Liminality as a Framework for Composition: Rhythmic Thresholds, Spectral Harmonies and Afrological Improvisation. Stephen H.

Transcription

1 Liminalit as a ramework or Comosition: Rhthmic Thresholds, Sectral Harmonies and Arological Imrovisation Stehen H Lehman Submitted in artial ulillment o the Requirements or the degree o Doctoral o Musical Arts in the Graduate School o Arts and Sciences CLUMBIA UNIVERSITY 2012

2 ABSTRACT Liminalit as a ramework or Comosition: Rhthmic Thresholds, Sectral Harmonies and Arological Imrovisation Stehen H Lehman This aer will eamine the was in which involvement with both rench sectral music and Arological orms o imrovisation has inormed m current work as a comoser I resent a brie overview o the major concerns and reoccuations o both musics as well as an account o the overlaing histories o sectral music and Arological imrovisation, with articular attention to the concets o liminalit and rhthmic thresholds in the light o recent music ercetion research inall, through an in-deth analsis o two o m recent comositions, Echoes (2008) and Baltimore/Berlin (2008, rev 2011), I show how this ongoing inquir allows us to think about comosition in new and ruitul was

3 Table o Contents reator Remarks ii Sectral Music 1 Arological Imrovisation 3 Sectral Music and Imrovisation 5 Rhthmic Thresholds and Music ercetion Research 10 Analsis o Echoes 21 Analsis o Baltimore/Berlin 28 Conclusion 1 Bibliograh/Works Cited 3 Aendi 1: Echoes Score Aendi 2: Baltimore/Berlin Score 56 i

4 reator Remarks Ater ears as a erormer and comoser o imrovised music, I irst became aware o sectral music in 2001, while studing or an MA in Music Comosition at Weslean Universit Since then, much o m intense involvement with contemorar Western art music, and with sectral music in articular, has been suorted and encouraged b academic institutions like Weslean, Columbia Universit, The aris Conservator (CNSM), and the Institut de Recherche et Coordination Acoustique/Musique (IRCAM), and through m collaborations with new music grous like the International Contemorar Ensemble and the JACK quartet In June 2009, when m CD recording Travail, Transormation low was released on i Recordings, I began to receive a stead stream o inquiries about m snthesis o sectral harmon, highl structured rhthmic materials, and imrovisation Colleagues, mentors, critics, serious listeners and students reached out, wanting to know more about this articular asect o m work I hoe to resond to those inquiries more ull in this aer b eamining the was in which involvement with both rench sectral music and Arological orms o imrovisation has inormed m current work as a comoser I resent a brie overview o the major concerns and reoccuations o both musics as well as an account o the overlaing histories o sectral music and Arological imrovisation, with articular attention to the concets o liminalit and rhthmic thresholds in the light o recent music ercetion research inall, through an in-deth analsis o two o m recent comositions, Echoes (2008) and Baltimore/Berlin (2008, rev 2011), I show how this ongoing inquir allows us to think about comosition in new and ruitul was ii

5 Sectral Music In sectral music 1 the hsics o sound inorms almost ever comositional decision Timbre (attack, deca, overtone structure) rovides the source material or orchestration, harmon, duration and musical orm The most rominent overtones o a given sound a clarinet or a church bell, or eamle are used to create a rich harmonic ramework that is organized according to requenc relationshis, as oosed to the intervals o a musical scale This can be articularl useul when working with the harmonic series, where the interval structure is airl comle, but the requenc structure is rather simle In addition, individual overtones are assigned to seciic instruments in an ensemble, and blended together to create new harmonies derived rom the hsical structure o the original sound source This collection o comositional techniques, oten reerred to as orchestral snthesis or instrumental snthesis, draws smbolicall rom the idea o additive snthesis, in which simle sounds (traditionall, sine waves) are combined to create more comle aggregates The advent o comuter music rograms, digital snthesis, and digital sound analsis in the earl 190s was instrumental in the develoment o sectral music and rovided comosers with owerul new tools, caable o handling the considerable comutational strain associated with the detailed analsis and snthesis o comle sounds 2 ollowing these comositional techniques, both timbre and harmon are conceived o as the comosite o more elementar sounds, and the elision o these two musical categories ma be the most imortant and durable idea to have emerged rom the sectral movement M own engagement with sectral music has been eseciall inluenced b the work o Gérard Grise, and Tristan Murail, who became an imortant mentor or me at Columbia Universit While these are the two comosers most closel associated with the sectral movement, this music has develoed in the historical contet o earlier roto-sectral 1 Sectral music and sectral techniques reresent an etensive collection o ideas about harmon and orchestration and about comosition in general As a result, a comrehensive overview o the sectral movement and the various organizing rinciles o the music would be well beond the scoe o this aer ortunatel, there alread eists a good amount o ecellent scholarshi devoted to the basic comositional techniques o sectral music (ineberg 2000, Moscovitch 199, and Rose 1996), and the cultural and historical contet in which the music irst emerged (Drott 2009 and Anderson 2000) 2 See Dodge and Jerse (199) or a comrehensive overview and histor o additive snthesis techniques 1

6 comosers like Debuss, Scriabin, Varese, Messiaen, Scelsi, Ligeti, and Stockhausen There are also arallel streams, such as the Romanian sectral school, which includes Dumitrescu, Radulescu and Avram But the emergence o the rench sectral movement in the 190s, and its subsequent evolution, seems to reresent a articularl imortant oint o deinition in the last ort ears o contemorar Western art music In the contet o this brie overview o sectral music, it is imortant to note that both Murail and Grise have eressed reservations about the idea o an all-encomassing sectral school o comosition, and have been hesitant to reduce their music to a inite collection o comositional techniques Both comosers have instead sought to deine the sectral movement more broadl, as a collection o ideas and attitudes about comosition, lacing articular emhasis on the henomenolog o ercetion and the central role o hbrids and thresholds in their music Here is Murail in 2000: or me, this ascination with transorming objects and creating hbrids was alwas there: it s almost congenital I think retrosectivel that this idea, couled with the imortance I (and others) lace on working with harmon in a wa that comletel controls it giving strength to the ormal construction were the basic ideas o sectral music (Murail 2000) 2

7 Arological Imrovisation Like the rench sectral movement, Arological orms o imrovisation do not reresent a seciic musical stle or collection o techniques In his 1996 article, Imrovised Music Ater 1950: Arological and Eurological ersectives, comoser/theorist George E Lewis describes the terms Arological and Eurological as reerring metahoricall to musical belie sstems and behavior that eemli articular kinds o musical logic Lewis comares and contrasts Arological and Eurological modes o imrovisation and argues that Arological imrovisation can be deined b the ollowing tendencies (Lewis 1996): An understanding o imrovisation in which careul rearation, ormalism, and intellectual rigor are as rivileged as sontaneit and real-time decision making A collaborative model in which the internalization o alternative value sstems is suorted and encouraged A reoccuation with the articulation o ersonalit and the assertion o individual agenc through sound An emhasis on the social instrumentalit o sound and the otential or imrovisation to resist erceived restrictions on eression M own use o the term Arological is also intended to be understood in a larger contet o Arican-American musical aesthetics, which includes imrovisation, but also etends beond it Comoser/theorist ll Wilson (19) cites the ollowing concetual tendencies, among others, as characteristic o Arican-American music across a wide variet o artistic genres: Metronomic Sense: Musical ulse that is ercetuall salient and encourages a scho-hsical resonse to music Rhthmic Contrast: olrhthm and/or the o-beat lacement o melodic accents Dominance o ercussion: A ercussive aroach to instrumental ractice and a reoccuation with ercussion as an eressive musical element 3

8 A heterogeneous sound ideal that rivileges a diverse collection o instrumental timbres and musical ersectives In m view, Lewis s notion o Arological imrovisation and Wilson s analsis o Arican-American musical aesthetics can comlement and reinorce one another In articular, Lewis s notion o the internalization o alternative value sstems in imrovisation seems to echo Wilson s concet o a heterogeneous sound ideal in Arican-American musical ractices As a comoser/erormer deel engaged with Arological orms o imrovisation, I view m own work as art o a lineage o American creative music that includes, among man others, Charlie arker, Bud owell, John Coltrane, Jackie McLean, Bett Carter, Andrew Hill, Henr Threadgill, Anthon Braton, George Lewis, Evan arker, Mark Dresser and Greg sb 3 Desite reresenting a vast arra o ideas about music and imrovisation, all o these musicians have roduced inluential and highl ersonal bodies o work that remain rooted in the constellation o Arological and Arican- American music as understood b Lewis and Wilson urthermore, the have all ursued creative strategies that oreground the role o the comoser/erormer and rivilege a collaborative model in which the echange o ideas with erormers in an ensemble is an essential comonent o the comositional rocess In act, or man o these musicians, the careul selection o collaborators is viewed as a crucial comositional decision These ideas la a central role in m own understanding o Arological orms o imrovisation, and o establishing a highl collaborative musical environment driven b erormer agenc what music historian and cultural theorist Samuel A lod (1995) has reerred to as individualit within the aggregate 3 Having ursued ormal studies with Braton (Weslean Universit), Lewis (Columbia Universit), and McLean (Hartt School o Music, Universit o Hartord), I have been articularl inluenced b the musical ersectives o these three comoser/erormers See Lehman (2005) on Braton and Lewis and (2008) on McLean

9 Sectral Music and Imrovisation In terms o socio-cultural contet, geograh, and institutional ailiation, sectral music and Arological orms o imrovisation could hardl be more distinct Yet, these two musical histories do overla, oten in ver meaningul was that reveal an imortant set o shared attitudes and ideas about music The Duke Ellington comosition Dabreak Eress (1933) rovides one o the earliest and most comelling eamles o the intersection o sectral techniques and Arological orms o imrovisation Ellington s densel-acked, three-minute work makes use o an acoustic big band to recreate the sounds o a seeding train; in one o the iece s most remarkable assages, the brass and woodwind harmonies use together to imitate the wail o a train whistle [ig 1] Combining individual instrumental sounds to create a more comle comosite, Ellington s writing in this ortion o the iece clearl seems to intend an instrumental snthesis Though Dabreak Eress was written at least ort ears beore the emergence o the rench sectral movement, Ellington s use here o orchestral snthesis to recreate real-world sounds certainl oreshadows man o the undamental concerns o comosers like Murail and Grise More recentl, the work o John Coltrane and Thelonious Monk has been theorized in terms o the harmonic series, a central concet in earl sectral ieces like Gérard Grise s artiels (195) Music historian Bill Cole ([196] 2001), or eamle, views Coltrane s imrovised use o multihonics and unorthodo ingerings, in comositions like m (1965), as a real-time maniulation o the harmonic sectrum o the saohone 5 ianist and comoser Vija Ier (2010) has also argued that the harmonic series and the hsical roerties o sound are at the heart o Thelonious Monk s singular aroach to the iano Like Ellington, Charlie arker is another Arological imroviser connected to the rehistor o sectral music, in arker s case through his collegial ties to the eatriate rench comoser Edgar Varese Varese and arker had arranged to work together and had it not been or arker s untimel assing in 1955, it seems likel that he would have ursued ormal studies with Varese (see Desmond, McClellan and arker (195)) 5 Coltrane has also used saohone multihonics as a comositional remise See Coltrane s Harmonique and his arrangement o the George Treadwell comosition I ll Wait and ra as documented on the 1960 recording Coltrane Jazz 5

10 ig 1: Imitation o a train whistle in Duke Ellington s Dabreak Eress or Ier, Monk s strategic use o chord voicings that san several octaves is directl related to his intimate knowledge o the iano s acoustic roerties and overtone structure Monk s then unorthodo use o chord etensions like the shar our, the lat nine, and the simultaneous use o the dominant and major sevenths, can, in act, be viewed as a means o aroimating the uer artials o a undamental requenc [ig 6

11 2] In some was, the sectral nature o Monk s characteristic chord voicings and sound clusters is reminiscent o livier Messiaen s chord o resonance, in which targeted ig 2: Chord voicings in relation to the overtone structure o an acoustic iano

12 iano voicings are used to aroimate artials through 15 o the harmonic series 6 However, as Anderson (2010) has ointed out, Messiaen s chord o resonance is, in act, a middle-register comression o harmonics through 15, in which the aroimation o a harmonic sectrum is contained within the san o two octaves In this sense, Monk s highl resonant iano voicings ma be more closel connected to the roto-sectral harmonies emloed b Henri Dutilleu in his orchestral work Métaboles (196), in which chords modeled o o the requential structure o the harmonic series san several octaves Just as some imrovisers have used sectral techniques, imrovisation has laed an imortant, i little documented, role in the music o rench sectral comosers like Murail, Grise and hilie Hurel Grise, in articular, made regular reerences in the 1980s to the inluence o American jazz musicians on his concet o rhthm and luid ulse/eriodicit (Grise and Lelong 2008) Grise taught at UC Berkele rom 1982 to 1986, and man o the major works he comosed during and ater this eriod Talea (1986), Le Noir de l Etoile (1990), and Vorte Temorum (1995) bear witness to a new reoccuation with musical rhthm The inluence o jazz and other orms o Arological imrovisation is also deel elt in the music o hilie Hurel Like Grise, Hurel oints to jazz as a direct inluence on his concetion o the rhthmic, rather than the durational asects o musical time (Dénut and Hurel 2001) In chamber works like Si Miniatures en Trome l'eil (1991) and Kits (1995), Hurel calls uon the ensemble to erorm comle olrhthms while remaining connected to the underling ulse, which he considers to be a rhthmic concet derived rom contemorar orms o jazz It is also interesting to observe that, like man Arological imrovisers, rench sectral comosers initiall succeeded in gaining international recognition or their work through their own eorts as comoser/erormers Grise and Murail co-ounded Ensemble l Itineraire in 193 with comosers Hugues Duourt, Roger Tessier and Michael Levinas 6 See Messiaen (19) and Mittelstadt (2009) or a discussion o Messiaen s use o the chord o resonance in his iano writing in the comositions oemes our Mi (1936) and Quatuor our la in du Tems (191), or eamle See Anderson (2010) or a comrehensive discussion o roto-sectral harmonies and ormal organization in Henri Dutilleu s Métaboles (196) 8

13 and regularl erormed their own electro-acoustic 8 works (Cohen-Levinas [1991] 1998) Murail and Grise would both eventuall move awa rom such do-it-oursel methodologies, towards comositional techniques reliant on cutting-edge technolog and generous institutional suort In a letter written to comoser Hugues Duourt in 1980, Gérard Grise eressed his rustration with the term sectral music, inding it too vague and inclusive 9 Instead, he roosed the term liminal music as a more at descrition o the oundational concets in his work (Grise and Lelong 2008) I would argue that this clariication ma, in act, oint to the most signiicant link between rench sectral music and Arological orms o imrovisation Both o these musical traditions are built around thresholds o transition and becoming, where the eloration o a liminal terrain between two ied identities can lead to a transcendent musical eerience Musical boundaries are central to sectral music: the lines between harmon and timbre, itch and noise, electronic and acoustic, and rhthm and duration In Arological orms o imrovisation, inquir into such musical boundaries is urther reinorced b the traditional and undamental nature o imrovisation as a creative ractice situated at the thresholds o structure and disorder, individualit and communit, understanding and mstiication, and the known and the unknown 10 8 Tristan Murail has made several reerences to the imrovisational nature o realizing and erorming works involving live electronics during the earl 190s (Murail 2010 and Cohen-Levinas [1991] 1998) 9 The term sectral music irst aeared in Hugues Duourt s 199 article Musique Sectrale: our Une ratique des ormes de l Énergie, ublished in See Ruud (1995), or eamle, or a discussion o jazz imrovisation as a liminal eerience, and its alication in a variet o music thera techniques 9

14 Rhthmic Thresholds and Music ercetion Research Je ressens ceendant qu il eiste quelque art dans notre ercetion une limite, un degré zéro en deça duquel il est imossible de trangresser sans sombrer dans l absurde C est de ce seuil que je arle; c est a artir de ce seuil que devrait s organiser toute musique (Gérard Grise [198] 1986) 11 Beginning in the late 190s, Gérard Grise devoted more and more o his creative energ to the comositional recet o rhthmic thresholds, lacing articular emhasis on the idea o luid eriodicit in works like Temus E Machina (199) 12 In man o these ieces, Grise seeks to establish a kind o comositional homolog between the harmonic (harmonicit/inharmonicit) and durational (eriodicit/aeriodicit) asects o his music Later works, such as Vorte Temorum (1995), eand on these ideas and demonstrate a unique set o rhthmic strategies which music theorist Jean-Luc Hervé (2001) describes as situated on the narrow crest where the rhthm alls neither into the anesthetizing reetition o a simlistic ulsation, nor into a rhthmic comleit that loses its wa with all sensation o ulsation 13 Comoser/theorist red Lerdahl (1988) has also commented on these tes o rhthmic henomena, noting that constant change doesn t give rise to salient and distinctive transitions and neither does no change at all Babbitt and Reich have something in common ater all In the oening assage o Vorte Temorum, Grise uses reetition, shiting rhthmic eriods, and an accelerating rogression o registral changes to graduall transorm his musical material [ig 3] The oening gesture o the iece, a raidl reeating areggio, evolves into a much longer musical action, where quick shits in register mimic the shae o the original areggio 1 11 I sense, however, that somewhere in our ercetion there eists a limit, a degree zero, beneath which it is imossible to ass without sinking into absurdit It is o this threshold that I seak; it is beginning with this threshold that all music should be organized Translation b the author 12 See Chen (2010) or a detailed account o Temus E Machina and its rhthmic structure 13 Situé sur l étroite crete ou le rthme ne tombe ni dans la reetition anesthésiante d une ulsation simliste, ni dans la comleité rthmique erdant ied avec toute sensation d une ulsation Translation b the author 1 See Hervé (2001) or a comrehensive analsis o Vorte Temorum 10

15 ig 3: Reetition and rhthmic shits in Gérard Grise s Vorte Temorum To a certain etent, the rhthmic structure o Vorte Temorum ma be directl related to a kind o eureka moment that Grise eerienced in 198, while attending a rehearsal o Tristan Murail s Désintégration (1983): Desite the etreme rigor o thought and the comletel new treatment o sound that Murail uts orth so abundantl, I am discovering to what etent it is time or me to add ruture and raidit to the obsession with continuit and slowness o rocess Is this the inluence o Arican music, or o the jazz I discovered during m sta in Caliornia Is it the discover o Conlon Nancarrow the greatest rhthmic comoser since Stravinsk (Grise [198] 2008) 15 Grise s relections about his own comositional rocesses ma indicate a desire to anchor his use o rhthmic thresholds to a more comrehensive understanding o human 15 Malgré l etreme rigueur de la ensée et l asect a rorement arler inoui du traitement des sons que Murail disense a rousion, je decouvre a quel oint il est tems our moi d ajouter ruture et raidité a l obsession de la continuité et a la lenteur du rocessus Est-ce l inluence de la musique aricaine ou du jazz découvert lors de mon séjour en Caliornie Est-ce la découverte de Conlon Nancarrow le lus grand rthmicien deuis Stravinks Translation b the author 11

16 ercetion But in contrast to his work with harmon, which beneitted rom considerable amiliarit with the science o schoacoustics, an inquir into the nature o rhthm ercetion seems to have been based largel on intuition and ersonal eerimentation 16 In m own eorts to move towards a more thorough understanding o the concet o rhthmic thresholds resent in rench sectral music and Arological orms o imrovisation, and to adat these concets to m own work, I have ound a more sstematic review o the ield o music ercetion to be useul, and here resent a brie overview o the relevant current research Cognitivist Research on Rhthmic Thresholds In his article Cognitive Constraints on Metric Sstems: Some bservations and Hotheses, music theorist Justin London (2002) rovides a useul summar o the rhthmic henomena which have been studied in the ield o music ercetion Among the categories o research listed b London, several relate directl to the concet o rhthmic thresholds: The range o sontaneous temo: the longest and shortest eriods in which we are able to roduce a stead beat The values o reerred temos: the rate at which we are most comortable roducing a stead beat ur sensitivit to changes o temo at dierent initial rates and in dierent contets ur sensitivit to dierences o duration relative to the magnitude o the durations involved The shortest and longest durations musicians tend to roduce in rhthmicall alable atterns The etent and limits o the schological resent 16 See Grise (198) and (1998) or additional eamles o the comoser s written relections on the ercetion o musical rhthms 12

17 Music ercetion studies on these toics suggest that there are ercetual and cognitive limits on our abilit to hear, understand, and reroduce musical rhthms But as London is careul to oint out: It is imossible to determine hard and ast values or the various temoral thresholds Moreover, this research has shown that the various thresholds, acuities, and so on are heavil deendent uon task, stimulus, contet, and so orth Thus with the understanding that roosed thresholds ma be uzz, or shit according to contet, such thresholds nonetheless eist (London 2002) In research ocused on sensitivit to change in temo and duration, ercetual thresholds are usuall reerred to as the just noticeable dierence or JND (normall reresented as ercentage change) Much o the recent research dealing with cognitive constraints on rhthm and temo ercetion is redicated on the earl work o aul raisse, which heled to establish a connection between rhthm and the structure o the bod, and osited several ke categories o duration, including: (1) short durations: 00 milliseconds or shorter; (2) long durations: milliseconds; (3) the indierence interval: milliseconds, and () the ercetual resent: 3-8 seconds (raisse 1963 and 198) As music theorist Eric Clarke (1999) has noted, or raisse these categories o duration are not onl quantitativel but also qualitativel dierent, and it is now widel acceted that the manner in which listeners rocess hsical inut is strongl aected b these durational categories Temo raisse s indierence interval, which he deines as the san o time or which a listener s estimate o duration is most accurate: milliseconds (raise 198), seems to have a direct eect on the manner in which we erceive and entrain to various temi Richard arncutt (199) has done research that suggests that listeners reer to hear temos in the range o BM, or at an isochronous ulse rate o milliseconds, which is well within the range o raisse s indierence interval arncutt also suggests a standard temo range o BM, inding that listeners sto hearing durations as regular ulses below 33 BM (1800 seconds) and start grouing individual 13

18 ulses into larger units above 300 BM (200 milliseconds) arncutt s roosed limits on the ercetion o temo ( milliseconds) can also be directl related to a listener s hsical abilit to reroduce isochronous durations Bruno Re (2005) has cited 100 milliseconds as the shortest hsicall reroducible duration and 1800 milliseconds as the longest such duration 1800 milliseconds (33 BM) corresonds to arncutt s lower limit o temo ercetion and the duration o 100 milliseconds, is hal the value o arcutt s uer limit o 200 milliseconds 1 or man music theorists, the ver notion o temo is contingent uon the abilit to erceive smmetrical divisions o a regular ulse, usuall in ratios o 2:1 or 3:1 Given our aarent inabilit to reroduce, and erceive regular sub-ulses shorter than 100 milliseconds, arncutt s uer limit o temo ercetion (200 milliseconds) can be viewed as a logical threshold The schological resent The uer limits o temo ercetion ma also bear witness to another imortant rhthmic threshold normall reerred to as the schological resent or the secious resent Michon (198) deines the ercetual resent as the time interval in which sensor inormation, internal rocessing, and concurrent behavior aear to be integrated within the same san o attention raisse (1982) cites 2 to 3 seconds as an average range or the schological resent, acknowledging that it can last as long as 5 seconds deending on contet This roughl corresonds to 33 BM as a lower limit on temo ercetion Michon s (198) indings are similar, though he laces the uer limit o the schological resent at to 8 seconds Relecting on the relationshi between temo ercetion and the threshold o the schological resent, London suggests that: I 2 seconds seems to be the limit or hearing successive events as temorall connected outside o a metric hierarch, then it makes sense that the absolute value or a measure might be rom about to 6 seconds (ie, twice or three times the length o the slowest ossible beat [sic]), (London 2002) 1 In assessing the longest hsicall reroducible duration, it is oten diicult to determine when listeners begin sub-dividing long durations into smaller grous in order to reroduce them more accuratel (Re and Doggett 200) 1

19 Building on this idea, it seems reasonable to conclude that the boundaries o the schological resent corresond to a qualitative shit in our ercetion o rhthm and musical time or eamle, rancoise Maçar (1985 cited in Kramer 1988) has ound that listeners are much less sensitive to changes in duration or time sans lasting seconds or longer Just Noticeable Dierence (JND) The concet o just noticeable dierence (JND) in music ercetion research can also rovide valuable insights into the nature o rhthmic thresholds JNDs reresent the smallest amount o detectable dierence between two sensor inuts In the case o rhthm ercetion, duration and temo-rate (interonset interval) are the stimuli that are most commonl studied Dowling and Harwood (1986) cite a JND ranging rom 2% to 3% or listeners taing along to a stead beat and a JND between 5% and 10% or (assive) listening estimations In other words, a change in duration or a ulse lasting 1 second (1000 milliseconds) a quarter note at 60 BM, or eamle might onl be detected once it reached the JND threshold o 900 milliseconds (10% decrease) or 1100 milliseconds (10% increase) As noted in the revious section, Maçar (1985 cited in Kramer 1988) has ound that the JND increases signiicantl or durations lasting to 30 seconds, citing 16% as an average JND or those time-sans With regard to sensitivit to changes in temo, Mark Ellis (1991) has ound that the JND can var considerabl, deending on temo range In articular, Ellis argues that it is harder to detect increase in temo at a range o 8-8 BM and, likewise, slightl more diicult to detect decreases in temo at a range o BM His indings are summarized below: Temo Rate (BM) JND (Decrease in Temo) JND (Increase in Temo) 8 6% 13% 8 65% 9% 120 % % 156 % % 192 8% 60% 228 % 55% 15

20 Ecological and Categorical ercetion Traditional cognitivist aroaches to rhthm ercetion rovide a useul oundation or the understanding o rhthmic thresholds As reviousl suggested, the overview o ercetual thresholds resented here is best understood as a collection o uzz data that can var, in signiicant was, deending on the broader musical ramework Nevertheless, man music theorists have criticized research in the ield o music scholog or reling too heavil on the analsis o abstracted and simliied musical tasks that are taken out o contet Drawing on the work o schologist James Gibson, Eric Clarke is one music theorist who has roosed an ecological model o music ercetion: Rather than considering ercetion to be a constructive rocess, in which the erceiver builds structure into an internal model o the world, the ecological aroach emhasizes the structure o the environment itsel and regards ercetion as the ick-u o that alread structured ercetual inormation What is imortant is to consider what is directl seciied [sic] b environmental inormation not what a erceiving organism can interret in or construct rom, a stimulus (Clarke 2005) With regard to rhthm ercetion in articular, Clarke (198) has suggested that it can be viewed as [the rocess o] inding solutions in a three-dimensional sace that includes meter, beat sub-division, and eressive transormations Building on this concetual remise, Clarke has argued or a categorical aroach to rhthm ercetion in which small whole number ratios o duration unction as ercetual categories 18 According to Clarke, once the temoral inormation or rhthm has been ercetuall categorized into ratios o 1:1 or 2:1, or eamle, an duration that deviates rom those categories is considered to be either eressive or accidental lacing emhasis on the otential shit rom one ercetual categor to another in lace o the more traditional notion o a JND this view o rhthm ercetion has a direct eect on the concet o rhthmic thresholds In one eeriment, listeners were resented with a short musical sequence in a trile meter (6/8) and asked to identi targeted two-note hrases as 18 raisse heled to establish the oundational nature o whole number ratios in rhthm ercetion, articularl 1:1 and 2:1, which he views as closel tied to the motor roerties and the smmetrical structure o the human bod (raisse 1963) 16

21 belonging to either a 1:1 or 2:1 ercetual categor The total duration o the two-note hrase remained constant at 960 milliseconds and the individual values o each note were sstematicall varied between a ratio o 1:1 and 2:1, with several intermediate values His indings are summarized below (Clarke 198): Note Values (Milliseconds) % o Listeners Identiing as 2:1 Ratio 60/320 (erect 2:1 Ratio) 100% 560/00 80% 50/20 50% 80/80 (erect 1:1 Ratio) 0% As Clarke s data indicates, in the contet o a trile meter, hal (50%) o the listener continued to categorize the ratio o 50/20 milliseconds as 2:1 Comared to the erect 2:1 ratio o 60/320, the 50/20 ratio reresents a 15% change in the long value (60 to 50) and a 31% change in the short value (320 to 20), which is a ar cr rom a JND or duration o 5-10% Like Clarke, Re (1992) has also emloed ecological models o rhthm ercetion in his research In a stud on eressive timing, Re suggested that a listener s eectation at ke structural moments in a comosition has a direct eect on his or her abilit to detect small changes in duration Re s indings showed that i listeners eect to hear an eressive ritard at the end o an imortant musical hrase or section, or eamle the are much less likel to classi the music as slowing down Thus, a temorar shit in temo, as imlied b the structural contet o a comosition, can obscure the ercetion o rhthmic change i it doesn t reresent a deviation rom stlistic norms o erormance ractice As both Re and Clarke s research strongl suggests, it seems likel that a thorough understanding o rhthmic thresholds must also account or the methodological aradigm o ecological ercetion as it relates to comositional structure and categorical boundaries 1

22 Embodied Cognition Drawing in art rom research done b raisse, which suggests a close correlation between the structure o the human bod, motor unctioning, and rhthm ercetion, Neil Todd, Vija Ier, and others have roosed a model o rhthm ercetion grounded in the concet o embodiment Citing Varela, Ier describes the aradigm o embodied cognition in the ollowing manner: The viewoint known as embodied or situated [sic] cognition treats cognition as an activit that is structured b the bod and its situatedness in its environment -- that is, as embodied action In this view, cognition deends uon eeriences based in having a bod with sensorimotor caacities; these caacities are embedded in an encomassing biological, schological, and cultural contet Sensor rocesses (ercetion) and motor rocesses (action), having evolved together, are seen thereore as undamentall insearable, mutuall inormative, and structured so as to ground our concetual sstems (Varela 1991 in Ier 1998) Contributing to this methodological oint o view, Todd (199), or eamle, has roosed a model o rhthm ercetion based around the idea o a sensor-motor ilter, where our abilit to eel and recognize rhthms is deined b our motor caacities Todd cites 600 milliseconds as the center requenc or the sensor-motor ilter, and the rate at which it is easiest or listeners to erceive a regular temo (100 BM) Not surrisingl, the rate o 600 milliseconds also corresonds to raisse s indierence interval the san o time or which a listener s estimate o duration is most accurate Eanding on Todd and raisse s research in similar areas, Ier (2002) has roosed a table o rough musical correlates to bodil motion which is summarized here: 18

23 Bod Motion Aroimate Musical Correlate Duration Breathing, Bod Swa 1 to 10 Musical hrase Seconds Heartbeat, Walking, 333 to 1000 Musical Temo Seual Intercourse, Milliseconds Head Nod Seech, Lingual Motion, 100 to 333 ast Notated Digital Motion Milliseconds Rhthm, Smallest Salient Subdivision o Musical ulse With regard to rhthmic thresholds, Ier s table seems to suggest a categorical model o rhthm ercetion in which dierent tes o bod movement hel deine ercetual categories And, as one might eect, the aroimate boundaries searating breathing, walking, and seaking in Ier s table corresond rather well to raisse s categories o duration Bodil Motion Aroimate ercetual Aroimate Categor (Ier) Duration Categor (raisse) Duration Breathing 1 to 10 schological resent 2 to 8 Seconds Seconds Walking 333 to 1000 Indierence Interval 00 to 2000 Milliseconds and Long Duration Milliseconds Seaking 100 to 333 Short Durations 100 to 00 Milliseconds Milliseconds Given the wealth o music ercetion research ointing to the undamental relationshi between rhthm and human movement 19, it seems reasonable to conclude that a comrehensive understanding o rhthmic thresholds must also account or thresholds o embodiment as the have been deined in the ield o embodied cognition 19 See Clarke (1999) or a summar o current research on rhthm, timing, and movement in the ield o music ercetion 19

24 Concluding Remarks on Rhthmic Thresholds Relecting on the nature o heuristics in music ercetion, Albert Bregman writes: Having evolved in a world o [sound] mitures, humans have develoed heuristic mechanisms caable o decomosing them Because the conditions under which decomosition must be done are etremel variable, no single method is guaranteed to succeed Thereore a number o heuristic criteria must be used to decide how to grou the acoustic evidence These criteria are allowed to combine their eects in a rocess ver much like voting (Bregman [1990] 199) I roose that the music ercetion research discussed here be viewed not as the basis or a theoretical model o rhthmic thresholds, but as a collection o heuristics that ma rovide useul and meaningul aroaches to rhthm in music comosition In m own music, I have tried to draw rom current research in the ield o music ercetion, and tend to believe, as red Lerdahl (1988) has stated, that the music o the uture will emerge less rom twentieth-centur rogressivist aesthetics than rom newl acquired knowledge o the structure o musical ercetion and cognition I also believe that twent-irst centur musical orms and other new modes o creativit will rovide us with crucial and unoreseen insight into the structure o the mind and how it rocesses musical activit and inormation 20

25 Echoes M comosition Echoes (2008), one o eight works comrising the ccle Travail, Transormation and low, rovides a useul eamle o the integration o sectral techniques and rhthmic thresholds with Arological orms o imrovisation Commissioned b Chamber Music America in 200, Echoes is written or an eight-iece ensemble that includes trumet, alto and tenor saohones, tenor trombone, vibrahone, tuba, acoustic bass, and drum set ormal Structure Echoes is aroimatel ive minutes long with a comositional orm comrising three sections: eosition (mm 1-25), interlude (mm 26-38), and drum coda (mm 39-5) The eosition (mm 1-25) is laed twice, with the alto saohonist erorming an imrovised solo during the second reetition The interlude (mm 26-38) is erormed as written and the drum coda (mm 39-5) is reeated our times During all our reetitions o the drum coda, the drum set laer erorms an imrovised solo Harmonic Structure The harmonic language o Echoes is loosel based on the sound sectrum o a vibrahone, which roduces a ver clear sense o itch desite the resence o some inharmonic artials, as well as a relativel loud 15 th artial which sounds three octaves and a major seventh above the undamental 20 In the irst measure o the iece, or eamle, the written harmon is derived rom the harmonic sectrum o the vibrahone note E-1 (12 Hz): the tuba and the acoustic bass la the second harmonic (E 82 Hz), the tenor saohone sounds the seventh harmonic (C ¾ Shar 2853 Hz), the alto saohone and the trombone la the ninth and tenth harmonic (resectivel # 30 Hz and G# 153 Hz), the trumet sounds the eleventh harmonic (A ¼ Shar 529 Hz), 20 It is imortant to note that though the harmonic series and the overtone structure o acoustic itched instruments are oten discussed in the contet o sectral techniques, it is actuall more common or comosers like Murail and Grise to use inharmonic sectra as oundational elements in their music (see Moscovich (199) on Murail s Gondwana (1980), or eamle) 21

26 and the vibrahone las both the iteenth and the thirt-second harmonic (D# 6223 HZ E Hz) The notated itches in this measure are, o course, onl aroimations o the eact requential structure o the harmonic series In a ractice commonl associated with sectral harmon, each note in the chord is rounded to the nearest quartertone in an eort to kee the underling requenc relationshis intact [ig ] ig : Harmon and requential structures in Echoes 22

27 The loud ercussive attack o the vibrahone and the crash cmbal at the beginning o the measure also contribute to the auditor sensation o sectral usion B masking the individual attacks o the brass and woodwind instruments, the vibrahone and the crash cmbal unction somewhat like attack transients, creating a kind o comosite ensemble attack As a result o these comositional techniques, the individual itches in the chord seem to use together, much like the harmonics o a single note on the vibrahone The harmonic rhthm o Echoes is airl slow, with strategic shits in orchestration and metric structure, rather than requent root movement, used to create comositional change at the local level The second measure o the iece, or eamle, is almost identical to the irst, ecet that the itches originall laed b the alto saohone, tenor saohone, and tuba have been removed The second measure is urther transormed b changes in dnamics and a metric shit rom 6/ to 5/ B means o these somewhat subtle shits in color and teture, the second measure o the iece is meant to unction as a kind o relection or echo o the irst Measures ive and si share a similar relationshi, but here the written harmon is based on the harmonic sectrum o C-1 (32 Hz) The A ¼ Shar (529 Hz) sounded b the trumet in these measures is an aroimation o the ourteenth harmonic o C-1, whereas in measures one through our it had unctioned as the eleventh harmonic o E-1 This change in virtual undamental unctions as a kind o common tone modulation, revolving around the hub o A ¼ Shar [ig 5] Rhthmic Structure The rhthmic structure o Echoes is organized around grouings o our, ive, si, seven, and nine beats Each grouing is subdivided into our arts o equal duration, accented to varing degrees b the alto and tenor saohones, trombone, tuba, acoustic bass, and drum set 21 As a result o these henomenal accents, each measure-length acquires a distinctive olrhthmic identit that remains unchanged throughout the entire iece The division o each measure into our equal arts also creates a ver seciic kind o 21 The 6/ measures (mm 1, 3, 6, 12, 15, 22, 26, 39) are actuall divided into eight equal arts b the alto saohone, trombone and drum set However, these measures can also be viewed as a continuous sequence o two 3/ measures divided into our equal arts 23

28 rhthmic ambiguit with regard to ulse articularl in the measures o 5/, it is ossible or a listener to entrain to grouings o ive siteenth notes and erceive them as a new, slower temo o 96 BM ig 5: Common tone modulation in Echoes 2

29 In the measures o / and 9/ this henomenon is still resent, though less rominent due to the increased disarit between the notated quarter-note temo o 120 BM and the temi that emerge with the grouings o seven siteenth notes (69 BM) and nine siteenth notes (53 BM) In the 6/ measures o Echoes, or eamle, listeners and erormers oten eel the grouings o three siteenth notes as a new, aster temo o 160 BM one that is easier to entrain to than the slower notated quarter-note temo o 120 BM eters and Schwarz (1989 cited in Summers and Rosenbaum 1993) have shown that when asked to entrain to a simle olrhthmic ulse comrised o two arallel temi, both musicians and non-musicians ound it much easier to consistentl eecute the aster o the two ulse-trains Handel (198), however, has suggested that while listeners do tend to avor the aster o two ulse-trains in the ercetion o olrhthms, the also consistentl gravitate towards temi that are hsicall eas and comortable to eecute Given arncutt s (199) reviousl cited reerred temo range o BM, it ma ollow that olrhthms comrised o two ulse-trains within the range o BM are most likel to evoke the ercetion o a rhthmic threshold between two discrete temi In Echoes, then, the measures o 5/ ma be most eective in rovoking the sense o two simultaneous temi, recisel because the listener is resented with two ulse-trains that all roughl within arncutt s reerred temo range: the quarter-note temo (120 BM) and the temo which emerges as a result o the our equal grouings o ive siteenthnotes (96 BM) Imrovisation The central ramework or Arological modes o imrovisation in Echoes is rovided b its sectral chord changes In measures one through our, or eamle, the alto saohonist is asked to imrovise based on a musical scale comrised o harmonics eight through siteen o E1, rounded to the nearest quartertone This chord-scale relationshi is marked in the score as C# (H8-H16) with the E transosed to C# or the alto saohone [ig 6] In measure 5, when the harmon shits to relect the change in the virtual undamental rom E1 to C1, the chord smbol notation also changes and is marked as A 25

30 (H8-H16) As is the case with an sstem o chord changes, man o the decisions regarding itch choice and octave transosition are let to the imroviser ig 6: Chord smbol notation or imrovisation in Echoes In m own eerience, I ve ound that in negotiating the sectral chord changes o Echoes I tend to emhasize harmonics nine, eleven, twelve, and ourteen in addition to incororating itches derived rom other scales when the musical contet calls or it Each measure o music in Echoes is conceived o as a unique sound object: a comosite o harmon, rhthm and ensemble teture As a result, the imrovisational recet o changes is eanded to include all three o these elements In measures our and ive, or eamle, the alto saohonist is eected to construct an imrovisation inormed b (1) the metric shit rom 5/ to /, (2) the change in teture brought about b the tenor saohone and the tuba, and (3) the modulation o the virtual undamental rom E1 to C1 As a ramework or Arological imrovisation, the comositional structure o Echoes can be diicult to internalize However, man o the challenges resented b the iece also rovide oortunities or creative aroaches to imrovisation An imrovised solo on Echoes can be built around the microtonal itch content o the sectral chord changes, but it is also ossible to imagine an imrovisation that uses the iece s rhthmic, tetural, and dnamic changes as its oundation or eamle, the drum coda at the end o the iece (mm 39-5) can be seen as a latorm or imrovisation that rivileges both rhthmic and tetural variation In lieu o chord changes, the ercussionist is asked to negotiate a set o dnamic changes, which are the result o raid shits in the number o 26

31 accomaning laers rom seven (m 39) to three (m 0) to two (mm 1-2) to ive (mm 3-) to one (m 5) [ig ] ig : Dnamic changes in the drum coda in Echoes 2

32 Baltimore/Berlin Written or a mied quintet that includes Bb clarinet, trombone, iano, acoustic bass and drum set, Baltimore/Berlin (2008, rev 2011) is one o our comositions in the eveninglength ccle Imossible low, which was commissioned b the International Contemorar Ensemble in 2010 and remiered on Aril 1, 2011 in New York Cit In the ollowing analsis o Baltimore/Berlin, I resent a brie overview o the comosition s ormal structure and harmonic underinning beore moving through a more detailed and comrehensive account o the iece s rhthmic structure, lacing secial emhasis on the was in which I have sought to incororate rhthmic thresholds into a work or a small chamber ensemble ormal Structure In Baltimore/Berlin, eressive timing, comound meter, rubato hrasing, changing temi, olrhthm, instrumental gesture, and memor are treated as a seamless continuum designed to elore the scholog o musical time and its connection to musical meaning The iece is aroimatel eleven minutes long and comrises si sections: irst assacaglia (mm 1-22 [3 ]), irst rhthmic interlude (mm [2 ]), iano interlude (mm 0-8 [1 ]), second rhthmic interlude (mm 9-59 [1 ]), rubato interlude (mm [2 ]), and second assacaglia (mm [2 ]) Each section is conceived o as a comositional scene which eamines the rhthmic remise o Baltimore/Berlin rom a unique vantage oint As a result, the work demonstrates a kind o kaleidoscoic ormal logic, in which distinctive melodic motis, instrumental gestures, and chord voicing are resented to the listener in a variet o comositional contets There are, however, several instances in Baltimore/Berlin in which comositional material is transormed and develoed in a more linear manner The recaitulation o the assacaglia in m 82, or eamle, can be understood both as a more traditional ormal device and as a means o eloring the nature o long-term memor in the maniold o rhthmic structures driving the iece 28

33 Harmonic Structure The harmonies in Baltimore/Berlin are derived rom the hsical roerties o an acoustic iano; the sound sectrum o the iano is slightl distorted, which results in inharmonic overtones, starting with the 16th artial The lowest octave o the iano is also deined b the act that, in man cases, the second harmonic has a higher amlitude than the undamental requenc Throughout Baltimore/Berlin, the sound o the iano and its hsical structure rovide a smbolic oundation or an arra o harmonic devices In the oening measures o the iece, the natural resonance o the iano assumes a harmonic role In order to reinorce the acoustic roerties and overtone structure o the iano, the irst assacaglia is written in the instrument s lowest register, allowing a greater number o the overtones to all within the range o human hearing The ianist is also asked to kee the sustain edal deressed throughout the entiret o the irst section in order to urther reinorce and rolong the natural resonance o the iano s uer artials [ig 8] ig 8: ening assacaglia in Baltimore/Berlin 29

34 In mm 1-15, the uer harmonics o the iano are reinorced b the clarinet and trombone The iano las a D#1 (389 Hz), which unctions as a undamental requenc, while the trombone sounds a rough aroimation o the eleventh harmonic (A 0 Hz) and the clarinet las the ourteenth harmonic (C ¼ Shar 5386 Hz) The quiet noise o the cmbal roll in mm 1-15 and the mezzo-iano attack in the iano (with the damer edal removed) hel to mask the entrance o the clarinet and trombone and allow those instruments to use more easil with the natural resonance o the iano [ig 9] ig 9: Aroimation o uer iano harmonics b the clarinet and trombone in Baltimore/Berlin The harmonies in the second rhthmic interlude (mm 9-59) are also modeled ater the slightl distorted sectrum o the iano In the beginning o m 9, or eamle, the acoustic bass and the iano sound itches derived rom the overtones o a virtual undamental sounding at C-0 (16 Hz) The acoustic bass las the second artial (C 32 Hz) and the iano aroimates the eleventh and iteenth artials (# 185 Hz B 2 Hz), as well as the 16 artial (C# 21 Hz), which is slightl inharmonic 30

35 Throughout the second rhthmic interlude (mm 9-59), the harmonies are constructed in this ashion and make requent use o erect ourth and erect ith intervals Demonstrating qualities o quartal harmon in a sectral contet, the chords sounded b the iano and acoustic bass in this section take on a distinctive character [ig 10] ig 10: Mitures o quartal harmon and sectral itch organization in Baltimore/Berlin Rhthmic Structure The rhthmic structure o Baltimore/Berlin elores the concet o rhthmic thresholds rom multile ersectives Using a unique and meaningul aroach to rhthm rooted in the nature o human cognition, each section o the iece elores a seciic acet o rhthm ercetion In the irst assacaglia (mm 1-22), the notated temo o eighth-note = 96/quarter-note = 8 laces the temoral low o the music at the lower threshold o arncutt s normal temo range (6 BM) and at the temo rate which both arncutt (199) and Re and 31

36 Doggett (200) have cited as the oint at which listeners are unable to erceive/anticiate a regular ulse (33 BM) As a result, the oening section o Baltimore/Berlin demonstrates a kind o uzz eriodicit, even when the ianist is asked to la several consecutive notes o equal length The notated durational shits in the oening assacaglia also contribute to this henomenon and urther comlicate the notion o ulse salience in this section o the iece Centering the irst assacaglia around the quarternote value o 8 BM and making requent use o siteenth-note grouings o 3, 5, and 6 to oster an asmmetrical ulse is intended to create a comositional tension between the ercetion o discrete changes in duration and the human reerence or and roensit to hear temoral ratios o 1:1 (See raisse (1963) and Clarke (198), among others) [ig 11] ig 11: uzz eriodicit in the oening assacaglia o Baltimore/Berlin The irst rhthmic interlude (mm 23-39) is largel deined b the introduction o the drum set as a rhthmic instrument The unison hrase laed b the acoustic bass and drum set at the end o m 22 situates the oening assacaglia within a more elicit 32

37 rhthmic structure, introducing a ragmented and asmmetrical sense o ulse that nevertheless remains highl snchronized The material in this section o the comosition elores the etent to which rhthmic unisons and snchronized attacks can inluence the ercetion o musical ulse Though the literature on this area o music cognition aears to be virtuall non-eistent, I believe that this kind o inquir is crucial to a comrehensive understanding o rhthm ercetion In Rai (2006), or eamle, I make use o a seemingl random row o durations, which increasingl evokes the sense o an underling cognitive grid with notated unison attacks [ig 12] ig 12: Unison attacks o asmmetrical rhthms in Rai In Baltimore/Berlin, the meticulous alignment o musical materials is also reinorced b the etensive use o the bass and snare drum Though it ma seem sel-evident that ercussive timbres, in and o themselves, can contribute to a sense o ulse and rhthmic 33

38 stabilit, here again there is little schological literature on the toic 22 In measure 31 o Baltimore/Berlin, a raidl shiting and highl asmmetrical organization o musical time is made to sound more rhthmic as a result o unison attacks shared b the iano, acoustic bass, and drum set, and densel notated material eecuted b the bass and snare drum As evidenced b the material in this measure, the irst rhthmic interlude in Baltimore/Berlin is intended to elore the relationshi between timbre, alignment, and the rhthmic threshold searating the ercetion o rhthm and ure duration [ig 13] ig 13: Unison attacks in a raidl shiting rhthmic contet in Baltimore/Berlin In the last our measures o the irst rhthmic interlude (mm 3-39), the listener is resented with a raidl shiting constellation o simultaneous ulse-trains As Lerdahl (1988) has noted, simultaneous temos can comete or attention and obscure the underling rhthmic structure o a comosition erkins and Howard (196) have ound 22 Writing on the nature o ecological ercetion in music, Vija Ier (2002) has noted that we connect the ercetion o musical motion at the ecological level to human motion rom this oint o view, the ver sound o a snare drum, or eamle, ma evoke the eeling o a human action (the striking o a drum) that culturall, we associate with rhthm 3

39 that when resented with multile temos, listeners will attend to the rhthmic structure in one wa while remaining aware o alternate ossibilities or entrainment, in some cases moving back and orth between two or more otions In mm 3-39 o Baltimore/Berlin, the simultaneous resence o multile ulse-trains is intended to create a comositional tension between serial and segregated modes o listening [ig 13 and 1] Jones and Jagacinski (1995) deine serial listening as a mode o attending in which two or more rhthmic tetures are erceived as art o one sequential stream o inormation Segregated listening, or streaming, on the other hand, occurs when a rhthmic sequence is erceived as two or more segregated streams ig 13: mm 3-38 o Baltimore/Berlin 35

40 ig 1: m 39 o Baltimore/Berlin Bregman (1990) has suggested that eriodic rhthms can reinorce the ercetion o an auditor stream, and has also roosed that simultaneous ulse-trains searated b more than 3 to semitones encourage segregated modes o rhthmic attending (streaming) In measure 39 o Baltimore/Berlin, the listener is resented with three searate isochronous ulse-trains sanning several octaves: the clarinet las a C ¾ Shar, just above C, in a stead quarter-note ulse; the right hand o the iano sounds G#6 as quarter-note trilets, and the let hand o the iano alternates between G2 and A#1 in grouings o ive siteenth notes Establishing multile ulse-trains that comete or attention across a wide registral san, I hoe to evoke a ercetual threshold in the listener, simultaneousl encouraging segregated and serial modes o listening The rhthmic structure o the iano interlude (mm 0-8) is oriented around the boundaries o the schological resent In mm 39-0, the duration o the reeating moti in the bass cle o the iano art is eanded rom a regular ulse o ive siteenth- 36

41 note grouings to a ulse o hal notes and dotted hal-notes At the written temo o quarter-note = 8, grouings o ive siteenth-notes last aroimatel 15 seconds and hal notes and dotted hal notes last about 25 seconds and 35 seconds resectivel Given the average range o the ercetual resent 2 to 3 seconds, as deined b raisse (1982) the eansion o the iano moti in mm 39-0 can be understood as a strategic shit which laces the musical material in a new ercetual ramework In measure 2, the duration o the iano moti is eanded urther to include a whole-note with a duration o aroimatel 5 seconds raisse s uer limit or the schological resent Having reached a ercetual threshold in m 2, the musical material in mm 3- is intended to create a smbolic link between the schological resent and a more eanded notion o short-term memor The reeated G#6 laed b the iano in m 3 is an allusion to m 39, where G#6 also igures rominentl in the notated iano art In measure, the iano makes a veiled reerence to the iece s oening assacaglia, which is eanded in mm 5-6 [ig 15] ig 15: Rhthmic structure in relation to the schological resent in Baltimore/Berlin The second rhthmic interlude o Baltimore/Berlin (mm 9-59) demonstrates the most rominent and consistent sense o ulse, where the tactus is elt at aroimatel 96 3

42 BM, at the eighth-note level The notated drum set art in this section o the iece establishes a semi-consistent temoral low that is disruted reeatedl at short intervals, b the asmmetrical subdivision o the ulse In this rhthmic contet, comound meter serves both to create segmentation and to rescribe a rough hierarch o rhthmic emhasis Winold (195) has suggested that the use o mied meters, articularl those that result in unequall timed beats, will bring about a strong sense o irregularit and disrution in rhthmic structure However, given the human reerence or temoral ratios o 1:1 and 2:1, a eeling o disrution at the hrase level can oten be diicult to achieve Re (1992), or eamle, has shown that listeners are oten ver good at detecting small changes in duration at the ulse level, and much worse at the hrase level Re has also suggested that this ma, in art, be due to the act that eressive deviations in timing in Western Classical music tend to be lengthenings, as oosed to shortenings, with the ormer oten occurring at hrase boundaries ollowing Re, the strategic use o comound meter to shorten individual ulses in the second rhthmic interlude o Baltimore/Berlin can be understood as a means o rovoking at the hrase level a sense o rhthmic unbalance that is more likel to be ercetuall salient This comositional eect is reinorced b the act that shortened ulses in this section o the iece are sstematicall ollowed b unison attacks in the iano, acoustic bass, and drum set, which mark imortant hrase boundaries The maniulation o rhthm to ostone and anticiate listener eectation has long been understood as a kind o henomenal accent in music 23 Indeed, the rhthmic structure o Baltimore/Berlin in mm 9-59 is intended to create a heightened sense o comositional tension b simultaneousl maniulating eectation at both the beat and the hrase levels Structuring m rhthmic materials in this wa, I hoe to achieve a careul comositional balance where the imression o a stead ulse is constantl deconstructed and transormed, without being comletel obscured [ig 16] In stark contrast to the second rhthmic interlude, the rhthmic structure in the rubato interlude (mm 60-81) is intended to romote a sense o what ierre Boulez (1960) has reerred to as smooth time, where the listener is unable to erceive the resence o a musical ulse 23 See Cooer and Meer (1956), or eamle, on rhthmic ostonement 38

43 ig 16: Mied meter and rhthmic disrution in Baltimore/Berlin This eect is achieved through the use o musical gestures which do not demonstrate a discrete beginning or end, and are thus more diicult to situate within a rhthmic contet: iano tremolos with the sustain edal deressed; quiet glissandi in the trombone and acoustic bass, and cmbals rolls in the notated drum art Here again, the distinctive reetition o G#6 in the uer register o the iano is intended to reerence mm 39 and 3 where the G#6 is irst introduced In this contet, the G#6 can be viewed as a smbolic comositional gesture, evoking the role o long-term memor in the rhthmic ramework o the iece In measure 65, the notated tremolo in the lower register o the iano is transormed into a more rhthmic gesture, which suggests a distinct eeling o ulse that remains largel obscured as a result o the notated register and the consistent use o the sustain edal [ig 1] 39

44 ig 1: mm o Baltimore/Berlin 0