Brower - A Cognitive Theory Of Musical Meaning.pdf

Yale University Department of Music

A Cognitive Theory of Musical Meaning Author(s): Candace Brower Source: Journal of Music Theory, Vol. 44, No. 2 (Autumn, 2000), pp. 323-379 Published by: Duke University Press on behalf of the Yale University Department of Music Stable URL: http://www.jstor.org/stable/3090681 . Accessed: 04/06/2014 13:28 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp

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A COGNITIVE THEORY OF MUSICAL MEANING

CandaceBrower

1. Introduction This articlepresentsthe outlines of a theory of musical meaningthat drawsupontwo ideasthathaverecentlyemergedin the cognitivesciences. First is the notion thatthinkingconsists, at least in part,of matchingpatternsof thoughtto patternsof experience.Second is the notionthatmuch of ourthinkingconsists of mappingpatternsof bodily experienceontopatternsin otherdomains.Althoughthe theorydrawsupon work carriedout across the cognitive sciences, it focuses upon the work of two writerssocial scientistHowardMargolisand philosopherMarkJohnson. According to Margolis (1987), all thinking-from the recognitionof a musical motive to the proof of a mathematicaltheorem-is based on patternmatching.1That is, we make sense of the world aroundus by matching perceived patterns to patterns stored in memory. Margolis describes the cognitive process as beginning with the selection of a patternto matchan incoming stimulus.Selection is carriedout throughwhat he calls jumping, or a leap of intuition.Selection may be immediate,as when we see a familiarobject. Or it may take a certainamountof time, as when we see someone whose appearancehas changed significantly since we last saw them. If the match is exact, or nearly so, the searchfor 323

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meaningmay end there. If the matchis only approximate,however,this may initiate a second step in the cognitive cycle, called checking, in which we compare patternsand note their similarities and differences. Checkingmay then give rise to higherlevels of meaning,as we initiatea search for a higher-level patternto account for similarities and differences found in patternsmatchedat a lower level. Patternmatchingalso plays an importantrole in MarkJohnson'stheory of embodiedmeaning(Johnson1987).2Johnsonclaims thatmuch of ourthinkingis metaphoricalin thatit involves a mappingof patternsfrom one domain of humanexperience to another.The patternsthat Johnson describes as most basic to our thoughtprocesses derive from the immediate experienceof our own bodies. Beginning with our firstattemptsto reach out and grasp a toy or a morsel of food, we learn about such phenomena as cause and effect, motion, force, energy, and balance through the ways in which they play a partin our own goal-directedactions.This learning is capturedin the form of patternsthat Johnson calls image schemas.Accordingto Johnson,we use image schemasto make sense of our experiencesin more abstractdomains-domains as diverseas visual art, emotion, social interaction, and mathematics. For example, the BALANCEschema, which we learnthroughthe balancingacts of our own bodies, allows us to make sense of such diverse concepts as visual balance, emotional balance, balance of power, and balancing an equation. Bodily image schemas-especially those involving force and motionappearto underlieour understandingof music as well.3We findevidence of this in the languageused to describeit: strong and weak beats, rising andfalling lines, voice leading, leading tones, harmonicgoals, and so on. Musicalpatternsparticularlylend themselvesto this sortof metaphorical mapping,being markedby changesof rateandintensitythattranslateeasily into force and motion. These two theoriesprovidethe basis for the theory of musical meaning to be offered here. Margolis's theory of patternmatching suggests thatmusic takes on meaningwith respectto itself as a resultof our mapping the musicalpatternsthatwe hearonto those storedin memory.Johnson's theory of embodied meaning furthersuggests that these patterns take on metaphoricalmeaning as a result of our mapping them onto image schemasderivedfrom bodily experience.Accordingto the present theory,musical meaningarisesmore specificallythroughthe mappingof the heardpatternsof a musical work onto three differenttypes of stored patterns:(1) intra-opuspatterns-patterns specific to the work itself; (2) musical schemas-patterns abstractedfrom musical convention;and (3) image schemas-patterns abstractedfrom bodily experience. These threetypes of patternmatchingare shown in Figure 1. The firsttwo types give rise to intra-domainmapping,while the thirdgives rise to metaphorical, or cross-domainmapping.4 324

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bodilyexperience Figure 1. Musical patternmatching A centralpremiseof the theoryis thatmanytonalconventionsarethemselves groundedin bodily experience.Thatis, the image schemasthatlend coherence to our bodily experience are metaphoricallyreflectedin conventionalpatternsof melody,harmony,phrasestructure,and form.These conventional mappings are the everyday metaphors of music-crossdomainmappingsthat are carriedout easily and unconsciouslyby experiencedlisteners.Understandinghow tonalconventionreflectsbodilyexperiencecangive us insightintothenovelmetaphoricalmeaningsof a musical work,just as examiningeverydaylinguisticmetaphorscan provideinsight into the more complex metaphorsof poetry(LakoffandTurner1989). Conventional cross-domain mappings-the everyday metaphors of tonal music-can be representedin the form of music-metaphorical schemas. These schemas show in a generalway how the variousaspects of tonal organizationare shaped by the image schemas that underlie them. The conjoiningof musical and image-schematicstructurein these schemas is representedby double arrows in Figure 1. Each musical schema serves as a templateupon which can be mappedthe concretepatterns of a musical work. Correspondencesbetween concretepatternand musical schema yield generic-level metaphoricalmeanings, which then serve as the backdropfor the interpretationof their differences on the basis of more complex metaphoricalprojections. Intra-opuspatternmatching adds yet anotherlayer of meaning. Patterns that recur within a musical work map not only onto schemas for tonal convention,but also onto versions of the same patternheardearlier in the work.Each pattern,or paradigm,establishesits own paradigmatic axis, with each new statementof a patternmappingonto those that precede it, as shown in Figure 2.5 Drawing upon the basic-level metaphors MUSICAL EVENTS ARE ACTIONS

and

A MUSICAL WORK IS A JOURNEY,

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325

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Figure 2. Intra-opuspatternmatching can interpretsuccessive statementsof a patternas a sequence of related actions making up a musical narrative.It is intra-opuspatternmatching thatallows us to assign relativelyprecise meaningsto surface-levelmusical events. The close correspondencebetween the patterns matched heightens our sensitivity to their differences,allowing even subtle alterations to take on meaning through their contributionto the narrative structureof the work. The remainderof this articleexpandsupon the theoryoutlinedabove, with the aim of developingtools for analysis thatcan help to uncoverthe metaphoricalmeanings of individualmusical works. Parttwo examines the image schemas that are most pervasivein our everydayexperience, schemas that play an especially importantrole in our embodied understandingof music. Partthree shows how these image schemas map onto conventionalfeatures of tonal melody, harmony,key, and phrase structure, capturedin the form of music-metaphoricalschemas. Partfour offers an overview of musical narrativeand musical plot structure,showing how variedpatternrepetitioncontributesto the narrativeunfoldingof a musical work. Partfive presentsa narrativeanalysis of Schubert's"Du bist die Ruh"' that serves to illustratethe analytictechniquesintroduced and to reveal the richly integratednetwork of cross-domainmappings through which the meaning of the song is conveyed. The article concludes by consideringthe theory'srelevancefor music outside the common-practiceperiod, as well as its potentialfor furtherdevelopment. 2. Embodied Image Schemas The image schemasthat appearto play the most importantrole in our embodiedunderstandingof tonal music-CONTAINER, CYCLE,VERTICALITY, BALANCE, CENTER-PERIPHERY,and SOURCE-PATH-GOAL-are also

amongthe most pervasivein everydayexperience.These schemasreflect 326

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basic featuresof our bodily experienceof space, time,force, and motion, as follows: 1) We experience space as made up of boundedregions. 2) We experiencetime as markedoff into cycles. 3) We experience the body as centered,balanced, and extending upwardfrom a stable ground. 4) We experience motion as following pathwaysleading to goals. Mapping these features of our bodily experience of the physical world (the source domain) onto music (the target domain) yields the musicmetaphoricalconcepts of musical space, musical time, musical force, and musical motion.6 Certaingeneral characteristicsof the image schemas to be discussed here shouldbe kept in mind. First,althoughthey arerepresentedin visual form, the understandingthat they convey is primarily somatosensory. Ourunderstandingof the interactionof such propertiesas motion, force, and balance derives from our own bodily motions, from ourselves exerting force and having forces act upon us, and from maintainingour own sense of balance. Second, two or more image schemas may combine in cross-domainmappings,allowing for the constructionof more complex metaphoricalmeanings. Because image schemas are both simple and abstract,they are easily adaptedto one anotherand a varietyof structural featureswithinthe targetdomain.Finally,each image schemalends itself to elaborationon the basis of its entailments,consequences of its structurethatgive rise to moreextendedinferencesandthus to moreelaborate metaphoricalinterpretations. The following discussion focuses on those entailmentsand combinations of schemas thatplay a significantrole in the constructionof musicmetaphorical meaning. In some cases, this will involve combining schemas that govern aspects of bodily experience that are likely to cooccur.Forexample, ourexperienceof an orderedrelationshipamong stable and unstabletones appearsto result from the simultaneousmapping of pitches onto threedifferentimage schemas-CENTER/PERIPHERY, VERTICALITY,and BALANCE-reflecting our association of bodily stability with centeredness,uprightness,and balance. The CONTAINER schema, by which we conceptualize space, consists of a boundaryand two regions, inside and outside, as shown in Figure 3. Entailmentsof the schema that can be inferredfrom the propertiesof physical containersinclude the following: (1) An object must be either inside or outside of a container. (2) Motion from inside to outside (and vice-versa) is constrainedby the walls of the container. 327

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outside

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Figure 3. CONTAINERschema

NESTEDCONTAINERS + CENTER-PERIPHERY

Figure4. Schema for hierarchy (3) A containermay itself be in motion. (4) Smallercontainersmay be nested inside largerones. (5) The boundariesof a containermay be fixed or flexible. (6) A flexible containermay expandor contractin response to changes in internalor externalpressure. Inthephysicalworld,we experiencecontainmentmostdirectlythrough our bodies. We experiencethe body itself as a containerwith other containersnestedwithinit-the lungs, the stomach,andotherinternalorgans. We experience containmentat a particularlyvisceral level throughthe expansionandcontractionof the lungs, which give rise in turnto feelings of tension and relaxation.We also experienceourselves as nested within a series of ever-largercontainers-a room, a building,a neighborhood,a city, a state. The schema for nested containersmay also combine with a CENTER-PERIPHERY schema, as shown in Figure 4. Figure 4 shows one way in which we understandthe concept of hierarchy-that is, as successive layers radiatingoutwardfrom a core. We tend to conceive of its structureas originatingin the center,with each addedlayer mirroringin some way the structureof the core.7 The CYCLE schema serves to organize our experience of time and the changes by which we measuretime. Figure 5 representsthe CYCLE 328

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schema in two forms, each highlightingdifferentfeaturesof the schema. As a circle in Figure 5a, the schema implies continuousmotion along a closed pathway,each iterationof the cycle ending where it began. As a wave in Figure 5b, the cycle takes the shape of a repeatingpatternof peaks andtroughs,suggesting climaxes alternatingwith points of repose. Figure5b emphasizesthe periodicityof the cycle, its capacityto markoff equal, or functionallyequivalent,units of time. The CYCLE schema combines easily with the CONTAINER schema,

incorporatingmuch of its structure.The circle, being closed, can be conceptualized as a containerfor motion aroundits perimeter.In its wave form, individualiterationsof the cycle mark off units that can be conceptualized as temporal containers, their boundariescorrespondingto beginnings and ends. These temporalcontainersmay be of fixed duration, as in the case of conventionalcycles such as minutes, hours, and weeks, or they may be subjectto expansionandcontraction,as in the case of most bodily cycles. Cycles may also be nested, with largercycles subsuming smallerones, producinga temporalhierarchycomparableto the spatialhierarchyshown in Figure 4. An importantfeatureof the CYCLEschemathatis revealedby its wave

a.

b.

Figure 5. CYCLE schema

up vs. down tension vs. relaxation Figure 6 329

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form is its inherentbinarystructure.As Figure6 shows, each iterationof the cycle is made up of complementaryhalves. This reflects the alternation of processes or states relatedby binaryopposition:up versus down, tension versus relaxation,in versus out, departureversus return.We observe this sort of opposition in many bodily cycles-the alternationof left andrightin walking,in andout in breathing,back andforthin swinging. The alternationmay be balanced,so thatthe halves of the cycle mirrorone anotherexactly.Orthe alternationmay be asymmetrical,as in the case of most bodily processes of tension and relaxation,with the climax sometimes coming well after the midpoint of the cycle. A wave can assume an infinite varietyof forms, and in fact it is this kind of flexibility that allows the schema to play such a pervasive part in our understandingof temporalexperience. The schema shown in Figure 7 combines aspects of schemas for and BALANCE. It reflects the way that CENTER-PERIPHERY, VERTICALITY,

the force of gravityacts uponthe body,causing us to maintainan upright, balancedposition with respectto the earth'ssurface.The downwardpull of the force of gravitycauses us to interpretthe groundas both a point of origin and a maximally stable position. The closer we are to the ground, the more stable we feel ourselves to be. The central,verticalaxis can be interpretedsimilarlyas a maximallystableposition withinthe horizontal dimension.We experiencethe body as maximallystable when its weight is evenly distributedaroundits verticalaxis. Any change in this distribution will cause the force acting on one side of the body to temporarily outweigh thaton its opposite,resultingin an impulse to adjustthe body's position so as to restoreequilibrium. An important entailment of the CENTER-VERTICALITY-BALANCE schema

is the establishmentof a consistentrelationshipbetween stabilityandtension. We experiencebodily tension wheneverwe extendthe body upward in opposition to the force of gravity,and likewise we experience relaxation when we allow the body to fall back downward.In a similar way, we tense our muscles when we shift the body away from its centralaxis

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center schema Figure 7. CENTER-VERTICALITY-BALANCE 330

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forceof propulsion x

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motion path

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schema Figure 8. SOURCE-PATH-GOAL so as to keep ourselves from being pulled over sideways, and we relax them again once we realign ourselves vertically. schema shown in Figure 8 organizes our The SOURCE-PATH-GOAL

experienceof motion, specifically goal-directedmotion.8The basic components of the schema are (1) the source, or point of origin, (2) the goal, (3) the pathleading from sourceto goal, (4) the trajectoryof motion, and (5) the force propellingthe motion. Relevantentailmentsof the SOURCEschema include the following: PATH-GOAL

(1) Motion is carriedout by an agent who wills the motion to take place. (2) Goal states tend to be maximallyor minimally stable within a local context. (3) Lower-levelgoals tend to be subsumedby higher-levelones. (4) The endpointof motion may or may not coincide with the goal. (5) Motion may or may not follow a path leading to the goal. (6) Otherforces, including gravityand inertia,may enhance, inhibit, deflect, or block motion towarda goal. (7) Blockage producedby otherforces may be overcome by repeating the action, increasingthe force of propulsion,or by seeking alternatepathwaysof motion. The (8) approachto a goal tends to be accompaniedby an increase in tension and arrivalat a goal by relaxationand the slowing and/orstoppingof motion. Entailment 1 describes a feature of the SOURCE-PATH-GOALschema that plays a centralrole in its mappingonto tonal music: an agent who conceives of the goal and who causes motion to take place.9This entailment in turngives rise to many others. Entailment2 suggests that there are two distincttypes of goals, reflectingthe humanneed for movement, activity,and challenge on the one hand, and for rest, security,and stability on the other. We tend to move through life in cycles in which the attainmentof one type of goal is followed by striving for the other. In leaping, we extend the body to its highest possible point, only to seek a stable landingimmediatelyafter.Entailment3 likewise reflects our need for a largersense of purpose.When we pursuea higher-levelgoal thatcan

331

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only be reachedthrougha series of small-scale actions, we imbue those actionswith a meaningbeyondtheirimmediatefulfillment.Fromthe taking of a single step, to the executionof a series of steps from one location to another,to the completionof an entirejourneyinvolving departureand return,each completedmotion takes on meaningin relationto the whole. Entailment4 distinguishesbetween the goal of motion and its endpoint, while entailment5 makesa similardistinctionbetweenthepath for motionandits trajectory.Both goal andpathwaymustbe conceptualized before goal-directedmotion can take place. Yet, motion directedtoward a goal may not reach its goal, or may diverge from the pathwayleading to it. As entailment6 suggests, otherforces may preventmotionfrom following its expectedcourse. This may resultin the repetitionof action, an increasein the force of propulsion,or the searchfor an alternativepathway, as suggestedby entailment7. Entailment8 reflectsthe way we experiencespeed andtension as they play a partin our own goal-directedactions.As we approachan unstable goal, we tend to move towardit with increasedspeed, tension, and anticipation. Upon reachingthe goal, we tend immediatelyto seek its opposite-stability, relaxation, and the slowing and/or stopping of motion. Thus, each completed motion correspondsto a completed cycle of tension and relaxation. The correspondencebetween completed motions and cycles of tension and relaxationallows for the superimpositionof the SOURCE-PATHGOAL schema onto the CYCLE schema.A single completedmotion is representedin Figure9a, a series of completedmotions in Figure9b. In this superimposition,stable and unstablegoals map onto troughsand peaks, respectively,while beginnings and ends of motion map onto beginnings and ends of cycles.

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3. Music-Metaphorical Schemas 3.1 Melody. Among the conventions for tonal melody that can be representedimage-schematicallyare the following: (1) Melody moves primarilyby diatonic step, secondarilyby chromatic step or arpeggiation. (2) An unstablemelodic pitch normallyresolves downwardand/orto its neareststable neighbor. (3) Melody normallycomes to a point of final rest on the tonic. Evidence of the embodied origins of these conventionsis to be found in the languageused to describethem.The descriptionof melody as moving by step clearly reflects the bodily experienceof walking. Interpreted according to the SOURCE-PATH-GOALschema, it suggests a step-by-step

progression along a pathway leading to a goal. Just such an image is brought to mind by Schenker's description of the fundamentalline: "Since it is a melodic succession of definitesteps of a second, the fundamental line signifies motion, striving towarda goal, and ultimately the completionof this course. In this sense we perceiveour own life-impulse in the motion of the fundamentalline, a full analogy to our inner life." (Schenker,[1935] 1979, 4) The schema in Figure 10 makes explicit the cross-domainmapping that underliesthe metaphorof goal-directedmotion, allowing us to observe specific points of correspondencebetween musical and imageIt representsthe diatonicscale as a pathwaythrough schematicstructure.10 melodic space ascending from 1 to 8, with the chromaticscale and the arpeggiatedtonic triadappearingas alternativepathways.The pitches of the tonic triadappearas stable pillars, showing that they are likely resting points for melodic motion. Differences in the width of these pillars representdifferences in stability,the widest pillar being occupied by 1, followed by 8, 5, and then 3. Solid and dottedhorizontallines convey differing degreesof stabilityas well, with diatonicpitches shownto be more stable than chromaticones.11 Thatthe tones occupying stablepillarsarerankedin the orderin which they appearin the overtoneseries suggests thatit is in relationto the overtone series thattheir stabilityis understood.12Figure 11 providesan embodied explanation.Its mapping of the overtone series onto the VERTICALITY schema portraysthe fundamentalas metaphorical"ground,"the lowest, most stable location within the musical space of a single tone. By extension, harmonicroot and tonic pitch can be interpretedas "ground" tones within triadicspace and key space, respectively.13Since the VERTICALITY schema correlatesstability with vertical height, the relative stability of the othertones of the tonic triadcan be correlatedwith theirheight above this metaphoricalground. 333

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Figure 10. Melodic paths, forces, and stable goals in a majorkey As a consequence of our interpretingmelodic tones as having differing degrees of stability,we experiencethem as acted upon byforces. We feel these forces to act most strongly on the unstabletones of a melody, pulling them upward or downwardto the closest stable tones. Rudolf Arnheim (1984) points out that the sensation of forces plays an analogous role in our experienceof visual art.Accordingto Amheim, in viewing art, we experiencevisual objects as if they were governedby forces of attractionand repulsion.The most pervasiveof these forces he likens to the force of gravity,which causes us to experienceall visual objects as if they were pulled downward. More localized forces are felt to be exerted by the individual objects themselves, which we experience as pulled towardor repelledby otherobjects.Overall,the individualobjects seem to strivetowardlocationsthatwould allow these forces to come into balance. In a similar way, Arheim proposes, we experience musical tones as subject to both a constant downwardpull of gravity, which acts with equal strengthat all locations, and a more variable force of attraction exertedby the tonic. He suggests thatthese two pulling forces act to reinforce or oppose one another,the downwardforce of gravitylessening the upward pull to 8 in the motion from 7 to 8, while strengthening the downward pull to 1 in the motion from 2 to 1. Steve Larson (1993) has elaborated upon Arnheim's theory of melodic forces, invoking a third force of inertia, which he defines as the tendency for melodic motion to continue in the same direction. He attributes the force of tonal attraction not to the tonic pitch alone, but to each member of the tonic triad, each of which he describes as exerting a pull on the 334

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unstablepitches on eitherside. He explainsthatjust as the attractiveforce of a physical magnet increases with proximity,so does the pull exerted by stable tones on their unstable neighbors.As a result, we experience this force as strongor weak, dependingupon whetherthe tones are separatedby half step or whole step. Thus, we experiencea strongpull from 7 to 1 and 4 to 3, but only a weak pull from 2 to 1 and 6 to 5. The melodic forces of inertiaandgravitythatLarsondescribesappear to be the resultof the metaphoricalprojectionof ourbodily experienceof these forces in the physical world. That we experience the pull of the tonic with similar vividness suggests that this force also has embodied origins. In The Body in the Mind, Johnson accounts for the interplayof visual forces described by Amheim-the experience of objects being attractedor repelled by one another-in terms of the workings of the BALANCE schema. I propose that the BALANCE schema similarly underlies our experienceof the pull of the tonic.14 We have alreadyobserved that mappingthe overtone series onto the VERTICALITY schemayields the metaphoricalconcept of tonic as ground. Yet another image-schematic mapping, that of NESTED CONTAINERS,ap-

pearsto underlieourunderstandingof tonic as center. Based uponexperimentaldataon the perceivedrelatednessof tones, Krumhansl(1979) has proposeda three-tieredhierarchicalarrangementof triadic,diatonic,and chromaticpitches, which she representsin the form of a three-dimensional cone. Figure 12 shows how this arrangementof pitches can be represented image-schematicallyas a set of nested containers.The pitches of the tonic triadconstitutethe core, the remainingdiatonic pitches the

-E -C -G less stable more stable C

C fundamental a ground schema Figure 11. OVERTONE-VERTICALITY 335

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middle layer, and the chromaticpitches the outermostlayer.This schema combines the NESTEDCONTAINER schema with CENTER-PERIPHERY and BALANCE schemas to

representthe pitches of the central tonic triad as maximally stable, and the remainingdiatonic and chromaticpitches as progressivelymore unstableas a result of their increasingdisplacement from the center. Note that the schema in Figure 12 attributescentricity to the tonic triadas a whole. In this schema,the pitches of the tonic triadjoin together to form a central axis, the most stable location within the horizontal dimension. Yet the pitches of the tonic triad, being of different height, occupy different positions along the central, vertical axis. Thus, the BALANCEschema applies both horizontally(i.e., to horizontaldisplacement from the central axis) and vertically (i.e., to vertical displacement from stable locations along the central axis). As a result, unstabletones seem to gravitatetowardthe stable tones that are closest in height, each one acted upon most stronglyby the stable tones immediatelyabove and below. These two stable tones exert opposing, but unequalforces thatwhen combinedwith the force of gravity-determine the overall strength and directionof the pull towardone tone or the other. Figure 13 providesa physical analogy,showing the change in the balance of forces acting upon a block rotatingfrom a lower to an upperposition along an inclined plane. Like a tonal melody moving through the space of an octave, the block can occupy four differentstable positions, one for each side of the block. As the block rotatesfrom one stable position to the next, at first the unequalforces acting on either side sum to a force that strongly favors motion back to the lower position (point b). Once the block has rotatedhalf way (point c), the force on the left still slightly outweighs thaton the right,reflectingthe overall downwardpull of gravity,thus favoring motion once again to the lower position. Continued rotationof the block eventually results in a change in the overall direction of the pull (point d), so that the sum of the forces now favors ^Bf

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Figure 13 rotationto the higher position. In a similarway, an unstablepitch that is closer to its lower stable neighbor (i.e., 4), is felt to be pulled strongly downward,an unstablepitch thatis equidistantfrom its two stableneighbors (i.e., 2) is felt to be pulled weakly downward,while one thatis closer to its upper neighbor (i.e., 7), is felt to be pulled strongly upward.This distributionof strongand weak forces of attractionis shown in Figure 10. Figure 14 reveals a slightly differentdistributionof melodic forces for the minor mode. Withinthe lower tetrachord,we might expect the lowering of 3 to b3in minor to result in a weakening of the pull from 4 to 3 and a change in the directionof pull for 2. Yet 4 and2 resolve in minoras they do in major, suggesting that the OVERTONE-VERTICALITYschema,

with its implied majortriad,overridesthe schema for the minormode in determiningthe strength and direction of the pull of the tonic. In the upper tetrachord,on the other hand, the lowering of 6 to 16 results in a much strongerdownwardpull to 5. Of the unstabletones of the scale2,4,6, and7-only 6 changes its location in the shift from majorto minor mode. This may explain why i6, much more than ,3, has been exploited-especially by Romantic composers-as an expressive marker of the minormode. In harmonicminor,the downwardpull from L6to 5 is intensified by the opening of a gap between k6 and #7, which impedes continuedmelodic ascent. It is here that we find the motivationfor raising both 6 and 7 in the ascending melodic minor scale, and for reverting to the lowered scale degrees in the descending form. In melodic minor, forces of inertiaand tonal attractionwork togetherto allow both ascending and descending motion to follow the path of least resistance. Differences in the experienceof ascendingand descendingmotion in majorand minor modes appearto underliedifferences in their affective associations as well. As far back as the Renaissance, major mode has been associated with happiness and minor mode with sadness (Zarlino 1558). Arheim (1984) offers a bodily explanation for these feelings, 337

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B4

C

Figure 14. Melodic paths and forces of tonal attractionin a minorkey attributingthe feeling of "vigor"associated with the majormode to the ease with which melodic motion seems to ascendwithin the majorscale, andconverselythe feeling of sadnessassociatedwith minorto the apparent effortfulness of the ascent in minor.15Arheim argues that rising motionis facilitatedin the majormode by the placementof half steps and whole steps within the scale. Within each tetrachord,the "vigorous" motion of the first two whole steps is followed by an easier half-step ascent at the end, the repetition of this patternof intervals within the space of an octave causing us to hearthe motion from 3 to 4 as parallelto thatof 7 to 8. In the minormode, on the otherhand,the lowering of scale degree3 makestraversalof the lower tetrachordmore difficultby robbing us both of the vigor of the motion from 2 to 3 and the feeling of resolution in moving from 3 to 4. The lowering of scale degree 6 makes ascent within the uppertetrachordeven more difficult,with the ascent from5 to 6 hinderedby the strongpull from L6back to 5 and the ascent from 6 to 7 by the widening of the gap between them. Figures 10 and 14 provide a "snapshot"view of the distributionof melodic forces for major and minor scales, implying that the center of tonal gravity remains fixed. Yet just as we continually shift the body's center of gravity so as to maintainstability while in motion, we realign ourharmoniccenterof gravityover the course of a musical work in order to maintainour sense of stability with respect to harmonyand key. Reflecting the nested structureof the tonal hierarchy,we interpretthe root, third, and fifth of the sounding harmonyas most stable at a lower level while interpretingthe first,third,and fifth degrees of the key as more stable at a higherlevel. As a result,we experiencethe forces of tonal attraction as fluctuatingover the course of a work accordingto local conditions of harmonyand key.

338

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Our experience of pitches an octave apartas not merely closely related, but in some sense identical, gives rise to yet anothermapping of melodic space, this time onto the CYCLEschema. In Figure 15, the major scale is representedas a circularpathalong which motionleads firstaway from the tonic and then back to its startingpitch. Thus, the path that is representedas continuously ascending in Figure 10 is representedas doublingback upon itself in Figure 15. This experienceof pitches an octave apartas both same and different allows for a perceptualparadox.On the one hand,we can interpreta scale as a verticalpathextendinginfinitelyupwardanddownward.Onthe other, we can interpretit as a closed circle traversingthe space of a single octave. It is this propertyof musical pitch space-that we experience it as both "open"and"closed"-that Douglas Hofstadter(1979) bringsto ourattention as anexampleof the phenomenonhe calls "StrangeLoops."He points out how this propertywas exploited by J. S. Bach to create a seemingly infinite ascending sequence in The Musical Offering,which he likens to the endlessly rising staircasesof M. C. Escher.Shepard(1964) bringsthis paradoxeven more vividly to our attentionthroughhis computer-generated "Shepard's tones," which continuously ascend while remaining within the space of an octave, much as the bands on a barbershoppole spiralever upwardwhile the pole itself remainsin place.16 Differences in the way we interpretharmonicversusmelodic distance give rise to a similarparadox.Comparisonof Figures 10 and 12 reveals that the distance between pitches-our experience of "nearness"and "farness"-differs for each schema. In Figure 10, closeness is correlated with pitches that are close in frequency. Thus, C and Db are close together,and C and G are far apart.In Figure 15, on the otherhand,closeness is correlatedwith the closeness of the harmonic relationshipbetween pitches. In this space, C and G are close together,while C and Db are far apart.Highly chromaticmusic tends to exploit this propertyof "near-yet-far," using chromaticvoice leading to move easily, yet seemingly mysteriously,to distantregions of harmonicspace.

/

B-[(-D,

\

Be

return

D

A A, r1.

Ei,

departure

E

\-

F

Figure 15. Circularmelodic path 339

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3.2. Harmony. Tonalharmonyappearsto be structuredby the same image schemas as tonal melody, with a similarset of mappings.That we describe harmonyin terms of progression suggests that the orderingof harmony,like that of melodic tones, is governed by the SOURCE-PATHGOALschema. On the one hand, tonal harmonyprovides supportfor the tones of the melody, its "pillars"making motion along an underlying melodic pathway seem secure; on the other, it traces its own course throughtonal space towardits own goals. The simplest mapping of tonal harmony onto the SOURCE-PATH-GOAL

schema is the one Schenkerproposedas the harmoniccounterpartto the motion of the fundamentalline. According to Schenker,in the progression I-V-I,"arpeggiationof the bass signifies movementtowarda specific goal, the upperfifth, and the completion of the course with the returnto the fundamentaltone" (Schenker 1935, 2). Schenker'sderivationof the I-V-I progression from the overtone series-the "chord of nature"schema, with its mapping of tonic as brings into play the VERTICALITY the As a result, progressionI-V-Ievokes the experiencenot only ground. of departureand return,but also of rise and fall, tension and relaxation. Figure 16 shows how Schenker'sinterpretationof the fundamentalstructure can be representedimage-schematicallyas a single goal-directed motion from 3 to 1 in the uppervoice accompaniedby two goal-directed motions-from 1 to 5 and back to 1-in the bass. Completion of the I-V-I progression brings into play the CYCLE schema, and with it implicationsof closure and containment.By itself, the I-V-I progressionrepresentsa completed cycle of departureand return,tension and relaxation.Yet the oppositionbetween tonic and dominant also lends itself to continuedoscillation, producingthe wave form schemawith its familiarpeaks andtroughs,as shown in Figof the CYCLE 0

a

3

2

I

V

1

I

Figure 16. Image-schematicrepresentationof Schenker's fundamentalstructure 340

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V

I

V

..... .-

V

,....I

.

V

.

I

I

- -

I

tonic > ground

Figure 17. I-V-I cycle

. -IV (IV -vii

-)

iii

vi

- vii ii -

I

Figure 18. Schema for harmonicpathways ure 17. Oscillationbetween I and V can provide an impulse for continuous motion like that of a bouncing ball or an oscillating spring. Dance movements,in particular,often make use of the oscillationbetween I and V to feed continuousmotion in the foregroundwhile avoidingthe implication of largerarcs of motion in the background. The I-V-I cycle may be expandedto bring into its compass other diatonic harmonies, as shown in Figure 18. This figure offers an imageschematicview of harmonicconventionsof the common-practiceperiod, representingthe most commonly traveledharmonicpathways for both major and minor.17It shows the I-V-I cycle nested within a series of expanded cycles, each of which representsa longer path through harmonic space beginning and ending at I. The longest path for harmonic motion can be interpretedas the backwardsextension of the pathfromV to I to form a completed diatonic circle of fifths, along which harmonic motion progressesindefinitelyby falling fifth (as indicatedby the rightward arrows), suggesting once again the influence of a metaphorical force of gravity.Justas continuousmelodic descent along a diatonicpath brings us back to our startingpitch after seven steps, harmonicdescent along the diatoniccircle of fifths bringsus back to where we began after a sequence of seven fifths. The asymmetricalarrangementof chordswithin the schemaof Figure 18, with its proliferationof chords and arrows on the right-handside, suggests that we experience harmonicmotion as if it were carriedout under the influence of the centripetal force of the tonic. The schema shows IV and vii appearingtwice-at the beginning of a cycle of fifths and above ii and V, respectively-suggesting that we interpretthese chords as the intersectionof two harmonicpathways.Although IV and 341

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vii can function as the first steps within a descending fifth progression, more often thannot they substitutefor ii andV, respectively,providinga shorterroute back to I. Alternatively,they may function as intermediate steps within an interwovencircle of thirds,as indicatedby the downward arrowsfrom IV to ii andvii to V. Figure 18 also shows IV leadingdirectly to I as partof a I-IV-Icycle thatinverts,andthuscounterbalances,the rise and fall of I-V-I.Otheralternativepaths-shown by arrowsleading from iii to IV, vi to V, and V to vi-can be interpretedas resulting from one chord substitutingfor anotherof similarpitch content;that is, iii substitutes for I and vi for IV or I. In most cases, similarityof pitch content translatesinto similarityof meaning, an importantexception being the deceptive cadence. For we interpretmotion from V to vi not as an alternativepathwayto I, but as the deflectionof harmonicmotion precisely at the point of expected arrivalat the tonic. The harmonicspace of Figure 18 may be furtherexpandedby substituting chromaticallyaltered chords (secondary dominants, augmented sixths, modal mixture, and Neapolitansixths) for their diatonic equivalents. The raising and/or lowering of individual tones within altered chordsdoes not so much changethe expectedcourse of harmonicmotion as heighten the effect of the melodic forces that contributeto musical expressiveness.In particular,secondarydominantsand augmentedsixth chordstend to heightenour experienceof goal-directedmotion by creating temporaryleading tones thatstrengthenthe feeling of pull towardthe next chord.By contrast,the chromaticalterationsthat give rise to modal mixtureand the Neapolitansixth are experiencedprimarilyas a change in affect. Modal mixturehighlights the contrastingaffective qualities of majorand minorby juxtaposingthem, the effect being much like that of chiaroscuro-the juxtapositionof darkand light areasin visual art.The Neapolitansixth takes on its own special affective characterthroughthe lowering of 2 to form a majortriadin place of one that would otherwise be diminished. It connotes the positive affect of major in a context in which the chord itself-built upon a root outside the key-is tonally unstable. Perhaps reflecting this, nineteenth-centurycomposers often used the Neapolitanto portraytransientor illusory states of happiness.18 Higher levels of tonal organization-levels at which we experience modulationas motion from one key space to another-are represented image-schematicallyin Figures 19-25. These figures combine CYCLE, PATH, and CONTAINER schemas to reveal the image-schematicorganization of the nested hierarchiesof pitch, harmony,and key. Each figure elaboratesupon the precedingone, showing a progressiveexpansion of harmonicspace from diatonicto chromaticand from fifth to triadic. Figure 19a begins by representingthe diatoniccollection as a circular pathwaythrough"fifth space,"reflecting our intuitionthat tones a fifth 342

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,FF

G ---

B

D

>

A

Eb E

Ab

'Db,. F .-B' Gb a.

b.

Figure 19. Circularpathwaysin "fifthspace" apartare in some sense adjacent;that is, maximally close.19In Figures 19a and b, we see how image-schematiclogic plays a role in modifying the sounds given to us by nature.A series of pure fifths never doubles back upon itself to form a perfect circle but ratherextends infinitely upward and downward.That is, motion by pure fifth never returnsto its startingposition within the chromacircle. However,a nearlyperfectcircle can be constructedout of a seven-note series by joining top and bottom pitches, B and F, to form a diminishedfifth. This diatoniccircle can then be expandedoutwardto the next point of near-perfectionby extending the series from seven notes to twelve. Whereas a diatonic series of fifths can be representedimage-schematicallyas a closed circle by accepting the presence of a single diminishedfifth, in the case of the chromatic circle, closure is attainedby temperingeach fifth to bring F# into alignment with Gb, thus spreadingthe imperfectionout over the entire cycle.20 These two paths throughfifth space are superimposedin Figure 20, highlighting an important correlation between CONTAINER and PATH

schemas. When we project the diatonic collection onto the chromatic circle, the diatonic collection appearsnot only as a segment of a longer path,but as a containerenclosing seven pitches of the circle. This divides chromatic space into two regions, diatonic pitches appearing"inside" and chromaticpitches "outside"the container.Througha mappingof the MOVING CONTAINER schema, we can then interpret modulation as motion

of the diatoniccontaineralong the chromaticcircle of fifths.Accordingly, the distance between two keys correspondsto the distancethe container must move around the circle of fifths-either clockwise or counterclockwise, "upward"or "downward"-to get from one key space to the other. 343

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It is here that we find an embodied explanationfor the tendency to interpretmodulationtowardthe sharpside of the circle of fifths as tensing and towardthe flat side as relaxing, for these are the very sensations that we associate with the upwardand downwardmotions of the human body. This interpretationof the sharp vs. flat dichotomy has a history nearly as long as that of majoras happy and minor as sad. Theoristsand composers of the eighteenthand nineteenthcenturiesdescribedmodulation to the sharpside as "tensing,""strengthening,"or "hardening,"and modulationto the flat side as "relaxing,""softening,"or "weakening."21 Such terms were used to describe not only modulation,but the characteristics of sharpand flat keys themselves in relationto C major(Steblin 1981). In some cases, these attributionstook the form of conventional associations of particularkeys with particularsettings; for example, F majorbecame known as the "pastoral"key. Since F majoris reachedby moving down one step from the "natural"key of C major, suggesting relaxation, it may have seemed particularlywell suited to portraythe simplicity of natureand the relaxed characterof rurallife. The paradox of "same-yet-different"comes into play once again in our experience of modulation, since continuous upward ("tensing") motion or downward("relaxing")motion along the circle of fifths eventually doubles back on itself; movementby six sharpsbringingus to the same place as movementby six flats.Yet Beethoven (and others)claimed to have had no difficulty distinguishingthe "hardness"of the key of C# majorfrom the "softness"of Db major(Steblin 1981). That enharmonically equivalent sharp and flat keys can be experienced as having different characterssuggests that the distinction is made on the basis of whether one understandsthe key to have been reached throughmotion upwardor downwardfrom C major. Figure 21 representsthe outwardexpansion of fifth space to "triadic" space, constructedby adding to each fifth a major third, thus capturing our intuition that these three tones are maximally close, reflecting their Ebmajor circleof 5ths pathway

Cmajor modulation

.-'~ I

diatoniccollection container

~\l

'

motionof container clockwisej up E counterclockwise= down

diatonicj inside chromatic outside

Db.. Ft.

Figure 20. Schema for modulation 344

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D.A.

' Bb .'.

.

.--.E.

D..: i .

44?

Figure 21. Triadicspace adjacency within the overtone series. The added major thirdsjoin together to form a second circle of fifths, interlockedwith the first as part of a chain of alternatingmajorand minorthirds.Once again, we see how the impulse for containment and closure serves to shape the musical material provided by nature. Pure thirds, in exact imitation of nature, would producea set of tones thatareclose to, but not identicalwith, those of the first circle of fifths, resulting in a potentially infinite outward expansionof pitch space. In orderto achieve closure in triadicspace, the thirdsmust be tempered-as were the fifths in chromaticfifth space-so as to bring the tones of the second circle into correspondencewith the tones of the first. Triadic space, like fifth space, brings into play NESTEDCONTAINER

andPATHschemas,as shown in Figure22. Figure22 representseach triad not only as a set of three adjacenttones, but also as a containernested within the successively larger containersof the diatonic and chromatic pitch collections. Furthermore,just as any two adjacenttones of the inner circle of fifths may join with the interveningtone in the outer circle to form a major triad, any two adjacenttones of the outer circle may join with an interveningtone of the inner circle to form a minor triad.Thus, the minor triad,despite its absence from the overtone series, assumes a prominenceequal to that of the majortriadin triadicspace. Figure 22 also shows how the NESTED CONTAINERschema combines with the CENTER-PERIPHERYschema to represent the tonic triad as cen-

ter. As Figure 22 shows, the tonic triadoccupies the central,most stable position withindiatonickey space, being balancedby overlappingIV and V chords arrangedsymmetricallyon either side. This helps to explain why the I-V-I cycle so often expands to I-IV-V-I,the latter being the resultof joining togetherthe ends of the diatonicsegmentof triadicspace to form a circle (thus reversingthe process of expansion carriedout in fifth space). The I-IV-V-Icycle can be representedin wave form by plac345

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IV

a minor triad *close

cths& 3rds pathways "pathways

V

Dths E' :,5ths&3rds= :A c: ' C,,,..\w **L;'#

C major triad *> center

B

A;

Gb major triad : distant

triadic & diatonic collections 0 nested containers

B*G

Figure 22 V I ...-j-

.j.\

I

tonic X center

IV Figure 23. I-IV-V-Icycle ing IV at the lowest point, V at the highest, and I at the midpointof the wave, as shown in Figure 23. This schema representstension and relaxation as a functionof displacement-not from tonic as ground-but from tonic as center. Thus, the I-IV-V-I cycle emphasizes the opposition between dominantand subdominant,with the tonic triadappearingat the point where opposing forces come into balance. Figure 22 representsin more concrete form the harmonicpathways shown in Figure 18. Harmonic progression can be interpretedimageschematicallyas motion of the triadiccontaineralong one of three alternative paths: the inner circle of fifths, the outer circle of fifths, or the interwoven circle of thirds. Harmonicdistance thus correspondsto the distance traveledaroundthe circle in moving from one chord to another. Modulationcan be representedsimilarly as motion of the key container along one of these three pathways,in this way introducingan additional degree of freedomfor change of key. Whereasin fifth space, C majorand a minoroccupy the same space, in triadicspace, they occupy distinct,but overlappingspaces. Thatis, modulationfrom C majorto a minorappears as motion of the diatonic containeralong the circle of thirdsby a single step in the counterclockwise direction, as shown in Figure 24. This causes D, the "highest"note within the space of C major,to reappearas 346

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the "lowest"note within the space of a minor.It also causes the main axis containingthe structuralfifths of the key (tonic, dominant,and subdominant)to shift from the innerto the outercircle, these now being filled in not by majorthirds,butby minorones. Thus, key space undergoesa kind of inversion,reflectingthe flipping of all of the triadsacross the central axis, so that the triads that were majorbefore are now minor, and viceversa. Figure25 shows the furtherexpansionof triadicspace to major-minor space, formed throughthe addition of a third circle of fifths inside the first to form two interlockingchains of thirds.This schema allows us to representparallel major and minor as overlappingcontainers,which in turncan combine to form the expandedspace of modal mixture.Figure 25 shows that the move from major to parallel minor does not involve motion along any of the three pathways,but ratherthe "flipping"of diatonic space across the central axis, capturingour intuition that parallel keys lie side by side.22 a minor

* C major

circle of 3rds 0 pathway

Figure 24. Modulationfrom C majorto a minor

C majorandC minor E overlapping containers

. .B A#"

'

,c ?

c"/.'

. C",--'FI, G.: j~"/ .J A-..D. D~* *~~B~*G1

Figure 25. Major-minorspace 347

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The shift frommajorto parallelminorpreservesthe structuralfifthsof the key, thus heighteningour perceptualawarenessof the loweredthirds. This throws into relief the affective propertiesof the change of mode, which combines the characteristicsof the move from majorto minorfrom happyto sad-with that of softening associatedwith the addingof flats. In this case, the effect of softening is due not to downwardmotion of the key container,but to the lowering of 3, 6, and 7 in melodic space. That a shift either to the minor mode or to the flat side of the circle of fifths is accompaniedby downwardmotion-whether in harmonic or melodic space-may help to explain why eighteenth- and nineteenthcenturytheoristsattributedmany of the same qualitiesto minor and flat keys, and likewise to majorand sharpkeys, with minorkeys having multiple flatsthoughtto be particularlysad and languid,and majorkeys with multiple sharps thought to be particularlycheerful and lively (Steblin 1981). The schemas that underlieour interpretationof harmonyas stable or unstableappearto be the same as for melodic tones, namely, the OVERTONE-VERTICALITY

and NESTED

CONTAINER/CENTER-PERIPHERY

schemas.

It is the latterschema that appearsto govern our perceptionof harmonic stabilityin relationto a tonic. This is conveyedmost clearlyby Figure26, which lays out the circularspace of Figure22 in horizontalfashion, with the chain of interlockedtriadscontinuingindefinitelyin eitherdirection. Like the melodic schema of Figure 12, it representsthe tonic triad as a containernested at the centerof diatonicspace, itself nested within chromatic space. It representsboth tonic triadandkey as centrallylocatedand thus maximally stable, and other harmonies and keys as increasingly unstablethe greatertheir displacementfrom the tonal center. The schema of Figure 26 relates to that of Figure 22 much as our embodied experience of the earth'ssurfacerelates to reality;that is, we experiencethe earth'ssurfaceas flatbecause its curvatureis hiddenfrom us. In a similar way, the curvatureof triadic space remains unnoticed, allowing us to interpretthe continuouschain of interlockedtriadsas the "horizontal"dimension of harmonicspace, in contrastto the "vertical" dimension that dictates the arrangementof pitches within individual chords.Like the surfaceof the earth,triadicspace lacks a fixed center,the symmetricalarrangementof tones in triadicspace giving no inherentpriority to any particularpitch, triad,or key over any other.Only with the establishmentof the key of a musical work do the hierarchicalrelations of the NESTED CONTAINER/CENTER-PERIPHERY schemabecome a perceptual reality. While our perceptionof harmonicstabilityin relationto a tonal center appearsto be governed by the NESTED CONTAINER/CENTER-PERIPHERY schema, our perceptionof the stabilityof individualchords appears 348

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IV

I

V

- - -Bb - -,F *- -C - - G - D- /V

.---G'B-----A,F---

ESB

F--

unstable --

-F - - C --G?- --- Dt --. At - -

: A:---" ---"- Fi#---"C--E --'(O---D-

stable --

unstable

Figure 26. Schema for harmonicstability schema. That is, the overto be governed by the OVERTONE-VERTICALITY

tone series serves as a prototypeagainst which we measurethe stability of each vertical sonority.23Since the overtone series representsthe most stable harmonicconfigurationof pitches, the more closely the arrangement of pitches correspondsto the overtone series, the more stable the sonority will seem to be. Thus, in tonal music, the preferencefor chords with the root in the bass at beginnings and endings of arcs of tonal motion, and especially the preference shown for a spacing that comes close to duplicatingthat of the overtone series-i.e., root, octave, fifth and third-appears to be not just a matterof preferencefor good sonority, but a reflectionof the psychological desire for maximumstability at points of musical repose. Likewise, the preferencefor ending works in the minormode in the parallelmajoror with a Picardythirdcan be taken to reflectthe closer correspondenceof the majormode to the OVERTONEVERTICALITYschema, causing us to experiencemajoras more stablethan minor. We have distinguishedhere between the "horizontal"and "vertical" dimensions of harmonicstability on the groundsthat the formeris governed by the NESTEDCONTAINER/CENTER-PERIPHERYschema and the latter by the OVERTONE-VERTICALITYschema. Yet from an experiential

standpoint,the two dimensions are not entirely separable.As we have alreadynoted, mappingtonic as groundsupportsour interpretationof the bass of I-V-I as ascending from the groundand then returningto it, thus contributingto our sense of the stabilityof the tonic. If insteadof returning to tonic, harmonicmotion continues in the same directionalong the circle of fifths, ascent will also appearto continue, with the root of each successive chordseeming to move to its upperfifth.The resultis the paradoxical sensationof motion ascendingcontinuouslyalong a closed pathway, once again bringingto mind the endless staircasesof M. C. Escher. 3.3. Phrase Structure. Figure 27 shows how the phrasestructureof a musical work maps onto a combination of CYCLEand SOURCE-PATH-

GOAL schemas, showing how the phrasesof a musical workcan be under349

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t

T

t

speeding slowing

rising tensing relaxing falling -.'-*- "" -.\

peak m

unstable stable

4^ 4^~ ~ 4^~ 4

-

.=

melodic t

....---

---tonally

?--;-

I

,V-I I

o

departure

..

.i

V V

most distant

.X X

s

.V-I

*0 o--return --

Figure 27. Schema for phrasestructure stood as a series of goal-directedmotions, with smaller arcs of motion nested within largerones. It capturesthe way thatharmony,melody, and rhythmwork togetherto articulatea series of completedmotions within an overall progressionof departureand return.In its depiction of a specific numberof phrases and relatively specific tonal plan, it constitutes more of a prototypethan a schema, illustratinghow the conventions of phrasestructuremight be realized in a typical work or section. The rise and fall of each arc of motion reflectsthe normativeshape of the melodic line-the way thatmelody tendsto rise andfall over the span of a phrase. Underlying this interpretation is the VERTICALITYschema

andthe implicationthatmotionis carriedout underthe influenceof gravity. We naturallyinterpretrising lines as requiringan output of energy and tension in orderto overcomethe force of gravity,and falling lines as giving into it. It is in the domain of melody that the mapping is most clearly iconic, since the rise and fall of each arc of motion correspondsto the actualtrajectoryof the melodic line. Horizontalarrowsrepresentcompletedarcs of harmonicmotion, each supportinga completed arc of motion in the melody. The overall trajectory of harmonicmotion shows the expected cycling of harmonyaway from the tonic and expansionof the tonic-dominantcycle. Thus, the initial arc of harmonicmotion-leading from I to V and back to I-undergoes expansionover the next threephrases,revealinga generaltendency towardmotion leading away from tonic to a point of greatesttonal distance followed by motion of return. Each phraseis representedas having two distinctgoals: the climax of the phrase-the turningpoint between tension and relaxation,and the cadence-the maximally stable event at the end of the phrase.The climax is nearerthe end thanthe beginningof each phrase,reflectinga pattern of tension and relaxationfamiliarto us from everydayexperience.24 350

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The rise and fall of each wave reflects a general correlationamong five pairsof oppositions:speeding vs. slowing, tensing vs. relaxing,rising vs. falling, unstable vs. stable, and departurevs. return.We have already observed correlationsamong the last four of these in mappings of harmony and melody onto the OVERTONE-VERTICALITYand NESTED CONschemas. In laying out the music along a TAINER/CENTER-PERIPHERY temporalaxis, we can see how rhythmalso contributesto our experience of music as goal-directed motion through our mapping of changes in durationonto motion startingand stopping, speeding and slowing. Rhythm makes the metaphor of goal-directed motion particularly vivid, for musicalrhythmsmap notjust metaphorically,butliterally,onto the sounds of bodily motion, in particularthe soundof our own footsteps in walking or running.It is primarilyrhythmthattells us where each arc of motion begins and ends. The rise and fall of each arc of motion in Figure 27 reflects this, showing the tendencyfor musical motion to accelerate leading up to a climax, followed by deceleration and the eventual stoppingof motion with the arrivalat a stable goal. The slurs underneaththe harmonyshow that phraserhythmtends to be both regularand binary,at its most regularforming hierarchiesof 2-, 4-, 8-, and 16-barunits.Suchrhythmicregularityclearlyreflectsthe workings of the CYCLEschema.At manylevels of temporalexperience,human activity tends to organize itself into cycles. From low-level patternsof walking and breathingto higher-level patternsof waking and sleeping, working and resting, we use these cycles to locate ourselves within the flow of time, anticipatingthe timing of upcomingevents throughthe regularityand predictabilityof the cycles thatthey help to define. In a similar way, we attuneto the periodicitiesof tonal music to anticipateupcoming events within a musical work. Tonal music reflects the regularityof the rhythms of everyday life while emphasizing the synchronization among simultaneouslyunfolding events, yielding a multi-leveledrhythmic hierarchythat is regular,yet flexible. At the phraselevel, this regularity allows us to anticipatewhere arcs of motion will end, thus to hear phraseexpansionas a delay in the expected arrivalat a tonal goal. Together,the music-metaphoricalschemas of Figures 10 through27 show that the bodily metaphorsthat underlietonal conventionare both complex and systematic. They show that the basic metaphorof goaldirectedmotion is supportedby mappingsof tonic as centerand ground, triadsandkeys as nested containers,scales andarpeggiosas pathwaysfor melodic motion, circles of fifths and thirds as pathways for harmonic motion, andtonal motion as subjectto forces of gravity,inertia,and tonal attraction.These basic-level metaphorsmay undergoextensive elaboration in the context of a musical work organized according to narrative principles. The MUSIC-AS-NARRATIVEmetaphor, which portrays the events

of a musical work as a coherentseries of actions, supportsmany higher351

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level conventionsof tonal music, includingthose of form.As the following section will show, many of these conventionscan be capturedin the form of schemas for musical plot structure. 4. Music as Narrative Accordingto Ivan Todorov,an ideal narrativebegins in a stable state, progresses toward disequilibrium,then reaches a new state of equilibrium by the end.25The general outlines of such a narrativestructurecan be seen in the rising and falling contoursof Figure 27. If Figure 27 portraysthe overall shape of a musical narrative,then the music-metaphorical schemas of Figures 10 through 26 provide us with more detailed informationabout its possible content. Figure 28 illustratessome of the ways that the three most importantfeaturesof these schemas-containers, pathwaysand goals-can play more specific roles in the elaboration of musical plot.26 Figure28a suggests thata musical container,at its simplest,functions metaphoricallyas a containerfor motion. Among the musical elements that can serve as metaphoricalcontainersare an interval,a chord, a key, anda registralspan.One of the most vivid meansof evoking containment is throughthe use of a stable intervalas a containerfor the motion of the melodic line. In particular,the octave-the outsideintervalof the chroma circle-combines the propertiesof stability and closure that we associate with physical containers.Many simple melodies remain entirely or mostly within the span of an octave, either from 1 to 8 or 5 to 5, suggestcombined with either TONICing a mapping of OCTAVE-AS-CONTAINER AS-GROUND or TONIC-AS-CENTER. These two mappings are portrayed

image-schematicallyin Figure29. Some musical containers,once established,may expandandcontract, as shown in Figure 28b, giving rise to feelings of tension and relaxation. We have alreadyseen thatthe schema for an expandingcontainerunderlies the gradualexpansionof the I-V-I cycle over the course of a musical work. It is also reflectedin the expansion of key space to include chromatically alteredchords. Figure 30 offers an image-schematicinterpretation of the expansion of diatonic key space to incorporatemodal mixture,augmentedsixth chords,the Neapolitan,andthe two most common secondarydominants,V/IV and V/V. The expanding containerschema may also come into play in our experience of melodic containment.A melody may remainwithin the bounds of an octave only to extend this range upwardby a single step at the climax. The feeling of tension that results can be attributedboth to the ascent and the force needed to overcome the resistanceof the upperboundaryof the octave. Perhapsthe most visceral experience of expansion comes from the registralexpansionthatresults when the rise and fall of the melodic line 352

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a. containerfor motion

b. expansion of a container

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Figure 28. Schemas for musical plot structure

is mirroredby contrarymotion in the bass. From a bodily perspective, registralexpansion and contractionmap most naturallyonto motion of the chest and lungs as we inhale and exhale. The lungs firstexpand,filling with air, as a result of the tensing of the muscles of the diaphragm, and then contractas a result of their relaxation.Roger Sessions (1950) once defineda musical phraseas "thatportionof music thatmust be performed ... figurativelyin a single breath."This suggests that we experi353

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ito8 octave 4J

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ence the expansion and contractionof registralboundariesin the typical phraseas mirroringthe motion of the chest and lungs in respiration. Figure28c shows the schema for a containerin motion, alreadyfamiliar to us as a means of representingchange of key. We have seen that modulationcan be portrayedimage-schematicallyas the motion of a key containeralong the circle of fifths. Figure 28d offers an alternativeview of modulation-one thatrepresentschange of key as motion leaving one containerand enteringanother,thus crossing a boundarybetween them. Whetherwe interpretchange of key accordingto one schemaor the other is likely to depend in partupon the relative smoothness or abruptnessof whetherthe passage tou ches upon the n and the tr ansitio between keys, interveningkeys over the course of the movementfrom one key space to the other.27 of Figure re 28 flect The remainingschemas agement of higher eng the levels of cognitive processing. To interpretmusic according to these but also be schemas, one must not only be familiarwith tonal convention, able to bringboth partsof the cognitive cycle-jumping and checking354

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into play. In Figures 28e-g, featuresthatappearin parenthesesrepresent parts of a schema recalled from memory but not actually heard, correspondingto the listener'sunfulfilledexpectations.In orderto experience melodic motion as departingfrom and returningto a pathway,as shown in Figure 28e, the completedpathwaymust firstbe constructedin imagination.To experiencemotion as blocked, as in Figure28g, one must first imagine the goal towardwhich motion is directed. WhereasFigures 28e and f show how meaningresultsfrom the divergence of a musical patternfrom schemas for tonal convention, Figures 28g-j show how meaning results from the divergenceof a patternfrom earlierversions of itself. In Figures 28g-j, each schema featuresa series of repeatedmotionsdirectedtowardthe same goal. These schemasreflect ways in which entailments 6 and 7 of the SOURCE-PATH-GOALschema

work in conjunctionwith one anotherto suggest the need for repeated action. Entailment6 suggests thatpursuitof a goal may be frustratedby forces that inhibit, deflect, or block motion, while entailment7 suggests thatthese forces may be overcomeby repeatingthe action, increasingthe force of propulsion,or by seeking alternatepathwaysof motion. It is in Figures28g-j thatwe see how intra-opuspatternrepetitioncontributesto our experience of music as narrative. Because in the case of intra-opuspatternmatching,the patternheard and the patternrecalled from memory are equally concrete, mappings can be relativelyprecise, allowing even subtle differencesto take on significance. Mappings involving intra-opus patterns and tonal schemas often work together, the mapping of intra-opuspatternsmaking overt those based on tonal convention.That is, they make it possible for us to hear literally what we would otherwise only imagine. In the final action representedin Figure28g, continuationof motion confirmsthe existence of a pathwayand goal that were previously only imagined. Likewise, in Figure 28i, the continuation of motion that previously ended at the boundaryof the containerallows us to understandthe boundaryof the containeras having blocked earlierattemptsat escape. To see how intra-opuspatternmatchingand schemasfor plot structure work togetherto give rise to musical narrative,it will be useful to examine a work in which these come fully into play. Schubert's"Du bist die Ruh"' (Example 1) provides a useful illustration.In analyzing a work with text, we can considerhow meaningemerges not only from the three forms of patternmatchingalreadydiscussed, but also from the matching of the image-schematicstructureof the music to thatof the text. In music, as in poetry,differentmetaphoricalmappingsoften work togetherto create a unified effect. Image schemas for containers,cycles, and pathways share structuralfeaturesthat allow them to be combined, each mapping onto differentdimensions of a musical work at the same time. The various alignments among these mappings contributeto the music's meta355

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phorical resonance, resulting in an intensificationof meaning like that found in poetry.28In a textedwork,this effect is furtherheightenedby the resonancesestablishedbetween music and text. 5. Analysis of Schubert's "Du bist die Ruh"' Before examiningthe image-schematicstructureof the music, it will be useful to considerthatof the text. Figure31 shows the text of "Dubist die Ruh"' side by side with its translation.Wordsand concepts thathave particularresonancewith respect to the poem itself are underlined.The text, like the music, takes on meaning with respect to itself throughthe recurrence of certain sounds and images: "peace," "longing," "joy," "pain,""eyes,""heart,"and "fullness." The poem is structured image-schematically

by CONTAINER and

schemas. The schema for goal-directed motion is evoked in connection with entering and filling two bodily containers, the eyes and the heart, two metaphoricaldwelling places for the soul. The image of a filled containerbecomes increasinglyvivid as the poem progresses,reaching a climax at the very end with the words, "O fill it full!" The poem gains much of its emotionalforce from two pairsof expressive oppositions-peace versus longing and pain versusjoy-providing an opportunityfor the heighteningof expressionthroughtheirjuxtaposition. At the beginning of the poem, the heart-metaphorically, the bodily containerfor emotion-is filled with joy and pain. The beloved is bid to enterthe dwelling place of the heartthrougha doorthatopens andthen closes, to drive out the pain and fill the heartwith joy. The poem closes by juxtaposing two complementarypositive images-the filling of the heartwith joy and the filling of the eyes with radiance. These are the metaphoricalmeanings of the poem for which we shall seek correspondencesin the music. As the analysis will show, the images conveyed by the music do not form a one-to-one relationto those of the text, but rathercomplement them, elaboratingupon and extending the metaphoricalmeaningsof the text. Figures 32 and 33 providethe main frameworkfor the analysis of the song. They reveal generic-level metaphoricalmeanings that result from the song's conformanceto tonal convention,as well as the more specific meanings that result from deviations from convention and from intraopus patternsestablishedearlier. Figure 32 shows how the music of "Du bist die Ruh'" maps onto the schema for phrasestructure.The upperpartof the figure shows the precise trajectoryof melodic motion and placementof stable and unstable goals within each phrase;phraserhythmandarcs of harmonicmotion are representedbelow. As the figure shows, the music divides clearly into SOURCE-PATH-GOAL

356

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1) Du bist die Ruh, Der Friede mild, Die Sehnsuchtdu, Und was sie stillt,

You are rest, Mild peace, You are longing, And that which stills it

2) Ich weihe dir Voll Lust und Schmerz, Zur Wohnunghier Mein Aug' und Herz,

I consecrateto you, Full of joy and pain, As a dwelling here My eyes and heart,

3) Kehr'ein bei mir, Und schliesse du Still hinterdir Die Pfortenzu,

Come enter in, And close The door quietly Behind you.

4) Treib'andernSchmerz Aus dieser Brust! Voll sei dies Herz Von deinerLust,

Drive otherpain Fromthis breast! May this heartbe filled With yourjoy,

5) Dies Augenzelt, Von deinem Glanz Allein erhellt, O full' es ganz!

The tabernacleof these eyes, By your radiance Alone is lit, O fill it full!

Figure 31. FriedrichRiickert's"Du bist die Ruh"' three sections: a piano introduction,a first phrase group, to which are sung the first four stanzas,and a second phrasegroup, to which the fifth and final stanza is sung twice. For convenience, individualphrases are numbered one through seven. Notable departuresfrom conventionthose for which we shall seek metaphoricalexplanation-are markedby exclamationpoints. As Figure 32 shows, the song exhibits many featuresof conventional phrase structure-the regular nested cycles of tension and relaxation, rise and fall, stability and instability, and departureand return.As we might expect, the song as a whole reachesboth its climax and its melodic high point in its penultimatephrase.Most lower-level arcs of motionsections, phrases, and subphrases-exhibit a similar patternof tensionrelaxationand melodic rise and fall. Yet two phrasesdepartin a notable way from the schema for melodic shape:in phraseone, the melodic peak occurs very close to the beginning;in phrasesix, it occurs at the very end. Arcs of harmonicmotion and phraserhythmlargely conform to conventions governed by the CYCLEschema. Arcs of harmonic motion 357

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Figure 32. Phrasestructureof Schubert's"Du bist die Ruh"' (piano interludesand postlude omitted) exhibit the progressiveexpansionof the I-V-I cycle, leading to and away from the tonic in ever-widening circles. Phrases one, two, and three returnimmediatelyto I, while phrasefour cadences on V followed by a returnto I at the end of phrasefive. The point of greatestdeparturefrom tonic coincides-as we might expect-with the climactic sixth phrase, which cadences on IV aftertonicizing bVI. The phraserhythmis for the most partregularand binary,showing a predominanceof two- and four-barunits. Once again, the most notable departuresfrom conventionare to be found in the firstand sixth phrases, which departin strikinglysimilar ways. Each consists of a single uninterruptedarc of tonal motion seven measureslong. These two phraseswhich stand out by virtue of their length and melodic shape-relate to 362

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one anotheras do the complementaryimages of eyes and heart;that is, througha combinationof similarityand contrast.In the analysis thatfollows, we will discover other ways in which these two phrases complement one another,highlightingtheir special relationshipto the song as a whole. Figure 32 also shows how the melody takes on more specific metaphorical meaning through mappings of the CONTAINERFOR MOTIONand EXPANDING CONTAINER schemas. In the piano introduction and first phrasegroup, the registralspace occupied by the melody is framedby 1 and8, the melody reachingup repeatedlyto 8 yet neverextendingbeyond it. The firstpartof the song thus establishesthe octave as a containerfor melodic motion, with 8 as ceiling and i as floor, allowing us to hear the melodic ascent of phrasesix as expandingthis container. Figure 33 shows how the varied repetition of intra-opuspatternsespecially those of melody-contributes to our hearing of the song as narrative.As in most tonal works, patternsrecurat many differentlevels, from individualmotives to entire sections. Figure 33 focuses our attention on one level in particular;namely,that of the phrase.It is largely at the phrase level that the musical plot structureof "Du bist die Ruh"' unfolds.29 While the narrativestructureof "Du bist die Ruh'" is largely articulatedthroughthe variedrepetitionof phrase-levelpatterns,motivic recurrence also contributesto our sense of an unfolding narrative;in particular,the recurrenceof the suspension/appoggiatura figurethatfirstappears in measure3. Figure 33 shows all statementsof this motive, allowing us to see how the motive takes on meaningin relationto the whole. In Figure 33, the music has been reducedto an outer-voiceframework that focuses attention on tonal motion just beneath the surface. The reductionrevealsthreedifferentlevels of melodic motion.At the surface, appearingas small, unstemmednotes, are the suspension-appoggiatura figures. At the first level of reduction, appearingas stemmed notes, is what I will refer to as the underlying melodic line, a reduction of the melody to one note per harmony.It is largely the motion of the underlying melodic line that gives rise to our experience of an unfolding narrative. Within this line, the reduction distinguishes between motion following a pathway and motion departingfrom a pathwayusing beamed half notes and quarternotes, respectively.Harmonicmotion is differentiated in a similarway using half notes and quarternotes in the bass.30 In Figure 33, different statementsof the same patternare vertically aligned, making it easier to observe similarities and differences in successive statementsof each pattern.Aside from the piano interludesand postlude,all of the music of "Dubist die Ruh'" can be assigned to one or the otherof the two paradigmaticaxes shown.Axis 1 tracesthe evolution of a patternof melodic ascent from 5 to 8, while axis 2 traces the evolu-

363

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364

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V7

tion of a patternof melodic descent from 6 to i. The piano introduction combines the initial rise of axis 1 with the fall of axis 2, thus introducing the two "plotlines" to be developed over the course of the song. We are now in a position to examine "Du bist die Ruh"' from the standpointof how each phrasecontributesto the meaning of the song as a whole. Once again, exclamationpoints are used to indicate significant deviations from pre-existentpatterns,whetherpatternsof tonal convention or intra-opuspatternsheardearlierin the work. The piano introductiondoes much to establishthe mood of the song's title, conveying restfulness through its treatmentof melody, harmony, key, rhythm,and texture.The underlyingmelodic line moves entirelyby step, rising gently from 5 to 6 before descending to the tonic. This is set harmonicallyby a series of sixth chords, its parallel voice leading suggesting smoothnessand fluidityof motion. The tonality of Eb majorand the pure diatonicism contributeto its relaxed character,as do the slow tempo, the unchanging harmonic rhythm, and the repetitive rocking motion in the right hand.All musical forces-propulsive, inertial,gravitational,and attractive-appear to be at a minimum,allowing the melody to remain momentarily suspended at its modest peak before drifting slowly to a point of repose. The only apparentdisturbancein the serenityof the stepwise descent is the suspension figure that appearsunadornedin measures3, 4, and 5, then echoed in ornamentalform in the obbligato voice that comes to the fore in measure6. The suspension, one of the most conventionalmodes of expression in tonal music, can be interpretedmetaphoricallyas the musical agent's momentaryresistanceto the downwardforces of gravity and tonal attraction.That the agent eventuallyyields to these downward forces may explain why the suspensionhas so often been describedas a "sigh."The pervasivenessof the suspensionfigurein phraseone overlays the sense of restfulnesswith its opposite, longing, conveying an amalgam of feelings that musically capturesthe words of the second line of the poem, "Youare longing, and that which stills it." Phrase two maintainsthe restful characterof the piano introduction while continuingits initial melodic ascent to a new point of repose on 8. It is in this phrasethat we hear the first melodic and harmonicdeparture from tonal convention. Melodic motion skips upwardto Eb, departing from an ascending pathwayfrom 5 to 8; harmonicmotion is simultaneously divertedto I6before closing on the expectedV7-Icadence. Melodic and harmonicdepartureand returncombine with registralexpansionand contractionto markthe ELas the climax of the phrase. The expressivequalityof the Ebof measure 10 is similarto thatof the suspensionfigureheardin the piano introduction.Justas we can interpret a suspensionas the musical agent's resistanceto the forces of gravityand tonal attraction,we can interpretmelodic departurefrom a pathway as 365

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the musical agent's willful shifting of motion away from its expected course.31Furthermore,the strong correlationbetween measures 10-11 and measures 6-7 encourages us to map the former onto the latter, as shown by the dotted lines. The Eb-D of measure 10 echoes the Eb-D of measure6, evoking similarfeelings of longing. Following a literalrestatementof the music of phrasetwo for phrase three, the course of action shifts smoothly,almost imperceptibly,to axis two. As the dottedlines show, phrasefour maps onto the descendingportion of phraseone. The substitutionof the sharplydissonantvii07 of V of measure 16 for the vi6 of measure2 introducesnew tension, as does the move towardthe sharpside of the circle of fifths, reflectingthe introduction of the word Schmerz(pain). Melodic and harmonicmotion at first continue as in phraseone, with the C-Bb suspensionover V6 in measure 17 recallingmeasure3. Yetthe phraseremainsin the key of the dominant, with Ah substitutingfor Ab in measure 18. The resultingupwardforce of tonal attractioncounteractsthe downwardforces of inertiaand gravity, blocking the continueddescent heard in phrase one and deflecting motion back upwardto 5. Yet the surfacemelody does not stop on 5, butcontinues all the way to 8, as if the chromaticallycharged,#4gives the line the momentumit needs to attain,if only briefly,its previousheight. This is again accompanied by an outward expansion that reaches its greatest extension on the Eb. Significantly, the EL resolves prematurelyto D, recalling the earlier EL-Dfigure of measures 6 and 10 while deflecting motion back to its expected place of rest on 5. It is in the final phraseof this group that intra-opuspatternrepetition makes its most significantcontributionto the narrativestructureof the song. The firsttwo measuresof phrasefive areidenticalto those of phrase four, stronglyinducing us to map the formeronto the latter.As a result, we expect to hearAMin measure22. When Al appearsin its place, this note takes on an affective characterthatits surfacenormalitybelies. For as Figure 33 shows, the harmonyand underlyingvoice leading are identical to that heardin measures3-7. It is only when we trace the precise course of change in the patternunfolding along axis 2 that the significance of the Abbecomes clear.Havingheardthe AMof phrasefour as creating blockage, we hear the Ab of phrasefive as undoing that blockage, thus reopening a pathway that had been closed just a moment before. This is reflected in the close alignment between text and music in the fourth stanza, the two contrastinglines of text, "Drive other pain from this breast"and "May this heart be filled with your joy," being underscored musically by tension and blockage giving way to a release of tension thatallows melodic motion to continue-as it did in the piano introduction-to a state of repose. This phrasealso illustrateshow patternrepetitionitself may be experienced as a force that governs the trajectoryof melodic motion. In the 366

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physical world,our actionsarepropellednotjust by force of will, butalso by force of habit. Having performedan action once, we are predisposed to repeatthat action.32In a similar way, intra-opuspatternsseem to give rise to theirown repetition,like precutgrooves thatchannelmotion, even if somewhatarbitrarily,in a particulardirection.It is to this metaphorical force thatwe might attributethe seeming inevitabilityof musicalpatterns that unfold along the lines of those heardearlier.Thus, the arc of rising motion initiatedin measure 18 preparesthe way for its variedrepetition in measures22-23 and 24-25. Furthermore,the changes introducedinto the patternwith each repetitionecho earlierpatterns,with the Eb-D-ELof measures 22-23 recalling the Eb-D-Ebof measures6-7 and 10-11 and the Bb-AM-Bb recallingthe EL-D-Ebfigureof measures22-23. Thus, what might otherwisepass for motivic unity can be understoodmetaphorically as the tendency of musical behaviors, like other human behaviors, to repeatthemselves. The piano interludesof measures 26-29 and 49-52 reflect upon the preceding text and music while setting the stage for musical events to come. They reflect upon the opposition between joy and pain described in stanzas two and four througha highly conventionalmode of expression; namely, the immediatejuxtapositionof parallel major and minor. Variedpatternrepetitionat the measurelevel over a tonic pedal focuses our attentionon the contrast,as do the stress accents thatmarkthe alternationbetween 46and b6.The referenceto the immediatemusical past is made more vivid by the resolutionof b6to 5 in alternatemeasures,bringing to mind the similarresolutionof b6to 5 in the suspensionfigurethat appearsin the piano in measures 18 and 41. After repeatingthe music of the first phrase group for stanzas three and four, Schubertreturnsto axis one for the climax of the song. Phrase six begins in precise imitationof phrasestwo and three. But in measure 55, the chromaticalterationof C to Cb,foreshadowedby the piano interlude, opens up an alternativepathwaythat passes throughthe key space of Cbmajor.When the melody ascends to Eb,we no longer hearit as 8 in the key of Ebmajorbut as 3 in Cbmajor.Whereaspreviouslythe 7-8 resolution put a halt to the ascent on the Eb,the change of key bypasses the expected cadence, allowing the ascent to continue all the way to Ab. This melodic ascent, like the descent of the precedingphrase,takes on moredefinitemeaningin relationto earlierevents.As alreadynoted,each phraseof the firstphrasegrouprises up to and then falls away from Eb5, as if it were a ceiling beyond which motion cannot go. Each time, the familiarsuspension figure expresses a yearningthat we come to associate with falling away from this ceiling. When in the climactic phrase,the ascent continues,we experiencethe removalof blockage, as if once again a door has been opened that was closed before, making it possible to ascend to a previously unattainableheight. Just as the Ab of measure22 367

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opens the door to continueddescent to the cadence, the Cbof measure55 opens the door to continuedascent to the climax. The resultingmelodic expansionis mirroredby similarexpansionsof register and duration.The registralexpansion heard in phrases two and three here continues to the very end of the phrase, allowing us to interpretthe earlierexpansionof registralspace-like thatof melodic spaceas having been blocked by the Eb5. Success in overcoming blockage is communicatedthrough other changes in the treatmentof melody, harmony, rhythm,and texture.In contrastto the melodic fluctuationsof earlier phrases,melodic motionis entirelystepwise with no changein its rate and direction, implying an absence of opposing force. In place of firstinversionharmoniesand stepwise motion in the bass, we hearroot-position chords and bass motion by falling fifth, which-along with the parallelfifths and octaves and graduallythickeningtexture-suggest stability andstrength.The suspensionsthatgave the openingphraseits sense of longing are here transformedinto appoggiaturasin an innervoice that suggest the overcomingof gravitywith their ascending leaps. The modulationfrom Eb majorto Cb majorcontributesfurtherto the feelings evoked by the climactic phrase.As Figure 34a shows, Cb major lies a full four steps below El majoralong the circle of fifths, nearly the other side of the circle. Yet Schubertmakes the transitionfrom Eb major to Cb majorseem particularlysmooth by hinting at Eb minor in the preceding piano interlude,thuspreparingus to hearmotion along the shorter route throughmajor-minorspace shown in Figure 34b. The sensation of motion throughkey space thus minimized, attention focuses on the change in emotional state. The CLof measure55 bridges two opposing emotional states, appearingfirstas b6'in Ebminorand then as i in Cb major,reflecting the transitionfrom pain to joy described in majo.r

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C"

depressed Figure 35. Expressiveoppositions stanza four. After the tension created by the move to the sharp side of the circle of fifths in phrases4 and 5, the additionof four flats in phrase 6 takes us far to the side of relaxation.Combiningthese two expressive oppositions-major/happy versus minor/sadand sharp/tenseversus flat/ relaxed-makes possible theexpressionof four"mixed"emotions:happytense (eager), happy-relaxed(peaceful), sad-tense (anxious), and sadrelaxed (depressed),as illustratedin Figure 35. The additionof four flats and the returnto the puremajormode in the climactic phraseshifts us to the leftmost side of the affective plane. The change of key, the melodic ascent, and the registralexpansion combine to evoke feelings of peacefulness and expandingjoy. In the climactic phrase, the image-schematic structureof the music does not so much reflectthe meaningof the text as amplify and extendit. In the poem, the eyes and heartare representedas metaphoricalcontainers, filled, respectively,with the radianceof the beloved and feelings of joy. What the words do not specifically describe,yet the music conveys, is the expansion of these two metaphoricalcontainers.It is not until we hearthe finalwordsof the text, Ofiill'es ganz! (O fill it full!) thatwe fully graspthe meaningof the climactic phrase.Its remarkableexpansionconveys the image of these two bodily containersbeing filled to theirfullest extent, an image thatbecomes increasinglyvivid as we approachthe end of the phrase.Forjust as the melody reaches3 in measure59, suggesting the likely arrivalat a cadence, V7 of IV takes the place of the expected I, causing the melody to ascend yet one more step to 4. To accommodate the unexpectedlengtheningof the phrase,the final syllable (-hellt) undergoes an expansionof its own.33At the same time, the suddenstoppingof surfacemotion in measure59 and the diminuendoover the last two bars suggests that all availableenergy has been taken up by the ascent to the climax. The vocal line remainssuspendedin this elevated state for a full 369

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measureof rest before picking up where it left off in phraseseven on 4, an octave lower, to retracethe path of descent heardin phrasesone and five. In recalling the descent of phraseone immediatelyafterthe ascent of phrase six, Schubertsets the emotional content of these two phrases in relief. Though widely separatedin time, the two phrasesand their associated web of affective states establish a relationshipto one anotherthat contributesgreatlyto the emotionalcharacterof the song. Their similarities-their lack of internal subdivision and their unusual length and melodic shape-serve to heighten our sensitivity to their differencesbass motion by step, invertedtriads, and falling melodic motion in the introductionversusbass motionby fifth,root-positiontriads,andmelodic ascent at the climax. In this way, Schuberthighlights an affective opposition thatis only hintedat by the text, yet is centralto the music.Whereas phrasesfour and five focus on the contrastbetween pain andjoy, phrases one and six highlightthe oppositionbetween peace andjoy, the two positive emotional states associatedwith love. 6. Conclusion Havingcompleteda narrativeanalysisthatshows how variousaspects of the presenttheoryapplyto a tonalwork,we may findit useful to return to our starting premise to reflect upon its broader implications. The groundingof the theoryin principlesof humancognition suggests thatit should be applicablein some way to all musics. Given its emphasis on the mediatingrole of tonal conventionin cross-domainmappings,what relevancedoes the theoryhave for music outsideof the common-practice period? What evidence do we find that the bodily image schemas describedhere also underliethe music of othertimes and cultures? Froma historicalperspective,we findevidence of the shapingforce of embodied metaphorin the changes in compositionalpracticethat led to the evolution and eventualdissolution of functionaltonality.From rules governingthe range and placementof structuraltones for chantmelody, to the preferencefor contrarymotion between outer voices with the advent of polyphony,to the gradualexpansionof harmonicspace from fifth to triadic and from diatonic to chromatic,to the hierarchicalnesting of arcs of tonal motion throughthe stratificationof melody, harmony,and key, and finallyto the openingup of new harmonicpathwaysandregions within the fully expandedchromaticspace of the Tonnetz,it is possible to understandthe evolution of tonal convention as reflecting the exploration over many centuries of tonality's potential for metaphorical expression. By the end of the nineteenthcentury,the expressivepotentialof conventional tonality seemingly exhausted, composers began to seek new 370

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tonal languages with fresh expressive resources. Schoenberg made the most radicalbreak,not only emancipatingdissonancebuteliminatingthe centralityof the tonic, yet manyof his atonalandeven twelve-tone works appearto be organizedaccordingto narrativeprinciples, with plots unfolding along paradigmaticaxes like those found in "Dubist die Ruh'."34 Many of his more conservativecontemporariessimply redefinedtonality, incorporatinginto their music fresh material-new modes, scales, and harmonies-that offered new possibilities for metaphoricalexpression. The presenttheory may have particularrelevancefor this body of music, for much of it appearsto be governed,at least at times, by metaphorsof goal-directedness,verticality,groundedness,andcontainment.The musicmetaphoricalschemas presentedhere could be modified to make them more suitable for mapping onto the post-tonal and neotonal works of Debussy,Stravinsky,Bart6k,andothers.Pentatonic,whole-tone,andoctatonic pitch collections suggest different musical geometries, each with differentintimationsof grounding,centering,stability,balance, containment, and strongand weak forces of tonal attraction.An investigationof these pitch collections from the standpoint of their image-schematic structurecould provide the basis for more meaningful analyses of this repertoire.35 Ethnomusicologistshave just begun to investigatethe role of bodily metaphorsin non-Westernmusic, yet early evidence suggests that metaphorplays an equally importantrole in organizingthe music and musical theoriesof othercultures.Justas eighteenth-andnineteenth-centurycomposers andtheoristsassociatedparticularmelodic figures,harmonies,and keys with particularemotional effects, the Kaluli of PapuaNew Guinea associate certainmelodic figureswith particularemotions and emotional behaviors;for example, they attributeto the descendingminorthirdfeelings of sadness, isolation, and loss (Feld 1981). Yet the Kaluli conceptualize melody metaphoricallynot as motion of the humanbody, but as the motion of water as it flows throughstreams,waterfalls,and pools. The predilectionfor expressing human agency and goal-directedmotion on an epic scale may in fact be unique to Western art music, with other musics, includingmuch contemporaryWesternartmusic, derivingmuch of its meaning from metaphorsthat come from nature.Debussy saw his music as evoking "the movement of the waters... the play of curves describedby the changingbreezes";Messiaen, "theeternityof space and time";Steve Reich, "thechanginglight as clouds move slowly across the sky."These descriptionsprovide a strong contrastto the emotional evocations of theirRomanticpredecessorsjust a centuryearlier.In the words of Liszt, "onesymphonyexpressesto a supremedegreethe severalphases of passionate, joyous feeling, another-elegaic mourning, anotherheroic enthusiasm,still another-sorrow over an irreparableloss." Music speaks to us with an immediacy that leaves us largely uncon371

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scious of the means by which it achieves its effects. Yet the fact that it is capable of evoking such powerful and varied emotions suggests that it reflectsupon embodiedexperienceat a very deep level. By extendingour explanationsof musical structureinto the metaphoricaldomain, we can better understandmusic's capacity-long recognized but little understood-to convey the innermostrealms of humanexperience.

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NOTES 1. Margolis'stheoryof patternmatchingfinds supportin the theoryof neuralnetworks,which explainsour capacityfor patternrecognitionandcategorizationas resultingfrom the selective strengtheningand inhibitingof neuralconnections. Fora discussionof theimplicationsof theneuralnetworkmodelformanyhumanistic disciplines,includingmusic,see Churchland1995. 2. Althoughthe ideasdevelopedherearebasedprimarilyuponJohnson'sTheBody in theMind(1987), theyalso drawuponthe workof LakoffandJohnson1980 & 1999,Turner1991& 1996,LakoffandTurner1989,TurnerandFauconnier1995. TheBody in the Mindprovidesthe most detailedaccountof the image schemas thatunderliethe music-metaphorical schemasto be developedhere. 3. LakoffandJohnson'sworkandthe relatedworkof TurnerandFauconnierhave inspireda rapidlygrowingbodyof writingsby musictheoristson embodiedmeaning in music.See, for example,Feld 1981,Walser1991, SaslawandWalsh1996, Saslaw1996& 1997,Larson1997,Zbikowski1997& 1999,Cox 1999,andCook 2001. 4. The presenttheorydoes not exhaustthe possibilitiesfor musicalmeaning;for to a waltz,a gigue, or a milexample,it does not explainthe meaningattributable itarymarchby virtueof its associationwitha particularsocialcontext.In semiotic terms,the theorycan be said to deal with the firstof CharlesPeirce'sthreecategoriesof sign, the icon, to the exclusionof the othertwo, the indexandthe symbol. Symbolicand indexicalmeanings,sometimesdescribedin termsof topic, havebeentheprimaryfocusof manytheoriesof musicalsemiotics.See, forexample, Agawu 1991,Hatten1994,Tarasti1994,andMonelle2000. It wouldbe possible, drawinguponcognitivemodels alreadyavailable,to expandthe cognitive basisof the presenttheoryto accountfor suchculturallybasedmeaningsin terms of patternmatching.Deacon(1997) has theorizedthatthe symbolicandindexical meaningsof languagegrowoutof iconicmeaningthroughhigherlevels of cognitive processing.The same is likely to be true-if to a more limitedextent-of music.Formusiclies at the otherend of the spectrumfromlanguagewithrespect to the balanceit maintainsamongthe threetypes of sign function.Musicrarely achieves-primarilybecauseit rarelystrivesfor-the puresymbolismthatlies at the heartof language. 5. The conceptof a paradigmaticaxis, along which unitsare relatedby similarity, comes fromstructurallinguistics.Structurallinguistsdevelopeda systemof paradigmaticanalysisfor languagethatwas laterappliedto musicby Ruwet(1972) and Nattiez (1975). The paradigmaticanalysesof Ruwet and Nattiez divide a musicalworkintoits recurrentpatterns(motives,phrases,sections,etc.), aligning these verticallyto revealtheirsimilaritiesanddifferences.Paradigmatic analysis will be usedlaterto showhow narrativemeaningresultsfromthevariedrepetition of intra-opuspatterns. 6. Such concepts,which combinefeaturesof two differentdomains,are examples whathas been called conceptualblending(Turnerand Fauconnier1995, Turner 1996, FauconnierandTurner1998).Blendingconsistsof the projectionof structurefrom two or more inputmentalspaces (often a sourcedomainand a target domain)to a single "blended"space, which takes on structurenot foundin the

373

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individualinputspaces.Formoredetaileddiscussionof conceptualblendingas it appliesto music,see Zbikowski1999. 7. Anothermeansof conceptualizingof hierarchicalrelationsis offeredby various mappings of the VERTICALITYschema. Zbikowski (1997) has shown that the ver-

ticalityschemaplaysanimportantrolein themodelingof tonalandrhythmichierandthe latter"bottom-up." archies,withthe formertendingto be "top-down" 8. In The Body in the Mind, Johnson refers to this as the PATHschema, but in his later writings he follows Lakoff in referring to it as the SOURCE-PATH-GOALschema

(Lakoff1987,Johnson1993,LakoffandJohnson1999). 9. While agency plays a centralrole in how we interpretmusic as goal-directed schema its role may be negmotion, in some mappings of the SOURCE-PATH-GOAL

ligible, as whenwe use it to predictthe behaviorof a fallingleaf or a rollingball. 10. Figure10 elaboratesupona similarschemausedby Arheim (1984). In this and featuresof the schemaappearin italics. all followingfigures,metaphorical 11. Lerdahl(1988) establishesa similarhierarchyof stabilityrelationsamongtriadic, diatonic,and chromaticpitches.However,becausehis model applies to pitchclasses,not pitches,his hierarchyexhibitsfive levels ratherthansix. 12. Althoughnot consciouslyperceived,the overtoneseriesfindsits way into memoryas a componentof speechandmusicalsound,whereit servesas a basisforpatternmappingat an unconsciouslevel. Evidenceof thisis providedby the factthat we areable to recognizea complextone as its fundamental,or its "virtualpitch" (Terhardt1974, 1979), even when the fundamentalis missing (as in the case of mostpocketradiosandtelephonereceivers). hasbeennoted of themappingof harmonicrootontofundamental 13. Thenaturalness by Terhardt(1984), who statesthat"thenatureof the fundamentalnote (root)of musicalchordsis identicalwith that of the virtualpitch of individualcomplex tones."(293) Languageitself providesus with evidencethattonic,root,andfunmeans damentalhavesimilarmetaphorical meaning.InFrench,thetermfondement "bottom";in English,the term"root"suggestsattachmentto the ground;andin German,the wordfor tonic-Grundton-literally translatesas "ground-tone." 14. The explanationofferedhereexpandsuponan earlieraccount(Brower1997). 15. Lakoffand Johnson(1980) have noted the cross-culturalpervasivenessof the generic metaphors HAPPYISUP and SAD IS DOWN, suggesting that these metaphors

arebothembodiedanduniversal. 16. Thiscyclic aspectof musicalpitchspaceis sometimesmodeledas a three-dimensional helix, thus superimposingthe spaces representedin Figures 10 and 15. (R6vesz1913/1954,Shepard1964).Thehelix,however,tendsto obscuretheparadox of "same-yet-different" by reconcilingthe conflict betweenharmonicand melodicdimensions.Forfurtherdiscussionof the perceptualimplicationsof this model,see Butler1992. 17. A similardiagramcan be foundin KostkaandPayne1995. 18. For example,Schubertuses a tonicizedbIIin Erlkoinigto set the Erlking'sfinal seductivecall to the child,thenresolvesit to V in g minoras the childis snatched of bIIin fromthe father'sarms.Similarly,Hatten(1994) interpretsthe appearance the F# minorslow movementof Beethoven'sHammerklavier Sonata,Op. 106, as "a [brief]vision of gracein the midstof tragicgrief"(p. 16). 19. Balzano(1980)similarlyconstructsdifferentpitchspacesfromdifferentintervals: the semitone,the fifth,andthe third.My melodicspacecorrespondsto his semi374

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tonal space,my fifth space to hisfifths space, and my triadicspaceto his thirds space. 20. CareyandClampitt(1989)havenotedthatthediatonicandchromaticscalesshare with the pentatonicscale the propertyof well-formedness,which they definein termsof a local conditionof symmetry(thediatonicscale, e.g., is generatedby a single interval,the fifth, always spanningfive scale steps), and alternativelyin termsof a moreglobalconditionof closure.Thepropertyof well-formednesscan be explained image-schematically in terms of PATHand CYCLEschemas: the sym-

metryconditioncan be understoodas favoringmaximalsmoothness,while the closureconditionfavorsthosepathwaysthattakethe shapeof nearlyperfectcircles. (In the case of the pentatonicscale, the imperfectintervalthat"closes"the circleis a minor6th.) 21. Accordingto Rameau(1754), "theside of the dominant,thatof the risingfifth,is rightlythe side of strength,so thatthe morefifthstherearein going up, the more this strengthincreases;the samereasoningholds converselyfor softness,on the side of the subdominant." This is echoedby Vogler(1779):"if we go up by fifths throughG, D, A, andE, thereis alwaysanincreaseof strength,effect,cuttingquality andpenetration.If we go downby fifthsthroughF, Bk,Eb,andAb, all strength is reducedandthe impressionbecomesdulleranddarker." Similarly,in an eighmusicalnovelby JohannJakobHeinse,the protagonist-conductor teenth-century explainsthatsharpkeys "climbeverhigheruntilheavenis reached;flatkeys sink to everdeeperlevels of solemnityandearthlypower"(Steblin1981). 22. If onewereto continueindefinitelytheprocessof addingcirclesof fifths,onewould eventuallyproducea gridthatdoublesbackuponitselfto takethe shapeof a threedimensionaltorus.In thatform,it wouldbecomeidenticalto the Tonnetz,a twodimensionalgrid used by many theoriststo representspatialrelationsamong pitches,triads,andkeys.WhileRiemannandhis Germanpredecessorsconceived of the Tonnetzas madeup of purefifthsandthirds,thusextendinginfinitelyoutwardin all directions,morerecentrepresentations of the Tonnetzassumeequal thusalso theunderlyinggeometryof thetorus.Lewin(1984, 1987), temperament, Hyer(1995), Cohn(1996, 1997),andothershaveusedthe spaceof the Tonnetzto thatit is along mapout alternativepathwaysto those shownhere,demonstrating such pathwaysthatmuchof the highly chromaticharmonicmotionof late ninemusic takesplace. Such applicationsof the modelof the Tonnetz teenth-century could be viewed as intersectingwith and even extendingthe image-schematic modelof tonalspacepresentedhere. 23. As Krumhansl(1990) describesit, "whencombinationsof tones areheard,tonal meaning(virtualpitches)are evokedto the extentthatthe soundedfrequencies matchsomepartof thetemplateof intervalpatterns"(p. 53). Fromtheperspective of the presenttheory,the overtoneseries servesnot only as template,but also as prototype. 24. In somephrases,the climaxmayactuallycoincidewiththe arrivalat the cadence, causingthesetwo goals to collapseinto a singlemusicalevent. 25. Todorov(1981) describestheidealnarrativeas follows:"anidealnarrativebegins with a stablesituationthatsome force will perturb.Fromwhichresultsa stateof disequilibrium; by the actonof a force directedin a conversedirection,the equilibriumis reestablished; the secondequilibriumis quitesimilarto the first,butthe two arenot identical"(p. 51). 375

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26. Saslaw(1996, 1997)hasshownthatmanyof theseschemasappearin thewritings of Riemann,Schenker,andSchoenberg,includingexpansionof a container,mofromandreturnto a pathway,andthe tionfromone containerto another,departure overcomingof blockage. 27. Inherinterpretation of Riemann'stheoryof modulation,Saslaw(1996)represents modulationyet a thirdway;namely,as motionfromone key containerto another alonga pathwayconnectingthe two. 28. The idea thatwe may experiencemusicalmeaningas a kind of resonance,also proposedby Newcomb(1984),mayin facthavea neurologicalbasis.Neurologists havefoundthatthe meaningof individualobjectsandeventsdoes not registerin any single place in the brain(Damasio1989 & 1999, Edelman1989). Instead, meaningappearsto involvethe simultaneousactivationof sometimeswidelyseparatedneuronalgroups.Repeatedexposureto the same stimulusstrengthensthe connectionsamongthese groups,increasingthe likelihoodthatactivationof one groupwill resultin activationof the others. 29. The phraseappearsto occupya privilegedpositionwithinthe groupinghierarchy as theunitcorresponding mostcloselyin lengthto thepsychologicalpresent-that spanof timeoverwhicheventsof theimmediatepastremainin consciousnessand thusavailablefor cognitiveprocessing.Becausewe can hold an entirephrasein consciousness,we are able to map a phraseonto earlierversionsrecalledfrom memoryandheartheirsimilaritiesanddifferencesin relationto the whole. 30. Figure33 adoptscertainconventionsof Schenkeriannotation;i.e., the use of differentrhythmicvalues to distinguishamonghierarchicallevels, beamsto show underlyingstepwisemelodiclines, andslursto showunstablepitchesresolvingto stableones. I haveused somewhatdifferentcriteriain carryingout the reduction, however,in thatI haveattemptedto preserveat eachlevel thoseelementsof a patternsharedby its variants. 31. Thefactthatthe Eb,unlikethe earliersuspensions,is sungratherthanplayedalso contributesto its expressiveness.EdwardCone (1974) suggeststhatwe attribute the expressivequalitiesof the vocal line to the fictionalcharacterwhosethoughts the singerto be the living andemotionsthe text conveys,andthatwe understand embodimentof this character. 32. Margolismakes no distinctionin his theorybetween patternsof thoughtand at the level at which patternsof behavior,notingthatthey are indistinguishable they arerepresentedin the brain;botharesubjectto patternmatchingcarriedout largelyat an unconsciouslevel. 33. I thankDavidLewinfor bringingthis detailof the image-schematicstructureof the song to my attention. 34. We can infer that Schoenbergconceivedof music in narrativetermsfrom his descriptionof a piece of musicas "aphotographalbum,displayingunderchanging circumstancesthe life of its basic idea-its basic motive"(Schoenberg1967, 58). Schoenberg'sfirstatonalwork, Opus 11, Number1, for example,exhibits of a drama,lendingitself to interpretation on thebasis manyof the characteristics axis establishedby its principaltheme of a plotthatunfoldsalonga paradigmatic (Brower1989). structureof theoctatonicscalesup35. Foranillustrationof howtheimage-schematic of Varese'sDensity21.5, see Brower1997. portsa narrativeinterpretation

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WORKS CITED of ClassicMusic. Agawu,V.Kofi.1991.PlayingwithSigns:A SemioticInterpretation Princeton:PrincetonUniversityPress. Arnheim,Rudolf.1984. "Perceptual Dynamicsin MusicalExpression."TheMusical Quarterly70 (3): 295-309. Balzano,Gerald.1980. "TheGroup-Theoretical Descriptionof 12-Foldand MicrotonalPitchSystems."ComputerMusicJournal4/4: 66-84. Brower,Candace. 1989. "DramaticStructurein Schoenberg'sOpus 11, Number 1."Music ResearchForum4: 25-52. 1997. "Pathway,Blockage,andContainmentin Density21.5."Theoryand Practice22: 35-54. Butler,David. 1992. TheMusician'sGuideto Perceptionand Cognition.New York: SchirmerBooks. Carey,Norman,andDavidClampitt.1989. "Aspectsof Well-FormedScales."Music TheorySpectrum11/2: 187-206. Churchland,PaulM. 1995. TheEngineof Reason,the Seat of the Soul. Cambridge, The MITPress. Massachusetts: Cohn, Richard. 1996. "MaximallySmooth Cycles, HexatonicSystems, and the TriadicProgressions." MusicAnalysis15/1:9-40. Analysisof Late-Romantic . 1997."Neo-Riemannian Trichords,andTheirTonOperations,Parsimonious netz Representations." Journalof MusicTheory41/1: 1-66. Cone,Edward.1974.TheComposer'sVoice.Berkeley:Universityof CaliforniaPress. Cook,Nicholas.2001. "TheorizingMusicalMeaning."MusicTheorySpectrum23/2: 170-95. Cox,Arie. 1999.TheMetaphoricLogic of MusicalMotionandSpace.Ph.D.dissertation,Universityof Oregon.AnnArbor,Michigan:UniversityMicrofilms. ActiDamasio,Antonio.1989."TheBrainBindsEntitiesandEventsby Multiregional vationfromConvergenceZones."NeuralComputation1: 123-32. 1999. TheFeelingof WhatHappens.New York:Harcourt,Brace,andCo. Deacon,Terrence.1997. TheSymbolicSpecies.New York:W.W.Norton. Present.New York:Basic Books. Edelman,Gerald.1989. TheRemembered Fauconnier,Gilles,andMarkTurner.1998."Conceptual IntegrationNetworks."CognitiveScience22/2: 133-87. Feld, Steven.1981. "'FlowLikea Waterfall':The Metaphorsof KaluliMusicalThefor TraditionalMusic 13:22-47. ory."Yearbook Hatten,Robert.1994.MusicalMeaningin Beethoven.Bloomington:IndianaUniversity Press. Hofstadter,Douglas.1979.Godel,Escher,Bach:AnEternalGoldenBraid.NewYork: Basic Books. Riemann." Journalof MusicTheory39/1: 101-38. Hyer,Brian.1995."Reimag(in)ing Johnson,Mark.1987. TheBodyin theMind:TheBodilyBasis of Meaning,Imagination,and Reason.Chicago:Universityof ChicagoPress. .1993. MoralImagination.Chicago:Universityof ChicagoPress. Kostka, Stefan, and Dorothy Payne. 1995. Tonal Harmony.3rd ed. New York: McGraw-Hill. Krumhansl,Carol. 1979. "ThePsychologicalRepresentationof MusicalPitch in a TonalContext."CognitivePsychology11:346-74. 377

This content downloaded from 143.107.252.11 on Wed, 4 Jun 2014 13:28:18 PM All use subject to JSTOR Terms and Conditions

. 1990. Cognitive Foundations of Musical Pitch. New York:Oxford University

Press. Lakoff, George. 1987. Women,Fire, and Dangerous Things. Chicago: University of

ChicagoPress. Lakoff,George,andJohnson,Mark.1980.MetaphorsWeLiveBy. Chicago:University of ChicagoPress. 1999. Philosophy in the Flesh. New York: Basic Books. Lakoff, George, and Mark Turner. 1989. More than Cool Reason: A Field Guide to

PoeticMetaphor.Chicago:Universityof ChicagoPress. Larson,Steve. 1993. "Scale-DegreeFunction:A Theoryof ExpressiveMeaningand Its Application to Aural-Skills Pedagogy." Journal of Music Theory Pedagogy 20:

69-84. .1997. "MusicalForces and Melodic Patterns."Theoryand Practice 22: 55-72.

Lerdahl,Fred.1988. "TonalPitchSpace."MusicPerception5: 315-50. Lewin,David. 1984."Amfortas's Prayerto Titurelandthe Role of D in Parsifal:The Music 8/3: TonalSpacesof the Dramaandthe EnharmonicCb/B."19th-Century 336-49. 1987. Generalized Musical Intervals and Transformations.New Haven: Yale

UniversityPress. Margolis, Howard. 1987. Patterns, Thinking, and Cognition: A Theory of Judgment.

Chicago:Universityof ChicagoPress. Monelle,Raymond.2000. TheSenseof Music.Princeton:PrincetonUniversityPress. Nattiez, Jean-Jacques. 1975. Fondements d'une semiologie de la musique. Paris:

UnionG6enraled'Editions. Newcomb,Anthony.1984."SoundandFeeling."CriticalInquiry10:614-43. Rameau, Jean-Philippe. 1754. Observations sur notre instinct pour la musique. Paris:

Praultfils. Ratner, Leonard. 1980. Classic Music: Expression, Form, and Style. New York:

SchirmerBooks. Revesz, Geza. 1913. Zur Grundlegung der Tonpsychologie. Leipzig: Veit. English trans., Introduction to the Psychology of Music. Norman: University of Oklahoma

Press, 1954. Ruwet, Nicholas. 1972. Langage, musique, poesie. Paris: Seuil.

Saslaw,Janna. 1996. "Forces,Containers,and Paths:The Role of Body-Derived of Music."Journalof Music Theory Image Schemasin the Conceptualization 40/2: 217-44. 1997. "LifeForces:ConceptualStructuresin Schenker'sFree Composition and Schoenberg's The Musical Idea." Theory and Practice 22: 17-34.

Saslaw,Janna,andJamesWalsh.1996."MusicalInvarianceas a CognitiveStructure: In IanBent,ed., MusicThe'MultipleMeaning'in theEarlyNineteenthCentury." ory in the Age of Romanticism. Cambridge: Cambridge University Press.

Schenker,Heinrich.1979. Free Composition.Translatedby ErnstOster.New York andLondon:Longman. Schoenberg, Arnold. 1967. Fundamentals of Musical Composition. London: Faber

andFaber. Sessions, Roger. 1950. The Musical Experience of Composer, Performer, and Lis-

tener.Princeton:PrincetonUniversityPress. 378

This content downloaded from 143.107.252.11 on Wed, 4 Jun 2014 13:28:18 PM All use subject to JSTOR Terms and Conditions

Shepard,R. N. 1964. "Circularityin Judgmentsof RelativePitch."Journalof the Acoustical Society of America 36: 2345-53. Steblin, Rita. 1981. A History of Key Characteristics in the Eighteenth and Early

NineeenthCenturies.Rochester,NY:Universityof RochesterPress. Tarasti,Eero.1994.A Theoryof MusicalSemiotics.Bloomington:IndianaUniversity Press. Ernst.1974. "Pitch,Consonance,andHarmony." Journalof theAcoustical Terhardt, Society ofAmerica 55/5: 1061-69. 1979. "Calculating Virtual Pitch." Hearing Research 1: 155-82.

1984. "TheConceptof MusicalConsonance:A Link betweenMusic and Psychoacoustics." Music Perception 1/3: 276-95.

to Poetics.Translated Todorov,Tzvetan.1981.Introduction by RichardHoward.Minneapolis:Universityof MinnesotaPress. Turner,Mark.1991.ReadingMinds.Princeton:PrincetonUniversityPress. 1996. TheLiteraryMind.New York:OxfordUniversityPress. Turner,Mark, and Gilles Fauconnier.1995. "ConceptualIntegrationand Formal Expression." Metaphor and Symbolic Activity 10/3: 183-204.

DeutscheEncyclopadie,oder (musikalisch)." Vogler,GeorgJoseph.1779."Ausdruck, Allgemeines Real-Worterbuch aller Kiinste und Wissenschaften. Edited by H. M.

G. KosterandJ. F.Roos.23 vols. Frankfurt-am-Main: SohnundWenVarrentrapp ner, 1778-1804. Walser,Robert.1991. "TheBody in the Music:Epistemologyand Musical Semiotics." College Music Symposium 31: 116-26. Zarlino, Gioseffo. 1558. On the modes: Le istitutioni harmoniche, part 4. Translated

by VeredCohen.New Haven:YaleUniversityPress, 1983. Zbikowski,Lawrence.1997."ConceptualModelsandCross-DomainMapping:New Journalof MusicTheory41/2: Perspectiveson Theoriesof MusicandHierarchy." 193-225. 1999. "TheBlossoms of 'TrockneBlumen':Music and Text in the Early NineteenthCentury." MusicAnalysis18/3:307-45.

379

This content downloaded from 143.107.252.11 on Wed, 4 Jun 2014 13:28:18 PM All use subject to JSTOR Terms and Conditions