repp, b. h. (1992). a review of carol l. krumhansl's cognitive foundations of musical pitch....

7/29/2019 Repp, B. H. (1992). a Review of Carol L. Krumhansl's Cognitive Foundations of Musical Pitch. DOCUMENT RESUM

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HCJBkins Laboratoria Status Report on Speech R e ~1992, SR-109 / 110, 277282

A Review of Carol L. Krumhansl'sCognitive Foundations o/Musical Pitch*

Bruno H. Repp

The psychology of music percept ion andcognition, nearly dormant 15 years ago, has madeconsiderable strides in the last decade. Severaltextbooks and edited collections of articles haveappeared, two new journals have beenestablished, societies have been formed, and manyreports of empirical studies have been published,including one in monograph form (Serafine, 1988).However, the field is still new and small,l and fewresearchers have had the persistence and the goodfortune of continuous grant support to develop andbring to fruition an extended and coherentprogram of research. Carol Krumhansl, ofCornellUniversity, has accomplished that feat, and hermonograph documents a decade of individualachievement, resulting in a critical mass ofpsychological data organized in a tight conceptualframework. This publication is a landmark eventin a young field striving for definit ion andrecognition.The brill iance of Krumhansl' s approach wasrecognized early on by her peers who bestowed onher the American Psychological Association'sDistinguished Scientific Award for an EarlyCareer Contribution in Psychology (see AmericanPsychologist, March 1984, pp. 284-286). Thecitation honored her for "a dazzling interplay ofexperimental techniques, music theory, andmultidimensional scaling" that had uncovered"new cognitive structures of great richness andbeauty" (ibid., p. 284). This methodologicalvirtuosity as well as it s satisfying results areevident throughout the book. AlthoUgh nearly allthe results have been published previously inaccessible journals, they are brought together herefor the benefit of the reader, who is led throughthe complex issues by lucid explanations anddiscussions. The clear organization and sense ofdirection make reading the book an aesthetic aswell as an intellectual pleasure.

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The book is divided into 11 chapters. Chapter 1introduces the reader to the author's objectivesand methods. Some general remarks about theapproach of cognitive psychology are provided fornonpsychologists. The general aim is "to describethe human capacity for internalizing thestructured sound materials of music bycharacterizing the nature of internal processesand representations" (p. 6). The more specific aimof Krumhansl's research is "to describe what thelistener knows about pitch relationships [mainlyin traditionalWestern music], how this knowledgeaffects the prOcessing of sounded sequences, andhow this system arises from stylistic regularitiesidentifiable in the music" (p. 9). Krumhansl 'sdistinctive way of characterizing internalrepresentations is to depict the similarityrelationships within sets of basic elements asdistances in a multidimensional space.

The basic elements are said to be single tones,chords, and keys. (That keys are rather moreabstract entities than are tones and chords is notimmediately pointed out, but perhaps obvious.)Krumhansl does not further defend this axiom,which would be accepted by most musicpsychologists and musicologists. Witness,however, what Seraf'me (1988}-not cited in thebook-had to say: "On this view, the elements andprocesses ofcognition will be exactly isomorphic tothe factors we are able to find ... and manipulatein experiments" (p, 26) and "we know that thestimuli used in such studies are never, under anycircumstances, considered or listened to as music"(p. 25). And, further along, Seraf'me argued that"much psychological research has mistakenlyfocused exclusively [on], and also misinterpreted,merely the results of reflection-that is, scales,chords, and discrete pitches-rather than beenconcerned with music itself" (p. 52). I will returnto these arguments at the end of this review.


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Chapter 2 introduces the reader to the conceptof tonal hierarchy, and to Krumhansl's way ofderiving and depicting this cognitive structure. Theterm "hierarchy" here refers to a simple orderingof tones according to their relative importance orstability within a given key, not to a structurewith several nested levels (as in Lerdahl andJackendoff, 1983). The hierarchy of the toneswithin a givenkey is likened to the organization ofcategory members around a prototypical exemplar,in this case the base note or tonic, which serves asa cognitive point of reference. Krumhansl'sexperimental probe tone method (developed incollaboration with Roger Shepard) presentslisteners with a sequence of notes thatunambiguously define a particular key (e.g., ascale or a tonic triad chord), followed by a singlenote of variable pitch. Subjects judge on a ratingscale how well this final probe tone fits into thecontext of the established key. The resulting pattern of average ratings across all tones of thechromatic scale describes the tonal hierarchy: Thetonic (scale step 1) is rated highest, followed inmajor keys by scale step 5, steps 3 and 4, steps 2and 7, and finally the chromatic tones that are notmembers of the key. In minor keys, the order is 1,3, 5, then steps 2, 4, and 7, and finally the chromatic tones. These hierarchies correspond to thefunctional importance of the scale notes in traditional tonal music, as described by musicologists.By computing the auto- and cross-correlationsbetween the rating profiles for all possible pairs ofmajor and minor keys, Krumhansl derives amatrix of interkey similarities that she thensubjects to nonmetric multidimensional scaling toobtain a spatial configuration of interkeydistances. The configuration is strikingly regular,due to the constraints built into the data, and italso makes sense: Two dimensions in which thepoints representing the keys are arrangedaccording to the circle of fifths are convolved withtwo dimensions in which the keys are arranged ina circle that reflects re lative and pa rallelrelationships between major and minor keys. Thetotal four-dimensional pattern can be v i ~ u a l i z e das the surface of a torus (a doughnut), or thesurface can be spread out in two dimensionsrepresenting the angular coordinates of the keysin the two circular configurations. This latter, twodimension. key map resembles maps drawnintuitively by musicologists: The key of C major,for example, is adjacent to the major keysdiffering in one note (G and F major), to therelative minor key (a minor), and to the parallelminor key (c minor). Thus it provides an empirical

validation of musicologists' insights throughlisteners' probe tone ratings.2 Krumhansl adds a. cautionary note by pointing out that her modeldoes no t account for possible directionalasymmetries in key similarity.Following this methodological tour de force, theauthor turns in Chapter 3 to a discussion of thefactors that may underlie listeners' knowledge oftonal hierarchies. She considers two: the phenomenon of tonal consonance, and the statisticaldistribution of pitches in tonal music. Strong correlations oftonal hierarchies with consonance hierarchies would suggest that tonal hierarchiesoriginate in the acoustics of complex tones andtherefore are relatively fixed and universal.Stronger correlations with the1listribution oftones in familiar music, on the other hand, wouldsuggest that tonal hierarchies are learned andculture-bound. Krumhansl briefly reviews acoustically-based theories of tonal consonance and thenproceeds to describe the correlations between hertonal hierarchies and consonance hierarchiesculled from various studies in the literature.s Thecorrelations are moderately high for major keysbut lower and mostly nonsignificant for minorkeys. Krumhansl then proceeds to compare thetonal hierarchies with the statistical frequencydistributions of tones in various selections of tonalmusic, again obtained from the literature. Thesecorrelations are much higher and significant forbothmajor and minor keys. Finally, a multiple regression analysis is performed which demonstrates that tonal consonance does not account forany aspect oftonal hierarchies that is not also accounted for by tonal frequency distributions. Onthe basis ofthese results, Krumhansl argues thattonal hierarchies are learned through listening totonal music and hence are a product of musicalacculturation. Research by Lynch et at {1990a,199Ob}-too recent to be cited by Krumhansl-indeed suggests that this acculturation begins in thefirst year oflife.In Chapter 4, Krumhansl turns to a practicalappl icat ion of her tonal hierarchy results:determination of the key for a musical excerpt,and of changes in key as music progresses. Herkey-finding algorithm (developed with MarkSchmuckler) is simple: The total duration of eachnote in the musical excerpt is determined bycombining repeated occurrences of the same note,regardless of octave or ord inal position. Theresulting relative durations of the 12 notes in theoctave (with zero for notes that do not occur) arethen correlated with the tonal hierarchy profilesfor the 24 major and minor keys, as described in


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A review ofurol L. Krumhansl's Cognitive Foundations ofMusiCilI Pitch 279

Chapter 2. The largest correlation identifies thedominant key. Other large correlations identifyrelated keys that may also be suggested by themusical passage. Indeed, the major virtue of thealgorithm is seen in its ability to yield a keyhierarchy, rather than just a single dominant key.As Krumhansl demonstrates, music theoryexperts can rate the relat ive strengths ofcandidate keys for short musical excerpts.The effectiveness of the key-finding algorithm isdemonstrated in three specific applications and iscompared to other procedures proposed in the literature. In the first application, the algorithm isused to determine the nominal keys of preludes(24 each) by Bach, Shostakovich, and Chopin,based on the first four notes only. The results arequite accurate for Bach and Shostakovich, but lessso for Chopin. In the second application, 24 fuguesubjects ofBach and Shostakovich are analyzed interms ofhow many notes are needed to determinethe correct key. The average number of notes isabout 5, considerably less than required by alternative algorithms proposed in the literature. Inthe third and most elegant application, the keymodulations in a single Bach prelude are trackedmeasure by measure and compared to judgmentsby two experts. There is good agreement, thoughthe algor ithm does not quite match the experts.The key changes are represented graphically as apath on the surface of the torus representing theconfiguration of interkey distances (Chapter 2). Afinal section of Chapter 4 acknowledges the current limitations of the algorithm, which include itsinsensitivity to temporal order, melodic patterns,harmonic structure, and rhythmic stress.In Chapter 5, Krumhansl returns to perceptualdata and in fact reports an original study notpublished elsewhere, which replicates and extendsone of her ear ly exper iments. The topic is theperceived relation between two musical tones.Whereas in the experiments that led to the tonalhierarchy profiles the subjects' task was to judgehow well a single note fit in to the tonal contextestablished by a precursor sequence, listeners nowhear two notes following the key-defining context,and the task is to rate how well the second notegoes with the first. The goal is to demonstrate thatthese perceived relations depend on the tonalcontext-for example, that the notes C-G areperceived as a better sequence than the notes C#-G# when the key is C major, even though bothnote sequences represent the same musicalinterval (a fifth). Krumhansl starts ou t bydiscussing various spatial representations of thepsychological pitch relations among tones, which

increasingly take the functional roles oftones intoaccount. Although the author persists in talkingabout the perceived relations among successivetones, what her experiment is really about is thefunctional role of two-note sequences within agiven key. It comes as no surprise, then, that theorder of the two notes plays an important role, afactor that cannot be accommodated by traditionalmultidimensional scaling of similar ity data.Krumhansl nevertheless presents the results ofsuch an analysis, bu t also notes its shortcomings.The spatial solution that best approximates theperceived tonal relations shows the tonic at thevertex of a cone, along whose circumference theother tones are arranged according to pitch, butwith their distance from the tonic being an inversefunction of their position in the tonal hierarchy. Amore complete pic ture including order effectsemerges from a multiple-regression analysis:Listeners' judgments were most stronglyinfluenced by the position in the tonal hierarchy ofthe second tone, with weaker bu t significantcontributions of the tonal hierarchy of the f irsttone, the pitch distance between the two notes,and the distance between the two notes along thecircle of fifths. The chapter concludes with ademonstration that the resul ts are positivelycorrelated with the relative frequencies ofmelodicintervals in several musical corpora, as tabulatedpreviously by others.Chapter 6 first summarizes three principles thathave emerged from this research and from thework of others on perceptual organization andmemory. The principle of contextual ident itystates that stable tones (i.e., tones high in thetonal hierarchy) are remembered better thanunstable tones. The princ ip le of contextualdistance states that two tones are perceived as themore closely related (and hence are also moreeasily confused in memory) the more stable eitherofthem is. The principle of contextual asymmetrystates that two tones are perceived as more closelyrelated when the second tone is more stable thanthe first than when they are in the opposite order.These principles are expressed formally in termsof perceptual distances, and relevant findings arecited from the literature. The principles are saidto support basic tenets of Gestalt theory, withtonal ity providing a kind of Gestalt quality,though (to this reader) this argument does not addany explanatory power. The second half of thechapter discusses perceptual grouping principlesin music, with data from several recent studies bythe author and he r collaborators. These studiesshow that pitch and rhythm make independent


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contributions to perceived phrase structure, thatthere are reliable boundary cues in performancesof pieces by Mozart as well as Stockhausen, and,most intriguingly, that 6-month old infants prefermusic that is interrupted at phrase boundaries tomusic that is inte rrupted in the middle of aphrase. Lowering of pitch and increases in tonalduration are identified as boundary cues likely tohave been salient to these infants, and theanalogy to speech prosody is noted.Chapters 7 and 8 are easily summarized. Theyreport the results ofexperiments with chords thatreplicate in all essentials the experiments withtones described in Chapters 2 and 3. Chapter 7reports data not published previously. Listenerswere presented with one (Chapter 7) or two(Chapter 8) triadic chords following a keyestablishing context and judged how well theyfollowed the preceding context. The results areshown to reflect the relative stability ofthe chordsin the tonal system, and they illustrate each ofthethree general principles discussed in Chapter 6.Memory for chords in a sequence is also shown toreflect relat ive stabi li ty , and chord stabil ity isfound to correlate with frequency of occurrence ofchords in tonal music. Krumhansl concludes bysummarizing the many parallels between theperceptual organization oftones and chords.All the work up to this point can be consideredas concerned with establishing basic facts concerning tonal organization in perception and memory.In Chapter 9, Krumhansl summarizes two studiesthat make use of these basic data in addressingtwo more complex scenarios: key modulation andpolytonality. In the key modulation experiment,probe chords are presented after every singlechord of chord sequences thatmodulate to close ordistant keys. By correlating subjects' judgmentswith the tonal hierarchy profiles obtained previously in unambiguous key contexts (Chapter 2),the relative strengths of different keys can be assessed as the chord sequence unfolds. By treatingthese strengths as distances, the changing senseof key through the chord sequence can be represented as a path in the toroidal key-distance mapderived in earlier studies. The analysis reveals listeners' initial resistance to radical key changes,followed by abrupt shifts into the new key whenthe following context confirms it. In the experiment on the perception of polytonality, a famousexcerpt from Stravinsky's "Petrouchka" is used inwhich two distant keys (C# and F# major) areused simultaneously.5 Probe tones are presentedafter the bitonal passage, as well as af te r eachtonal component played separately. Detailed anal-

ysis of the results suggests that subjects' judgments are governed by the notes presented, andhence also by both keys, but that no clear sense ofeither tonality develops. Listeners were generallyunable to focus on one or the other tonality, evenwhen instructed to do so. Thus it seems that polytonality, in this instance at least, prevents the establishment of either a single or a multiple tonalframework; instead, it creates ambiguity.The author ventures farther afield in Chapter10, which reports studies that applied the probetone technique to 12-tone serial music, to NorthIndian classical music, and to Balinese gamelanmusic (the last s tudy done by Kessler and col-leagues). The resulting probe tone profiles, ob-tained at various points during and/or followingmusical excerpts from these various styles, wereanalyzed to determine the factors that played arole in subjects' judgments. In the study of 12-tonemusic (excerpts from two of Schoenberg's works),two groups of subjects could be distinguishedwhose patterns of responding were almost exactopposites of each other: One group, generally morefamiliar with 12-tone music, avoided tonal implications like the plague, whereas the other groupwas governed by whatever tonal implications theycould derive from surface features such as notelength and recency. Similarly, in the experimentusing North Indian music in different keys (thats),experienced subjects gave probe tone profiles thatenabled Krumhansl to recover through multidimensionalscaling analysis the key (that) distancemap postulated a priori, whereas other subjectsgave a much less clear pattern and seemed to begoverned by surface features of the music ratherthan by the underlying scales. Krumhansl's conclusion that "listeners can set aside ... expectationsand hea r the pitch events in style-appropriateterms quite independently of their prior musicalexperience" (p. 268) is perhaps premature, but herresults demonstrate that musical compositions indifferent styles often provide the "surface" information (emphasis, repetition, lengthening ofimportant notes) a listener needs to infer thecharacteristics of the style, so the prior experienceis simply not needed to appreciate simple structural features. Interestingly, orthodox 12-tonemusic is different in that it studiously avoids suchsurface aids to the listener, so, in order to respondappropriately to this music, listeners need to knowwhat not to expect. This is an interesting demonstration of the inherent radicalism of dodecaphonic music, and an indication that it negatesnot only traditional (i.e., 19th century) aestheticvalues but psychological principles as well


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A reTJiew ofCllrol L. KrumNl1ISl's Cognitive Foundaticms o[MusiCllI Pitch 281

In he r final chapter, Krumhansl first discussesrather briefly some formal properties of the tonalsystem an d of some other scale systems,6 andspeculates that these properties may have arisenfrom psychological constraints, thereby suggestinginteresting future research to be done. The finalpages summarize the principal findings from theempirical studies. The perception of tonal music issaid to exhibit "one of the hallmarks ofa cognitivesystem: th e categorization an d classification ofsensory information in terms of a stable, internalsystem o f s tr u ct ur a l relations (p. 282). Thatsystem, Krumhansl claims, is a bs tr ac te d a n dinternalized by listeners from th e sound events inthe music they encounter; that is, it is learned andstyle-specific, though it makes use of generalcognitive architecture to represent th e externalregularities.Krumhansl's book is a superb accomplishmentand represents cognitive psychology at its best.This does not mean that it is beyond criticism. Thequestion is, quit e simply, whether cognitivepsychology a t its (current) best is good enough toexplain musical phenomena. Music is a veryhighly developed art form whose complexitieshave kept musicologists busy for centuries.Cognitive psychology is n ot p ar ti cu la rl y wellsuited to studying art forms, or at least has notyet proven to be. What, to Krumhansl, are majorinsights gained from a decade of research may beplatitudes to a musicologist (Butler, 1990) ormusician. This problem is endemic to cognitivepsychology, which searches for general principlesthat cut across many domains. However, it is withthe specific properties of music that th e study ofmusic proper begins. I t could be argued thatcognitive psychology an d th e serious study ofmusic ar e mutually exclusive, though perhapscomplementary. If so, then even a tour de forcesuch as Krumhansl's research will inevitably missth e significant issues in music perception.Nevertheless, it may provide a general frameworkwithin which these music-specific issues may beaddressed in a more rigorous manner.The probe-tone task has been cri ticized byButler (1989) as being insensitive to th e dynamicunfolding ofharmonic implications in tonal music,as permitting alternative listener strategies, andas being more sensitive to the tone distributions inthe key-defining context than to the implied tonality. Krumhansl's reliance on tabulations of notedurations and frequencies was likewise attackedby Butler as being a crude method. The resultingexchange (Krumhansl, 1990; Butler, 1990) has notsettled these issues completely, a nd f ur th er re-

search will be necessary. It certainly would be inappropriate to conclude (as Butler tends to do)that any of Krumhansl's results ar e artifactualuntil they have been proven to be so by careful fol-low-up experiments.7 For one thing, most of herfindings are in good agreement with conventionalmusical wisdom, which makes it likely that theywill s ta nd t he test of time. It seems to this reviewer that Krumhansl ha s justifiably ignoredsome significant musical detail in order to arriveat generalities, bu t the detail will have to be dealtwith eventually. The dynamic tracing ofharmonicexpectations described in Chapter 9 certainly is aninteresting beginning in th a t direction.Unfortunately, th e probe tone method becomesprohibitively time-consuming as a tool for investigating modulations in real music, and trained musicologists' judgments may ultimately prove notonly more convenient bu t also more reliable.Like most cognitive psychology studies,Krumhansl's research is not concerned specificallywith expert knowledge. After finding early on that

musically untrained subjects tend to us enonmusical response strategies in the probe tonetask, she relied in the following on listeners whoha d considerable musical training but were notnecessarily p ro fe ss io na l m us ic ia ns ormusicologists. This is both a strength and aweakness. I t is a strength in so fa r as itdemonstrates th e solid, ingrained knowledgemusically informed listeners have of th e tonalsystem. I t is a weakness in that it does no tc ha ra ct er iz e w ha t, if anything, musicallyuninformed listeners know about music, and,more importantly, in th at it misses th e specialskills an d insights provided by highly trainedmusicians and musicologists. In any investigationof a highly developed art, expert judgments mustbe th e measure of validity-even if thosejudgments sometimes diverge. The consensus ofaverage l isteners can tell us w hat th e averagelistener knows, bu t it will no t capture th e fullsubtlety ofthe phenomena under investigation.What about Serafine's (1988) warnings, cited atthe beginning of this review? I t is certainly truethat Krumhansl took certain musical elementsth e "results of reflection-a s given an d proceededto develop he r representations of mental structures in terms of those units (tones, chords, andkeys). Her claim is undoubtedly that, even whennot reflected upon, these units play a functionalrole in mental processing. It is also true, however,that th e probe tone task directs th e listener's attention to a particular unit (a tone or chord) andrequests a judgment about it in the context of an


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often stereotyped and much-repeated, musicallytrivial context that, moreover, is rendered in electronic sound and with mechanical timing and dynamics. There are- exceptions, such as the experiment using actual excerpts from Schoenberg's music as the context for probe tones (Chapter 10). Onthe whole, however, it is quite possible that themusical samples in Krumhansl's experimentswere not "listened to as music" by which Serafine(1988) presumably means that they were not perceived as musically meaningful or expressive. It isthe more remarkable, then, that these meaningless sequences inevitably and strongly engagedthe listeners' knowledge of tonal hierarchy structures; in a sense, then, they had some musicalmeaning, after all. It is the cognitive psychologist's trump card that even highly schematicstimuli often engage mental structures designedfor much more complex and ecologically validevents. It is the expert's wild card, however, thatonly a very limited subset of pertinent structurescan be probed in this way, so that an impoverished view ofcomplex phenomena may result.In her introduction, Krumhansl refers severaltimes to "musical experience," bu t her researchdoes not really deal with listeners' experiences.They made judgments that followed certain patterns; what they experienced, we do not knowprobably boredom. Krumhansl's spatial maps pre

sent us with crystallized configurations-mentalstructures in vitro, as it were, that can be regarded with awe, like a piece of modem architecture. They convey none of the excitement andpleasure that comes from exploring the building,its comers and hallways. For an appreciation ofmusical meaning, we must read Langer (1953) orZuckerkandl (1956) or Clynes (Clynes &Nettheim, 1982)-

repp, b. h. (1992). a review of carol l. krumhansl's cognitive foundations of musical pitch....

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