- electronic proceedings available at http://cmr.soc.plymouth.ac.uk/cmmr2015/proceedings.pdf-- paper proceedings published by Springer in the LNCS series, in 2016- the article win the best student presentationInternational audienceIn this project, we created an agent-based model of music group playing under four di↵erent interaction mechanisms. Based on real music data, added randomness and simplifying assumptions, we examine how agents synchronize and deviate from the original score. We find that while music can make synchronization complex, it also helps reducing the total deviation. By studying the simulation process, several conclusions on the relationship between di↵erent growing speeds of total deviations and di↵erent interaction schemes are drawn. With interpretation from a musical point of view, we find that, in a music ensemble, listening to neighbors helps the players end up in sync. However, if people do not listen carefully enough, the deviation becomes larger than when people do not listen at all. On the issue of whom one should listen to, the results show no significant di↵erences between listening to the immediate neighbors and to the whole group. Finally, we also observe that large deviations can be reduced by making the musicians move while playing

Doursat, René

Giavitto, Jean-Louis

Yuping Ren, Iris

HAL-Polytechnique

Synchronization in Music Group PlayingIris Yuping Ren, Rene´ Doursat, Jean-Louis GiavittoTo cite this version:Iris Yuping Ren, Rene´ Doursat, Jean-Louis Giavitto. Synchronization in Music Group Play-ing. Mitsuko Aramaki; Richard Kronland-Martinet; Sølvi Ystad. International Symposiumon Computer Music Multidisciplinary Research (CMMR), Jun 2015, Plymouth, United King-dom. Springer, http://cmr.soc.plymouth.ac.uk/cmmr2015, 510–517 (in electronic proceedings),Lecture Note in Computer Science. <http://cmr.soc.plymouth.ac.uk/cmmr2015/>. <hal-01257540>HAL Id: hal-01257540https://hal.archives-ouvertes.fr/hal-01257540Submitted on 17 Jan 2016HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.Synchronization in Music Group PlayingIris Yuping Ren1, Rene´ Doursat2, and Jean-Louis Giavitto31 Erasmus Mundus Master’s in Complex Systems Science,Graduate School, Ecole Polytechnique, Paris, France2 Complex Systems Institute, Paris Ile-de-France (ISC-PIF),CNRS (UPS3611), Paris, France3 Institut de Recherche et Coordination Acoustique/Musique (IRCAM),CNRS (UMR9912), Paris, Franceyuping.ren.iris@gmail.comAbstract. In this project, we created an agent-based model of musicgroup playing under four di↵erent interaction mechanisms. Based on realmusic data, added randomness and simplifying assumptions, we examinehow agents synchronize and deviate from the original score. We find thatwhile music can make synchronization complex, it also helps reducing thetotal deviation. By studying the simulation process, several conclusionson the relationship between di↵erent growing speeds of total deviationsand di↵erent interaction schemes are drawn. With interpretation froma musical point of view, we find that, in a music ensemble, listening toneighbors helps the players end up in sync. However, if people do notlisten carefully enough, the deviation becomes larger than when peopledo not listen at all. On the issue of whom one should listen to, theresults show no significant di↵erences between listening to the immediateneighbors and to the whole group. Finally, we also observe that largedeviations can be reduced by making the musicians move while playing.Keywords: synchronization, collective behavior, agent-based modeling,deviation, music playing1 IntroductionMany questions have been asked about the rhythmic complexity of music. Is itmore di cult to synchronize over a melodic rhythm or a drum beat? Is it betterto listen to people around you or just play as written in a music ensemble? Howcan we obtain better synchronization? Several research papers and books haveaddressed synchronization problems in biological and social/human interactionsystems [1–5], but few have answered this line of questions. In this project, wesimulate music ensembles using agent-based models, a method known for its abil-ity to produce complex behaviors from simple rules. Although it is not possiblefor simple models to accurately represent every interaction among musicians, itis still possible to gain valuable insights from abstractly simulated music ensem-bles.Two important concepts embedded in this project are derived from the well-known “firefly” model of synchronization [5]. Like this model, we define phaseProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155102 Iris Yuping Ren, Rene´ Doursat, and Jean-Louis GiavittoFig. 1. Initial configuration of the music group program, with a conductor symbolizedin red and four di↵erent groups of musicians in “white”, “green”, “yellow”, and “blue”.and frequency variables to characterize the system. Herre, the frequency of eachagent will be called “tempo” and the phase lag, the “the waiting time”. Im-portant di↵erences with the firefly model are the incorporation of actual musicdata and conditional interactions between musicians. Another important con-cept is the unavoidable deviation of the played stream from the written music,which has been investigated in [6–8] and experimentally proven. Although we donot have such a small time resolution, the implementation can be justified withamateur music players.2 ModelIn this model, we use real music data in the form of duration datasets (withoutpitch), extracted from Beethoven’s quartets. The players follow these durationsand di↵erent interaction schemes among themselves. We simulate music ensem-bles consisting of four sections, “white”, “green”, “yellow”, and “blue” (Fig. 1),so that we can observe the di↵erences between schemes applied inside each sec-tion. Musical interactions between two sections are ignored for simplicity. Someamount of spatial interaction between players will be introduced at a later stage.2.1 ParametersThe parameters of the model are the following (Table 1):– Number of agents: how many agents there are in one musical section.– Music sheet: 10 di↵erent music datasets (rhythmic parts only, no pitch); 1-8 are the Beethoven string quartets Nr. 1-8; 0 and 9 are drum beats withintervals of 1 and 3 seconds.– Avg freedom: mean of the freedom of agents (with default standard devia-tion, modifiable from the program itself).– Tempi std: standard deviation of the tempi of agents (with default meanvalue, modifiable from the program itself).Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015511Synchronization in Music Group Playing 3Parameter Range NotationNumber of agents 1-28 xMusic sheet 0-9 N/AAvg freedom 1-100 FTempi std 0-20 ↵Max reaction 0-100 RConfidence 0-8 CWaiting resolution 1-1000 NWith/Without Conductor true/false –Move/No move true/false –Table 1. Table of model parameters with the range of acceptable values and mathe-matical notations– Max reaction: maximum value of the reaction skills of agents (where actualskill is a random integer number under this cap, modifiable from the programitself).– Confidence: how many actively playing neighbors one musician must have,in order to be confident that s/he is playing at the right time.– Waiting resolution: a normalizing factor controlling in part how much timeresolution a musician has.– With/without conductor: this is just for the yellow group; the tempo will beset uniformly to 100 if this is on and the players became aware that they areplaying “wrongly”.– Move/no move: agents will move randomly if this is on, as shown in Fig. 2.Their neighbors will therefore also change.To have a concrete view of the e↵ect of these parameters, we explain the dy-namics of the model in the next section.2.2 DynamicsThe mechanism used to synchronize the musicians is based on the music. Forevery note duration in the dataset, we approach it using a timer, which is resetat the beginning of every step. The value of the timer is denoted by t(i), wherei is the step number in the process, which is equal to the number of durationvalues in the dataset. Then, once the timer’s value and the note’s duration m(i)are su ciently close, we ask the agents, which are by default in color gray, tochange to the color belonging to their group (white, green, yellow, blue), henceachieve an e↵ect of “playing” the event. We will also use the word “recoloring” todenote music playing. We denote each agent by x, as mentioned in the parametertable. For describing the relation between a parameter and the turtles-ownedvalue controlled by it, we use a functional notation. For example, each turtle’sreaction skill will be denoted by R(x). Considering all the parameters we usedabove, this part of the dynamics can be expressed as:if m(i)  ↵(x)100⇥ t(i) > F (x)N, wait for R(x)/N, and set color := gray, t(i) := 0Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155124 Iris Yuping Ren, Rene´ Doursat, and Jean-Louis GiavittoFig. 2. Typical motion dynamics.otherwise, recolor. The next time the agent becomes gray can happen at thenext step, when the timer discovers that there is still a certain amount of timeuntil the end of the next duration.Finally, we add interactions among players to the process, asking agents to“look” whether there are enough players around them who are playing. If thatnumber is larger than the confidence level of a player, C, then s/he must changethe tempo according to the mean of the active neighbors, denoted by {xk}k2[0,28](explained in detail in the next paragraph). We denote the number of the graylinked-neighbors by nx, and write this part of the dynamics:if nx   C, tempo(x) := tempo(xk)After all this decision making, we record the actual di↵erence between thewaiting time and the duration, and plot this deviation. Di↵erences between thefour group reside in how they react to other players’ tempi, i.e. the di↵erencesbetween the {xk}:– Players in the white group listen to other neighboring white players and takethe mean tempo from them.– Players in the green group listen to other neighboring green players, butfollow a normal distribution whose mean is equal to the average tempo ofthe neighbors.– Players in the yellow group have two choices: when the conductor option ison, they sync to the conductor, i.e. adopt a uniform tempo; otherwise, theylisten to all other players in all groups.– Players in the blue group listen to all other blue players and take the meantempo from them.We also introduce a motion dynamics, while the “Move” option is on, we askthe players to move randomly, including changes in their links; that is, theirneighbor will change according to where they are.Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015513Synchronization in Music Group Playing 5(a) Time series of the total deviationsof the white (shown in black), green,yellow and blue groups, featuring thelarge deviation of the green group. Othergroups have similar lower total devia-tions. The “conductor switch” for theyellow group is on. Other di↵erent grow-ing patterns between the white, yellowand blue groups are caused by the speci-ficties of the music at hand.(b) Time series of the total deviations ofthe four groups when musicians are mov-ing. Here, the blue group is strongly in-fluenced by the bad tempi of the greenplayers. In other runs, the group thatgets most influenced might change. Ingeneral, however, there is no outliercurve of total deviation like the green onein (a).Fig. 3. Time series of total deviations: (a) static players; (b) moving players.2.3 StatisticsThe following statistics are used to measure the outcome of our model:– Each group’s total deviation from the music, called “total deviation 1”, etc.– Each player’s deviation from the music (because the total deviation loses theinformation about whether individual players are lagging or leading).– The tempo distribution of the players over each group; synchronizationamong players can be observed when these distributions converge.– The deviation distribution of the players; most are centered around zero, oth-ers account for the cumulative deviation that we show in the total deviationwindow.3 ResultsIn the beginning of the simulation, tempi are scattered in all four groups, andtotal deviations grow with time in a similar manner. We can also see the conver-gence of tempi in certain groups. After observing the process for a while, we finddi↵erent growing speeds of the total deviation between di↵erent groups. Thegreen group exhibits a particularly big deviation as shown in Fig. 3(a). Afterrunning for a period of time, the program slows down. This should not matterProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155146 Iris Yuping Ren, Rene´ Doursat, and Jean-Louis Giavitto(a) Time series of the total deviationsof the white group for di↵erent musicpieces. Real music is adding complex-ity to the drum-beat music. Listening toneighbors results in larger deviation thanthe group with the conductor for drum-beat music, but smaller deviation for realmusic.(b) Time series of the total deviationsof the green group for di↵erent musicpieces. Compared to the Beethoven mu-sic, the drum-beat music leads to fastgrowth in deviation. The complexity ofmusic prevents the generation of devi-ation upon deviation. The curve withlarger curvature is the drum beat of 3-second intervals.(c) Time series of the total deviationsof the yellow group for di↵erent musicpieces. Real music is adding complex-ity to the drum-beat music. With theconductor, the drum-beat music has theleast deviation. The linear growth ratesare close, also resulting from having aconductor in lead.(d) Time series of the total deviations ofthe blue group for di↵erent music pieces.The linear growth of the drum-beat mu-sic is at around the same level of theBeethoven music. The linear growth withlarger slope is the drum beat of 3-secondintervals.Fig. 4. Total deviation time series of all four groups with di↵erent music piecesmuch for the project because when deviations become large, the ensemble usu-ally stops playing. However, there are cases when musicians sight-reading newmusic are not able to know for a while whether they are playing out of step ornot. So it is also useful to look at the dynamics for a longer period of time, andrecord observations of large deviations.One way to improve on large deviations is by actually making the playersmove (Fig. 3(b)). By “improve”, we mean that the slopes of total deviations inProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015515Synchronization in Music Group Playing 7the four groups are more or less similar, so there is no more single large deviation(as the green curve in Fig. 3(a)), which is the most disruptive to music groupplaying. This can happen because, as the completely o↵-beat players encounterthe right players, they can exchange information, not through tempo, but justby looking at whether their linked neighbors are playing or not. However, thismethod has an obvious flip side, which is that bad influence can be proliferating,too, as can be seen in Fig. 3(b).Given the above results and diagrams, we can already draw musical conclu-sions such as: listening to your neighbors helps the ensemble end up in sync;furthermore, if people do not listen carefully (as in the green group) the resultscan be a disaster. In the case of the yellow group, it is safe to say that theyshould not listen to people who do not listen; instead, they should look at theconductor. Finally, for the blue group, the lesson we can learn is that listeningto the whole group or only to your neighbor does not make much di↵erence,therefore it is su cient to listen to a small number of people around you.Besides running the simulation and observing statistics under a given setof parameter values, we also explored the “music” parameter axis. The totaldeviation time series of all four groups with di↵erent music pieces are shown inFig. 4(a)-4(d). There are two regular-looking curves in each graph, because musicNr. 0 and music Nr. 9 are drum-beat intervals of 1 second (the line correspondingto the group color) and 3 seconds (the red line), not music. In the green groupcase, the growth is fast in comparison with the other linear growth of deviation.We can also see one common feature out of the drum-beat cases: the smaller theintervals are, the easier they are to sync.Excluding Fig. 4(b), in most of the cases, we can see that music definitelymakes it harder for people to minimize their deviation, especially as shown inFig. 4(c). However, in Fig. 4(b), it is actually helping with a reduction of thetotal deviation. If we recall the phenomenon of many people trying to clap in acertain tempo but unavoidably just getting faster and faster, this fast-growingcurve may bear some resemblance to that phenomenon. A plausible explanationof the seemingly helpful function of music would be that the varying intervallengths are suppressing further growth of the deviation during the process.4 Conclusion and Future WorkWe have presented a model consisting of di↵erent mechanisms of synchronization,which was able to tell us some non-trivial facts about music group playing.In future work, we can implement minor modifications such as changing thedistribution of di↵erent parameters in addition to their values; di↵erent neighborselection strategies can be used, since musicians are not necessarily just listeningto their immediate neighbors in the ensemble.However, the most important factors omitted here are the many musicologicalnuances which are no doubt used by individual musicians; for instance, the factthat a certain amount of rest in the music will help synchronization, or that o↵-beat notes are harder to sync, etc., are not considered. Moreover, the model didProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155168 Iris Yuping Ren, Rene´ Doursat, and Jean-Louis Giavittonot account for musical interactions across the four groups, although they clearlyinfluence musical interpretation and synchronization, too. Therefore, we will takeintroducing musical rules in the agent behavior as a priority in future work.While such projects are mostly based on subjective observation and rather non-exhaustive, they also open the door for more critical inquiry and opportunitiesfor interesting discoveries at the same time.References1. Keiko Yokoyama and Yuji Yamamoto. Three people can synchronize as coupledoscillators during sports activities. PLoS computational biology, 7(10):e1002181,2011.2. Peter J Beek. Timing and phase locking in cascade juggling. Ecological Psychology,1(1):55–96, 1989.3. Arkady Pikovsky, Michael Rosenblum, Ju¨rgen Kurths, and Robert C Hilborn. Syn-chronization: a universal concept in nonlinear science. American Journal of Physics,70(6):655–655, 2002.4. Arthur T Winfree. Biological rhythms and the behavior of populations of coupledoscillators. Journal of theoretical biology, 16(1):15–42, 1967.5. Steven Strogatz. Sync: The emerging science of spontaneous order. Hyperion, 2003.6. H Hennig. Synchronization in human musical rhythms and mutually interactingcomplex systems. Proceedings of the National Academy, 2014.7. Holger Hennig, Ragnar Fleischmann, Anneke Fredebohm, York Hagmayer, Jan Na-gler, Annette Witt, Fabian J Theis, and Theo Geisel. The nature and perceptionof fluctuations in human musical rhythms. PloS one, 6(10):e26457, January 2011.8. H Hennig, R Fleischmann, and T Geisel. Musical rhythms: The science of beingslightly o↵. Physics Today, 2012.Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015517

Synchronization in Music Group Playing

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HAL Id: hal-01257540https://hal.archives-ouvertes.fr/hal-01257540Submitted on 17 Jan 2016HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestinée au dépôt et à la diffusion de documentsscientifiques de niveau recherche, publiés ou non,émanant des établissements d’enseignement et derecherche français ou étrangers, des laboratoirespublics ou privés.Synchronization in Music Group PlayingIris Yuping Ren, René Doursat, Jean-Louis GiavittoTo cite this version:Iris Yuping Ren, René Doursat, Jean-Louis Giavitto. Synchronization in Music Group Playing. Inter-national Symposium on Computer Music Multidisciplinary Research (CMMR), Jun 2015, Plymouth,United Kingdom. 510–517 (in electronic proceedings). ￿hal-01257540￿Synchronization in Music Group PlayingIris Yuping Ren1, René Doursat2, and Jean-Louis Giavitto31 Erasmus Mundus Master’s in Complex Systems Science,Graduate School, Ecole Polytechnique, Paris, France2 Complex Systems Institute, Paris Ile-de-France (ISC-PIF),CNRS (UPS3611), Paris, France3 Institut de Recherche et Coordination Acoustique/Musique (IRCAM),CNRS (UMR9912), Paris, Franceyuping.ren.iris@gmail.comAbstract. In this project, we created an agent-based model of musicgroup playing under four di↵erent interaction mechanisms. Based on realmusic data, added randomness and simplifying assumptions, we examinehow agents synchronize and deviate from the original score. We find thatwhile music can make synchronization complex, it also helps reducing thetotal deviation. By studying the simulation process, several conclusionson the relationship between di↵erent growing speeds of total deviationsand di↵erent interaction schemes are drawn. With interpretation froma musical point of view, we find that, in a music ensemble, listening toneighbors helps the players end up in sync. However, if people do notlisten carefully enough, the deviation becomes larger than when peopledo not listen at all. On the issue of whom one should listen to, theresults show no significant di↵erences between listening to the immediateneighbors and to the whole group. Finally, we also observe that largedeviations can be reduced by making the musicians move while playing.Keywords: synchronization, collective behavior, agent-based modeling,deviation, music playing1 IntroductionMany questions have been asked about the rhythmic complexity of music. Is itmore di cult to synchronize over a melodic rhythm or a drum beat? Is it betterto listen to people around you or just play as written in a music ensemble? Howcan we obtain better synchronization? Several research papers and books haveaddressed synchronization problems in biological and social/human interactionsystems [1–5], but few have answered this line of questions. In this project, wesimulate music ensembles using agent-based models, a method known for its abil-ity to produce complex behaviors from simple rules. Although it is not possiblefor simple models to accurately represent every interaction among musicians, itis still possible to gain valuable insights from abstractly simulated music ensem-bles.Two important concepts embedded in this project are derived from the well-known “firefly” model of synchronization [5]. Like this model, we define phaseProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155102 Iris Yuping Ren, René Doursat, and Jean-Louis GiavittoFig. 1. Initial configuration of the music group program, with a conductor symbolizedin red and four di↵erent groups of musicians in “white”, “green”, “yellow”, and “blue”.and frequency variables to characterize the system. Herre, the frequency of eachagent will be called “tempo” and the phase lag, the “the waiting time”. Im-portant di↵erences with the firefly model are the incorporation of actual musicdata and conditional interactions between musicians. Another important con-cept is the unavoidable deviation of the played stream from the written music,which has been investigated in [6–8] and experimentally proven. Although we donot have such a small time resolution, the implementation can be justified withamateur music players.2 ModelIn this model, we use real music data in the form of duration datasets (withoutpitch), extracted from Beethoven’s quartets. The players follow these durationsand di↵erent interaction schemes among themselves. We simulate music ensem-bles consisting of four sections, “white”, “green”, “yellow”, and “blue” (Fig. 1),so that we can observe the di↵erences between schemes applied inside each sec-tion. Musical interactions between two sections are ignored for simplicity. Someamount of spatial interaction between players will be introduced at a later stage.2.1 ParametersThe parameters of the model are the following (Table 1):– Number of agents: how many agents there are in one musical section.– Music sheet: 10 di↵erent music datasets (rhythmic parts only, no pitch); 1-8 are the Beethoven string quartets Nr. 1-8; 0 and 9 are drum beats withintervals of 1 and 3 seconds.– Avg freedom: mean of the freedom of agents (with default standard devia-tion, modifiable from the program itself).– Tempi std: standard deviation of the tempi of agents (with default meanvalue, modifiable from the program itself).Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015511Synchronization in Music Group Playing 3Parameter Range NotationNumber of agents 1-28 xMusic sheet 0-9 N/AAvg freedom 1-100 FTempi std 0-20 ↵Max reaction 0-100 RConfidence 0-8 CWaiting resolution 1-1000 NWith/Without Conductor true/false –Move/No move true/false –Table 1. Table of model parameters with the range of acceptable values and mathe-matical notations– Max reaction: maximum value of the reaction skills of agents (where actualskill is a random integer number under this cap, modifiable from the programitself).– Confidence: how many actively playing neighbors one musician must have,in order to be confident that s/he is playing at the right time.– Waiting resolution: a normalizing factor controlling in part how much timeresolution a musician has.– With/without conductor: this is just for the yellow group; the tempo will beset uniformly to 100 if this is on and the players became aware that they areplaying “wrongly”.– Move/no move: agents will move randomly if this is on, as shown in Fig. 2.Their neighbors will therefore also change.To have a concrete view of the e↵ect of these parameters, we explain the dy-namics of the model in the next section.2.2 DynamicsThe mechanism used to synchronize the musicians is based on the music. Forevery note duration in the dataset, we approach it using a timer, which is resetat the beginning of every step. The value of the timer is denoted by t(i), wherei is the step number in the process, which is equal to the number of durationvalues in the dataset. Then, once the timer’s value and the note’s duration m(i)are su ciently close, we ask the agents, which are by default in color gray, tochange to the color belonging to their group (white, green, yellow, blue), henceachieve an e↵ect of “playing” the event. We will also use the word “recoloring” todenote music playing. We denote each agent by x, as mentioned in the parametertable. For describing the relation between a parameter and the turtles-ownedvalue controlled by it, we use a functional notation. For example, each turtle’sreaction skill will be denoted by R(x). Considering all the parameters we usedabove, this part of the dynamics can be expressed as:if m(i)  ↵(x)100⇥ t(i) >F (x)N, wait for R(x)/N, and set color := gray, t(i) := 0Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155124 Iris Yuping Ren, René Doursat, and Jean-Louis GiavittoFig. 2. Typical motion dynamics.otherwise, recolor. The next time the agent becomes gray can happen at thenext step, when the timer discovers that there is still a certain amount of timeuntil the end of the next duration.Finally, we add interactions among players to the process, asking agents to“look” whether there are enough players around them who are playing. If thatnumber is larger than the confidence level of a player, C, then s/he must changethe tempo according to the mean of the active neighbors, denoted by {xk}k2[0,28](explained in detail in the next paragraph). We denote the number of the graylinked-neighbors by nx, and write this part of the dynamics:if nx   C, tempo(x) := tempo(xk)After all this decision making, we record the actual di↵erence between thewaiting time and the duration, and plot this deviation. Di↵erences between thefour group reside in how they react to other players’ tempi, i.e. the di↵erencesbetween the {xk}:– Players in the white group listen to other neighboring white players and takethe mean tempo from them.– Players in the green group listen to other neighboring green players, butfollow a normal distribution whose mean is equal to the average tempo ofthe neighbors.– Players in the yellow group have two choices: when the conductor option ison, they sync to the conductor, i.e. adopt a uniform tempo; otherwise, theylisten to all other players in all groups.– Players in the blue group listen to all other blue players and take the meantempo from them.We also introduce a motion dynamics, while the “Move” option is on, we askthe players to move randomly, including changes in their links; that is, theirneighbor will change according to where they are.Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015513Synchronization in Music Group Playing 5(a) Time series of the total deviationsof the white (shown in black), green,yellow and blue groups, featuring thelarge deviation of the green group. Othergroups have similar lower total devia-tions. The “conductor switch” for theyellow group is on. Other di↵erent grow-ing patterns between the white, yellowand blue groups are caused by the speci-ficties of the music at hand.(b) Time series of the total deviations ofthe four groups when musicians are mov-ing. Here, the blue group is strongly in-fluenced by the bad tempi of the greenplayers. In other runs, the group thatgets most influenced might change. Ingeneral, however, there is no outliercurve of total deviation like the green onein (a).Fig. 3. Time series of total deviations: (a) static players; (b) moving players.2.3 StatisticsThe following statistics are used to measure the outcome of our model:– Each group’s total deviation from the music, called “total deviation 1”, etc.– Each player’s deviation from the music (because the total deviation loses theinformation about whether individual players are lagging or leading).– The tempo distribution of the players over each group; synchronizationamong players can be observed when these distributions converge.– The deviation distribution of the players; most are centered around zero, oth-ers account for the cumulative deviation that we show in the total deviationwindow.3 ResultsIn the beginning of the simulation, tempi are scattered in all four groups, andtotal deviations grow with time in a similar manner. We can also see the conver-gence of tempi in certain groups. After observing the process for a while, we finddi↵erent growing speeds of the total deviation between di↵erent groups. Thegreen group exhibits a particularly big deviation as shown in Fig. 3(a). Afterrunning for a period of time, the program slows down. This should not matterProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155146 Iris Yuping Ren, René Doursat, and Jean-Louis Giavitto(a) Time series of the total deviationsof the white group for di↵erent musicpieces. Real music is adding complex-ity to the drum-beat music. Listening toneighbors results in larger deviation thanthe group with the conductor for drum-beat music, but smaller deviation for realmusic.(b) Time series of the total deviationsof the green group for di↵erent musicpieces. Compared to the Beethoven mu-sic, the drum-beat music leads to fastgrowth in deviation. The complexity ofmusic prevents the generation of devi-ation upon deviation. The curve withlarger curvature is the drum beat of 3-second intervals.(c) Time series of the total deviationsof the yellow group for di↵erent musicpieces. Real music is adding complex-ity to the drum-beat music. With theconductor, the drum-beat music has theleast deviation. The linear growth ratesare close, also resulting from having aconductor in lead.(d) Time series of the total deviations ofthe blue group for di↵erent music pieces.The linear growth of the drum-beat mu-sic is at around the same level of theBeethoven music. The linear growth withlarger slope is the drum beat of 3-secondintervals.Fig. 4. Total deviation time series of all four groups with di↵erent music piecesmuch for the project because when deviations become large, the ensemble usu-ally stops playing. However, there are cases when musicians sight-reading newmusic are not able to know for a while whether they are playing out of step ornot. So it is also useful to look at the dynamics for a longer period of time, andrecord observations of large deviations.One way to improve on large deviations is by actually making the playersmove (Fig. 3(b)). By “improve”, we mean that the slopes of total deviations inProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015515Synchronization in Music Group Playing 7the four groups are more or less similar, so there is no more single large deviation(as the green curve in Fig. 3(a)), which is the most disruptive to music groupplaying. This can happen because, as the completely o↵-beat players encounterthe right players, they can exchange information, not through tempo, but justby looking at whether their linked neighbors are playing or not. However, thismethod has an obvious flip side, which is that bad influence can be proliferating,too, as can be seen in Fig. 3(b).Given the above results and diagrams, we can already draw musical conclu-sions such as: listening to your neighbors helps the ensemble end up in sync;furthermore, if people do not listen carefully (as in the green group) the resultscan be a disaster. In the case of the yellow group, it is safe to say that theyshould not listen to people who do not listen; instead, they should look at theconductor. Finally, for the blue group, the lesson we can learn is that listeningto the whole group or only to your neighbor does not make much di↵erence,therefore it is su cient to listen to a small number of people around you.Besides running the simulation and observing statistics under a given setof parameter values, we also explored the “music” parameter axis. The totaldeviation time series of all four groups with di↵erent music pieces are shown inFig. 4(a)-4(d). There are two regular-looking curves in each graph, because musicNr. 0 and music Nr. 9 are drum-beat intervals of 1 second (the line correspondingto the group color) and 3 seconds (the red line), not music. In the green groupcase, the growth is fast in comparison with the other linear growth of deviation.We can also see one common feature out of the drum-beat cases: the smaller theintervals are, the easier they are to sync.Excluding Fig. 4(b), in most of the cases, we can see that music definitelymakes it harder for people to minimize their deviation, especially as shown inFig. 4(c). However, in Fig. 4(b), it is actually helping with a reduction of thetotal deviation. If we recall the phenomenon of many people trying to clap in acertain tempo but unavoidably just getting faster and faster, this fast-growingcurve may bear some resemblance to that phenomenon. A plausible explanationof the seemingly helpful function of music would be that the varying intervallengths are suppressing further growth of the deviation during the process.4 Conclusion and Future WorkWe have presented a model consisting of di↵erent mechanisms of synchronization,which was able to tell us some non-trivial facts about music group playing.In future work, we can implement minor modifications such as changing thedistribution of di↵erent parameters in addition to their values; di↵erent neighborselection strategies can be used, since musicians are not necessarily just listeningto their immediate neighbors in the ensemble.However, the most important factors omitted here are the many musicologicalnuances which are no doubt used by individual musicians; for instance, the factthat a certain amount of rest in the music will help synchronization, or that o↵-beat notes are harder to sync, etc., are not considered. Moreover, the model didProc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 20155168 Iris Yuping Ren, René Doursat, and Jean-Louis Giavittonot account for musical interactions across the four groups, although they clearlyinfluence musical interpretation and synchronization, too. Therefore, we will takeintroducing musical rules in the agent behavior as a priority in future work.While such projects are mostly based on subjective observation and rather non-exhaustive, they also open the door for more critical inquiry and opportunitiesfor interesting discoveries at the same time.References1. Keiko Yokoyama and Yuji Yamamoto. Three people can synchronize as coupledoscillators during sports activities. PLoS computational biology, 7(10):e1002181,2011.2. Peter J Beek. Timing and phase locking in cascade juggling. Ecological Psychology,1(1):55–96, 1989.3. Arkady Pikovsky, Michael Rosenblum, Jürgen Kurths, and Robert C Hilborn. Syn-chronization: a universal concept in nonlinear science. American Journal of Physics,70(6):655–655, 2002.4. Arthur T Winfree. Biological rhythms and the behavior of populations of coupledoscillators. Journal of theoretical biology, 16(1):15–42, 1967.5. Steven Strogatz. Sync: The emerging science of spontaneous order. Hyperion, 2003.6. H Hennig. Synchronization in human musical rhythms and mutually interactingcomplex systems. Proceedings of the National Academy, 2014.7. Holger Hennig, Ragnar Fleischmann, Anneke Fredebohm, York Hagmayer, Jan Na-gler, Annette Witt, Fabian J Theis, and Theo Geisel. The nature and perceptionof fluctuations in human musical rhythms. PloS one, 6(10):e26457, January 2011.8. H Hennig, R Fleischmann, and T Geisel. Musical rhythms: The science of beingslightly o↵. Physics Today, 2012.Proc. of the 11th International Symposium on CMMR, Plymouth, UK, June 16-19, 2015517

Abstract. In this project, we created an agent-based model of music group playing under four different interaction mechanisms. Based on real music data, added randomness and simplifying assumptions, we examine how agents synchronize and deviate from the original score. We find that while music can make synchronization complex, it also helps reducing the total deviation. By studying the simulation process, several conclusions on the relationship between different growing speeds of total deviations and different interaction schemes are drawn. With interpretation from a musical point of view, we find that, in a music ensemble, listening to neighbors helps the players end up in sync. However, if people do not listen carefully enough, the deviation becomes larger than when people do not listen at all. On the issue of whom one should listen to, the results show no significant differences between listening to the immediate neighbors and to the whole group. Finally, we also observe that large deviations can be reduced by making the musicians move while playing

Synchronization in Music Group Playing

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