State University; David Butler, School of Music, Ohio StateUniversity.This results of Experiment 1 were reported at the November 1991meeting of the Psychonomic Society in San Francisco.This research was supported inpart by a grant from the Center forCognitive Science of Ohio State University toDavid Butler and MariRiess Jones. We are indebted to Angie Fankhauser, Lisa Schmakel,Rocki Strader, Elizabeth Zinober, Mark Peter, and Leo Schmidt fordata collection and also to Caroline Palmer for comments on a versionof this article.Correspondence concerning this article should be addressed to MariRiess Jones, Department of Psychology, Ohio State University, 1827Neil Avenue, Columbus, Ohio 43210. Electronic mail may be sent viaInternet to [email protected].

F'). Notice that in this context, the cognitive anchor is now thepitch F. Further, in this tonal context, C becomes the fifth scalemember, meaning that its function has been transformed froma keynote to a dominant pitch (i.e., the fifth scale note of Fmajor). In these two tonal contexts, the pitches F and C changetheir meanings. This can also be seen in special three-notegroups drawn from the two scales, for example, C-E-G andF-A-C. Musically, such groups correspond to a level ofanalysis analogous to morphemic or word units in language.When such pitches are sounded together, as a simultaneousgroup, they form harmonic relationships known as chords (seeFootnote 1). Again the issue of context arises in interpreting

1 A fundamental musical scale is the equal-tempered chromatic set,which consists of twelve pitches spaced in equal logarithmic steps(semitones, for example, adjacent notes on the piano keyboard)bounded by a 2:1 (or octave) frequency ratio. Diatonic scales can beconceived as seven-pitch subsets of the chromatic scale in whichdistances between successive pitches are prespecified by patterns ofsemitones (s; half steps) and whole steps (w = 2 s). Major diatonicscales are named according to their first scale degree, and subsequentscale degrees are defined by the pattern w w s w w w s. Scale degreesare given special names reflective of their importance in the scale: forexample, thefirstscale degree is the tonic, and the fifth, the do minant.In the text, we refer to the tonic scale degree as the keynote. The termstonic and dominant arealso assigned tochords built on thefirstandfifth scale members (degrees), respectively. As defined in this study,explicit chords are groups of tones that are separated in pitch byprescribed scale intervals and played simultaneously, implicit chordsare sequences of tones that are heard asperceptually grouped. Eventhough a scale may contain notes that a re not found in a given musicalpassage an d, conversely, a tonal passage may contain notes not foundin a given musical scale, musical passages in which pitches largelyconform to a particular scale and follow certain conventions (to bediscussed later) are commonly said to be in the key with the same nameas that scale. Thus, a tonal passage is one in which a single pitchfunctions as a psychological reference frame for other pitches withinboth that scale set and related scales. The system of tonal harmonyaims to describe the interactions of simultaneous and successivepitches (chords and melody) within this framework.737


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738 S . HO LLE RAN . M. JON ES . AND D. Bl 'T l .E Rthese harmonic units. Although both of the chords C-E -G andF-A-C appear in C and F major scales, they mean differentthings in the two tonal contexts. When the C of the C-E-Gchord is identified as a keynote in the C major scale, thenC-E-G is a I chord.2 This chord thus implies that C is itscognitive ancho r. How ever, when the pitch C is the fifth note ofthe F major scale, then C -E -G becomes a V chord. In thiscontext, F functions as a cognitive anchor. In short, contextdependency is evident at several levels of musical analysis.

Meaning conventionally arises from inferences an individualmakes about something to effectively place it within a largerdomain. Musical meaning, as we use it here, refers to infer-ences listeners make about events, such as single tones orchords, that place them within a larger musical context. Suchinferences are possible because these events consist of units atone level of analysis that carry implications about specificreferents at another level: for example, what key (if any) isimplied by a particular chord (e.g., C-E-G), or what chord (ifany) is implied by a given tone (e.g., C). As previouslydiscussed, a tone or chord by itself is ambiguous and canparticipate in several different chords or keys; its meaningmust derive from aspects of its context. However, in actualmusic, this context seldom consists solely of sequences ofchords, or of tones arrang ed in musical scales. Rather, musicalcontext is dynamic and relational, comprising patterned se-quences of melodic pitches and chords that permit listeners toanticipate certain forthcoming chords and pitches (Butler &Brown, 1984; Jones, 1981, 1990; Lerdahl, 1988; Narmour, 1990,1992). In Western tonal music, various chord patterns realizechanging harmonies, with each chord constituting a localharmonic unit. Some chord sequences are common, such asI-V-I, whereas others are quite uncommon, such as V-FV-IH(Piston, 1987). Listeners genera te harm onic expectancies con-forming to the more common chord patterns (Schmuckler,1989). Together with the musical conventions outlined abovewhich relate pitches of individual tones to chords, and chordsto keys, the principles governing the patterning of suchharmonic relationships can be considered a tonal "grammar."Applying such a grammar to a simple C major melody revealshow its dynamic context perm its meaningful anticipa tions offorthcoming elements. Imagine a tune that opens with athree-note melodic sequence, say C-E-G; recall that thesepitches form the I chord in the key of C major. If this melodycontinues, such that the next three pitches are drawn from theset B, D, G (from the V chord), then knowledgeable listenersmight expect the following ones to be derived from the I chord(C , E, G). This is because the example melody is based on asuccession of pitches that is consistent with the common chordsequence I-V-I. Thus , if listeners with knowledge of the tonalgrammar can infer from the melody one (or more) of theseinitial chords, then they may also be able to infer thatsubsequent tones are consistent with this chord sequence, inspite of the fact that such pitches, taken out of context,logically imply several alternative chords or keys. There issome evidence that listeners' expectancies about underlyingchords do influence their judgments about the strength of asense of key in melodies (e.g., Boltz, 1989a, 1989b, 1991;Brown, 1988; Brown & Butler, 1981; Butler, 1989; Butler &Brown, 1984). However, this example assumes that listeners

knowledgeable about musical convention1; should actually heable to track the pattern (if harmonic relationships implied by amelody, inferring various chords at different points within it.On this topic there is no current evidence.Our research considered whether people could infer theappropriate chord from pitch eleme nts of an unfolding m elody.We had three goals. The first was to assess whether listenerscould make reliable harmonic inferences on the basis ofindividual tones within a changing tonal melody. Our secondgoal was to examine contextual prop erties, both harmonic andmelodic, that might affect the strength of these inferences, ifthey exist. The final goal was to determine how listeners withdifferent levels of musical knowledge differed in their inference-making abilities.To achieve the first goal we used typical Western tonalmelodies to assess listeners' sensitivity to melodic changes thatconform to or conflict with commonplace local harmonicimplications. Local harmonic implications are those gen eratedby a small group of neighboring tones within the overallmelody; here, we call such groups measures, with each measurecomprising three or four tones and suggesting a chord consis-tent with its tones. We can distinguish two forms of localharmony: explicit and implicit. Explicit local harmony refers tothe case in which a chord is actually sounded as an accompani-ment to the melody in that measure. Implicit local harmonyrefers to the case in which a chord is not sounded, but themelodic pitches within that measure imply it; that is. if thosepitches had occurred together, they would form that chord.Some theorists contend that listeners routinely make localharmonic inferences, even when the melodic line does notcontain all members of an implied chord (e.g., Dahlhaus,1965-1966/1990; Piston, 1987: Schenker, 1979). Others havequestioned this time-honored opinion (e.g., Povel & vanEgmond, 1993).We used a standard-comparison task to determine listeners'sensitivity to changes in local implied harmony. Listenersheard two patterns, a standard and a comparison, that weresimilar in that they contained the same basic melody andexplicit chords. In fact, the comparison pa ttern differed fromits standard only with respect to the pitch of one tone. Thispitch change was always an in-key pitch change. The catch isthat the new pitch either conformed to or conflicted with themelody's local (implied) harmony in that measure. When itconformed to the harmonic implications of other pitches inthat m easure, the pitch change was an implied (I) one; when itdid not fit with these harmonic implications, the pitch changewas nonimplied ( NI) . If listeners monitor pa tterns of changingharmonies (implicit or explicit) that occur in the surroundingcontext, then they should judge comparison patterns with NIpitch changes to differ more from their standards than compari-sons with I pitch changes. The reason for this is that if listenersinfer the chord implied at this point in the melody, then the NIpitch change will "stand out" as a violation of their expectancies.To achieve our second goal, we considered aspects of thelarger context that influence listeners' abilities to monitor

2 Symbols for musical chords appear in bold to distinguish themfrom abbreviations in the text.


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IMPLIED HARMONY 739changing harmonic information. We assumed that tracking amelody is affected by its overall tonal clarity, namely thedegree to which it follows conventions (described above) thatspecify chord sequences within an established key. When atonal melody is accompanied by explicit chords that reinforceits key, this should provide a clear tonal context; by contrast,tonal clarity is reduced if the melody is accompanied by chordsthat do not reinforce the key. We also considered the possibil-ity that a melodic line, taken by itself, can convey importantharmonic information, and hence tonal clarity should begreater when a melody is intact than when it is not.

A number of current approaches address the influence oftonal context on musical inferences at various levels (e.g., tone,chord, and key levels; Krumhansl, 1990; Krumhansl & Kessler,1982; Shepard, 1982). Krumhansl has maintained that a "tonalhierarchy" scheme summarizes acquired musical knowledge.With this knowledge, listeners can make inferences about agiven pitch and its relative stability within a contextuallyestablished key level (Krumhansl, 1990; Krumhansl & Kessler,1982). Others have relied on associative networks and patternsof network activations to model different levels of pitchrelationships that figure in harmonic implications (e.g., Bha-rucha, 1987, 1991; Gjerdingen, 1990, 1992). Thus, Bharuchaproposed a tonal network scheme in which tones activate thelowest level units, which are tuned to pitch equivalence classes.Harmonic inferences about specific chords come about whenlower level units (e.g., single pitches) activate associative linkswith higher level chord units. These units are, in turn, linkedhierarchically to still higher key levels in a way that alsopermits downward activations from a key-based tonal scheme.

All of these views suggest that a tonal scheme, which linksunits across hierarchical levels, underlies tonal clarity; thus,tonal clarity should be greater when melody and chords arelinked by the same key. Further, a tonal scheme should morereadily assimilate to itself those elements that are stronglylinked across levels (i.e., implied) than ones that are weaklylinked (nonimplied). Supporting evidence for these viewscomes largely from research that addresses inferences at thelevel of key (e.g., Krumhansl, 1990; Krumhansl & Kessler,1982) and chord (e.g., Bharucha & Stoeckig, 1986; Tekman &Bharucha, 1992). In addition, findings that out-of-scale pitchchanges are more noticeable than in-scale pitch changes inmusical contexts (e.g., Cuddy, Cohen, & Miller, 1979; Dowling,1978; Frances, 1958/1988) are explained in terms of schemeassimilation at the level of key.

Nevertheless, Povel and van Egmond (1993) disputed thetonal scheme hypothesis, and the idea of harmonic inference.They presented to their listeners standard-comparison pairs ofnine-tone melodies; in some trials, only the melodic tones wereplayed, whereas in others, each of the nine melodic tones wasplayed with an accompanying chord. Each of the chordscontained the melodic tone that it accompanied, but some ofthe sequences of chords used as accompaniment were arbi-trarily chosen and did not consistently follow the conventionsof the tonal grammar. Listeners were asked to detect pitchchanges in the melodies of the comparison patterns, and theirperformance was not affected by the type of chordal accompa-niment used. Accordingly, Povel and van Egmond proposed anindependence hypothesis, which asserts that melodies are coded

strictly in terms of steps along a musical scale in a given key.and independently of explicit or implicit chords. Thus, theindependence hypothesis casts doubt on the existence of localharmonic inference in any tonal context.

Some findings of Platt and Racine (1994) are relevant to theindependence hypothesis. They used nine-tone melodies inwhich the first eight tones all derived from the same three-notechord; thus, local harmonic implications of successive pitchgroups remained constant across these eight pitches. Listenerswere to decide if a ninth (target) pitch resulted in a change inharmony. When the target pitch was a member of a differentchord, most listeners were able to determine that a change inharmony had occurred. Thus, these data are contrary toexpectations that are based on an independence hypothesisbecause they suggest that in certain melodic contexts listenersare sensitive to harmonic implications. However, because agiven chord can occur in multiple keys, these melodies may nothave been heard as occurring in a specific key, a prerequisitefor the independence hypothesis. Our design used explicitlytonal melodies (i.e., in a specific key). In addition, unlike thedesign of Povel and van Egmond (1993). in our design thesemelodies were built on conventional, not arbitrary, impliedchord progressions. We therefore not only provide a test of theindependence hypothesis but also assess whether listeners candraw timely harmonic inferences from a tonal melody withlawfully changing harmonic implications.

Our third goal involved comparisons of the performance oflisteners with different levels of musical training. Most theoriesimply that sensitivity to implicit chords should increase withtraining; therefore, it seems reasonable that musicians willshow greater sensitivity to pitch changes (including harmoni-cally implied ones) than nonmusicians. In fact, the literature isnot unequivocal on this point. In some cases, less musicallyskilled participants produced patterns of discrimination simi-lar to those of musicians, although performance was poorerand more variable (e.g., Cohen, Trehub, & Thorpe, 1989;DeWitt & Samuel, 1990; Monahan, Kendall, & Carterette,1987; Smith & Cuddy, 1989). In other tasks, level of musicaltraining did not significantly affect performance (Cuddy et al.,1979). Where differences did emerge, the favored interpreta-tion assumes that musicians possess better developed tonalschemes (Monahan et al., 1987) or more efficient higher levelencodings (Cohen et al., 1989). In these cases, such interpreta-tions raise questions about the role of acquired tonal schemesin harmonic inference, as the recent work of Trainor andTrehub (1992) illustrated. They compared detection of dia-tonic (in-scale) versus nondiatonic (out-of-scale) pitch changesin brief melodies by using both infant listeners and adultsvarying in musical skill. Diatonic changes in a comparisonmelody formed a greater pitch interval from the standard thandid the nondiatonic changes, yet adult listeners had greaterdifficulty detecting the in-scale changes; 8-month-old infantstested on the same patterns detected both change typesequally well. (In fact, in conditions in which both groups weregiven training with nondiatonic changes, adults were actuallyworse than infants at detecting diatonic pitch changes.) Over-all, there was no relationship between adults' performance andtheir level of musical skill. Trainor and Trehub suggested thatall adults had more difficulty discriminating diatonic changes


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740 S. HOLLERAN. M. JONES. AND D. BUTLERbecause these "fit" readily into tonal schemata acquiredthrough exposure to Western musical structure. Becauseinfants lack such schemes, they showed no difference insensitivity to diatonic and nondiatonic pitch changes.These studies raise the following question: What role doesmusical training actually play in the ability of skilled listenersto detect certain tonally consistent implications? If the in-creased exposure to Western tonal structures afforded bymusical training results in better developed tonal schemes,then in the present research high-skill participants may actu-ally find the harmonically implied changes less obvious thanlow-skill listeners. Alternatively, if both groups of listenershave acquired these tonal schemes (low-skill listeners presum-ably by listening to Western music), then they should performsimilarly in judging I versus NI changes.

Another facet of acquired knowledge concerns whether it istacit knowledge. If listeners' performance is shaped, in part, byprinciples of tonal gramma r, are tonal inferences verbalizable?Most of us who enjoy music cannot articulate its principles.However, research on tacit knowing has not addressed themusical domain; instead it typically relies on categorization orwell-formedness (grammaticality) judgments of artificially gen-erated serial pattern s (e.g., Reber, 1989; Reber, Kassin, Lewis,& Cantor, 1980; Reber, Walkenfeld, & Hernstadt, 1991). Thegrammars of choice have been Markovian finite state gram-mars, in part because of their potential for generating complexsequences (for a discussion see Jones, 1974). The usual findingis that people's categorizations reveal abstract knowledge ofthese probabilistic gramm ars, with postsession questionnairesindicating that they cannot articulate this knowledge. Rebermaintained that implicit knowledge of complex rule systems isacquired "in the absence of conscious, reflective strategies tolearn" (Reber, 1989, p. 219). The rules of Western tonalharmony are not Markovian, but they must be at least ascomplex because they incorporate elements of uncertaintywhile remaining basically relational in nature. As such theyshould offer a basis for implicit knowledge. The typical musiclistener presumably has not engaged in a conscious andreflective strategy to learn these tonal grammars. There fore, ifaverage listeners have acquired a tacit knowledge of the tonalgrammars through general enculturation, then they should beable to reliably detect differences between changes that areharmonically implied and those that are not implied; at thesame time, they should be unable to describe the rules theyuse. On the other hand, it is possible that listeners with moretraining will have greater ability to articulate grammaticalrules, but they will not necessarily have enhanced ability todetect harmonically consistent pitch c hanges. Accordingly, wequestioned listeners in both skill groups about the propertiesof the pitch changes they heard.

Exper imental Rat ionaleIn these experim ents we used a standard-comparison task inwhich an in-key pitch change could occur somewhere in acomparison pattern, with this change representing either ashift in local harmony or no such shift. Two primary manipula-tions corresponded respectively to the type of pitch change andto the context surrounding a pitch change.

The type of pitch change was manipulated relative to themelodic structure of standard and comparison patterns. Allmelodies followed conventional tonal grammar rules in thatcommon chord arrange ments dictated the harmony implied bypitches within successive measures. For example, a standardmelody in A major is shown in Figure 1 (top ); it opens withthree pitches in the first measure (C #5 , E5, and A4, where thenumeral indicates the octave; C4 is middle C) that imply a Ichord. Over the eight measures of the melody, successivemeasures contain similar groups of pitches, each implying aplausible (missing) chord. The key and the chord sequencespecify "what" chords should occur (i.e., those in A major) and"when" they should occur (given a common chordal se-quence). In the comparison versions of this melody, a singlepitch change can occur in one of several test measures. In thisexample, the third test measure illustrates the target changemanipulation. It comprises three pitches (B4, E5, and G#4),with G#4 as the to-be-altered target. Together these pitchesimply the V chord in A major. Given this, one of three types oftarget change can occur (Figure 1, top). A target can be thesame (S) pitch as in the stand ard, or a new pitch that reinforcesthe harmony of the V chord, an I change, or a new pitch thatconflicts with that harmony, an N I change. With the I change,G#4 becomes E4, another pitch in the V chord, and with theNI change, it becomes F#4, a pitch that is not in the V chord.Note that both F#4 and E4 are in the key of A major.However, the I pitch change results in a comparison patternthat preserves the local harmony of its standard, whereas theNI change does not. If listeners perceive a melody in terms ofits harmonic implications, then NI changes should seem moreobvious than I changes; furthermore, the extent to which theobviousness of the NI changes exceeds that of the I changesshould reflect the strength of harmonic implications. Con-versely, if listeners perceive the melodic line independently ofany chordal implications, then they may respond only todifferences in the pitch intervals created by the target changes.In this case, because NI changes always result in a smallerchange in pitch interval from the standard than do I changes,NI changes may seem less obvious than NI changes.

Two aspects of context are considered to contribute to tonalclarity: Melodic context, which consists of all melodic pitchesforming a continuous melodic line (excluding the test mea-sure), and harmonic context, which refers to explicit chords thatsurround the test m easure. Figure 1 shows the m elodic line(top) and the same melody in three harmonic contexts (bot-tom); in this figure, melodic context does not vary. In the firstcontext (control), the melody has no chordal accompaniment;in the other two contexts (which we refer to as consistent andnonconsistent), explicit chords are present. In the consistentchord condition, the chords that accompany the melody are inA major, the key of the melody, and they support its changinglocal harmo nies: Each chord is implied by the pitches app ear-ing within that measure of the melody, and in most casesactually consists of those same melodic pitches. Notice thatchords are never present in test measures; harmonies in thesemeasures are always implicit. In the nonconsistent chordcondition, the accompanying chords realize the harmony of adifferent key, G major; in this condition, many pitches in thesechords do not correspond to those in the melody. However, in


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IMPLIED HARMONY 741TestMeasure 1 TestMeasure 2 TestMeasure 3

Impl ied Chords(A M ajor): V I V 7 IT Y PE S OF T A R GE T C HA N GE :

Same: No Target Change (S) I f' (j(J)liG

Implied Target Change (I) | P' [? A |

C ON T E X TC ON D IT ION S: Non lmplied Target Change (NI) | Ft

g n r LiConsistent Chords

(A M ajor)(I

NonConsistent Chords

(0 Mjor)( ii

i *

i

I

Figure 1. A standard melody along with three target changes (S, I, and NI) is shown. Also shown arecontrol, consistent chord, and nonconsistent chord contexts. Asterisk denotes an inverted chord.

both cases, within their respective keys the consistent andnonconsistent chords follow identical chord sequences typicalof the Weste rn tona l grammar (Piston , 1987) . Furthermore ,target pitch changes (I and NI), when they occur, are alwayspitches that are in the key of the melodic line (A major) andalso in the key of the nonc onsistent chords ( G major).

This design perm its assessmen t of l isteners' use of context todisambiguate a melody's local harmonic implications. Recallthat the independence hypothesis predicts that l isteners useneither explicit nor implicit chords to do this. By contrast, weassume that tonal clarity provided by these contexts shouldsystematically affect the strength of harmonic implications.Tonal clarity is greatest in conditions predicted to be leasttonally ambiguous. Thus, the consistent chord conditions, inwhich key-consistent information is provided jointly by a

melody and its chords, should provide greatest tonal clarity.For example, in this condition both m elodic and chord contextunambiguously specify the key of A, meaning that a majorchord, such as E - G # -B , will function in a test measure as a Vchord and not, say, a I chord. This reduction in tonal ambiguitysuggests that in such contexts pitch changes that do not fit (NItargets) within this local harmony should be much moreobvious than ones that do fit (I targets), relative to contextswith greater tonal ambiguity. The nonconsistent chord condi-tions supply greater ambiguity about key and hence about thetonal function of a given chord; accordingly, if tonal clarityinfluences harmonic inferences, then differences between NIand I targets should be smallest in this condition. Finally, thecontrol condition, which presents an unaccompanied butcontinuous melodic line, is interesting because it implies the


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742 S. HOLLERAN. M. JONES. AND D. BUTLERsame information about key and chord progression that isexplicit in the consistent chord condition. This conditionperm its an evaluation of the claim that a melodic line conform-ing to the rules of the tonal gramm ar is alone sufficient to implyits "missing" ch ords.In two experiments we considered the relative influence ofharmonic and melodic context on listeners' tendencies to makeharmonic inferences. In both studies we sampled from popula-tions of listeners with different degrees of musical training. Inthe first experiment, tonally coherent melodies containedin-key pitch changes that were congruent with harmonicimplications of the melodic line (S or I) or that conflicted withthese implications (NI). Different groups of listeners wereasked to judge the obviousness of such changes in threerespective chord contexts. In the consistent chord context,melodies were accompanied by chords that reinforced themelodic line; in the nonconsistent chord context, accompany-ing chords did not reinforce the melodic line; and in a controlcondition, no accompanying chords were presented. In thisexperiment, we anticipated that listeners would find N I changesmost obvious, especially in the consistent chord context. In thesecond experiment, the coherence of the melodic line wasdisrupted by removing some par ts of it that did not contain therelevant pitch changes. In all other respects the experimentaldesign pa ralleled that of Experiment 1. In Experiment 2, weanticipated that if listeners rely more heavily on surroundingchords to make harmonic inferences than on a continuousmelodic line they would perform as in Experiment 1. In bothexperiments, if musical training desensitizes listeners to changesthat fit a tonal scheme, then listeners with more musicaltraining should find the I changes less obvious than wouldlisteners with less training.

Experiment 1In the first experiment we presented musical patterns thatdiffered in harmonic context to different groups of listeners.Some listeners (controls) heard standard-comparison pairsthat were strictly based on monophonic (unaccompanied)melodies; others heard the same melodic line accompaniedeither by consistent chords or by nonconsistent chords (seeFigure 1). Explicit chords never appeared in potential testmeasures, which were always Measures 2, 4, and 6. Both thetest measures of a given melody and its entire melodic linewere identical in all three context conditions.We a ddressed several questions in this experiment. First, weasked: A re listeners sensitive to local harmonic implications inthese contexts? If so, then we would expect to find that NI

targets are judged more obvious than I targets, overall. Second,does the tonal clarity of a musical context affect the strength ofharmonic implications? If so, then we would expect to find aninteraction of type of target change with harmonic context:The greatest difference between obviousness ratings of I andNI target changes should occur in the consistent chordconditions, and the smallest difference between judgments ofNI and I targets should occur in the nonconsistent conditions.Third, do these effects, if they exist, hold for all listeners?Specifically, are listeners with more musical training moreresponsive to implied harmonies than those with less training,

perhaps because they are less sensitive to pitch changes thatpreserve the local harmony? If so, then we would expect to findinteractions of skill level with these variables. Alternatively, ifhigher skilled listeners perform equivalently to less skilledlisteners with respect to target changes, we should find no suchinteractions. Finally, assuming that obviousness ratings reflectsensitivity to the implications of tonal grammar, we assessedthe extent to which these ratings, together with after-sessionquestionnaire responses, reveal tacit knowledge.Method

Participants. A total of 66 participants served in Experiment 1; 36qualified as low-skill listeners, and 30 as high-skill listeners.Low-skill listeners from introductory psychology classes at OhioState University volunteered to participate in return for course credit.All had at least 5 years of musical experience (defined as playing in aband or o rchestra, singing in a choir or chorus, or taking private lessonson an instru men t), but none had extensive formal musical training, andnone were music majors. The mean number of years of private lessonson the participants' primary instrument was 5.7. Fifteen of theparticipants had additional experience on a second instrument, with anaverage of 3.9 years of formal training.High-skill listeners participated in the study in return for monetaryreimbursement (each received $6.00). All were professional m usiciansfrom the Columbus, Ohio, area, graduate students in music at OhioState University, or undergraduates who had completed or werecurrently enrolled in the second year in a two-year sequence of auraltraining courses required for the music major at Ohio State University.Participants had a mean of 8.74 years of formal training on theirprimary instrument; 23 had formal training on a second instrument,with a mean of 6.41 years.

Design. The design was a 2 x 3 x 2 x 3 x 3 mixed factorial. Thetwo within-subject variables were target change (same, implied, andnonimplied) and melodic instance (1, 2, and 3). The three between-subjects variables were musical skill level (low and high), context (con-trol, consistent chords, and nonconsistent chords), and counterbalanceorder (1 and 2), yielding a total of 12 (2 x 3 x 2) different between-subjects conditions. Participants from each skill level were randomlyassigned to each of the remaining 6 between-subjects conditions.Apparatus. Stimuli were generated by the MIDILAB softwaresystem (Todd, Boltz, & Jones, 1989), through a Yamaha TX81Z FMtone generator controlled by an AT-2000 computer. Stimuli wererecorded on a Nakamichi LX-3 cassette deck onto professional-qualitycassette tapes, and played to participants on a Nakamichi 550 cassettesystem, amplified by a Kenwood KA-5700 stereo integrated amplifier,through AKG K240 headphones at a comfortable listening level.These levels could vary according to listener, but none were less than65 dBA or greater than 75 dBA (GenRad sound-level meter model1982).Materials and conditions. Three different core melodies (melodicinstances 1, 2, and 3) were developed and then modified to includechordal accompaniment (context manipulations) and target notechanges (target change). All three melodies were generated byfollowing elementary rules of the tonal grammar (Berkowitz, Fron-trier, & Kraft, 1986; Piston, 1987). One of these melodies appears inFigure 1; all three are shown in the Appendix. They were generated torepresent a selection of common chordal arrangements, with eachusing a distinctive serial pattern of chords (implicit or explicit). Theyobserved the following constraints: (a) All were eight measures long;(b) all contained the I chord, thus implying the keynote, in the firstandlast measures; (c) all were in the same key (A major); (d) the melodicsequence of each measure implied some chord (not necessarily thesame chord) in the key of A major; (e) all chord progressions (explicit


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IMPLIED HARMONY 743and implicit) followed conventional rules over the eight measures; (f)melodic lines included no pitch skips greater than an octave andminimized the number of unisons (immediately repeating notes); and(g) all pitches were realized as sine tones. With respect to timingconstraints, all melodies manifested (a) a V, time signature; (b)nonisochronous rhythms with the possibility of five different notedurations: eighth note, quarter note , dotted quarter note, half note,and dotted half note; and (c) a final lengthened note (dotted half).These core melodic instances served as the basis for developing thefollowing three context conditions (see Figure 1):

1. Control co ntext involved strictly monophonic melodies; that is, noexplicit chords were present.

2. Consistent chord context involved homophonic (accompanied)melodies in which three- or four-pitch chords (sometimes in invertedforms) from the key of A major were sustained for the duration of ameasure in Measures 1, 3, 5, 7, and 8 of all three instances. For eachmeasure, the chords presented were consistent with the key of the melodicline and in fact reinforced the implied harmony of each measure.

3. Noncon sistent chord context involved hom ophonic tunes in whichthree- or four-pitch chords from the key of G major occurred for theduration of a measure in Measures 1, 3, 5, 7, and 8. In this condition,explicit chords were not consistent with the key of the melodic line. Allchords were exact transpositions of the A major chords of theconsistent chord condition to G major for that melodic instance.

Several precautions were taken in introducing the chords in theconsistent and nonconsistent chord conditions: (a) All tones withinchords were sine tones, (b) onsets and offsets of tones within eachchord were slightly asynchronous (i.e., beginning 10 ms later thanmelodic pitches at the beginning of the measure) to create a morenatural sound, and (c) chord intensities were adjusted to be softer (bybetween 4 to 6 dB) than the melodic line, but always distinctly present.

The core melodic instances served as standard melodies in astandard-comparison task for a given context condition. To increasetask difficulty and to encourage listeners to attend to transformationalaspects of the tunes, we played all standard sequences faster (.8 beatperiod) and higher (one octave) than their respective comparisonsequences. Specifically, quarter notes in standard and comparisonsequences corresponded, respectively, to stimulus onset asynchronies(SOAs) of 320 (312 ms on and 8 ms off time) and 400 ms (390 ms onand 10 ms off time). Standard sequences began in the fifth octave andcomparisons in the fourth (where C4, or middle C , is located).

Three d ifferent kinds of comparison tunes, corresponding to levelsof the target change variable, were created for each context condition:5, I target change, and NI target change. The S comparisons incorpo-rated no target changes. The other two conditions incorporated asingle in-key changed pitch (target) that could occur in one of the threemeasures in tunes that contained no explicit chords: Measures 2, 4, or6. The I comparisons included in-key pitch changes that were in theimplied chord of the test measure. The NI comparisons used in-keypitch changes that were not in the implied chord of the test measure.Local melodic context was identical across all manipulations of targetchange and global context; together with the changed pitch, other testmeasure tones always formed a prominent in-key chord in the Iconditions but not in the NI conditions. In the NI conditions, testmeasure and target tones d id not form a chord in all melodic instancesand test measures except one: In melodic instance 2, test measure 2,the NI change formed a part of a II chord in A major, a highly unlikelychord given this key and chord context (Piston, 1987). (In fact, thelatter might be expected to reduce the p redicted I versus NI difference,thus working against predictions about implied harmony.) Finally, Itargets always formed a larger pitch interval difference from thestandard than did NI targets.

Additional constraints determined targets: (a) A target could notbreak the m elodic contour of the seq uence; (b) a target could not forman immediately repeating tone within the sequence; (c) targets were

always quarter notes (400-ms SOA); (d) targets always replaced thefinal note in a test measure; (e) targets and test measures wereidentical across the three context conditions; and (f) for each of thethree melodic instances, only two of the three potential test measureswere functional test measures. Thus, for a given melody, a pitchchange could occur in either of two of the three measures that weredesignated test measures. (The unused test measure in each melody islabeled as such in the Appendix.) This constraint insured greateruncertainty with respect to target location.

Eighteen standard-comparison pairs were construct ed: 6 S pairs, fi Ipairs, and fi NI pairs . Each melodic instance had two different targetlocations for each of the two changed-note conditions (3 x 2 = 6pairs) ;for S pairs, each melodic instance occurred unchanged twice. Twodifferent counterbalance orders (1 and 2) arranged sequence pairswith the following constra ints: (a) N o melodic instance followed itself;(b ) pairs that occurred in the first half of one counterbalance orderwere assigned to the second half of the other, minimizing the occur-rence of the same sequence in both counterbalance orders; and (c) nomore than two S or changed target sequences could occur in a row.

Procedure. Participants were run in groups of 1 to 4. Recorde dinstructions explained that they should rate each of the standard andcomparison pairs of sequence s. Listene rs heard 21 trials in all; the first3 trials consisted of all three melodic instances played with samecomparisons. These trials were not scored. Participants were told thatthe second sequence could sometimes contain a changed note in itsmelodic line; in consistent and nonconsistent context conditions it wasstressed that if a pitch change occurred it would never occur in th echordal accompaniment but always in the higher p itched melodic line.Participants used a 7-point scale (6 = very obvious change, 1 = lessobvious change, and 0 = same or no change) to indicate detection of amelodic change and to rate its obviousness. They were specifically toldto use a 0 rating whenever they thought the comparison melody wasthe same as the standard. Following this, the participants received twopractice trials using a different melody in a similar style (comparisonswere respectively same and different) and received feedback withregard to their responses; at this time, experimenters clarified thatuniform shifts of a comparison's tempo and overall pitch level were notrelevant to the task.

Each trial began with a high-pitched (D7; 2349 Hz) 1-s warningsignal followed by a 2-s silence and then a standard pattern. T hecomparison sequence occurred 2 s after the offset of its standard.Following this, listeners were given 5 s to respond, in writing, beforethe warning tone sounded for the next trial.

After the session listeners filled out two questionnaires. The firstcomprised six questions probing their understanding of the musicalstructure manipulations. They were asked (a) if they noticed morethan one kind of (target) change and if so to explain the differences,(b) how the change affected the sound of the comparison, (c) to statespecific strategies they used to perform the task, and (d) for generalcomm ents. The second questionnaire solicited information regardingthe participants' musical background.

Results and DiscussionOverall, the results of Experiment 1 suggest that all listenerswere sensitive to harmonic implications and were heavilyreliant on context to make these inferences. Details arediscussed in two sections, which consider, respectively, obvious-ness ratings and questionnaire resp onses.Obviousness judgments. Ratings from the two test mea-sures per melodic instance were averaged, yielding one obvious-ness score for each m elodic instance. Figures 2a and b presen tmean obviousness ratings for listeners of low and high musicalskill levels, respectively, as a function of context (control,


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744 S. HOI.LERAN. M. JONES, AND D. BUTLER

a) b)Low Skill High Skill

TARGET CHANOEH Sun* (S)g H Impl ied ( I )I I Nonlm plitd (Nl)

Control NonContlaMit Control Conltont NonConlt*ntCHORD CONTEXT CHORD CONTEXTFigure 2. Mean obviousness ratings for (a) low- and (b) high-skill listeners as a function of target change(S, I, and NI) and chord context (control, consistent, and nonconsistent) in Experiment 1 are shown.

consistent chords, and nonconsistent chords) and target change(same, implied, and nonimplied).Our first question concerns whether listeners were sensitiveto harmonic implications. The main effect of target changesuggests that they were, F(2,108 ) = 114.84,p < .0001, MSE =2.75. Overall, NI changes were most obvious (M = 3.80) with I(2.53) and S (1.33) following in the a nticipated o rder. Pairwisecom parisons ( a = .025 per con trast ) confirmed the signifi-cance of all three differences: I versus NI, F( 1,108) = 6.86; Iversus S, F(l,108) = 6.50; and NI versus S, F(l,108) = 13.39.This general ordering was true of listeners in both skill groups.Overall, for all listeners, comparison pitch changes that did notfit with the local harmony established in the standard patternseemed to pop out.It is possible that the main effect of target change arisessimply from local melodic context effects, an issue we pursuedin E xperiment 2. However, note that if greater obviousness ofNI targets were du e to this factor in Experiment 1, then only amain effect for target change should occur. However, theinfluence of chordal context was also evident: chord contextprovided not only a significant main effect, F(2, 54) = 9.69,p < .0005, MSE = 4.03, but also a significant interaction withtarget change , F(4 , 108) = 2.66, p < .05, MSE = 2.75. Overall,obviousness ratings were highest with the control condition(M = 3.08) and lowest with th e consistent chord condition(M = 2.25). Planned pairwise contrasts on the context maineffect indicated that ratings in the control condition weresignificantly higher than in either of the chord co nditions, F( l,54) = 15.45, for consistent chord versus control, and F (l , 54) =12.81, for th e parallel nonconsistent com parison, but ratings inconsistent chord conditions did not differ significantly fromthose in nonconsistent. However, when target type is consid-ered, the interaction reveals that differences in ratings of Iversus NI targets were greatest in the consistent chord condi-tions and least in the nonconsistent chord condition. Becausedifferences between I and NI are diagnostic of harmonicinference, we consider this interaction in more detail next.The interaction of context with target change, evident in

Figure 2, speaks to the question of whether context affects thestrength of harmonic implication. The answer here appears tobe "Yes" as well. Planned nonorthogonal contrasts (eachevaluated at a of .025) indicated that differences between I andNI targets did not differ significantly between the control andconsistent chord c onditions, but together the mean differencesbetween I and N I, averaged over control and consistent chordconditions, were significantly greater than corresp onding differ-ences (I vs. NI) in the nonconsistent chord conditions, F(l,108) = 8.38. Thus, the strength of harmonic implication, asindexed by differences in obviousness between I and NItargets, was reliably greater in conditions predicted to havegreater tonal clarity, namely the control and consistent chordconditions.A final issue concerning obviousness ratings pertains todifferences arising from musical training. Overall there was noreliable difference in rating scores as a function of skill, F(l,54) < 1.00. More important, as already indicated, the patternof mean ratings across target change and context was fairlysimilar for listeners of both skill levels. High-skill listenersyielded somewhat higher obviousness ratings (2.63 vs. 2.49)and appeared to make clearer differentiations among S versusI and NI target changes (Figure 2), producing a significantinteraction of skill with target change, F(2, 108) = 7.26, p


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IMPLIED HARMONY 745evidence that listeners with more musical training were signifi-cantly less sensitive to target changes that preserved the localharmony than were listeners with modest amounts of training.'

Questionnaire responses. How aware were listeners of theseinfluences on their judgments? We assessed questionnairesprobing listeners' descriptions of differences between standardand comparison sequences. Each listener was assigned to oneof four mutually exclusive categories on the basis of his or herresponses, as determined by two scorers: (a) Harmony partici-pants mentioned changes related to harmony, tonality, key, orchords; (b) Interval listeners heard changes in interval size or inmelodic motion (movement by step or by leap); (c) Characterparticipants reported general character changes regardingchanged notes or the comparison melody (e.g., the note "stuckout" or was "sour," or the melody seemed different or "off");and (d) Other listeners made only miscellaneous comments(e.g., about the sine tones, register, or tempo changes betweenstandard and comparison). One of the authors and an under-graduate student with moderate musical training who wasnaive as to the purpose of the experiment served as scorers.Scorers agreed on category assignment for 82% of responses.Discrepancies were decided by a third scorer, another author.

Table 1 (top) presents the distribution of low- and high-skilllisteners as a function of the categories listed above. The twoskill groups assessed the stimuli differently, x2(3, N = 36) =10.97, p < .025. Most low-skill listeners fell into the third(character) and fourth (other) categories, reflecting a lack ofawareness of the tonal and harmonic principles at play. Bycontrast, more high-skill listeners appealed to harmonic prin-ciples and were assigned to the harmony category. No differ-ences as a function of context appeared in either skill group.

As for explicit articulation of I versus NI distinctions intarget changes, only 1 of the 36 low-skill listeners (under 3%)was able to clearly articulate this manipulation, whereas 7 ofthe 30 high-skill listeners (under 24%) could do this. Thus,although skilled listeners did better in this respect than lessskilled listeners, in neither group could most of the listenersvolunteer precisely correct information about the tonal gram-maticality of target changes.

In summary, given melodies with dynamically changing har-monies, all listeners were sensitive to changes in local impliedharmony, as indexed by differences between their NI and Iratings. These differences were large even when the melodieswere unaccompanied by chords in the surrounding context(control). By contrast, differences between I and NI targetswere attenuated in conditions assumed to convey lower tonalclarity, namely where accompanying chords were not consis-tent with the melodic line (nonconsistent). These effects heldfor both skill groups. Although high-skill listeners were gener-ally more articulate about underlying harmonic principlesgoverning the melodies, relatively few listeners in either skillgroup could accurately explain differences between grammati-cal (I targets) and ungrammatical (NI) pitch transformations.

Experiment 2Experiment 1 demonstrated that all listeners made local

harmonic inferences and that the strength of these inferenceswas influenced by context. However, the way in which context

Table 1Percentage of Listeners in Questionnaire CategoriesSkill level

Experiment 1Lo w aHighbExperiment 2Lo w aHighb

Harmony5.633.35.626.7

Interval19.420.011.140.0

Character41.736.736.116.7

Othe r33.310.047.216.7

"n = 36 . b/i = 30.

affected harmonic inference remains unclear. Although har-monic (chord) context heightened implied harmony effects, itis also evident that listeners were sensitive to harmonicimplications, even in melodies lacking explicit chordal accom-paniment (controls). The latter finding suggests that a melodicline, by itself, may be an important determinant of impliedharmony.

In Experiment 2 we pursued the hypothesis that the melodicline has a significant influence on a listener's sensitivity to localharmonic implications. Specifically, we used patterns fromExperiment 1 in which the melodic line was rendered lesscoherent by removal of melodic information that connectedthe test measures. Thus, in both standard and comparisonpatterns only a broken melodic line remained. Figure 3 depictsa sample stimulus pattern. Three different context conditions(control, consistent, and nonconsistent chords) correspondedto those of Experiment 1. This means that listeners in controlconditions received only three melodic fragments (potentialtest measures) and no accompanying chords (top line only ofFigure 3), whereas those assigned to consistent and nonconsis-tent chord conditions received the same intervening chordsused in these conditions in Experiment 1, but with no concur-rent melodic line connecting test measures.

In this experiment harmonic context consisted of the sameexplicit chord progressions used in Experiment 1. Chordinformation is redundant with that supplied by the melodicline (in Experiment 1) insofar as key and changing harmoniesare concerned; therefore removal of the melodic line (inExperiment 2) should not necessarily change the pattern ofresults. If harmonic context alone determines harmonic infer-ence, then in Experiment 2 tonal clarity should continue to begreatest in the consistent chord condition and least in thenonconsistent chord condition. In short, in Experiment 2 weshould replicate the pattern of findings of Experiment 1 ifsurrounding chord progressions alone effectively determinefor listeners the "what" and "when" of the implied chords intest measures.

The role of local melodic context, namely the pitches withina given test measure, can be more directly assessed in this

3 Significant differences that were due to m elodic instance and inter-actions of melodic instance with target change, context, and counter-balance order were also found. Innone of these cases did the findingsreverse conclusions reported with respect to the order of obviousnessratings: NI > I > S. Complex interactions suggested that for skilledlisteners the magnitude of the implied harmony effect was greater insome melodies and experimental conditions than in others.


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746 S. HOLLERAN, M. JONES, AND D. BUTLERConsistent ChordsNo Target Change (S)

m 16

iFigure 3. Example s t imulus for Experiment 2, in which melodic line is absent in Me asu res 1, 3, 5, 7. and 8,is shown. Asterisk denotes an inverted chord.

design. The control condition of Experiment 2 presented testmeasures in isolation (i.e., lacking more extended melodic andharmonic context). If listeners are primarily biased by localcontext, then the differences in I versus NI ratings observed inExperiment 1 should appear in the control condition ofExperiment 2.

In summary, in Experiment 2 we broke the melodic line. Ifmelodic context contributes to listeners' dynamic expectanciesabout forthcoming chords, then the diagnostic evidence forlocal harmonic implication, namely differences between I andNI targets, should disappear in all contexts. However, if con-ventional tonal chord progressions alone can provoke expect-ancies about forthcoming chords, then we should replicate thefindings of Experiment 1 for the two chord context conditions.Method

Participants. A total of 66 listeners participated in Experiment 2.Thirty-six qualified as low-skill listeners , and 30 as high-skill listeners.The low-skill listeners w ere volunteers from introductory psychologyclasses at Ohio State University who participated in return for coursecredit. All met the criteria of Experiment 1, and none had participatedin the previous experiment. They had an average of 4.13 years ofprivate instruction on a primary instrument. Eighteen had experienceon a second instrumen t, with an average of 1.89 years of formal training.

The high-skill listeners met the same criteria as those in Experiment1, and none had participated in that experiment; each participated inreturn for monetary reimbursement ($6.00). They had an average of7.95 years of formal instruction on their primary instrument. Twenty-three had experience on a second instrument, with a mean of4.5 yearsof formal training.Design. The des ign w as a 2 x 3 x 2 x 3 x 3 mixed fa cto ria l. Thethree between-subjects variables were skill (high and low), context(control, consistent chord, and nonconsistent chord), and counterbal-ance order (1 and 2). The two within-subject variables were targetchange (same, implied, and nonimplied) and melodic instance (1,2,and 3) . Participa nts of each skill group were random ly assigned to eachof the six context by counterbalance order conditions.Apparatus. This was identical to Experiment 1. As in that study,listening levels of recorded events were adjusted for each participantto a comfortable level; these ranged between 64 and 70 dBA.Materials and conditions. In all respects, save one, the contextconditions were identical to those of Experiment 1. The one changeinvolved removal of all sine tones corresponding to the upper (me-lodic) line in Measures 1, 3, 5, 7, and 8 for all melodic instances. Incontrol conditions, this resulted in patterns containing three melodicfragments corresponding exactly in timing and pitch to potential testmeasures (i.e., Measures 2, 4, and 6); intervening measures were filled

with silence (to p musical line of Figure 3). In the two chord conditions,the same three melodic fragments (test measures) occurred andintervening measures were filled either with consistent chords ornonconsistent chords. Figure 3depicts a new standard melody corre-sponding to the same, consistent chord condition of Experiment 1 (cf.Figure 1). These manipulations insured that test measures remainedidentical across all contexts in both experiments.Procedure. The procedure was identical toExperiment 1, with thefollowing exceptions. Participants in the two chord conditions wereinstructed that the stimuli consisted of a "series of chords interruptedperiodically by higher pitched tones without chordal accompaniment"and that pitch changes (targets) could only occur in these upper,higher pitched melodic notes. Stimuli in the control condition weredescribed as "three brief pitch sequences which are separated bysilences; each sequence in turn consists of three pitches." To keepretention and response periods equivalent across all three conditions,we did not incorporate in the control condition the time periodscorresponding to the final measures (7 and 8) in the chord conditions.Thus, as in Experiment 1, in the two chord conditions, the com parisonpattern began 2 s after the offset of Measure 8 of the standard, and the5-s participant response period began after the offset of Measure 8 ofthe comparison pattern; in the control condition, however, thecomparison pattern began 2 s after the offset of the third pitchsequence (test measure) of the standard, and the 5-s participantresponse period began immediately after the offset of the third pitchsequence (test measure) of the comparison pattern.Results and Discussion

Overall, the findings of Experiment 2 suggest the impor-tance of melodic context as a source of tonal clarity. Relevantdata from ratings and questionnaires are discussed separately.

Obviousness judgments. Obviousness ratings were averagedover the two test measures for each melodic instance. Figures4a and b present the mean ratings for low- and high-skilllisteners, respectively, as a function of target change and con-text averaged over counterbalance order and melodic instance.

The pattern of results from an analysis of variance (ANOVA)on ratings in Experiment 2 differs markedly from that ofExperiment L The most important difference is the disappear-ance of evidence for harmonic implication. Although targetchange exerted a significant main effect on ratings, F(2,108) =117.57, p < .0001, MSE = 3.49, this does not indicatesensitivity to harmonic implication, as reflected in NI versus Idifferences. Instead, the effect rests entirely on differencesbetween S target changes, which were judged not especiallyobvious, and the other two kinds of target changes (I and NI),both of which were judged significantly more obvious than S


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IMPLIED HARMONY 747

a)w r yabvlouaChang*

obvlouaehang*

Low Skill

Control Cwialalaiil NonCmalalanlCHORD CONTEXT

b)High Skill

TARGET CHANGEMH Sama(3)US Impliad(I)CD Nonlmpllad (NO

Control Contlatant NonConl(*nlCHORD CONTEXT

Figure 4. Mean obviousness ratings for (a) low- and (b) high-skill listeners as a function of target change(S, I, and NI) and chord context (control, consistent, and nonconsistent) in Experiment 2 are shown.

changes. Three pairwise comparisons (a .025 per contrast)verified that the I versus S difference, F(l, 108) = 12.09, andthe NI versus S difference, F(l, 108) = 13.45, were bothsignificant, but the I versus NIdifference was not. Althoughtarget change produced a significant interaction with context inthis experiment, F(4, 108) =3.73, p < .005, MSE =3.49, thisinteraction does not reflect context-determined harmonicinference. Instead, it arises entirely from differences betweenNI and S, rather than NI and I, in the control and nonconsis-tent chord conditions, F(l, 108) =7.98,p < .025. This higherorder contrast indicates that the difference between NI and Starget chang es was larger in the nonco nsistent chord conditionthan in the control condition. However, most important fromthe perspective of harmonic implication effects is the findingthat pairwise contrasts of I versus NI were not statisticallysignificant in any of the three contexts. The absence of I versusNI differences in all context conditions, including the controlcondition, indicates not only that h armonic context was a weakdeterminant of harmonic inference in this task but also thatlocal melodic context cannot explain the harmonic inferenceeffects observed in the control condition of Experiment 1.Skill differences were again evident in Experiment 2. A maineffect of skill, F (l , 54) = 12.447, p < .001, MSE =4.54, indi-cates th at ov erall high-skill listeners pro duced higher obvious-ness ratings than did low-skill listeners. H owever, these overallmeans really reflect the fact that high-skill listeners tended tojudge any pitch change (I or NI) as highly obvious inall con-texts. This produced a Target xSkill interaction, F (2, 108) =20.36, p < .0001, MSE =3.49. Ratings of I versus NI did notdiffer significantly as a function ofskill level, but high-skilllisteners were be tter at distinguishing patterns w ith no changesfrom ones with true targets; hence contrasts involving I versusS, F(l, 108) =22.23, and NI versus S, F (l , 108) =25.33, didchange significantly with skill (a per contrast = .025).These findin gs indicate that although low-skill listeners hadmore difficulty than high-skill ones indistinguishing compari-son sequences that contained true pitch changes from ones

that did not, neither skill group relied heavily on impliedharmony to do this.Questionnaire responses. Questionnaire results were tabu-lated according to the same four categories as in Experiment 1.The two scorers agreed on category assignment for 67% of thequestionnaires, with discrepancies again decided by a thirdscorer. Table 1 (bottom) presents the number of participantsfrom each skill group assigned to each category. As inExperiment 1, the two skill groups differed significantly in theirassignment to the four catego ries, x2(3, N = 36) = 17.30,/?


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748 S. HOLLERAN. M. JONES, AND D. BUTLERfound in-key target pitches that conflicted with the localharmony implied by a melody much more obvious than in-keypitches that did not. This finding extends previous researchthat suggests that even listeners with fairly modest degrees offormal musical training respond to general aspects of diatonic-ity in Western tonal music. It also confirms a longstandingpremise of music theory that individual pitches of a melody canindeed imply certain underlying chords. At the same time, itundermines the hypothesis that people encode melodies inde-pendently of their harm onic implications.A second goal of this research concerned the impact ofcontext on harmonic inferences. In particular, we consideredwhether the tonal clarity of a surrounding context determinedthe strength of local harmonic inferences drawn from amelody. Together the findings of Experiments 1 and 2 permitus to conclude that context is important and that a clear andunambiguous tonal context is probably necessary for observa-tion of a strong harmonic inference. In particular, whensupplied with only a local melodic context (control conditionsof Experiment 2), listeners showed no clear evidence of havingmade harmonic inferences. T he fact that local melodic contextdid not have strong effects on judgments of I versus NI targ etsis not entirely surprising because , taken in isolation, the toneswithin a single test measure did not logically specify the key;therefore they could not, by themselves, tonally disambiguatean implied chord. The present data confirm this while alsotestifying to the fact that global melodic and harmonic contextcan supply the necessary disambiguating tonal information.

Originally we maintained that if the strength of harmonicinference depends on the tonal clarity provided by a musicalcontext, then differences in obviousness ratings between I andNI targets should be grea test in the consistent chord cond ition,in which chords explicitly reinforce various harmonies impliedwithin a continuous melodic line (i.e., in Experiment 1). Thisturned out to be the case. However, statistically speaking, itappears that the presence of a continuous melodic line is fairlyimpo rtant. In Experim ent 1, the listeners in the control condi-tion did not differ from those in the consistent chord condition.These findings, together with those of Experiment 2, indicatethat melodic context alone is highly influential in bringingabout judgments that are based on harmonic implications.We emphasized that the various manipulations of harmonicand melodic context designed to affect tonal clarity rested onestablishment of key and constraints of tonal grammar. Toinsure this, we played all melodies in the same key, or tonalframe, throughout a session. Pilot work using melodies indifferent keys produced greater variability and weaker impliedharmony effects than reported above. Because these melodicinstances, by necessity, were short relative to most musicalevents, it seemed clear that introduction of erratic key shiftswithin a session would violate the sort of normal listeningexperience people encounter in everyday musical settings,where longer tunes remain in the same key or modulate to arelated one in predictable ways. As with tempo and meter,which also offer stable frames for musical events (Jones, Kidd,& W etzel, 1981; Yee, H olleran, & Jone s, 1994), a tonal framecannot be haphazardly shifted about within a session withouttaking a toll on performance. We chose our design not only to

insure that listeners heard the melodies as tonal but also tominimize variability with respect to the particu lar key involved.As a result, it is most unlikely that listeners heard thesemelodies in unintended keys. At least in control and consistentchord conditions, this means that I targets and NI targets trulyreflected changes consistent and inconsistent, respectively,with the local harmony of A major. Other aspects of the designconfirm that listeners responded to manipulations of targetchange in terms of harmonic implications. For example, it ispossible that listeners would respond to these changes strictlyin terms of log frequency melodic differences between stan-dard and comparison patterns and not to tonal harmonicimplications. In these designs, comparison patterns containingNI targets turned out to be more similar to their standards withrespect to pitch interval structure than did comparisonscontaining I targets, in that they realized the smaller pitchinterval change. If listeners were responding only to pitchinterval differences, then the I targets should have seemedmore obvious than NI targets. In fact, there is some evidencethat larger melodic intervals may be taken (incorrectly) asevidence of harmonic change (Platt & Racine, 1994), acircumstance that might even have contributed to higherobviousness ratings of I targets in the present studies and thusworked against the NI versus I differences we predicted (andfound). Furthermore, because low-skill listeners appear to bemore responsive to interval size manipulations than are high-skill listeners (e.g., Platt & Racine, 1994), it could be arguedthat they might have found the I targets more obvious than theNI targets in the present studies. This was not the case. In fact,in Experiment 1 low-skill listeners did not rate the I targets asmore obvious than the N I targets in any context condition.Another interpretation of the target change effect could bebased on the spectral structure of the target tones. Becausesine tones were used, we can eliminate an explanation in which

the virtual pitch associated with targets within test measuresmight fit more readily with I target changes than with NIchanges. With pure tones, the mode of analytic listeningproposed by Terhardt (1984) applies; in this case, there is notheoretical basis for predicting I versus NI differences. Be-cause mo derate listening levels (around 70 dB SPL) were used,we cannot entirely rule out aural nonlinearities (e.g., Green,1976; Wegel & Lane, 1924), but it is highly unlikely that suchphenomena played any significant role in the pattern ofobserved results. The most telling evidence against any strictlypsychoacoustic-peripheral interpretation is the finding thatthe implied harmonic effect associated with the same set ofsine tones (i.e., melodic test fragment) did not occur when onlythe local melodic context was present (control conditions inExperiment 2), but it did appear when additional melodiccontext was present (Experiment 1).Other possible explanations of the target change effectappeal to principles that are not directly related to tonalgrammars. One maintains that the I pitch changes are lessobvious merely because they might belong to the same pitchclass as another pitch in the test measure. However, if thiswere the case, then we would expect NI versus I differences tobe evident in all context conditions of Experiment 2 (and inExperiment 1), but this was not found. A more sophisticated


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IMPLIED HARMONY 749explanation maintains that the greater frequency of the Itarget's pitch class (E) in the surrounding melodic contextmakes it less obvious than the pitch class of the NI targets. Therecurrence of E is an inevitable consequence of the tonalmanipulations that relied on a melodic sequence of impliedchords most common to the A major scale (vs. G major) toestablish high tonal clarity in A major. However, three piecesof evidence argue against this as the whole explanation of thetarget change effect. The first concerns the failure to find anysignificant I versus NI differences in Experiment 2 in thecontrol condition, where the surrounding test measures in-cluded melodic fragments containing more instances of the Ipitch than of the NI pitch. Second, if obviousness of any targetpitch (S, I, or NI) decreases with an increase in the frequencyof occurrence of that pitch in the context, then we wouldexpect the I targets to be even less obvious than the S targetchanges because they are more common in the melodic lines ofthese instances than are S targets. This was not found. Finally,if this were the entire explanation for target differences inExperiment 1, then we would anticipate no Target x Contextinteraction in that experiment because the lower tonal clarityof the nonconsistent chord condition should have no effect onperformance. This was not the case. At a larger level, however,this raises the issue of what constitutes a tonal context. Ourposition is that tonal context depends on key plus grammaticalarrangements of tones (implied harmonies), and thus inevita-bly involves an element of pitch repetition.

With respect to the influence of context on harmonicinferences, the pattern of results over the two experiments wasrather surprising. We anticipated that harmonic context ef-fects, taken alone, would at least rival those of melodic context,taken alone. Chord progressions alone have produced strongeffects on performance in other tasks. They were used, forexample, by Krumhansl and Kessler (1982) in a task in whichskilled listeners rated single probe tones of various sorts togauge a listener's developing sense of key. Such findingssuggest two plausible outcomes for the present experiments:First, that chord progressions and melodic line should affectharmonic inferences equally and, second, that the combinationof consistent chords with a continuous melodic line (i.e., inExperiment 1) should produce implied harmony effects substan-tially stronger than conditions involving either the melodic linealone (Experiment 1, control) or consistent chords alone(Experiment 2). However, insofar as judgments of I versus NItargets reflect harmonic influences, in Experiment 1 theconsistent chord condition did not produce stronger evidencefor such influences than did the control condition. In addition,in Experiment 2 there were virtually no reliable harmonicimplication effects associated with presentations of the consis-tent chords alone. Perhaps the latter two outcomes explainwhy, in Experiment 1, combining the melodic line withreinforcing chords did not yield distinctly better performancein the consistent chord conditions than that found in controlconditions, which presented only the melodic line: Consistentchords merely provided information that was redundant withthe melodic line. Therefore, when chords were presentedseparately, as in Experiment 2, they were not especiallyeffective at evoking harmonic implications. In any case, thefindings of both experiments converge to suggest that listeners

weight the melody itself fairly heavily in drawing harmonicinferences from it: Without a continuous melodic line theyjudged both kinds of pitch changes to be equally obvious.

The finding that a melodic line alone affords sufficient basisfor harmonic inference is strong evidence against the assertionthat a melody is perceived independently of its chordalimplications (e.g., Povel & van Egmond. 1993). Instead, itconfirms the time-honored music theoretic claim that a wcll-formed melody can imply its own harmony. This is one of ourmost interesting discoveries about how context works. Previousresearch has not systematically compared the relative influ-ence of chordal and melodic context (but sec Platt & Racine.1990). It does seem somewhat surprising that even musiciansdo not exploit more information from purely chordal contexts:If "hearing" chordal implications is what makes the I targetsseem less obvious than the NI targets, then shouldn't present-ing explicit chords in the surrounding context be at least asinfluential as presenting the melodic line alone? At least in thepresent task, in which listeners knew that if a change occurredit would happen in the melodic line, it is clear that this was notthe case.

One interpretation of the melodic context effect focuses onthe effectiveness of a continuous melodic line in guidingselective attending. When a melodic line is provided to alistener who knows that targets will always appear within thatsequence, a selective attending set is encouraged in whichlisteners monitor only the melody (e.g., Jones & Yec. 1993;Jones, Jagacinski, Yee, Floyd, & KJapp, 1995; van Noordcn,1975). In this case, perhaps the bitonality of nonconsistentchord conditions in Experiment 1 created a divided attentiontask in which listeners could not "tune out" the distractingchord conflicts. However, it would be misleading to dismiss thepresent findings as merely the result of a task-induced set.Such an interpretation does not do justice to the interactionsof context with target change and skill observed here. Further-more, others who have pitted instructions against structuraldeterminants of attending in a task involving detection of smallperturbations in polyrhythmic sequences found that the struc-tural aspects of the sequences themselves had more influenceon selective attending than an instructed "set" to attend in aparticular way (Jones et al., 1995).

There are other aspects of the structure of any multivoicedmusical event that may contribute to the salience of themelodic line. When chords accompany a melody, the melodicline is typically higher in frequency and slightly louder thanother voices, and this was true in the present case (Experiment1). These physical features undoubtedly contribute to themelody capturing listeners' attention. However, if only fre-quency and intensity differences were responsible for theseeffects, then we would expect no interaction of target changewith context in Experiment 1; all listeners would performequally well in all contexts. This was not the case. There is alsorecent evidence that harmonically related (in-chord) pitchchanges are as noticeable as harmonically unrelated oneswhen they occur in an upper voice that carries the melody, butthey are less noticeable in the upper voice when another voicecarries the melody (Palmer & Holleran, 1993). This suggeststhat selective attending to the melodic line may even attenuateevidence for harmonic inference.


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750 S. HOLLERAN, M. JONES, AND D. BUTLERThe finding hat listeners differentially weight various contex-tual determinants (melodic vs. chordal or harmonic) poses achallenge to current theo ries that addre ss implied harmony (asthese effects are revealed by responses to N I vs. I targets) butthat fail to accomm odate selective influences of context. Jonesfor example, maintains that a temporal context provokes anactive abstraction of key specific and grammatical relation-

ships, which direct, over time, specific attentional extrapola-tions (i.e., expectancies) about certain anticipated tonal rela-tionships (e.g., I changes) and not others (e.g., NI changes;Jones, 1976, 1981, 1982, 1990). Others incorporate rule sys-tems in which melodic and harmonic relationships will shapemusical expectancies in such a way that some expectancyviolations might seem more obvious than others (Carlsen,1981; Meyer, 1973; Narmour, 1990, 1992). Tonal schemetheories, including network models, are less specific about howexpectancies adapt over time to accommodate dynamicallychanging musical events; nevertheless, at a gene ral level theirdescriptions of tonal expectancies in terms of stronger linksamong chords and other harmonically salient structural levels(e.g., Bharucha, 1987,1991) mean that they too offer a basis forpredicting differences in obviousness ratings between NI and Itargets. However, none of these approaches explains howobviousness of I versus NI targe ts changes as a function of thepresence or absence of a continuous melodic line. This isbecause none currently accommodates selective influences onattending that may arise either from the task or from therelative prominence of certain-contextual relationships (e.g.,melodic vs. harmonic context). Yet our data argue for theimportance of these factors in explaining performance.

Our third concern relates to musical skill. Musically trainedlisteners did not make substantially stronger harmonic infer-ences, if it is assumed that inference strength is gauged bydifferences in ratings of I versus NI targets. Furthe rmo re, thebroad outline of their performance as a function of context inboth experiments was quite similar to that of less skilledlisteners. It seems clear that context suppressed I targetobviousness (relative to NI targets) for both skill groups.Consequently, we cannot conclude that increased trainingrende rs listeners correspondingly less sensitive to pitch changesthat preserve local harmony.These findings are similar to those of DeWitt and Samuel(1990), who reported that more experienced adult listenersshowed no greater tendency than inexperienced adults torestore missing tones in tonal melodies and, in some cases,seemed to be more discriminating. These results also convergewith other studies that found no relationship between amountof musical training and the ability to detect in-scale versusout-of-scale pitch changes (e.g., Trainor & Trehub, 1992).However, the outcome of the our experiments appears at oddswith Trainor and Trehub's main result, in which adults wereless sensitive to d iatonic changes th an infants. A resolution ofthese seemingly contradictory finding s is possible on the basisof the assumption that musical training not only confersknowledge of the tonal grammar but that it also heightensdiscriminative acuity of many structural features of an acousticpattern (e.g., Jones et al., 1993; Spiegel & Watson, 1984). Thenthe presence of an implied harmony effect reflects the opera-tion of contextually provoked tonal expe ctancies that suppress

listeners' sensitivity to expected events relative to their normaldiscrimination levels. Thus, if in a tonal context high- andlow-skill listeners give the same nonobvious rating score to achange in pitch, this score would reflect more suppression forthe trained listeners relative to their normal (but higher) pitchdiscrimination baseline. For exam ple, assume that Experiment2 performance indexed pitch change discrimination levels innontonal contexts; then high-skill listeners in this experiment,on average, were quite good at discriminating I targets (meanExperiment 2 obviousness rating of 4.52). However, in Experi-ment 1, these listeners scored, on average, 1.96 for I targets inthe consistent chord conditions; over the two experimentsthen, skilled listeners showed a reduction in sensitivity to thispitch change of 2.56 points. On the other hand, low-skilllisteners were less discriminating overall in Experiment 2;consequently, in E xperiment 1, they showed a drop of around1.18 for I targets in the consistent chord condition. It isprimarily in this respect that it might be argued that greaterreliance on a tonal scheme renders certain expected eventscorrespondingly less obvious.

Finally, skill-level manipulations and the probing of listen-ers' awareness of target manipulations relating to harmonicimplications extend the generality of tacit knowledge tononartificial grammars that are transformational rather thanMarkovian in nature. A demonstration of tacit knowledgetypically involves a juxtaposition of evidence that people doreliably respond to rule violations (i.e., NI vs. I obviousnessratings), with evidence that they seem unaware of the underly-ing principles (questionnaire responses regarding targetchanges). This juxtaposition was most prominent in Experi-ment 1, where most listeners reliably distinguished compari-sons that did not belong in the same grammatical category astheir standards (NI) from comparisons that did (I), while atthe same time very few could explain their performance,especially if they had little musical training: The NI compari-son sequences just "did n't seem right." We think this is a fairlystraightforward example of tacit knowledge of musical prin-ciples. Interestingly, even high-skill listeners, who have re-ceived training not only in attending to and identifying tonalrelationships but also in labeling relevant grammatical p roper-ties, showed this effect. Although these listeners were betterable to identify the changes as involving harmonic principles,less than a quarter could pinpoint the exact nature of thedifferences between I and NI target changes.

The present data make two additional points complemen-tary to the research on tacit knowing. The first relates to issuesraised by Vokey and Brooks (1992), who maintained thatpeople learn abstract similarities among exemplar patternswithin a category rather than grammars as such. At least inmusical events, it is difficult to separate abstract patternsimilarities from the underlying grammar. For example, in ourresearch there was substantial similarity between standard andcomparison members of any pair because pair membersdiffered only with respect to a single in-key pitch. Neverthe-less, a single tone change (NI vs. I) can have remarkablydifferent implied mean ings in light of conventions of Weste rntonal harmony. This suggests that determining similaritiesbetween instances is not a simple matter. That is, by astraightforward feature account it might be maintained that


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IMPLIED HARMONY 751comparison patterns containing NI targets are more similar totheir standards than those with I targets because the formerrepresent a smaller pitch interval distance. Such an analysis,however, would predict the opposite of our findings. Herepatterns judged most similar involved comparisons in whichtargets are defined by common tonal grammar transformations(i.e., S and I changes). It turns out that the criterion listenersadopted for categorization has little to do with the surfacefeatures of a single pitch change and everything to do withwhat it implies grammatically. The second point concerns theway listeners respond over time to grammatical sequences. Thefact that listeners were most effective in distinguishing NIcomparisons as "not right" when they could follow a continu-ous melodic line implies that some sequential properties (e.g.,a melodic line) may have more impact on attending and henceon categorization (of NI vs. I) than others (e.g., explicitchords). In short, a theory about what constitutes abstract tacitknowledge is not sufficient to explain performance; it is alsonecessary to know how grammatically generated structureguides attending.

ReferencesBerkowitz , S., Fontr ier , R., & Kraft, L. (1986). A new approach to

sight-singing. New York: Norton.Bha rucha , J. J. (1987).

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