Marjorie Thomas' schemas of Possible 2-voice canonic relationships

Transcription

1 Marjorie Thomas' schemas of Possible 2-voice canon Real Time Tempo Canons wih Anescofo Chrisopher Trapani Columbia Universiy, New York ABSTRACT Wih recen advances in score-following capabiliies, i has become possible o envision new iming sraegies, o realize previously impracical mehods of coordinaion beween a live performer and elecronics. Our work ceners on he challenge of synchronizing a he end of a musical phrase, where evens and processes are imed no from an iniial rigger, bu occur according o a relaive disance owards a prediced fuure aack. The key sofware componen is Anescofo, a score-following ool which relies on a srong coupling, hrough a dynamic programming language, beween a machine lisening module and a reacive engine. This language allows hierarchical, concurren, and heerogeneous compuer processes o be organized over ime, and for exernal evens o be anicipaed, wih a runime sysem ha riggers elecronic acions in response o variaions in performance. Various programming sraegies were implemened, honed and esed wih a live performer. The musical maerial of hese skeches focused on he idea of flexible canons, on ineracions beween a live insrumen and a second voice generaed from a buffered real-ime recording. The differen canonic sraegies make use of Anescofo s live empo calculaions o creae dynamic empo shifs, o force voices o converge, and o conrol precise canon effecs. 1. INTRODUCTION Elecroacousic performance has long relied on he mehod of fron-end synchronizaion, allowing live players o inerac wih elecronics by riggering evens in real ime, wih processes imed o unfold from hese inerspersed cues. Wih a reliable score-following ool coupled wih a domain specific language, differen sraegies of synchronizaion have become feasible, noably he possibiliy of aligning a he end of a musical phrase. Using he empo canon principles of Conlon Nancarrow ([1],[2]) as a model, voices a relaed bu independen speeds cach up a a predeermined convergence poin (Fig 1). Unlike Nancarrow s rigid grids however, a degree of rhyhmic flexibiliy and vialiy becomes possible wih he dynamic Copyrigh: c 2014 Chrisopher Trapani e al. This is an open-access aricle disribued under he erms of he Creaive Commons Aribuion 3.0 Unpored License, which permis unresriced use, disribuion, and reproducion in any medium, provided he original auhor and source are credied. José Echevese b. IRCAM UMR STMSconverging canon CNRS Sorbonne Universiés UPMC - INRIA Rocquencour voice a. convenional echevese@ircam.fr canon Marjorie Thomas' schemas of Possible 2-voice canonic relaionships Marjorie Thomas' schemas of Possible 2-voice ca score-following ool Anescofo, c. whose diverging programming canon srucure b. allows converging high-level canon macro conrols ha adap o realime racking daa, adaping he playback speed of he canons accordingly o accompany he ineviable b. converging flucuaions canon of a live performance. a. Elecronic convenional canon evens faser are voice imed novoice longer from a given saring poin, bu in relaion o an approaching momen whose disance is coninually prediced and recalculaed. c. diverging canon d. converging-diverging canon Marjorie Thomas' schemas of Possible 2-voice canonic relaion Marjorie Thomas' schemas of Possible 2-voice canonic relaionships b. converging canon c. diverging canon b. d. (a) (b) (c) converging converging-diverging canon canon c. diverging canon e. diverging-converging canon d. converging-diverging canon faser voice faser voice c. diverging canon poin of synchrony poin of synchrony (d) EXAMPLE 1: MODELS d. converging-diverging canon OF (e) TWO-VOICE CANONS e. diverging-converging canon e. diverging-converging canon faser (1c) faser diverging voice canon. faser d. converging-diverging canon poin of synchrony EXAMPLE 1: faser MODELS voice OF TWO-VOICE CANONS EXAMPLE 1: MODELS OF TWO-VOICE CANONS e. diverging-converging canon faser EXAMPLE 1: MODELS OF TWO-VOICE CANONS faser poin of synchrony Figure 1: (1a) convenional canon. (1b) converging canon. (1e) diverging converging canon. (1d) converging diverging faser canon. 2. ANTESCOFO faser 2.1 Synchronizing elecronic acions wih a musician poin of performance synchrony Research e. around he diverging-converging EXAMPLE 1: canon Anescofo sysem focuses on how o MODELS OF TWO-VOICE CANONS achieve a high-level musical ineracion beween live musicians and a compuer, specifically in he conex of mixed faser music, where he emporal developmen of musical processes depends faser on acive lisening and complex synchronizaion sraegies [3]. We have proposed in [4] a novel archiecure (Fig 2) ha relies on a srong connecion beween arificial machine lisening and a domain-specific real-ime programming language for composiional and performaive purposes. To insruc he arificial lisening engine, he user creaes an augmened score whose language inegraes boh programming ools and musical erms, allowing a unique and flexible emporal organizaion. The augmened score oulines boh he insrumenal and he elecronic pars and he insrucions for heir real-ime coordinaion during performance, he specific evens ha should be recognized in real

2 This excerp from an Anescofo score shows wo musical evens wih wo elecronic acions. The firs corresponds o a single noe (middle C) wih a duraion of one bea. An elecronic acion is riggered by Anescofo one eighh-noe afer he C is deeced, where he message $v1 $v2 is sen o he objec receive acion. Figure 2: General archiecure of Anescofo. The score is an inpu of boh he lisening machine and he reacive engine. The evens recognized by he lisening machine are signaled o he reacive engine which schedule he acions a he righ ime. 3. REALIZATION Skeches wrien by Chrisopher Trapani and played by he clarineis Jérôme Come from he Ensemble inerconemporain formed he basis of a six-monh sudy, culminaing wih a 3-minue final skech viewable here [5]. In his secion we will deail he various challenges addressed during his collaboraion. 3.1 Se-up ime, and he acions corresponding o hese riggers. During a performance, he language runime evaluaes he augmened score and conrols processes synchronously wih he musical environmen, wih he aid of arificial machine lisening. This approach has been implemened in he Anescofo sysem and validaed in many live performances. 2.2 Some elemens of he language An Anescofo score conains boh an insrumenal par and he accompanimen acions. As explained above, deails of boh noaed music and elecronics are combined in a single augmened score. During live performance, Anescofo reacs o daa from he lisening machine and from he exernal environmen. This reacive sysem dynamically akes accoun of empo flucuaions and he values of exernal variables, in order o synchronize accompanimen acions o he real-ime inerpreaion. The possibiliy of iming evens and he acions relaive o he empo, as in a classical score, is one of he main srenghs of Anescofo. Wihin he augmened score language, he composer can decide o associae acions o cerain evens wih delays (eiher in absolue ime or relaive o he empo), o group acions ogeher, o define iming behaviors, o srucure groups hierarchically, and o allow hese groups o ac in parallel. An augmened score is a sequence of insrumenal evens and acions. The synax for he insrumenal par allows he descripion (piches + duraion) of evens such as noes, chords, rills, glissandi and improvisaion boxes [4]. Acions are divided ino aomic acions which perform an elemenary compuaion and compound acions. Compound acions group muliple acions; hese are riggered more or less direcly by an even. NOTE C /2 receive_acion $v1 $v2 CHORD (D4 F#4) 1/2 receive_acion $v3 $v4 Figure 3: Anescofo follows he clarineis s performance which is recorded in parallel ino a buffer. Phase Vocoder objecs read his buffer a specific posiions and speeds conrolled by Anescofo as oulined in he score. These skeches were realized in he Max/MSP environmen. The live performer is recorded ino an audio buffer, while a Phase Vocoder objec (SuperVP [6], [7]) reads his buffer a specific posiions and speeds. The Anescofo program calculaes he correc posiion and speed values according o incoming real-ime daa, communicaing wih he Phase Vocoder. The challenge of creaing a dynamic canon lies in building, esimaing, and updaing in real ime he relaion beween he emporaliy of he score (in beas) and absolue ime. All parameers ha conrol he unfolding of he canon depend on his relaionship. The Anescofo language allows he composer o manage his kind of conrol in a precise fashion. 3.2 Descripion of Real-Time Canons A canon can be defined as he superimposiion of a phrase upon a version of iself. In our work, he live musician provides he firs voice of he canon, whereas he elecronics provide a manipulaed second voice in reply. A wo-voice canon can hus be characerized as a symbioic phrase wih wo componens: he canonic reply played back from a buffer (he line segmen [sar,end] in he figures 4),

3 he phrase performed live by he musician ono which he canonic reply is superimposed (he line segmen [sar,sync] in he figures 4). Keeping in mind ha he playback posiion can never overake ha of he live recording for obvious causal reasons, differen ypes of real-ime canons can be defined (Fig 4). (a) Figure 5: The diagram represens he differen values o be considered for he speed calculaion. A he curren ime, he daes end (he canon end) and sync (he final synchronizaion poin) are esimaed according o he empo value. The value corresponds o he ime a which he live musician played he curren posiion of he buffer. (b) (c) Figure 4: Differen ypes of real-ime canons The emporal daa peraining o each canon is specified in he score. These specificaions are virual and relaive o he empo so ha during performance, hese values can be ranslaed ino a real and absolue scale. The canon (4a) sars a he same ime as he musician bu unfolds a a speed. The canon (4b) sars afer he musician has played he end of a phrase. This corresponds o a superposiion of wo independen voices. The canon (4c) begins afer he live voice a a empo ha will gradually increase unil caching up he musician a a predefined convergence poin. 3.3 Canon speed calculaion In order o deermine he precise speed for each canon in he score, he Anescofo program uses real-ime empo calculaions as well as emporal esimaions of upcoming evens. The empo of he musician as esimaed by he lisening machine of Anescofo is he key o calculaing hese esimaes of fuure evens. Thus, he speed values are reesimaed hroughou he enire duraion of he canon as soon as new informaion concerning he posiion or he empo of he musician arrives. Figure 5 represens he differen relaionships which can be found in he hree ypes of canons menioned above. Le he curren posiion of he musician in he absolue scale; he compuaion of he speed follow his equaion: canonspeed = end sync where sync is he esimaion of he ime before he synchronizaion poin and end is he esimaion of he (1) ime ha remains o be played by he canon unil he synchronizaion poin. This is he main piece of code in he score ha compues he speed of he canon each ime he empo is updaed: whenever($rt_tempo) $ :=$ +((@dae($ )-$NOW)*$speed) $end:=$now+($end_pos-$rnow)*60/$rt_tempo $sync:=$now+($sync_pos-$rnow)*60/$rt_tempo $speed := ($end-$ )/($sync-$now) ph_voc speed $speed }unil ($RNOW $end_pos) $NOW, $RNOW, and $RT_TEMPO are inernal variables ha represen, respecively, he curren ime in seconds, he curren posiion of he musician in beas, and he curren value of he empo. The whenever saemen allows acions o be launched when a given condiion is verified. Each ime he variables corresponding o his condiion are updaed, he predicae is re-evaluaed. Here he body of he whenever is execued each ime he variable $RT_TEMPO changes. This process coninues unil he live musician has reached he end of he canon ($RNOW $\geq$ $end_pos). $ represens he audio ime-chunk in he buffer already ) is he dae of he las updae of $ variable. The empo esimaion is used o predic he daes of $end and $sync. $speed represens he speed of he playback and is used as he conrol parameer of he phase vocoder. 3.4 Real-Time Canons wih speed curve consrains Tradiionally, canons are defined by a consan speed raio. Phase vocoder playback however offers he possibiliy of dynamic empo flexibiliy following a predefined paern. These shifs in speed can be easily sored as a funcion graph, wih care aken o avoid increased playback speeds ha would cause he playback buffer o overake he recording. Equally applicable o prolongaion and converging canons, hese empo maps provide a funcion rans-

4 Figure 6: Real-Time Canons wih speed curve consrain fer, an inermediary muliple ha imposes a second se of speed relaionships ono he canonic reply. This sraegy is also used o creae a specific syle of canon (ype e in Fig. 1) where wo voices cover he same lengh, boh beginning and ending ogeher, bu wih dynamic changes of speed wihin his frame. Nancarrow makes frequen use of his effec, swiching he speeds beween a faser and a a he exac midpoin of he phrase for a flawless alignmen. In our example, he empo shifs dynamically. From an iniial shared saring poin, he playback voice unfolds a a speed han he live player s, giving he impression of a prolongaion canon wih a malleable empo. Laer in he canon, phrases in playback are repeaed faser han heir live rendiions, wih he empo again coninually calibraed agains he approaching convergence poin. Figure 7: Example of a curve specified by he composer o consrain he speed of he canon. The figure 7 shows a possible curve o consrain he speed of he canon. If is he relaive posiion of he musician in he score, he sen speed is: sync canonspeed = f() sync (2) f(x) dx where f() is he curren value of he curve, sync is he ime in beas ha remains o be played by he canon unil he synchronizaion poin and sync f(x) dx he inegral of he curve from he curren insan o he synchronizaion poin. In pracice, he speed calculaion is updaed every 0.05 seconds. 3.5 Meadaa ineracions Aack recogniion daa gahered in real ime by Anescofo also serves as a ool for soring and recalling he posiions of various evens. As he live voice is followed, he iming in ms of each deeced even is sored as a marker in he buffer. Though playback speed is coninually in flux, he posiions of hese markers remain consan and funcion as signposs for various mea-processes. As one basic example, hese markers can be read as muliple enry poins, so ha canonic replies can begin no only a he sar of he recorded buffer, bu a any recognized even wihin he musical phrase. They may also serve as signposs for dynamic ransposiion, sending predeermined ransposiion values o he phase vocoder when he playback voice reaches he maching phrase. Markers are also valuable for managing daa ouside of he signal realm. Using he onse and pich daa for each noe in an Anescofo score, i is possible o keep rack of he curren pich of each canonic voice, even as he playback rae changes. In our example, a process of adding and subracing he frequencies of acive piches is esablished, wih he resuls displayed in real ime using he Bach inerface [8]. The resuling piches are used o pilo he ransposiion of concaenaive synhesis in CaaRT [9], producing a consanly shifing halo of samples whose harmonic conen conforms o he sum and difference ones of he curren piches in he wo canonic voices. 3.6 Conrol a he Convergence Poin The mos significan challenge of creaing converging canons is how o rea he arrival poin, since perfec synchrony beween a live voice and a buffer is impossible. One shorerm soluion involves a las second crossfade in playback, from he buffer o he live voice. While his allows he final aack o be reliably aligned, he drawback is a loss of precision in he passage leading up o he convergence poin. The playback speed is also sysemaically rese o 1. (pariy) a he convergence poin o preven playback from overaking he buffer s playhead. A wachdog mechanism is execued o preven playback from overaking he buffer s playhead each ime he speed value of he canon is updaed: whenever($rt_tempo) abor wachdog... canon speed compuaion... group wachdog $delay:=($now-$ )/($speed-1) $delay ph_voc speed 1.0 } }unil ($RNOW $end_pos) The wachdog mechanism is managed in he same body as he speed compuaion. The ime needed for he posiion of he playhead ($ ) o cach up o he live player a he speed sen jus before ($speed) is compued in he variable $delay. The message ph_voc speed 1.0 is scheduled o be launched $delay seconds laer. If he empo is again updaed, he abor wachdog command will cancel he message launch and re-schedule a new one. The final momens of each converging canon involve increasingly perilous calculaions. As he prediced arrival

5 poin approaches, empo calculaions have more immediae consequences, and small changes in he live player s iming can creae drasic aleraions in playback speed. Wih less ime lef o correc course, he danger of veering ahead of he live buffer s recording poin increases. A provisional soluion has been he inroducion of a braking mechanism which performs a secondary predicion. If he nex even anicipaed by Anescofo has no ye arrived afer a given percenage of he alloed window (80% by defaul), he speed auomaically slows along an exponenial curve, so ha playback gradually slows unil he nex prediced poin of recalibraion arrives. A prooype braking pach was creaed and esed during he work period, and should be inegraed ino he pach afer furher experimenaion. 4. CONCLUSION The success of his projec demonsraes Anescofo s capaciy for sophisicaed ime-relaed processes, handling boh live performance and real-ime compuing hrough a single sreamlined engine. This could open he door o novel and imaginaive reinvenions in he realm of rhyhm, exending he exising paradigm and encouraging new experimens wih ancien musical devices in a wholly conemporary conex. The musical examples explored hus far have been brief and inuiive forays ha only scrach he surface of he new possibiliies offered by his approach. If empo canons can be realized in Anescofo wih jus a few lines of code, one can imagine a larger-scale work wih several local-level empo loops, converging and diverging in fracal-like paerns. The main barrier o composing such music oday is he noaion and execuion of such a highly inricae level of rhyhmic inerplay, bu a ool ha generaes canonic responses wih real-ime adapive capabiliies could lead o exciing new forays in he realm of labyrinhine rhyhmic layering and deailed canonic wriing. The mos imporan breakhrough for Nancarrowhe primary facor ha paved he way for his unprecedened experimenaion wih muliple layers of empo and imingwas being allowed o work ou his ideas in visual and mahemaical erms, direcly ono he piano roll. The oucome of his projec could signal a similar breakhrough in he elecroacousic realm: a new ool for inricaely-imed canonic wriing ha could prove o be useful for many composers, enabling hem o succincly and reliably describe complex numerical relaionships wihou recourse o noaion. [4], Anescofo: Anicipaory synchronizaion and conrol of ineracive parameers in compuer music, in Proceedings of Inernaional Compuer Music Conference (ICMC). Belfas, Augus [5] (2013, April). [Online]. Available: hps://www. youube.com/wach?v=cq1pqny5xjk [6] A. Roebel, Transien deecion and preservaion in he phase vocoder, in Inernaional Compuer Music Conference (ICMC), Singapore, Singapore, Ocobre 2003, pp [7] A. Roebel and X. Rode, Efficien specral envelope esimaion and is applicaion o pich shifing and envelope preservaion, in Inernaional Conference on Digial Audio Effecs, Madrid, Spain, Sepembre 2005, pp [8] A. Agosini and D. Ghisi, Bach: An environmen for compuer-aided composiion in max, in ICMC Inernaional Compuer Music Conference. Ljubljana, Slovenia: IRZU - he Insiue for Sonic Ars Research, Sep [Online]. Available: hp://hal.inria.fr/hal [9] D. Schwarz, G. Beller, B. Verbrugghe, and S. Brion, Real-ime corpus-based concaenaive synhesis wih caar, in 9h In. Conference on Digial Audio Effecs (DAFx-06), Monreal, Canada, Sepember REFERENCES [1] K. Gann, The Music of Conlon Nancarrow. Cambridge Universiy Press, [2] M. E. Thomas, Nancarrow s canons: Projecions of emporal and formal srucures, Perspecives of New Music, vol. 38, no , Summer [3] A. Con, On he creaive use of score following and is impac on research, in Sound and Music Compuing, Padova, Ialy, July 2011.