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An example of interactive score On this figure, we can find 8 temporal objects from different types: Every textures are simple ones except T 7.

This specific point is supposed to make sense with the process attached to T 1 for example the climax of a dynamic variation. T 0 and T 6 are rigid, then they force the two constraints: It forces a global Page 2 14 constraint on the volume.

As it is a global constraint, this volume is the volume of the mix of the textures that sets during T 8, i.

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We have implemented into OpenMusic a version of the interactive scores model limited to the case where every TOs are supple and where there is no linear constraints.

The composer can only define Allen relations and global constraints. The figure 3 presents some screenshots of our implementation of Iscore. There are two different steps in the interactive scores model: During the edition we have to support the add and remove of constraints and maintain these ones when the composer changes some characteristics while during the performance we have to take into account the performer choices and to maintain the constraints under a strong real-time constraint.

Since computation time is not critic during the edition time, we use a general constraints solver called Gecode [10] which propagates the new relations, constraints and values.

This cannot be done in a real time context since we are not able to control the computation time. In this case, the temporal constraints in the scores are limited to the Allen relations. So there are no intervals and all the textures are supple. This model is based on Petri nets to which we add a global constraints store. A Petri net is a specific states machine which can run concurrent processes that must synchronize at particular moments. Formally, it is a bipartite directed graph with two types of vertice called places and transitions.

An edge can only connect two vertices from different types. At last places contain a number of tokens greater or equal to zero. A state of the system is represented by a distribution of tokens among the places. In our case, we use a special type of Petri nets called Time Petri Nets [9] which allows to associate a time-range of wait in places before crossing the transitions.

After the edition time, we transform the interactive score into a Petri net by associating events with transitions while places are used to wait between events. We represent the Allen relations through edges connections. So we will be sure that the relation r is maintained.

In addition, we don t use fixed delays in places but ranges to permit synchronizations. Some screenshots of Iscore in Open Music Page 3 15 ated in a place P with a range [t min, t max ], an intern timer t is launched from 0.

While t t min, the token cannot be consummated this means that the transition that follows P cannot be crossed. Formally, the range forces the following transition of P to be crossed when t min t t max. If this transition waits for an external event to come as for a transition representing an interactive event, then the system doesn t take into account the performer s actions before the timer t reaches the value t min and if the performer doesn t trigger the crossing of the transition before t reaches t max, then the system automatically crosses the transition.

Each T i has a range [t mini, t maxi ] and a timer t i. In this case, T can be crossed when: In our system, we always try to prevent this kind of situation. In the limited system, we use 2 different temporal ranges in the places: The value translates the fact that a wait duration can be increased by an interactive event not directly connected to it but which can influence the wait duration through synchronization configurations.

Thus if no interactive events influences the wait duration, its value is score else it is a greater one. We can find an example of the transformation of a very simple score into a Petri net on the figure 4. In this example, there are 4 textures and an interaction point T 4.

The symbol X denotes the external control used to trigger T 4. At last, we lay emphasis on 3 intervals: An example of the transformation of a score is typically a synchronization transition. In this case, the ranges of 2 and 3 are [ 2score, ] and [ 3score, ]. This permits the synchronization. In fact, the modification of the date of s t 3 by the performer will propagate to e t 3.

Since the date of e t 3 may be modified, then values of 2 and 3 may also be modified. With the ranges we defined, we ensure that: On the contrary, if s t 3 is delayed, 2 will increase and 3score will be respected. At last, the composer can change the default ranges of intervals preceding a synchronization transition.

He can choose [0, ] for some intervals. This implies that the values iscore whith such a range will not be ensured. Then the composer can give a priority on intervals that he wants to last at least the written values while the other can be totally modified. For the edition time we still use a constraints solver such as Gecode, since we don t care about the computation time. But we have to modify our real-time model. In fact, to introduce qualitative constraints rises up the possibility for the performer to break some constraints of the score during the execution.

Our aim is to ensure that the score will bee totally played without any broken constraints. This aim is quite difficult to reach since we have to anticipate the actions of the performer that could lead to inconsistent situations.

The figure 5 shows a an example of this type of situation.

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So, the value 1 can change under the influence of T i. Since we have the equation: In the example, T i is delayed so we have to reduce the durations values. There are several ways to compute these values, so we guided the computation in adding an order of reduction chosen by the composer at composition time among 2 alternatives: Since duration values may change, we have to modify the time-ranges associated to the places of the Petri net.

Encoding the quantitative constraints directly in the Petri nets appeared to be inapplicable in the general case. As a consequence, we have to add to the petri net that holds the Allen relations, a constraints system or CSP consraints satisfaction problem that holds the quantitative constraints. This CSP is from the same type as the one we use during the edition step to maintain all the constraints. The difference with the edition step is that during the execution, we have the petri net that maintains the Allen relations without constraints computation.

Then, we want to put into this CSP only the constraints that cannot be hold by the Petri net. One can also see that some specific quantitative constraints can be very easyly represented in the Petri net. For example, an interval between a satic event and an interactive one that follows it such as 0 on the figure 4can be forced to be semi rigid with the range of values [V al min, V al max ] simply by using this range in the Pretri net in the place that represents this interval.

It is very important to deal with the smallest CSP as possible to prevent from excessive computation times, then we have to clearly identify the constraints that cannot be represented in the Petri net. To represent this CSP, we use a constraints graph which is a bi-partite graph in which variables and constraints are represented by the vertice and there is an arc between a vertex labeled by variable a V and the vertex labeled by a constraint C only if V is involved in C in the CSP.

We want to use this representation with a propagation algorithm that allow us to propagate the dates of the interactive events over the CSP and compute new values for the textures and intervals durations that take into account the actions and choices of the performer.

To determine which intervals will appear into the graph, we define for each interactive event e a durations set Z e called the influence area of e including all the durations that could be modified by e through qualitative constraints. Eventually the variables set of the constraints graph associated to a score s will be Z e where the du- e s rations are seen as the variables representing them. This means that the constraints graph will only include the intervals that may change during the execution.

Each variable of the graph is associated to a domain which is a range of values [V al min, V al max ]. Computing the variables domains of a general constraint problem is not easy. In our case we use a domain reduction algorithm inspired by Indigo [6] which reduces the domains from the initial range [0, ].

After the edition time, we turn the score into a Petri net and a constraints graph. Before the performance we run the domains reduction algorithm to compute the timeranges of the arrival of control inputs, because we want them such as whatever the anticipations or delays on interactive events there will be no incoherence with the quantitative constraints.

During the performance we run the reduction algorithm each time an interactive event happens to reduce the variables according to the anticipation or delay of this event. Of course, the domain of an interval in the constraints graph will be same as the time range we use in the Petri net for this interval.

Then, each time we recompute the domain of an interval with the propagation algorithm, we set the corresponding time range in the Petri net to the new domain. Unfortunately, the reduction algorithm is efficient only over acyclic constraints graphs which is not the general case.

If the graph is cyclic the domains after the reduction algorithm can contain some values that lead to an incoherence. This is particularly crucial for the domains of intervals involving interactive events because this means that when the performer will have to trigger such an event, we may accept some values that lead to inconsistent situations.

One solution could be to test each value of the domains after the use of the reduction algorithm but this one is clearly too expensive in time. To prevent from this expensive computation we are thinking about only test the extreme limits of the domains after running the propagation algorithm and use a property of convexity of the domains. That is for a variable V with a domain D and v 1 and v 2 in D: If solutions exist with this values, we accept the domain, if not, we recompute the domains.

This solution is still on the drawing board. But even if the acyclic graphs are not the general case, they present interesting cases. The example presented on figure 6 consists in interactively setting the tempo of 2 bars of the bossa-nova standard Blue Bossa by Kenny Dorham.

We turn the 2 bars into an interactive score with temporal objects representing the notes, Allen s relations designing the temporal organization and an interval T q representing a time-unit which is related to each duration by a linear constraint.

These constraints express the durations in time-unit. T 1 has interactive start and end, so during the performance d t 1 will be changed. Using the constraints graph, we will propagate this modification to d t q and then to all the other durations in order to simulate a change of the tempo. With similar configurations, one can define automatic accelerendo or descelerendo. An example of an interactive tempo setting 6.

This structures are bounded together and must be jointly used during the performance step. Then we gather all this structures in what we call a musical environement that will be executed during the performance. Formally, this environement will interpreted by an abstract machine that we call the and that we introduced in [8]. This is an abstract machine such that: In this implementation, OSC messages can be defined to be sent when temporal objects start and end.

The interactive events are also triggered by OSC messages. The figure 8 presents a part of the score. Precisely, the first object is used to control the recording of samples that are used in some granular synthesis processes controlled by the other temporal objects. According to Joseph Laralde: The figure 6 presents the schema of the ECO machine in a particular state during the execution.

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As we can see, the musical environement contains all informations needed to produce the outputs. We can see that we separate the musical envornement in two parts, one deals with the temporal structures and the other deals with the processes attached with the temporal objects and their parameters. Then after the edition step, we turn the score into a musical environement that will represent the temporal and musical informations and will be interpretable by the ECO machine.

This abstract machine is generic and will be stricly the same for each score, while the musical environement will depend on the score. During a step of the execution of the machine, the following operations occur: Trigger the events associated to this transitions. We used Allen relations and durations constraints to define temporal organization and specific models using constraints propagation and Petri nets to maintain these constraints.

We presented examples of the use of interactive scores including an original composition. The next step of this work will be to find a solution for scores with cyclic constraints graph and to continue implementing and testing Iscore. We are also involved into a project for adapting our model to the needs of theater stage managers.

Maintaining knowledge about temporal intervals. Communications of the ACM, 26 A model of interactive scores based on petri nets. Concurrent constraints models for interactive scores. Computer assisted composition at ircam: From patchwork to openmusic. A local propagation algorithm for inequality constraints.

A model for specifying temporal relations between interactive and static events. A study of the recoverability of computing systems, [10] C.

Views and iterators for generic constraint implementations. Finally, we discuss the advantages and limits of such an approach.

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As a starting point, we took as general model the situation of installation and the exploitation of immersive spaces or at least, "psychologically immersive" where there is also a certain degree of interaction with the spectator who becomes at the same time an observer and an user: In the following paragraphs, we will describe the first axis of this work under development: Our artistic motivation resides in the desire to exploit other forms of musical deployment, beyond the linear unidirectional sequence, in conformity with the situation in concert.

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