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Music Perception Spring 2002, Vol. 19, No. 3, 311–332 © 2002 BY THE REGENTS OF THE UNIVERSITY OF CALIFORNIA ALL RIGHTS RESERVED. 311 Address correspondence to Richard Ashley, School of Music, Northwestern University, 711 Elgin Rd., Evanston, IL 60208-1200. (e-mail: [email protected]) ISSN: 0730-7829. Send requests for permission to reprint to Rights and Permissions, University of California Press, 2000 Center St., Ste. 303, Berkeley, CA 94704-1223. Do[n’t] Change a Hair for Me: The Art of Jazz Rubato RICHARD ASHLEY Northwestern University This article examines a number of different performances of jazz ballad melodies in order to investigate the nature of expressive timing used by jazz soloists. Three performances of My Funny Valentine and two per- formances of Naima, taken from commercial recordings by master solo- ists, are examined. Expressive timing is seen to be a kind of tempo rubato involving a flexibility of melodic rhythm over a steady underlying beat. A typical strategy used is to begin the melody “late” relative to the ac- companiment, and speed up over the course of a phrase. This delay- accelerate strategy is modulated in a number of ways. First, the nominal rhythms of motives are modified so as to preserve their categorical iden- tity; below the level of the motive there is more expressive freedom. Sec- ond, there is a strong tendency for melodies to align with the accompani- ment at cadential locations, serving to clarify hierarchic phrase structure. Finally, notes belonging to the underlying harmonies tend to be displaced more than nonharmonic tones, a tendency which is more pronounced at downbeats. These rhythmic procedures are thus found to be related to musical structure in a variety of ways. T HE scientific study of musically expressive performance began de- cades ago, most notably with the pioneering work of Seashore and his colleagues (Seashore, 1938), and a large literature on the topic has developed over the years. Most of this literature has focused on West- ern art-music (“classical” music), most frequently in the form of solo piano music. In the study of this music, the aspect of musical expres- sion most frequently examined is expressive timing, the way in which a performer manipulates the rhythm of a work in order to make it sound musical rather than mechanical. Perhaps the most studied aspect of rhythm is attack-point rhythm—the distance in time between the onset of one tone and the onset of the next. The many studies that have looked at this aspect of musical performance have found a number of robust effects, including those listed next.
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Page 1: Do[nÕt]Change aHairforMe: TheArtofJazzRub ato · MusicPercep tion Spring2002,Vol.19,No.3,311Ð332 ©2002 BYTHEREGE NTS OFTHEUNIVE RSITYOFCALIFOR NIA ALLRIGHT SRESERVED. 311 Addr

Music� PerceptionSpring� 2002,� Vol.� 19,� No.� 3,� 311–332

©� 2002� BY� THE� REGENTS� OF� THE� UNIVERSITY� OF� CALIFORNIA

ALL� RIGHTS� RESERVED.

311

Address� correspondence� to� Richard� Ashley,� School� of� Music,� Northwestern� University,711� Elgin� Rd.,� Evanston,� IL� 60208-1200.� (e-mail:� [email protected])

ISSN:� 0730-7829.� Send� requests� for� permission� to� reprint� to� Rights� and� Permissions,University� of� California� Press,� 2000� Center� St.,� Ste.� 303,� Berkeley,� CA� 94704-1223.

Do[n’t]� Change� a� Hair� for� Me:� The� Art� of� Jazz� Rubato

R I C H A R D � A S H L E Y

Northwestern� University

This� article� examines� a� number� of� different� performances� of� jazz� balladmelodies� in� order� to� investigate� the� nature� of� expressive� timing� used� byjazz� soloists.� Three� performances� of� My� Funny� Valentine� and� two� per-formances� of� Naima,� taken� from� commercial� recordings� by� master� solo-ists,� are� examined.� Expressive� timing� is� seen� to� be� a� kind� of� tempo� rubatoinvolving� a� flexibility� of� melodic� rhythm� over� a� steady� underlying� beat.A� typical� strategy� used� is� to� begin� the� melody� “late”� relative� to� the� ac-companiment,� and� speed� up� over� the� course� of� a� phrase.� This� delay-accelerate� strategy� is� modulated� in� a� number� of� ways.� First,� the� nominalrhythms� of� motives� are� modified� so� as� to� preserve� their� categorical� iden-tity;� below� the� level� of� the� motive� there� is� more� expressive� freedom.� Sec-ond,� there� is� a� strong� tendency� for� melodies� to� align� with� the� accompani-ment� at� cadential� locations,� serving� to� clarify� hierarchic� phrase� structure.Finally,� notes� belonging� to� the� underlying� harmonies� tend� to� be� displacedmore� than� nonharmonic� tones,� a� tendency� which� is� more� pronounced� atdownbeats.� These� rhythmic� procedures� are� thus� found� to� be� related� tomusical� structure� in� a� variety� of� ways.

THE� scientific � study� of� musically� expressive� performance� began� de-cades� ago,� most� notably� with� the� pioneering� work� of� Seashore� and

his� colleagues� (Seashore,� 1938),� and� a� large� literature� on� the� topic� hasdeveloped� over� the� years.� Most� of� this� literature� has� focused� on� West-ern� art-music� (“classical”� music),� most� frequently� in� the� form� of� solopiano� music.� In� the� study� of� this� music,� the� aspect� of� musical� expres-sion� most� frequently� examined� is� expressive� timing,� the� way� in� which� aperformer� manipulates� the� rhythm� of� a� work� in� order� to� make� it� soundmusical� rather� than� mechanical.� Perhaps� the� most� studied� aspect� ofrhythm� is� attack-point� rhythm—the� distance� in� time� between� the� onsetof� one� tone� and� the� onset� of� the� next.� The� many� studies� that� have� lookedat� this� aspect� of� musical� performance� have� found� a� number� of� robusteffects,� including� those� listed� next.

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312 Richard� Ashley

Final� phrase� lengthening.� Performers� show� a� very� strong� tendencytoward� a� kind� of� tempo� rubato� in� which� the� overall� tempo� of� themusic� slows� near� the� end� of� phrases� and� sections� (cf.� Todd,� 1985).

Alteration� of� note-to-note� rhythms.� Rhythms� are� often� playedsomewhat� differently� than� the� mathematically� precise� ratios� givenin� a� score.� There� is� a� tendency� for� notes� written� in� a� given� ratio(such� as� 2:1)� to� be� played� in� other� ratios,� such� as� 1.7:1� (cf.Bengtsson� &� Gabrielsson,� 1983).

Melody� lead.� In� a� chordal� or� homophonic� context� such� as� is� com-monly� found� in� piano� music,� the� melodic� tones� tend� to� be� playedslightly� ahead� of� the� other� tones,� in� order� to� let� them� be� heardmore� clearly� (cf.� Palmer,� 1996).

Relationships� to� structure.� The� relationship� of� expressive� timingto� structural� factors� is� complex� but� unmistakable� (cf.� Desain� &Honing,� 1992).

Individual� performers’� differences� as� well� as� common� tendencies.Individual� performers� have� their� own� special� ways� of� treatingthe� rhythm� of� a� work,� but� some� common� approaches� to� a� givenwork� may� be� found� as� well� (cf.� Repp,� 1992).

One� of� the� most� typical� devices� used� to� illustrate� such� effects� is� a� “tempocurve,”� which� shows� how� performed� attack-point� rhythm� deviates� fromthe� average,� or� mathematically� perfect,� tempo� and� proportion.� This� tempocurve� is� a� functional� representation� of� tempo� rubato� and� tends� to� affect� allvoices� in� the� musical� texture� simultaneously.

However,� not� all� music� is� constructed� or� performed� the� way� Mozart� orSchumann� piano� compositions� are� constructed� and� performed.� This� studyis� concerned� with� the� expressive� performance� of� jazz� ballad� melodies,� whichexhibit� a� number� of� differences� from� the� classical� piano� repertoire.� Mostimportantly� for� this� study,� the� tempos� of� the� different� voices� may� not� covarytogether;� rather,� there� is� most� typically� a� steady� underlying� beat� (providedby� the� rhythm� section,� with� the� bass� and� drums� being� the� most� importantcontributors� to� this)� against� which� all� other� rhythmic� activity� is� measured.In� this� light,� expressive� alterations� of� rhythms� in� jazz� may� be� seen� as� simi-lar� to� the� “early”� rubato� described� in� pre-20th� century� treatises� (cf.� Hudson,1994).� The� purpose� of� this� study� is� to� outline� some� new� research� on� theways� in� which� master� jazz� musicians� alter� the� nominal,� notated� rhythm� ofa� ballad� melody—a� slow,� often� unornamented� tune—for� the� purposes� ofmusical� expression.

In� pursuing� this� question,� many� interesting� and� important� aspects� ofexpressive� jazz� performance,� especially� pitch,� vibrato,� and� timbre,� are� be-ing� left� unexamined.� These� dimensions� will� need� to� wait� for� other� studiesto� explore� them;� perhaps� the� results� presented� in� this� article� will� help� tomotivate� other� scholars� to� pursue� these� directions.

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313Do[n’t]� Change� a� Hair� for� Me

Study� 1:� The� “Standard”� Ballad:� My� Funny� Valentine

The� first� major� class� of� composition� to� be� considered� here� is� the� “stan-dard”� ballad.� “Standards”� are� compositions� that� are� widely� performed� andoften� began� as� popular� songs� before� becoming� vehicles� for� jazz� artists.� Thereare� many� examples� of� the� standard� ballad;� here� I� will� focus� on� one� of� themost� famous,� My� Funny� Valentine.� This� song� was� written� by� RichardRodgers� and� Lorenz� Hart,� and� it� was� a� part� of� the� 1937� musical� Babes� inArms.� From� that� time,� however,� this� song� has� taken� on� a� life� of� its� own� thatis� remarkable;� literally� hundreds� of� recordings� of� the� song� have� been� madeby� musicians� ranging� from� Sarah� Vaughan� to� Harpo� Marx� to� Fredericavon� Stade.� This� song� was� chosen� not� only� for� its� wide� use,� but� also� for� thehigh� level� of� artistry� found� in� recordings� of� it� and� the� lack� of� a� single� ca-nonical� recording� that� might� have� exerted� undue� influence� as� a� model� forlater� performers.

MATERIALS

The� materials� used� in� this� first� study� (as� first� reported� in� Ashley,� 1996)are� commercially� available� recordings� of� My� Funny� Valentine � as� interpretedby� master� musicians� (Chet� Baker,� Art� Farmer,� and� Miles� Davis).� The� use� ofsuch� recordings� helps� to� ensure� a� high� level� of� aesthetic� quality� in� the� inter-pretations� as� well� as� make� the� source� materials� available� for� other� researcherswho� might� wish� to� examine� them.� These� three� recordings� were� chosen� forthree� reasons.� First,� they� were� all� recorded� within� a� few� years� of� one� an-other.� The� Baker� recording� was� made� on� February� 15,� 1954� (on� PacificJazz� B2-92932-2),� the� Davis� rendition� (on� Prestige� 7094)� on� October� 26,1956,� and� the� Farmer� recording� (on� Columbia� CS-8116)� on� December� 23,1958.� Second,� the� three� musicians� were� widely� recognized� as� master� trum-peters,� were� active� at� the� same� time,� and� knew� one� another’s� work;� thus,they� come� from� a� kind� of� shared� community� of� jazz� artists.� Finally,� despitethese� commonalities,� these� recordings� display� a� number� of� diverse� charac-teristics.� The� very� well� known� Baker� recording� is� one� on� which� he� is� per-forming� as� a� vocalist� instead� of� an� instrumentalist,� whereas� in� the� othersthe� melody� is� played� on� trumpet.� Miles� Davis’s� version� takes� great� libertieswith� the� melody� at� points,� whereas� the� others� hew� more� closely� to� theoriginal� melody.� Finally,� the� three� versions’� accompaniments� vary� consid-erably� in� their� approaches,� with� Baker’s� using� no� drums� and� only� sparingpiano� at� the� outset,� Farmer’s� omitting� piano� and� drums� completely� butshowcasing� a� baritone� saxophone� countermelody,� and� Davis’s� using� a� moreconventional� drums-bass-piano� accompaniment.� From� taking� these� threerecordings� as� a� group� we� may� then� hope� to� obtain� a� kind� of� snapshot� ofboth� typical� approaches� to� jazz� performances� of� My� Funny� Valentine � andindividual� differences� as� well.

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314 Richard� Ashley

Analytic� Overview� of � My� Funny� Valentine

We� begin� with� the� notion� that� musicians’� expressive� performances� are� re-lated� in� some� manner� to� the� structure� of� the� music� they� are� performing,� as� wellas� personal� habits� and� general� stylistic� tendencies.� In� order� to� understand� thepotentials� for� expressive� performance� that� My� Funny� Valentine � offers� the� per-former,� then,� a� few� analytic� remarks� on� the� song’s� structure� follow.

My� Funny� Valentine� is� written� in� the� typical� AABA� 32-measure� song� form,with� each� section� lasting� 8� measures.� The� first� “A”� section� of� My� Funny� Val-entine � is� shown� in� notated� form� in� Figure� 1.� In� this� notation,� the� melody� isgiven� as� found� in� the� original� published� sheet� music� for� the� song,� and� thechords� are� given� in� one� commonly� found,� although� not� invariant,� version.1

This� harmonization� is� substantially� the� same� as� those� used� in� both� the� Bakerand� Farmer� recordings;� the� Davis� recording� has� a� number� of� different� harmo-nies� that� will� be� addressed� later� in� the� study� (fuller� transcriptions� of� theseperformances� are� available� from� the� author).� At� the� beginning,� the� most� no-table� harmonic� feature� is� the� C � pedal� tone,� which� is� overlaid� with� a� descend-ing� chromatic� line� of� C,� B,� B ,� and� A;� this� is� one� of� the� most� salient� harmonicfeatures� of� the� song� (see,� e.g.,� the� comments� of� Wilder,� 1972,� pp.� 205ff).

A� few� structural� issues� are� of� the� most� importance� for� this� study.� First,notice� the� alternation� of� two� rhythmic/motivic� figures� (marked� as� “x”� and

Fig.� 1. � My� Funny� Valentine,� by� Lorenz� Hart� and� Richard� Rodgers.� ©� 1937� (Renewed)Chappell� &� Co.� Rights� for� extended� renewal� term� in� U.S.� controlled� by� The� Estate� of� LorenzHart� (administered� by� WB� Music� Corp.)� and� The� Family� Trust� U/W� Richard� Rodgers� andThe� Family� Trust� U/W� Dorothy� F.� Rodgers� (administered� by� Williamson� Music).� All� rightsreserved.� Used� by� permission.� Warner� Bros.� Publications� U.S.� Inc.,� Miami,� FL� 33014.

1.� In� the� notation� used� here,� the� first� letter� and� any� accompanying� accidentals� show� theroot� of� the� chord.� The� following� letters� and� numbers� show� quality� of� the� triad� and� othertones:� m� =� minor� triad,� m7� =� minor� triad� with� minor� seventh� above� the� root;� mM7� =� minortriad� and� major� seventh� above� the� root;� m6� =� minor� triad� with� added� sixth� above� the� root;-5� or� 5� shows� lowered� fifth� above� the� root;� +5� or� 5� shows� raised� fifth� above� the� root.� Aletter� after� a� slash� indicates� the� bass� note� above� which� the� chord� is� played.

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315Do[n’t]� Change� a� Hair� for� Me

“y”)� and� their� derivations.� Second,� observe� the� alternation,� in� the� melody,of� harmonic� tones� (those� belonging� to� the� underlying� chord,� marked� witha� “+”)� and� nonharmonic� tones� (those� not� in� the� underlying� chord).� In� thissection� of� the� song,� the� harmonic� tones� are,� with� the� exception� of� the� Fheld� over� the� final� G� dominant� seventh� chord,� members� of� the� basic� triadsrather� than� higher� chordal� elements� such� as� the� seventh� or� ninth,� makingdistinctions� between� chord� and� nonchord� tones� rather� straightforward.� Thebalance� of� these� elements� in� the� tune� is� striking.� In� the� “A”� sections� of� themelody� there� is,� overall,� an� alternation� of� the� x� and� y� motives,� beginningwith� x;� this� pattern� is� reversed� in� the� B� section� (although� there� are� moreinstances� of� the� x� motive� and� its� related� transformations� than� of� the� y� mo-tive).� In� like� manner,� there� is� an� overall� alternation� between� melody� tonesthat� belong� to� the� underlying� harmonies� and� those� that� do� not;� some� of� theharmonic� tones� come� on� the� stronger,� more� metrically� accented� beats� ofthe� melody� (the� first� and� third� beats,� with� the� first� beat� being� the� strongest)and� the� weaker,� less� accented� beats� (the� second� and� fourth� beats� of� eachmeasure).

With� these� analytic� remarks� as� a� foundation,� let� us� proceed� to� an� exami-nation� of� some� rhythmic� aspects� of� these� performances.

METHOD

Direct� digital� transfer� from� the� CDs� produced� 16-bit� sound� files� that� were� 44.1� kHzmono� or� stereo,� depending� on� the� original� recordings’� format.� No� further� processing� wasperformed� on� the� sound� files.� These� files� were� then� analyzed� on� Macintosh� computers� usingSoundEdit� 16� software� to� determine� the� onset� timings� of� notes� in� two� different� lines.� Thefirst� of� these� produced� the� underlying� metric� “grid”� of� each� performance,� which� was� de-rived� from� the� attack� times� of� the� double� bass’s� tones.� The� bass� lines� were� used� for� tworeasons:� first,� the� bass� was� the� only� accompanying� instrument� found� in� all� of� the� musicalsegments� under� examination,� and� second,� the� bass� can� often� be� regarded� as� the� fundamen-tal� timekeeping� element� in� a� jazz� ensemble,� even� more� than� the� drums� (see,� e.g.,� Collier,1994).� The� other� musical� element� for� which� timings� were� established� was� the� attack� timesof� the� melodic� tones.� The� onsets� of� tones� were� found� by� inspecting� the� sound� files� by� eyeand� ear� and� consistently� applying� a� simple� rule.� This� rule� was� that� a� tone’s� onset� was� de-fined� to� be� the� amplitude� zero-crossing� most� immediately� preceding� the� beginning� of� the(quasi)periodic� portion� of� the� tone.� The� effect� of� this� rule� is� to� establish� the� onset� of� a� toneafter� the� initial,� more� noise-filled� attack,� and� where� the� pitch� is� becoming� more� important.This� approach� parallels� the� method� typically� used� in� laboratory� phonology,� where� the� onsetof� the� vowel,� rather� than� the� onset� of� the� consonant,� is� typically� used� in� timing� vocal� mate-rials.� The� attack� point� of� each� tone� was� measured� three� separate� times,� some� weeks� apart,each� time� without� reference� to� any� prior� measurements,� and� the� average� of� the� three� mea-surements� was� used.� This� approach� was� used� to� minimize� errors� in� measurement;� typically,differences� between� the� measurements� obtained� in� different� sessions� were� in� the� 3-� to� 5-msrange.� I� thus� consider� these� measurements� extremely� consistent� and� probably� as� accurate� aspossible� for� a� human� researcher.

With� this� attack-point� information� in� hand,� one� can� compare� the� actual� rhythmic� per-formance� to� a� “nominal”� rhythmic� version,� that� found� in� the� original� sheet� music.� Themajor� concept� used� to� understand� the� differences� between� these� two� is� that� of� attack-pointdisplacement� (AD).� A� tone� that� was� played� exactly� where� the� notation� indicates,� relative� tothe� underlying� accompaniment,� would� have� an� AD� of� zero;� a� note� played� “too� late”� would

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316 Richard� Ashley

have� a� positive� AD,� and� a� note� played� “too� early”� would� have� a� negative� AD.� This� ap-proach� is� taken� in� order� to� be� able� to� relate� all� recordings� to� a� single� baseline� in� the� currentcase,� where� no� canonical� recording� exists� (as,� e.g.,� in� contrast� to� the� approach� taken� inAshley� &� Trilsbeek,� 2001).� By� using� this� method,� no� claim� is� being� made� for� a� particularlyhigh� ontological� or� epistemological� status� for� the� notated� version� of� the� melody� as� a� con-sciously� used� model� by� these� performers;� although� one� hears� performances� and� finds� re-cordings� of� My� Funny� Valentine� that� follow� the� rhythms� and� pitches� of� the� original� sheetmusic� closely,� jazz� performers� take� extended� liberties� with� their� versions� of� the� song.� In-deed,� it� is� likely� that� some� jazz� performers� have� never� seen� or� heard� My� Funny� Valentine’smelody� performed� as� originally� notated� (I� played� this� song� for� more� than� 10� years� beforeseeing� a� notated� version� of� it� and� was� quite� amazed� at� the� rhythms� notated� for� the� melody!).It� is� exactly� the� degrees� of� liberty,� and� the� constraints� that� might� be� operating� on� this� free-dom,� that� are� of� interest� in� a� study� like� this,� and� comparison� with� Rodgers’� publishedversion� is� instructive� indeed,� as� we� shall� see.

RESULTS

Tempo

One� of� the� primary� assumptions� of� the� method� used� in� this� study� is� thatthe� underlying� beat,� as� given� by� one� or� more� rhythm� section� instruments,can� be� used� as� a� temporal� grid� against� which� to� measure� the� rhythmicdisplacement� of� the� melody.� For� this� assumption� to� be� tenable,� the� underly-ing� beat� must� be� very� steady,� so� that� the� soloist� could� measure� his� rhythmicactivity� against� it.� Let� us� examine� the� question� of� steadiness� of� beat� forthese� three� performances� of� My� Funny� Valentine.

Table� 1� shows� the� means� and� standard� deviations� for� the� tempi� of� thefirst� 16� measures� of� each� of� these� three� performances,� measured� as� theinteronset� interval� from� one� downbeat� to� the� following� downbeat,� takenfrom� the� bass� notes� of� each� recording.� As� the� table� indicates,� the� tempo� ofeach� performance� is� not� metronomic—there� is� some� constant� give� and� takeof� the� underlying� beat—but� each� recording’s� tempo� nevertheless� exhibits� ahigh� level� of� intraperformance� consistency.� The� standard� deviations� fromthe� mean� tempi� are� quite� remarkable,� given� that� prior� researchers’ � indica-tions� of� perception� and� control� of� tempo� indicate� that� something� in� therange� of� 6.2%� to� 8.8%� is� as� accurate� as� humans� can� achieve� (Drake� &Botte,� 1993).� In� this� case,� we� have� a� clear� window� into� extremely� skilled

TABLE� 1Tempo� Characteristics� of� Three� Performances� of

My� Funny� Valentine, � A� Section

Performer Mean� Tempo� (bpm) SD� (bpm) SD� as� %� of� Tempo

Baker 71.4 3.0 4.20Davis 66.1 0.8 1.21Farmer 74.3 1.9 2.56

SD� indicates� standard� deviation.

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317Do[n’t]� Change� a� Hair� for� Me

jazz� performers’� control� of� the� beat—what� jazz� players� call� “time.”� “Goodtime”� is� a� critically� important� skill� for� jazz� musicians,� especially� those� whoplay� rhythm� section� instruments,� and� the� data� shown� here� testify� to� thelevel� of� accomplishment� that� master� players� can� achieve� in� this� skill.

In� summary,� then,� the� tempo� measurements� support� the� use� of� the� underly-ing� beat� as� a� temporal� grid� against� which� the� melody� can� be� measured.� Thenext� step� is� to� look� at� the� performance� of� the� melodic� rhythms� themselves.

Patterns� of� Attack� Displacements

For� the� purposes� of� this� study,� only� the� first� 16� measures� of� the� melodyare� analyzed.� This� limited� approach� gives� a� reasonable� number� of� notes(42)� while� not� overwhelming� us� with� too� much� detail.� Because� only� threeperformances� are� under� examination� here,� the� results� will� be� viewed� with� amixture� of� quantitative� and� qualitative� methods,� in� order� to� avoidovergeneralizing� from� a� small� sample.

Figure� 2� shows� the� attack� displacements� of� the� melodic� notes� in� each� ofthe� three� performances.� The� x-axis� of� each� graph� represents� the� successivenotes� of� the� melody,� with� each� step� on� the� axis� representing� one� note,� re-gardless� of� its� duration.� The� y-axis� of� each� graph� shows� the� displacementof� the� melody� note� from� the� nominal� position� represented� by� the� notatedscore.� A� positive� deviation� means� that� the� note� was� played� late,� relative� tothe� notated� version,� and� a� negative� deviation� means� that� the� note� was� playedearly� relative� to� the� notated� version.� The� unit� of� measurement� on� the� y-axisis� a� percentage� of� the� length� of� the� measure� in� which� the� note� occurred,� soa� deviation� of� 0.5� would� mean� that� the� note� was� played� two� beats� laterelative� to� its� nominal� position.

When� looking� at� the� ADs� of� the� three� different� performances,� a� numberof� aspects� become� clear� immediately.� The� first� of� these� is� the� sheer� extent� oftempo� rubato � as� shown� by� the� size� of� the� attack� displacements.� The� devia-tions� from� the� underlying� rhythmic� framework� and� notated� melody� aremuch� more� extensive� than� one� might� expect� from� reading� the� research� lit-erature� on� expressive� performance� of� classical� music.� It� is� hard� to� imagine,for� example,� a� violinist� playing� the� Beethoven� D� Major� Concerto� in� a� waythat� involves� notes� being� a� full� beat� behind� the� orchestra—which� is� equiva-lent� to� some� of� the� displacements� seen� in� these� performances.� Nevertheless,within� the� conventions� of� jazz� performance� practice,� the� level� of� rhythmicchange� found� here� is� perfectly� acceptable� and� even� to� be� expected.� Thishelps� to� expose� the� differences� that� exist� in� expressive� performance� prac-tices� in� different� musical� domains� and� points� out� the� usefulness� of� examin-ing� repertoires� beyond� the� Western� art� music� tradition� and� repertoires� inwhich� improvisation� is� a� primary� means� of� musical� expression.

The� second� striking� finding� from� Figure� 2� is� that� motivic� structure� ispreserved� and� highlighted � through� the� rhythmic� alterations.� The� x� and� y

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motives� each� clearly� exhibit� a� typical� rhythmic� “contour”� or� “shape.”� Theuse� of� a� distinct� shape� for� each� different� motive� preserves� the� motive’s� iden-tity� and� can� be� understood� as� a� typical,� stylistically� appropriate� interpreta-

Fig.� 2.� Attack-point� displacements� in� three� performances� of� My� Funny� Valentine,� as� a� per-centage� of� bar.

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tion� of� each� of� these� motives.� The� x� motive� tends� to� be� played� with� a� notethat� is� delayed� very� significantly,� followed� by� one� note� close� to� the� zero� lineand� then� a� third� note� that� is� intermediate� in� its� delay.� The� y� motive� is� mosttypically� performed� in� a� contrasting� way,� where� the� first� note� is� delayedonly� a� very� small� amount,� with� the� two� following� notes� coming� early� rela-tive� to� their� nominal� position.� In� looking� at� the� pattern� produced� by� thepairing� of� the� x� and� y� motives,� one� can� see� that� it� tends� to� begin� quitedelayed� and� then� move,� in� a� clear� but� nonmonotonic� manner,� to� anticipat-ing� the� nominal� rhythmic� placement� of� the� notes.� The� overall� larger� pat-tern� that� emerges� is� one� in� which� the� first� note� is� played� quite� late� relativeto� the� score,� with� the� succeeding� tones� of� the� motive� serving� to� “catch� up”or� even� get� ahead� of� the� rhythm� section.� This� is� an� example� of� what� isknown� in� the� jazz� community� as� “back� phrasing”� and� is� characteristic� ofmany� well-known� vocalists� coming� from� the� jazz� tradition,� such� as� BillieHoliday,� Frank� Sinatra,� and� Tony� Bennett.

The� kind� of� timing� alterations� found� here� are� quite� different� from� thoseencountered� in� examining� the� expressive� performance� of� classical� music.Notably,� the� larger� delays� induced� here� are� in� marked� contrast� to� the� find-ing� of� “melody� lead”� in� classical� music,� where� the� melody� anticipates� theaccompaniment� by� a� small� but� perceptually� significant� amount� (anotherevidence� of� the� value� of� studying� a� variety� of� repertoires� to� understandexpressive� performance).� In� terms� of� the� empirical� study� of� expressive� rubato,one� can� consider� this� technique� to� be� like� the� application� of� a� local� tempocurve� in� which� the� notes� are� first� delayed� and� then� accelerate� over� the� courseof� the� motive.� This� delay-accelerate� strategy� is� widespread� in� jazz� perfor-mance� and� is� more� common� than� the� inverse,� anticipate-delay� (althoughexamples� can� be� found� of� the� latter� strategy� as� well).� Even� though� thispattern� is� widespread,� note� that� no� two� of� these� rubatos� use� exactly� thesame� pattern.� There� are� differences� between� each� x� and� the� others� and� eachy� and� the� others.� In� this� way� the� performer� preserves� coherence� and� com-prehensibility� while� allowing� for� expressive� freedom� within� the� categoriesthat� are� being� defined.

This� leads� to� a� third,� related� observation,� that� rhythmic� alteration� oper-ates� here� at� two� hierarchical� levels:� first,� a� “compositional”� one� that� pre-serves� motivic� relationships,� and� second,� an� “expressive”� one� that� altersthe� microstructure� of� the� rhythm� in� smaller� but� important� ways.� The� com-positional� level� is� the� one� that� is� easily� found� in� the� attack� displacementgraphs.� One� effect� of� the� kind� of� tempo� rubato� used� here� is� to� isolate� motivicunits� from� one� another� by� delaying� the� entrance� of� the� first� note,� creatingextra� space� between� the� last� note� of� one� motivic� group� and� the� first� note� ofthe� following� group.� This� lengthened� distance� between� attacks� serves� tomake� each� motive� function� as� a� group� on� its� own,� focusing� attention� onthese� small� units� of� three� to� four� notes.� Having� made� these� units� distinct,an� attendant� musical� issue� is� how� to� create� a� sense� of� interconnection� be-

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tween� them,� so� that� the� melody� does� not� disintegrate� into� a� pointillisticfabric.� The� use� of� similar� delay-accelerate� curves� for� related� motives� servesto� reinforce� the� compositionally� created� network� of� associations� betweenthese� motives,� helping� the� listener� to� be� reminded� of� the� recurrence� of� themotives� even� given� their� various� transformations.� Nevertheless,� the� simi-larities� are� shaded� by� numerous� differences� between� iterations� of� a� motive.It� is� fascinating� to� consider� this� as� an� example� of� musical� category� develop-ment.� In� order� to� learn� a� category,� there� should� be� enough� significant� fea-tures� in� common� between� exemplars� to� create� a� central� idea� of� the� cat-egory,� and� yet� there� should� also� be� sufficient� differences� to� gain� a� sense� forthe� scope� and� limits� of� the� category.� The� rubato� used� in� these� performancesserves� both� of� these� purposes� simultaneously.

A� fourth� significant� aspect� of� these� performances� is� the� presence� of� whatmight� be� termed� cadential� anchoring,� the� tendency� of� the� soloist� to� alignwith� the� accompaniment� at� important� cadential� positions.� This� is� a� tech-nique� that� can� be� found� implemented� at� different� structural� levels;� in� someballad� performances,� it� is� coupled� with� the� delay/accelerate� strategy� at� thelevel� of� each� bar,� with� downbeats� acting� as� mini-cadences;� a� fine� example� isfound� in� Bill� Evans’� famous� 1961� trio� recording� of� My� Foolish� Heart� (Riv-erside� 9376).� The� primary� musical� function� of� this� technique� in� these� re-cordings� of� My� Funny� Valentine� would� seem� to� be� that� of� clarifying� thehierarchic� phrase� structure� of� the� composition.� When� the� motives� havebecome� more� highly� individuated� as� groups� through� the� delay-acceleratestrategy,� the� overall� grouping� structure� could� easily� become� weakened,� witheach� motive� understood� episodically� and� disconnectedly,� like� beads� on� astring� with� no� larger� structural� organization� apparent.� Cadential� anchor-ing� has� the� effect� of� clearly� marking� major� points� of� structural� articulationand� is� most� clearly� seen� in� these� examples� at� the� downbeats� of� measure� 7,the� final� note� of� the� phrase� (on� the� word� “heart”).� This� location� is� theapparently� “missing”� bar� in� the� graph� of� the� Baker� recording,� where� theattack� is� within� 0.01%� of� its� nominal� position,� and� the� slight� anticipation(AD� of� -3%)� found� in� the� Farmer� performance.� The� Davis� recording,� inthis� as� in� other� ways,� demonstrates� that� jazz� soloists� are� not� bound� by� anykind� of� rule� in� their� interpretations;� although� this� note� is� not� displaced� asfar� as� its� immediate� predecessors,� it� is� still� quite� late� relative� to� the� notated,nominal� position.

Miles� Davis’s� performance� is� very� different� from� the� other� two� in� at� leasttwo� ways.� The� first� is� that� relatively� fewer� melody� notes� are� shown� on� thegraph.� This� has� to� do� with� Davis’s� handling� of� the� melody,� where� somenotes� in� the� original� melody� are� deleted� while� other� notes� and� passages� areadded� (a� transcription� is� given� in� Carr,� 1998).� Only� notes� that� occur� in� theoriginal� notated� melody� are� represented� in� the� graphs;� the� added� notes� areomitted.� These� added� figures� are,� of� course,� not� without� musical� impor-tance;� in� jazz,� such� improvisational� treatment� of� a� melody� is� often� a� pri-

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mary� means� of� musical� expressiveness.� In� the� more� narrow� domain� of� rhyth-mic� alterations� to� an� existing� melody,� the� addition� of� notes� to� the� melodyhas� a� significant� effect� on� the� timing� of� the� surrounding� notes� (indeed,� thisis� one� of� the� major� factors� in� the� original� meaning� of� tempo� rubato� as“stolen� time;”� an� added� note� steals� time� from� the� main� note,� altering� themain� note’s� rhythmic� characteristics).

The� second� intriguing� thing� about� Davis’s� performance� is� the� magnitudeof� the� largest� ADs,� which� are� more� than� six� beats� in� extent.� At� this� point� inthe� performance� (on� the� words� “with� my� heart”),� Davis� has� drifted� veryfar� out� of� alignment� with� the� accompaniment� and� begins� a� period� wherehis� line� has� little� if� anything� in� common� with� the� canonical� melody.� In� fact,to� many� listeners� it� must� seem� as� if� he� has� gotten� lost� or� has� abandoned� thetune� altogether� in� favor� of� some� new� and� individual� melodic� concept.� Davis’sapproach� is� centered� around� his� treatment� of� the� y� motive.� In� the� first� fourbars� of� the� melody,� Davis� plays� the� y� motive� (the� “valentine”� rhythm)� in� amanner� that� is� quite� similar� to� Baker� and� Farmer,� and� would� be� immedi-ately� recognized� by� a� knowledgeable� listener� as� a� normal� interpretation� ofthis� figure� in� this� style� of� jazz.� His� performance� of� this� motive� is,� thus,� akind� of� anchor� for� the� listener� at� the� beginning� of� the� melody—and� it� is� onthis� motive� that� he� reanchors� the� listener� after� his� long� soliloquy.� In� thisway,� he� first� establishes� a� context� and� a� set� of� expectations,� then� under-mines� these� expectations,� and� finally� returns� to� the� norms� that� he� had� ini-tially� established.

The� foregoing� observations� have� focused� on� temporal� structure:� rhyth-mic� motives,� phrases,� downbeats,� and� the� like.� However,� one� of� the� mostsurprising� results� to� be� found� here� lies� below� the� surface� and� requires� an-other� kind� of� investigation.� This� is� the� way� in� which� the� rhythmic� manipu-lations� of� the� melody� work� with� regard� to� the� interaction� between� meterand� harmony.� Figure� 3� introduces� this� topic� and� shows� the� attack� dis-placements� between� different� categories� of� notes.� The� first� set� of� bars� showsthe� relative� displacements� of� melody� notes� that� are� members� of� the� under-lying� harmony� and� those� that� are� nonharmonic� tones.� (For� the� Baker� andFarmer� recordings,� the� harmonies� used� were� those� given� in� Figure� 1;� in� theDavis� recording,� the� second� measure� is� Dmin7-5/A � and� then� G7-9,� andthe� fourth� is� F9.� Figure� 3 � and� the� following� discussion� map� melodic� tonesonto� the� chords� used� in� the� different� harmonizations.)� The� differences� seenin� Figure� 3� are� striking,� in� that� harmonic� tones� are� displaced� far� more� thannonharmonic� tones.� The� Baker� recording� is� interesting� here,� in� that� theplacement� of� nonharmonic� tones� is� almost� precisely� in� line� with� the� nomi-nal� placement� on� the� metric� grid;� the� average� ADs� in� each� case� are� lessthan� 1%� of� the� length� of� a� measure.� Surprisingly,� even� Miles� Davis’s� re-cording� shows� differences� between� harmonic� and� nonharmonic� tones� inthe� original� melody,� despite� its� apparent� freedom� of� approach.� The� secondset� of� bars� in� the� graph� reveal� something� still� more� interesting,� as� they

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bring� out� the� contrast� between� harmonic� tones� and� nonharmonic� tonesoccurring� on� downbeats� as� opposed� to� other� locations.� The� results� areclear:� harmonic� tones� that� nominally� occur� on� a� downbeat� are� displacedfar� more� than� nonharmonic� tones� on� the� downbeat.

What� sense� might� be� made� of� this?� The� results� suggest� that� thesesoloists� are� increasing� the� displacement� of� the� most� stable� tones� in� themelody—notes� that� belong� to� the� underlying� harmonies� and� come� on� adownbeat—and� are� minimizing� the� displacement� of� nonharmonic� tonesthat� are� nominally� on� the� downbeat.� The� hypothesis� advanced� here� isthat� the� performers� are� seeking� to� manipulate� musical� tension� by� desta-bilizing� the� least� active� tones� in� the� melody,� while� emphasizing� the� ten-sion� in� metrically � accented� nonharmonic� tones� by� having� them� occurstrongly� on� the� downbeats.� Such� a� strategy� is� not� unreasonable;� in-deed,� in� My� Funny� Valentine � it� is� suggested� by� the� structure� of� the� melodyitself,� where� the� peak� of� the� melodic� contour� in� measure� 6� is� a� disso-nant� note� on� the� downbeat.� Thus,� this� note� has� three� sources� of� accentcombining� at� once:� contour,� meter,� and� dissonance.� It� should� come� asno� surprise� that� sensitive � musicians� would� recognize� this� kind� of� struc-tural� premise� and� promote� it � throughout� their� performance� of� themelody.

It� is� not� clear� what� form� the� performers’� knowledge� took� during� theseperformances.� It� may� have� been� in� the� kinds� of� analytic,� propositional,� anddeclarative� terms� used� here,� or� not;� likewise,� it� may� have� been� explicit� ortacit.� Jazz� musicians� can� often� be� extremely� clear� and� precise� about� whatthey� are� doing,� but� may� also� be� working� in� very� intuitive� ways.� When� im-provising� in� jazz,� one� moves� in� a� world� of� sound� that� is� immediate� andprecise� but� most� often� nonverbal;� what� the� results� of� this� study� do� is� tomake� this� tacit,� thinking-in-sound� knowledge� more� apparent.

Fig.� 3. � Attack� displacements� by� harmonic� and� metric� categories,� three� performances� of� MyFunny� Valentine,� A� section.

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Study� 2:� The� “Jazz”� Ballad:� Naima

Not� all� ballads� are� standards� that� began� as� popular� songs,� however.� Thereis� a� long� tradition� in� jazz� of� composing� new� ballads� specifically� for� thepurposes� of� jazz� performance.� It� is� to� these� kinds� of� compositions� that� wenow� turn,� looking� at� two� performances� by� John� Coltrane� of� his� balladNaima.� Naima� was� named� for� Coltrane’s� first� wife;� he� considered� it� thebest� of� his� compositions� (Porter,� 1998,� p.� 156).� It� has� been� recorded� dozensof� times� by� different� musicians,� thereby� attaining� the� status� of� a� jazz� standardin� its� own� right.� It� is� a� composition� in� AABA� form,� with� a� single� rhythmicmotive� dominating� the� melody.� There� are� two� recorded� versions,� or� “takes,”of� Naima� by� Coltrane� dating� from� the� year� 1959:� the� “main”� take,� releasedon� the� Giant� Steps� album� (Atlantic� 1311)� and� recorded� in� October,� and� the“alternate”� take,� recorded� in� April,� on� Coltrane’s� first� recording� date� as� leader.This� alternate� take� was� only� released� years� later,� after� Coltrane’s� death� (it� iscurrently� available� on� the� CD� reissue� of� Atlantic� 1311).� Both� recordings� havethe� same� instrumentation� (tenor� saxophone,� piano,� string� bass,� and� drums),are� in� the� same� key,� and� are� at� roughly� the� same� tempo.� There� are� differences,however.� The� personnel� differ� on� the� two� sessions,� as� does� an� interesting� rhyth-mic� aspect:� the� alternate� take� contains� a� steady� high-hat� beat� on� counts� 2� and4� of� each� 4/4� bar,� which� is� eliminated� in� the� main� take.� Let� us� investigate� somerhythmic� aspects� of� Coltrane’s� two� performances.

MATERIALS

As� with� My� Funny� Valentine,� commercially� available� digital� recordingsof� the� main� and� alternate� takes� of� Naima� were� used� for� this� study.� Therecordings� were� transferred� directly� to� 16-bit� 44.1-kHz� digital� audio� files,and� no� further� audio� processing� was� carried� out� on� the� files.

Analytic� Overview� of� Naima

Although� Naima� and� its� recordings� are� almost� contemporaneous� withthe� Farmer/Mulligan� recording� of� My� Funny� Valentine, � a� new� kind� of� jazzidiom� is� apparent� here� that� contrasts� with� the� older� style� found� in� Rodgers’melody� and� harmonies.� In� addition,� this� composition� was� certainly� knownprimarily� through� its� recording� on� the� Giant� Steps� album� and� not� througha� printed� score.� In� fact,� a� number� of� published� versions� of� the� compositionare� in� print,� containing� a� number� of� variants� in� both� rhythm� and� harmo-nies.� This� being� the� case,� we� will� want� to� approach� the� use� of� the� scoreeven� more� deliberately� than� with� My� Funny� Valentine.

The� fragment� of� score� in� Figure� 4� shows� one� transcription� of� the� melodyand� one� possible� interpretation� of� the� accompanying� harmonies.� The� first

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thing� one� notices� about� Naima� is� the� sparing� use� of� motives.� In� fact,� thereis� basically� only� one� motive� for� the� whole� composition,� with� variations;this� motive� consists� of� one� long� note� followed� by� two� much� shorter� ones.Some� transcriptions,� such� as� the� one� in� Figure� 4,� use� triplets� for� the� shorternotes,� while� others� use� sixteenth� notes� (still� others� use� a� mixture� of� both),but� all� keep� the� long� note–two� short� note� distinction.� Naima� therefore� hasless� motivic� material� with� which� a� soloist� can� work� when� compared� withMy� Funny� Valentine.� In� addition,� the� harmonic� language� of� Naima� standsat� something� of� a� distance� from� the� conventional� functional� language� ofMy� Funny� Valentine � and� poses� new� and� interesting� issues� for� the� analystand� performer.� The� bass� line� in� Naima� is� a� kind� of� pedal� point,� a� sustainedor� repeated� note� over� or� around� which� the� harmonies� change� rather� thanbeing� a� functional,� chord-root-oriented� bass� line.� Over� this� bass,� one� findsdifferent� harmonizations� for� this� melody;� one� is� shown� in� Figure� 4,� andone� other� common� interpretation� of� the� harmonies� for� the� first� four� bars� isgiven� below.

B m7/E |E m7� |AMaj7/E � GMaj7 5/E � |A M7/EA� gloss� on� the� harmonies� may� be� of� assistance� to� many� readers.� The

harmonic� goal� of� the� phrase� is� the� A � chord� in� measure� 4.� Taking� this� as� theframework� on� which� the� rest� depends,� the� first� two� chords� may� be� seen� asan� alteration� of� the� standard� ii-V� progression;� the� ii� chord� appears� over� adominant� pedal� point� and� the� dominant� chord� is� minor� rather� than� major,but� these� emendations� do� not� fundamentally� alter� the� nature� of� the� pro-gression.� The� next� two� chords� can� be� read� in� a� number� of� different� ways,but� perhaps� the� simplest� interpretation� is� to� see� them� as� approaching� thefinal� A � from� above� (A )� or� below� (G ),� thus� pointing� in� a� linear,� melodicmanner� by� half� steps� toward� the� goal� tone.� Note� that� each� of� these� chordscontains� at� least� four� notes� (including� the� seventh)� and� that� the� harmoniesare� made� yet� more� diffuse� and� colorful� by� the� addition� of� the� nonharmonictones� in� the� melody� (the� long� notes� in� mm.� 1� and� 2),� the� use� of� the� majorseventh� of� the� chord� as� the� primary� melody� tones� in� measure� 3,� and� thepedal� E � throughout� the� phrase.� What� is� immediately� clear� is� that� many� of

Fig.� 4.� Naima,� first� transcription.

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the� chords� are� more� ambiguous� in� their� nature� than� was� the� case� with� MyFunny� Valentine.� Chord� function� has� a� lessened� importance,� the� melodicor� voice-leading� tendencies� of� specific� tones� are� handled� differently,� andharmonic� color� has� become� an� increasingly� important� element.� Thesechanges� in� harmonic� practice� are� hallmarks� of� the� newer� jazz� style� used� inNaima� and� many� other� compositions.

These� motivic� and� harmonic� complications� are,� in� fact,� major� reasonswhy� Naima� was� chosen� for� investigation� after� My� Funny� Valentine.� Thehope� was� that� studying� Naima� would� help� to� distinguish� those� aspects� ofballad� performance� that� are� more� generally� stylistic,� such� as� back� phras-ing,� from� those� that� are� more� closely� connected� with� the� idiostructure� of� aspecific� composition.� In� particular,� it� was� anticipated� that� the� harmonic/nonharmonic� metric� distinctions� found� in� the� performances� of� My� FunnyValentine � would� disappear� in� the� performances� of� Naima,� owing� to� the� lessclearly� defined� nature� of� the� harmonies.

Listening� to� the� two� recordings� of� Naima� is� instructive� in� and� of� itself.The� following� analyses� of� the� performances� help� to� clarify� some� of� thedifferences� in� these� two� recordings.

METHOD

The� same� methods� of� determining� performance� timings� were� used� as� in� Study� 1.� Soundfiles� were� analyzed� on� Macintosh� computers� using� SoundEdit� 16� software.� The� underlyingmetric� grid� was� determined� from� the� onsets� of� the� bass� notes,� and� the� melody� tones� weretaken� from� the� tenor� sax� solo.� The� beginning� of� the� note� was� taken� to� be� the� zero� crossingmost� immediately� preceding� the� quasi-periodic� part� of� the� signal,� after� the� more� noise-ladenonset� transients� have� begun� to� fade� away.

RESULTS

Tempo

As� was� the� case� with� the� performances� of� My� Funny� Valentine,� theserecordings� of� Naima� evidence� the� ensemble’s� high� level� of� rhythmic� con-trol.� Table� 2� shows� the� salient� aspects� of� tempo� in� the� two� versions.� First,

TABLE� 2Tempo� Characteristics� of� Two� Performances� of

Naima,� A� Section

Performance Mean� Tempo� (bpm) SD� (bpm) SD� as� %� of� Tempo

Main 60.0 0.7 1.7Alternate 59.7 0.4 0.7

SD� indicates� standard� deviation.

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notice� that� once� again� the� variability� of� the� tempo� is� quite� small.� Also� no-tice� that� the� standard� deviation� is� higher� in� the� later� recording—perhaps� anindication� of� decreased� rigidity� in� the� performance.� Finally,� notice� the� con-siderable� consistency� of� tempo� across� the� two� sessions,� 6� months� apart.

As� was� the� case� with� the� recordings� of� My� Funny� Valentine,� the� temposof� these� two� performances� of� Naima� are� extremely� steady,� and� thereforethe� underlying� beat� can� be� reliably� used� as� a� grid� against� which� to� measurethe� rhythm� of� the� melody.

Transcription� 1

Figure� 5� shows� the� attack� displacements� of� the� two� Naima� recordingscompared� with� the� first� transcription� (the� version� using� triplets� for� the� shortnotes).� It� is� immediately� apparent� that� the� earlier,� alternate� version� doesnot� exhibit� the� clear� rubato� patterns� revealed� in� the� My � Funny� Valentinerecordings.� The� attack� displacements� graph� shows� a� meandering� path,� madeup� almost� exclusively� of� positive� (i.e.,� late)� displacements.� The� melody� is,in� other� words,� performed� “correctly,”� a� little� behind� the� beat,� but� with� noovert� expressive� tendencies� in� the� rhythms.� The� contrast� with� the� secondperformance� is� quite� striking;� notice� the� emergence� in� the� later� recording� ofthe� delay-accelerate� strategy� that� dominated� the� performances� of� My� FunnyValentine.� The� later� version� of� Naima� is� performed� in� a� manner� much� morelike� that� found� in� the� three� recordings� of� My� Funny� Valentine,� making� useof� the� same� stylistically� appropriate� strategy,� which� seems� to� absent� inColtrane’s� earlier� recording.

Fig.� 5. � Attack� displacements� in� two� performances� of� Naima � (according� to� Transcription� 1).

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This� implies� a� further� avenue� of� research,� namely� that� of� the� harmonic/metric� interplay� found� in� My� Funny� Valentine.� In� what� ways� might� thisphenomenon� be� seen� in� Naima,� given� its� restricted� motivic� vocabulary� andmore� ambiguous� harmonic� language?� Figure� 6� gives� the� primary� answersto� this� question.� In� Figure� 6,� the� same� criterion� was� used� as� for� the� record-ings� of� My� Funny� Valentine,� which� is� that� the� melody� note� would� be� con-sidered� harmonic� if� it� was� a� member� of� the� labeled� triad,� and� nonharmonicotherwise.� This� ends� up� being� equivalent� to� a� triadic/nontriadic� distinctionin� this� case,� exactly� the� same� categories� as� used� in� the� Funny� Valentineanalyses.� The� results� are� intriguing� indeed.� For� the� alternate� recording,� thedifferences� between� the� ADs� are� minimal,� typically� ranging� between� 2.0%and� 2.6%� of� the� measure� regardless� of� category� (the� only� exception� is� har-monic� tones� on� the� downbeat,� which� includes� only� two� notes).� However,for� the� main� recording,� there� are� clear� distinctions� between� the� categories.These� are� differentiated� in� a� relatively� small� way� between� downbeats� andother� beats� (0.1%� vs.� 1.3%)� but� also� between� harmonic� and� nonharmonictones� (1.2%� vs.� 0.4%).� Tones� on� the� downbeat� see� to� be� less� displaced� herethan� in� My� Funny� Valentine,� and� the� question� is,� why?� In� a� closer� analysis,breaking� downbeats� into� those� notes� that� are� harmonic� and� those� that� arenonharmonic,� the� effects� become� more� differentiated.� We� see� that� the� har-monic� tones� anticipate� the� downbeat� by� a� noticeable� amount� in� the� mainrecording� and� come� near� the� beat� in� the� alternate� version,� whereasnonharmonic� tones� lag� behind� the� beats� in� both� cases;� the� magnitude� of� thedifference� is� far� greater� in� the� main� recording.� The� somewhat� surprisingfinding,� then,� is� that� these� two� performances� seem� to� show� Coltrane� com-ing� to� manipulate� the� resources� of� meter� and� dissonance� to� expressive� ef-

Fig.� 6. � Attack� displacements� in� two� performances� of� Naima,� by� category� of� note� (accordingto� Transcription� 1).

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fect,� as� was� the� case� in� the� previously� examined� recordings� of� My� FunnyValentine.� Harmonic� tones� tend� to� be� displaced� more� than� nonharmonictones,� and� downbeats� are� treated� with� special� care.� In� contrast,� however,there� is� an� avoidance� of� cadential� anchoring� in� the� later� version.� It� is� tempt-ing� to� see� the� overall� pattern� of� development� as� pointing� to� an� increasedapplication� of� Coltrane’s� well-learned� expressive� behaviors,� honed� in� yearsof� playing� with� Davis� and� others,� over� the� months� of� improved� familiaritywith� Naima� between� the� two� recordings.

Transcription� 2

These� results� are� really� rather� surprising� and� go� against� the� hypothesiswith� which� Naima� was� approached.� One� possible� explanation� is� that� theseresults� might� be� caused� by� some� problem� with� the� transcription� used� as� abasis� for� comparison,� caused� by� inaccuracies� or� some� kind� of� bias� con-tained� therein.� In� order� to� check� these� results,� let� us� follow� the� same� proce-dure� using� another� transcription� and� another� version� of� the� harmonic� pro-gression;� this� should� help� to� isolate� important� effects� in� the� performances.The� second� transcription� is� given� in� Figure� 7.

Figure� 8� shows� the� ADs� found� in� these� two� performances,� using� thesecond� transcription.� There� are� a� number� of� parallels� with� the� previousresults.� First,� the� alternate� take� once� again� involves� almost� exclusively� “late”notes,� shown� as� positive� ADs.� The� only� two� exceptions� are� on� the� first� ofthe� two� short� notes� in� measures� 5� and� 8,� which� anticipate� the� sixteenth-note� position� by� almost� 300� ms� (about� one� third� of� a� beat� at� this� tempo),followed� in� each� case� by� notes� that� delay� their� onsets� by� a� little� more� than200� ms.� This� sheds� some� light� on� the� reason� for� different� transcriptions� ofthe� melody:� the� categories� being� used� for� transcription� are� somewhat� coarse,leading� to� the� possibility� that� one� transcription� will� be� closer� to� a� perfor-mance� in� some� particulars� than� another.� The� main� take� provides� anotherpicture.� The� most� evident� finding� is� that� Coltrane� moves� to� being� ahead� ofthe� beat� over� the� course� of� each� four-bar� phrase.� In� the� first� phrase,� theADs� are� at� first� very� slight,� hovering� around� the� zero� line� and� then� moving

Fig.� 7.� Naima,� second� transcription.

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more� firmly� into� the� range� of� -100� ms� in� the� last� three� notes.� This� “rushed”quality� is� emphasized� yet� more� when� the� phrase� is� repeated;� in� measures� 5–7,� Coltrane� begins� by� playing� slightly� behind� the� beat,� peaking� on� the� down-beat� of� measure� 7� with� an� AD� of� almost� 200� ms� (very� perceptibly� behindthe� beat),� and� then� moving� aggressively� forward,� relative� to� the� beat,� toend� up� almost� 200� ms� ahead� of� the� bass.� This� pattern� is� only� partiallyfound� in� the� alternate� take,� which� tends� instead� to� remain� rather� shapelessin� measures� 5–8� even� though� its� variability� increases.� On� a� broader� level,one� can� see� the� main� take� as� following� almost� a� wavelike� motion� over� itscourse,� with� increasing� amplitude� over� the� two� phrases.

In� both� the� main� and� alternate� take,� the� higher� variability� in� the� secondphrase� is� notable.� After� stating� the� melody� first� in� a� rather� straightforwardmanner,� Coltrane� follows� with� a� freer� version.� However,� the� main� takeshows� more� influence� of� the� delay-accelerate� back� phrasing� strategy,� evenin� this� relatively� restrained� performance.� The� choice� of� precise� rhythmiccategories� used� for� the� tones� influences� the� kind� and� degree� of� effects� found,as� expected,� but� does� not� eliminate� them.

We� should� now� turn� to� looking� at� the� ADs� from� the� standpoint� of� cat-egories� of� tones,� which� raises� an� interesting� methodological� question.� Thisis� because� of� the� different� harmonic� framework.� If� tones� beyond� the� triadare� admitted� as� harmonic,� including� the� seventh� and� the� ninth� (which� isidiomatically� sound� in� the� harmonic� style� of� Naima),� then� no� tones� of� themelody� would� qualify� as� nonharmonic� and� we� could� examine� only� rhyth-mic� phenomena.� In� order,� then,� to� use� harmonic� categories� that� were� assimilar� as� possible� to� those� used� in� examining� My� Funny� Valentine � and� the

Fig.� 8. � Attack� displacements� in� two� performances� of� Naima� (according� to� Transcription� 2).

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330 Richard� Ashley

first� transcription� of� Naima,� only� members� of� the� triad� were� included� hereas� “harmonic”� tones.� This� is� admittedly� a� restrictive� measure� but� has� theadvantage� of� being� parallel� to� the� two� previous� cases.� Figure� 9� shows� theresults� of� the� harmonic/nonharmonic/metric� position� analysis� for� the� twoperformances� of� Naima,� compared� with� the� transcription� given� in� Figure7.

Not� surprisingly,� the� downbeats� produce� the� same� results� as� in� theprior� analysis.� However,� the� other� tones� (the� shorter� ones,� primarily)act� somewhat� differently.� The� main� take� shows� about� the� same� degreeof� displacement� of� these� tones,� but� they� now� occur� early� rather� thanlate;� the� alternate� take,� which� is� overall� the� “straighter”� of� the� two,shows� a� very� small� displacement� of� tones� not� on� the� downbeat.� Thedifference� between� harmonic� and� nonharmonic� tones� in� the� main� takeis� about� the� same� as� in� the� prior� analysis,� whereas� the� alternate� versionshows� greater� displacement� of� nonharmonic� tones� (as� is� fitting� if� down-beats� are� displaced� more� than� other� tones).� What� is� perhaps� most� inter-esting� here� is� that� the� differences� between� categories� in� the� main� takeare� of� the� same� order� no� matter� which� transcription� is� being� used� as� thebasis� for� comparison,� lending� support� to� the� idea� that� Coltrane� is� work-ing� out� his� expressive� strategy,� even� within� the� relatively� restrainedphrasing� used� in� Naima.

Therefore,� we� see� that� these� newly� composed� ballads� exhibit� some� ten-dencies� similar� to� those� found� in� performing� the� standard� ballads—but� toa� lesser,� more� subtle� degree.� Especially� interesting� is� the� concept� that� thedegree� of� overt� rhythmic� expression� used� on� the� melody� is� in� some� sense� afunction� of� the� melody’s� familiarity.

Fig.� 9. � Attack� displacements� in� two� performances� of� Naima,� by� category� of� note� (accordingto� Transcription� 2).

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Conclusions

Studying� performances� of� the� melodies� of� jazz� ballads� thus� revealstendencies� that� enrich� our� understanding� of� musical� expression.� As� wehave� seen� in� studies� of� the� Western� art-music� repertoire,� expressive� al-teration� of� “nominal”� rhythmic� patterns� in� a� manner� related� to� struc-ture� is� typical� of� jazz� musicians’� strategies.� Far� from� being� strictly� in-tuitive� and� “free,”� these� performances� show� a� remarkable� sensitivity� toand� use� of� motivic� structure,� phrasing,� and� the� interrelationship� be-tween� meter� and� harmony.� I � would� hasten� to� point� out,� however,� thatthe� way� in� which� ballad� melodies� are� performed� does� not� constitute� asingular� “jazz� approach.”� Järvinen’s� exploration� of� tonality� and� meterin� bebop� solos� (Järvinen,� 1997)� has� shown� that� in� that� corpus� there� is� astrong� tendency� to� employ� primary� tonal� pitches� on� strong� beats,� therebyreinforcing� a� tonal/metric� linkage� (with� results� strikingly � like� those� ofKrumhansl’s� tonal� hierarchies;� cf.� Krumhansl,� 1990),� rather� than� weak-ening� it� as� seen� here.� Jazz� musicians� are� too� much� the� masters� of� theircraft� to� have� only� one� approach� for� all� music� (cf.� Berliner,� 1994)—thestyle,� the� context,� and� the� performer’s� expressive� intent� guide� the� ap-proach� to� each� musical� moment� as� suits� it � best.

References

Ashley,� R.� (1996).� Aspects� of� expressive� timing� in� jazz� ballad� performance.� In� B.� Pennycook&� E.� Costa-Giomi� (Eds.),� Proceedings� of� the� International� Conference� on� Music� Percep-tion� and� Cognition � (pp.� 485–490).� Montreal:� McGill� University.

Ashley,� R.,� &� Trilsbeek,� P.� (2001).� All� his� yesterdays:� McCartney’s� performances� of� Yester-day.� Manuscript� submitted� for� publication.

Bengtsson,� I.,� &� Gabrielsson,� A.� (1983).� Analysis� and� synthesis� of� musical� rhythm.� In� J.Sundberg� (Ed.),� Studies� of� music� performance� (pp.� 27–60).� Stockholm:� Royal� SwedishAcademy� of� Music.

Berliner,� P.� (1994).� Thinking� in� jazz.� Chicago:� University� of� Chicago� Press.Carr,� I.� (1998).� Miles� Davis:� The� definitive� biography. � New� York:� Thunder’s� Mouth� Press.Collier,� J.� L.� (1994).� “Beat.”� In� B.� Kernfeld,� (Ed.),� New� Grove� Dictionary� of� Jazz� (p.� 86).

New� York:� St.� Martin’s� Press.Desain,� P.,� &� Honing,� P.� (1992).� Tempo� curves� considered� harmful.� In� Music,� Mind,� and

Machine� (pp.� 25–40).� Amsterdam:� Thesis� Publishers.Drake,� C.,� &� Botte,� M.-C.� (1993).� Tempo� sensitivity� in� auditory� sequences:� Evidence� for� a

multiple-look� model.� Perception� and� Psychophysics,� 54(3),� 277–286.Hudson,� R.� (1994).� Stolen� time:� The� history� of� tempo� rubato.� Oxford:� Clarendon� Press.Järvinen,� T.� (1997).� Tonal� dynamics� and� metrical� structures� in� jazz� improvisation.� Jyväskylä,

Finland:� University� of� Jyväskylä� Press.Krumhansl,� C.� (1990).� Cognitive� foundations� of� musical� pitch.� New� York:� Oxford� Univer-

sity� Press.Palmer,� C.� (1996).� On� the� assignment� of� structure� in� music� performance.� Music� Perception,

14, � 23–56.Parncutt,� R.� (1989).� Harmony:� A� psychoacoustical� approach.� Berlin:� Springer-Verlag.

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Porter,� L.� (1998).� John� Coltrane.� Ann� Arbor:� University� of� Michigan� Press.Repp,� B.� (1992).� Diversity� and� commonality� in� music� performance:� An� analysis� of� timing

microstructure� in� Schumann’s� ‘Traumerei.’� Journal� of� the� Acoustical� Society� of� America,92(5),� 2546–2568.

Seashore,� C.� (1938).� Psychology� of� music.� New� York:� McGraw-Hill.Todd,� N.� (1985).� A� model� of� expressive� timing� in� tonal� music.� Music� Perception,� 3, � 33–58.Wilder,� A.� (1972).� American� popular� song.� New� York:� Oxford� University� Press.