lerdahl - 2 ways in which music relates to world

8/13/2019 Lerdahl - 2 Ways in Which Music Relates to World

1/7

two ways in which music relates to the world 367

Essay:Two Ways in Which Music Relates

to the World

fred lerdahl

Of all the arts, music possesses the most technical vocabu-lary. This state of affairs gives music theorists the ability tospeak and write about music with enviable precision, but it

also isolates us. Technical training in music theory is a spe-cialized endeavor. Nonmusicians, and even musicians whoare not theoretically inclined, do not easily understand us.From our isolation and their incomprehension comes thetendency to regard music as existing in a bubble, unrelated toanything else in the world. This view is surely mistaken.Here, I shall discuss two respects in which music relates tothe world beyond itself: its common origin and shared struc-tures with language, and its projection of intuitions of ten-sion, attraction, and agency through the internalization of

motion. Both aspects are fundamental to musical emotion.Music exists in complex form only in the human species,

and it appears in all human societies. How did it arise? Earlyethnomusicologists were concerned with this question, butin recent decades the issue has largely been neglected. A signof recent reengagement is a rather speculative book, TheOrigins of Music, in which biologists, paleontologists, evo-lutionary psychologists, and anthropologists propose thatmusic-making conferred an evolutionary advantage upon ourdistant ancestors.1The hypothesized causes for the musical

capacity include Darwinian sexual selection, synchronizedgroup behavior, social bonding during grooming, mother-

infant interplay, and expressive gestural communication.These causes are not mutually exclusive.

One suggestive idea in this volume, by Steven Brown, isthat music first emerged together with language in a musi-language that eventually split into the two modalities thatwe recognize today. The notion that music and languagehave the same source goes back at least to Jean-JacquesRousseau, who wrote:

With the first voices came the first articulations or sounds formed ac-cording to the respective passions that dictated them . . . Thus verse,singing, and speech have a common origin. The first discourses werethe first songs. The periodic recurrences and measures of rhythm, themelodious modulations of accents, gave birth to poetry and music along

with language.2

Browns evolutionary argument is very general, but it canbe supported by two lines of contemporary evidence. Thefirst comes from the brain sciences. The neuropsychologistIsabelle Peretz has reached some telling conclusions basedon patterns of behavioral deficits in patients with brainlesions.3 First, musical processing divides into two broadcomponents, rhythm and pitch. Second, musical and linguis-tic processing share certain deficits but not others. On onehand, rhythmic processing takes place in the same areas of

the brain for both language and music. On the other, lexicalretrieval and syntax in language and pitch processing inmusic are activated in different areas of the brain. Contourrecognition appears to take place in a different brain areathan interval recognition and to precede it in processing, sothat tone-deaf people are usually able to speak with normalcontour but contour-deaf people are necessarily tone-deaf.These conclusions are supported in part by new imagingtechniques that track local brain activation.

The second line of evidence comes from theoretical ac-

counts of linguistic and musical cognitive capacities. The

1 Wallin, et al., 2001.2 Rousseau [1760] 1966, 50.3 Peretz 1993 and Patel & Peretz 1997.

679-125.MTS.Lerdahl_pp367-374 8/28/03 2:25 PM Page 367


2/7

linguistic capacity has three broad components: semantics,syntax, and phonology. Music does not, except peripherally,have semantics in a linguistic sense, which includes lexicalitems as well as concepts such as reference and entailment.Nor does music have a specifically linguistic syntax, whichincludes parts of speech, labeled phrase structures, negation,anaphora, and so forth. Rather, the linguistic componentthat most resembles music is phonology, which, like music,concerns the organization of sound in time. The sounds ofsentences break up into units of phrases and words; theseunits decompose into patterns of stressed and unstressedsounds and of long and short sounds, and they form risingand falling contours.

All of these phonological features have musical counter-parts. In a recent article I develop these parallels through atreatment of the sounds of a short poem, Nothing GoldCan Stay by Robert Frost, entirely as if they were musicalsounds, ignoring their meaning and syntax.4The sounds ofthe poem are put through the grouping, metrical, and reduc-tional components of Lerdahl & Jackendoff 1983 (hereafterGTTM), and through a newly devised method for the deri-vation of contour. The analytic procedure relies on aspects ofgenerative phonological theory, specifically the prosodic hi-

erarchy, stress theory, and contour theory.5

Briefly, theprosodic hierarchy describes the grouping of speech soundsinto the levels of the syllable, word or clitic group, phonolog-ical phrase, intonational phrase, and utterance. The stresstheory uses a notation similar to GTTMs metrical grid andrepresents hierarchical patterns of syllabic stress. Stresses areassigned cyclically over the prosodic groupings.

After these structures are established, the model assignsmetrical structure by finding the optimal match between apermissible metrical grid and the stress pattern, essentially as

in the musical case. Syllables are placed not only to matchstress and grid but also to maximize, through relative dis-tances between attack points, the perceptual projection ofthe constituents of the prosodic hierarchy. In this way longand short durations are assigned to syllables. It may be ob-jected that language and even metered poetry are not spokenwith periodicity between metrical accents. However, limer-icks and many short verses are recited with great metricalregularity,6 and music is never played by human performerswith complete isochrony.7 The difference is one of degree.Periodic meter is an idealized mental construct for bothmusic and poetry.

The derivation of contour follows largely from the stress

grid, since the perception of relative stress is primarily a re-sult of relative pitch height, not of intensity, as one mightsuppose.8 Following intonational theory and data,9 whichestablish focal pitches usually near the onset of syllables eventhough pitch height continuously modulates, the modelposits four levels of tone height, with glides assumed be-tween levels. In other languages the treatment of pitchheight might vary. Within the four-level framework, pitchheight is assigned via the stress grid from global to locallevels, guided by a few paradigmatic shapes.10

The addition of contour to the metrical and durationalassignments yields the normative realization of the poem inmusical notation shown in Example 1. Contained withinthis seemingly transparent notation are the structures of theprosodic hierarchy, phonological stress, the metrical grid,duration, and pitch height.11

368 music theory spectrum 25 (2003)

4 Lerdahl 2001a.5 For prosodic hierarchy, see Hayes 1989; for stress theory, Liberman &

Prince 1977; and for countour theory, Pierrehumbert 1980 and Ladd1996.

6 Oehrle 1989.7 Gabrielsson 1999.8 Handel 1989.9 Reviewed in Ladd 1996.

10 This method bears comparison to the pitch-contour tradition in musictheory, in particular the contour reduction algorithm in Morris 1993.

11 The phonologist William Idsardi recently apprised me of Frosts read-ing of this poem, recorded in Paschen and Mosby 2001. Frosts rendi-tion is extremely close to that represented in Example 1.



3/7

From a musical perspective there is another step to take.

Traditional poetic analysis treats verbal recurrences as simplerhyming patterns: aabb, abab, and so forth. Music theory, incontrast, has a highly developed approach to recurrence inthe form of prolongational structure. As in my theory oftimbral prolongations,12 prosodic prolongational structure isderived from global to local time-span reductional levels ofsyllabic prominence. Example 2 illustrates this for the firstcouplet. Noteheads signify relative structural importance. Inan adaptation of GTTMs threefold classification, dashedslurs represent the strong prolongation of rhyme, dotted slurs

the weak prolongation of alliteration or assonance, and solidslurs the progression of nonrepetition. The graph shows notisolated instances of alliteration and rhyme, as in standardpoetic analysis, but the richer relationship of partial repeti-tions nested within rhymesgreen is to gold as hue isto hold. Note that it is timbral similarity rather than pitchthat is connected prolongationally, for gold is in the highestpitch category while hold is in the lowest. This approachcan be extended to the poem as a whole.

Incidentally, text setting is a rich source of evidence for

the interface between music and poetry.

13

The present ap-

proach can contribute in turn to the study of text setting. It

should also be remarked that this treatment extends to theanalysis of nonpoetic speech, with the proviso that in ordi-nary speech there is little regularity in phonological stressand syllabic repetition, so that its metrical and prolonga-tional structures are attenuated.

To summarize the preceding, music and the the sounds oflanguage share more organization than has commonly beenrecognized. The subcomponents of this organization corre-spond to the pattern of neuropsychological evidence men-tioned earlier. Example 3 gives the hypothesized overall pic-

ture: those brain modules that process rhythm, contour, andtimbral relationships are the same in music and language,while those that process purely pitch-intervallic structuresand purely linguistic syntax and semantics occupy differentparts of the brain. The convergence between cognitive the-ory and neuroscientific evidence calls for further investigation.

The most plausible explanation for this convergence isthat music and language share the same evolutionary roots,in the form of pre-musical and pre-linguistic communicativeand expressive auditory gestures involving shapes of group-

ing, stress, duration, contour, and timbre. We still communi-cate with infants and higher mammals in this manner. Theseelementary shapes appear to lie at the basis of expressiveutterance in language and of musical expression. With evo-lution came specialization. Music and language diverged in


Na-tures first green is gold, Her hard- est hue to hold. Her early leafs a flow- er; But only so an hour.

Th en lea f s ub -s id es to lea f. So E- d en s ank to g rief . So d aw n g oes do wn to da y. N oth- ing go ld c an s ta y.

2 2

24

example 1. Metrical, durational, and contour realization of Nothing Gold Can Stay, by Robert Frost.

12 Lerdahl 1987.13 Ruwet 1972, Jackendoff 1989, Halle & Lerdahl 1994, and Hayes &

Kaun 1996.



4/7


their most characteristic features: pitch organization inmusic, and word and sentence meaning in language. Poetrystraddles this evolutionary divergence by projecting, throughthe addition to ordinary speech of metrical and timbral pat-terning, its common heritage with music.

Let us now consider a second way in which music relatesto the world beyond itself. Drawing on philosophical andlinguistic work by Lakoff & Johnson (1980), Jackendoff(1982), and others, the cognitive scientist Steven Pinkerwrites:

Location in space is one of the two fundamental metaphors in language. . . The other is force, agency, and causation . . . Many cognitive scien-tists have concluded from their research that a handful of conceptsabout places, paths, motions, agency, and causation underlie the literalor figurative meanings of tens of thousands of words and constructions,not only in English but in every other language that has been studied

. . . These concepts and relations appear to be the vocabulary and syntaxof mentalese, the language of thought.14

I have reached a similar conclusion about music from adifferent line of reasoning. In the early 1980s, it was estab-lished empirically that music listeners of varied training andbackground make essentially identical judgments about per-ceived distances of pitches, chords, and regions from a given

tonic.15

This striking discovery motivated me both to seek atheoretical explanation for regular patterns in the data and todevelop a model that would quantify the qualitatively statedstability conditions in GTTMs conception of prolonga-tional analysis. This research agenda culminated in TonalPitch Space,16which presents an algebraic model of the per-ceived distances of pitches, chords, and regions from one an-other. These distances are mapped onto multidimensionalgeometries that have precedent in the music-theoretic litera-ture. In addition to providing an explanatory framework

for the data, the model is used to trace event locations andpaths at multiple prolongational levels, thereby conveying in

15 Krumhansl 1990.16 Lerdahl 2001b.14 Pinker 1997, 3545.

Na- tures first green is gold Her hard- est hue to hold

example 2. Prolongational structure of the first couplet of Nothing Gold Can Stay, by Robert Frost.

exclusively musical structurespitches & intervalsscalesharmony & counterpointtonality

pitch prolongationstonal tension & attraction

common structuresdurational patternsgrouping (prosodic hierarchy)stress (contextual salience)metrical grids

contourtimbral prolongations

exclusively linguistic structuressyntactic categories & relations

word meaning (lexicon)semantic structures (reference, truth

conditions . . .)

phonological distinctive features(etc.)

example 3. Hypothesized brain organization of musical and linguistic structures.



5/7


a specific manner the otherwise vague intuition that listeningto a piece of music is like taking a journey. When allied towords, pitch-space paths take on a narrative dimension aswell.

The pitch-space theory also enables the prediction of pat-terns of tension and relaxation as events unfold. Four condi-tions are needed to make valid predictions. First, there mustbe a component that derives and represents hierarchicalevent structure, since tension is judged hierarchically morethan sequentially.17 This goal is accomplished by an im-proved version of GTTMs prolongational analysis. Second,there must be a calculation of the perceived distance betweenany two chords, something the model does with great accu-

racy. Third, there must be a treatment of surface or sensorydissonance. Although this topic has been studied extensivelyby psychoacousticians, its behavior in musical contexts iscomplex, and here the theory settles for an approximateimplementation. Fourth, there must be a model of melodicand harmonic attractions. The theory succeeds in this goal,subject to computational fine-tuning from experimental evi-dence that is only beginning to become available.18 CarolKrumhansl and I have undertaken an ongoing empiricalstudy of the predictions of the tension model over a wide

range of diatonic and chromatic music. The correlations be-tween predictions and data are generally very high, and theypermit detailed and illuminating interpretations about lis-teners responses.19

According to this theoretical and empirical perspective,then, not only the linguistic but also the musical capacityemploys space and motion in a constitutive way. This em-ployment is not just cognitive in a disembodied sense but is a

cause of the visceral sense of the ebb and flow of musicaltension.20

Recall Pinkers statement: Location in space is one of thetwo fundamental metaphors in language. The other is force,agency, and causation. The theory of tonal attraction bringsforce into the picture of musical space and motion. Like aspaceship moving among the moons of Jupiter, a melody orchord progression moves in a certain direction but is affectedin its velocity and direction by the relative gravitational orattractive force of other pitches and chords. A neighboringornament may have little effect on its motion, but a tonic hasconsiderable mass and may bring the tonal spaceship to rest.

But what of agency and causation? Pinker refers to a clas-

sic experiment by Heider & Simmel (1944), in which theymade a cartoon film using three dots that were perceived bysubjects as moving not as inanimate objects but as animateagents. Pinker writes:

Agents are recognized by their ability to violate intuitive physics bystarting, stopping, swerving, or speeding up without an external nudge,especially when they persistently approach or avoid some other object.The agents are thought to have an internal and renewable source ofenergy, force, impetus, or oomph, which they use to propel themselves,usually in the service of a goal.21

Similarly, a melody or chord progression does not simplyfollow the inertial path of least resistance. It would be dulland would quickly come to a stop unless enlivened by mo-tion away from places that pull it toward rest. Such motionworks against inertia and seems to be caused by an animateagent. Furthermore, such motion causes an emotional re-sponse. Echoing Pinker, the neurologist Antonio Damasiowrites:

You can find the basic configurations of emotions in simple organisms,even in unicellular organism . . . You can do the same thing with a

simple chip moving about on a computer screen. Some jagged fastmovements will appear angry, harmonious but explosive jumps will

17 This conclusion is sustained by empirical data on hierarchical and se-

quential predictions, as reported in Lerdahl, et al., 2000.18 See also Larson 2002 and Margulis 2003.19 A preliminary version of this research appears in Lerdahl and Krum-

hansl 2003. For a historical review of music theories of tonal motion,tension, and attraction, see Rothfarb 2002.

20 See Brower 2000.21 Pinker 1997, 322.



6/7

look joyous, recoiling motions will look fearful. A video that depictsseveral geometric shapes moving about at different rates and holdingvaried relationships reliably elicits attributions of emotional state from

normal adults and even children. The reason why you can anthro-pomorphize the chip or an animal so effectively is simple: emotion, asthe word indicates, is about movement, about externalized behavior,about certain orchestrations of reactions to a given cause, within a givenenvironment.22

Here is a central source of musical emotion. We internal-ize the motion of pitches and chords in reaction to contex-tual tonal forces in musical space. We attribute agency andcausation to musical motions that violate intuitive physicsand inevitability to motions that yield to musical inertia and

force. The character of the musical motions, which is shapedalso by their temporal realization, mirrors equivalent mo-tions in the real physical world. We map specific musicalmotions onto specific emotional qualities, again in reflectionof real-world equivalences.

This argument about musical space, motion, force,agency, and emotion rejoins the earlier discussion about theorigin of musilanguage in expressive auditory gestures. Butlanguage lacks pitch structure except in the most rudimen-tary sense. Perhaps music is the quintessentially emotionalart because its elaborate pitch structures so richly and pre-

cisely reflect motion, force, and agency, and therefore emo-tions, in the outer world.

references

Brower, C. 2000. A Cognitive Theory of MusicalMeaning.Journal of Music Theory44: 32379.

Brown, S. 2001. The Musilanguage Model of Music. InThe Origins of Music. Edited by N. L. Wallin, B. Merker,and S. Brown. Cambridge: MIT Press.

Damasio, A. 1999. The Feeling of What Happens: Body andEmotion in the Making of Consciousness. New York: Har-court Brace.

Gabrielsson, A. 1999. The Performance of Music. In ThePsychology of Music. Edited by D. Deutsch. Second edi-tion. New York: Academic.

Halle, J., and F. Lerdahl. 1994. A Generative TextsettingModel. Current Musicology55: 326.

Handel, S. 1989. Listening. Cambridge: MIT Press.Hayes, B. 1989. The Prosodic Hierarchy in Poetry. In

Phonetics and Phonology: Rhythm and Meter. Edited byP. Kiparsky and G. Youmans. New York: Academic.

Hayes, B., and A. Kaun. 1996. The Role of PhonologicalPhrasing in Sung and Chanted Verse. The LinguisticReview 13: 243303.

Heider, F., and M. Simmel. 1944. An Experimental Study

of Apparent Behavior.American Journal of Psychology57:24359.

Jackendoff, R. 1982. Semantics and Cognition. Cambridge:MIT Press.

. 1989. Rhythmic Structures in Music and Language.In Phonetics and Phonology: Rhythm and Meter. Edited byP. Kiparsky and G. Youmans. New York: Academic.

Krumhansl, C. L. 1990. Cognitive Foundations of MusicalPitch. New York: Oxford University Press.

Ladd, D. R. 1996.Intonational Phonology. Cambridge: Cam-

bridge University Press.Lakoff, G., and M. Johnson 1980. Metaphors We Live By.Chicago: University of Chicago Press.

Larson, S. 2002. Musical Forces, Melodic Expectation, andJazz Melody.Music Perception 19: 35185.

Lerdahl, F. 1987. Timbral Hierarchies. ContemporaryMusic Review 1: 13560.

.2001a. The Sounds of Poetry Viewed as Music. InThe Biological Foundations of Music. Edited by R. J.Zatorre and I. Peretz. Annals of the New York Academyof Sciences 930: 33754.

. 2001b. Tonal Pitch Space. New York: Oxford Uni-versity Press.

Lerdahl, F., and R. Jackendoff. 1983.A Generative Theory ofTonal Music. Cambridge: MIT Press.


22 Damasio 1999, 70.



7/7

lerdahl - 2 ways in which music relates to world

Documents