Manuele Kirsch-Pinheiro

Marlene Villanova-Oliver

Jerôme Gensel
email: gensel@imag.fr

Hervé Martin
email: martin@imag.fr

Marlène Villanova-Oliver

Jérôme Gensel

A Personalized and Context-Aware Adaptation Process for Web-based Groupware Systems

Keywords: context-aware computing, user adaptation, progressive access, web-based groupware systems, CSCW

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Introduction

Mobile technologies, such as PDAs, cellphones and wireless networks, are more and more adopted by mobile workers in order to collaborate with their colleagues. Webbased groupware systems, which allow collaborative work through a web system, have now to cope with these technologies. However, although these technologies have evolved, they still have several limitations (see [START_REF] Jing | Client-server computing in mobile environments[END_REF] [START_REF] Islam | Toward ubiquitous acceptance of ubiquitous computing[END_REF]). We may cite, for instance, the reduced display size and the limited memory and battery life capacities of mobile devices such as PDAs, or the limited bandwidth of wireless networks. Additionally, thanks to these technologies, users are not anymore constrained to access the system using a unique device or from a unique location. The same user now may access the system and collaborate with her/his colleagues from different locations (e.g. from home, from the airport, from the office…) or using different devices (a laptop, a PDA, a cellphone, etc.). Consequently, we cannot predict the circumstances under which the user will access the system. This mobility, as well as the limitations of mobile technologies, requires systems with some adaptation capacities. Systems should adapt the informational content, the presentation and/or the services to the users accordingly to the technologies and to the circumstances in which the users are acting.

The adaptation of a system according to the circumstances in which a user is accessing it is usually associated with the notion of context-aware computing [START_REF] Burrell | Context-aware computing: a text case[END_REF] [START_REF] Dey | Understanding and using context[END_REF]. Context-awareness is the capability of perceiving the user situation in all its forms, and of adapting in consequence the system behaviour, i.e., the services, the data and the interface. The adaptation is therefore the goal of context-awareness [START_REF] Chaari | Design of context-aware applications based on web services[END_REF]. Commonly, context-aware systems limit the notion of context, referring to the situation in which the user is acting, to the concepts of user's location and device (see [START_REF] Burrell | Context-aware computing: a text case[END_REF][15] [START_REF] Schilit | Context-aware computing applications[END_REF]). For instance, some systems propose to adapt the presentation of a given information according to the capabilities of the user's device (such as in [START_REF] Lemlouma | Context-Aware Adaptation for Mobile Devices[END_REF]), others propose the selection of a particular informational content according to the user's location (such as in [START_REF] Burrell | Context-aware computing: a text case[END_REF] [START_REF] Islam | Toward ubiquitous acceptance of ubiquitous computing[END_REF]). Nevertheless, this approach presents some drawbacks. In the one hand, the user's preferences related to the delivered information are often ignored. We believe that taking into account the user's preference may improve the adaptation process. This is particularly interesting for groupware systems in which users play roles that demand an adapted informational content. In the other hand, groupware systems should consider, as part of the user's context description, other elements related to the collaborative process (for instance, the notions of group, role, activity, shared object, and so on), since users on these systems are involved in such a process.

In this paper, we propose a new approach for adapting the informational content delivered by web-based groupware systems to a mobile user. In this approach, adaptation is performed by a twofold filtering mechanism, which filters the available information based on the user's current context and on the user's preferences for this context. We have proposed in [START_REF] Kirsch-Pinheiro | Representing Context for an Adaptative Awareness Mechanism[END_REF] an object-oriented model representing context which takes into account both the physical context (location, device, etc.) and the collaborative context (collaborative process, group, role, etc.). In this paper, we use this model to represent the user's context in order to adapt the information content delivered by a Web-based groupware system to the user's current context. The user's preferences are represented through a set of pre-defined profiles, which allow the organization of the delivered information into several levels of details. This organization is based on the Progressive Access Model (PAM) we have proposed in [START_REF] Villanova | A progressive access approach for web based information systems[END_REF]. In this paper, we propose new operations to navigate through these levels. These operations ("next", to present the content of the next level, and "previous", to show the previous one) are particularly concerned with the use of mobile devices and their limitations. The proposed filtering mechanism is therefore performed in two steps: first, it analyses the user's current context and selects, among the user's pre-defined profiles, those which match the user's current context. Second, it applies the progressive access model according to the selected profiles, filtering and organizing the available information.

This paper is organized as follows: Section 2 presents the models used by the proposed filtering mechanism (the context model, the user's preferences model, and the PAM). Section 3 presents the filtering mechanism, detailing each step, whilst Section 4 discusses some preliminary results. We conclude in Section 5.

Related Models

In this section, we introduce the models we propose as a base to the context-aware filtering process (see Section 3). This process uses the following interconnected models: (i) a context model to represent the user's context; (ii) the progressive access model to select and organize the informational content; (iii) a model to describe this informational content (i.e., the awareness information) and the user's preferences model. These models are described in the sections below.

An Object-Oriented Model of the User's Context

Any groupware system, in order to exploit the user's context, has to represent somehow the notion of context. However, in order to represent this notion, we need to understand and define it. When looking at the context-aware computing literature, one may perceive that there is no single definition (see, for instance, [START_REF] Dey | Understanding and using context[END_REF][6] [START_REF] Mostéfaoui | Context-aware computing: a guide for the pervasive community[END_REF]). In one of the pioneers works, Schilit et al. [START_REF] Schilit | Context-aware computing applications[END_REF] define context as "the location of use, the collection of nearby people and objects, as well as the changes to those objects over time". A largest view is given by Dey [START_REF] Dey | Understanding and using context[END_REF], who defines context as "any information that can be used to characterize the situation of an entity. An entity is a person, place, or object that is considered relevant to the interaction between a user and an application, including the user and the applications themselves". In this work, we adopt this definition since it applies particularly for designing context-aware systems.

Inspired by this definition, we have proposed [START_REF] Kirsch-Pinheiro | Representing Context for an Adaptative Awareness Mechanism[END_REF] an object-oriented representation of context, which focuses on a mobile use of Web-based groupware systems. Based mainly on a set of UML diagrams, this model represents both the user's physical context (including the concepts of location, device and application) and the user's collaborative context (which includes the concepts of group, role, member, calendar, activity, shared object and process). We claim that a groupware system should take into account the collaborative context, since the users of such systems are also involved in some collaborative process. Consequently, some information related to the group, such as its composition, its activities, its goals, etc., can be considered as relevant for such users, and consequently should be included into the user's context. The Fig. 1 shows all the concepts that constitute this model.

In this model (see Fig. 1), the concept of context is represented by a class context description, which is a composition of both physical (location, device, space and application) and collaborative elements (group, role, activity, shared object, etc.). These elements are represented by classes that are specializations of a common superclass, called context element. Furthermore, these context elements are related to each other, defining associations between the corresponding concepts. Each element of context is not an isolated information but does belong to a more complex representation of the user's situation. For instance, we consider that a member belongs to the group through the roles she/he plays in this group, and that each group defines a process, which is composed by a set of activities (or tasks, also composed by subtasks), and so on. A complete description of these associations is given in [START_REF] Kirsch-Pinheiro | Representing Context for an Adaptative Awareness Mechanism[END_REF].

The context of a user (member of a group) is then represented in this model by an instance of the class context description, which is linked by composition to instances of the class context element and its subclasses (see Fig. 1). The Fig. 2 illustrates an application of this context model. In this figure, we consider a user ('Alice'), who is the coordinator ('coordinator' role) of a team ('administration' group), which uses a groupware system with collaborative edition and asynchronous communication (through annotations) services. Let us suppose that Alice is accessing this groupware system through her PDA in order to consult the latest notes about a report that her team is writing. When Alice requests these notes, her current context can be represented by the context description object represented in the Fig. 2b. This object is composed by the context elements representing Alice's location ('office D322' object of the location class) and device ('PocketPC' object of the device class), her team ('administration' object), her role in this team ('coordinator' object), and so on. These objects are related through a set of associations: Alice belongs to the administration group through the role coordinator; this role allows Alice to perform the 'report edition' activity, which handles the shared object 'report2005' through the 'notes' application, etc. All these associations, as well as the context elements objects connected by them compose the current Alice's context. These classes form the schema of a knowledge base (KB), which allows us to describe the context of a user accessing the groupware system. This KB encompasses three kinds of knowledge. First, the classes and associations related to the system and the working environment are defined and instantiated. For instance, considering a collaborative editor, this knowledge refers to the definition of the classes and instances corresponding to the edition process and its component activities, the group's members, the application (services) the system offers, etc. Second, the KB stores the descriptions of potential contexts established for the different users (cf. section 2.3). Third, the KB keeps the instances of context description that represent the current context of the active users. These instances represent a knowledge that is created and dynamically updated by the system during each user's session, according to her/his behaviour. This knowledge can be discarded once the user is no longer active. In the opposite, the instances corresponding to the other kinds of knowledge are permanently stored in the KB, and they may evolve, following the evolution of the work performed by the group. We exploit the elements of this model in the filtering process (cf. section 3).

The Progressive Access Model

The central idea behind the notion of progressive access is that a user does not need to access all the information all the time. The goal is to make the system able to deliver progressively a personalized information to its users: first, information considered as essential for them is provided, and then, some complementary information, if needed, is available. The Progressive Access Model we have proposed in [START_REF] Villanova | A progressive access approach for web based information systems[END_REF] is a generic model, described in UML, which allows the organization of a data model in multiple levels of details according the user's interests. This model is based on some basic definitions that we present below (more details can be found in [START_REF] Villanova | A progressive access approach for web based information systems[END_REF]).

The notion of progressive access is related to the one of Maskable Entity. A Maskable Entity (ME) is a set of at least two elements (i.e. |ME| ≥2) upon which a progressive access can be set up. The progressive access to a ME relies on the definition of Representations of Maskable Entity (RoME) for this ME. These RoME are subsets of the ME ordered by the set inclusion relation. Two kinds of RoME, extensional or intensional, are distinguished. Extensional RoME are built from the extension (i.e. the set of elements) of the ME. In the case where the ME is a set of structured data having the same type, intensional RoME can be built from the intension of the ME. The intension of a structured ME is defined as the set of descriptions of variables, which constitute the structure of the ME. Whatever its nature -extensional or intensional -, each RoME of a ME is associated with a level of detail. Thus, RoME i is defined as the RoME of a ME corresponding to the level of detail i, where 1≤i≤max, and max is the greatest level of detail available for this ME.

The Fig. 3 shows a ME with three associated RoME. Some rules impose that a RoME i+1 -whether it is extensional or intensional -associated with the level of detail i+1 (1≤i≤max-1), contains at least one more element than RoME i . A stratification for a ME is a sequence of RoME ordered by set inclusion as illustrated in the Fig. 3. Please note that several and different stratifications can be defined for a given ME.

The progressive access relies traditionally on two operations that allow to switch from a RoME to another within a given stratification:

• from a RoME i , at level of detail i, the m ask operation gives access to the RoME i-1 , and to its possible predecessors as well, at level of detail i-1: When applying the unmask operation, the content of the next level is added to the content of the previous levels. In other words, the user will have all the previous information as well as the information selected by the next level. When the user is using a mobile device, this way of access can reveal itself inappropriate. For instance, let us consider a user consulting the address book on her/his cellphone. In this case, the ME is the address book, and we suppose a stratification S composed by two levels: RoME 1 = {contact's name, contact's phone} and RoME 2 = {contact's address}. Thus, at the first level, the user can consult the contacts' names and their phone numbers (content of the RoME 1 ). By applying the unmask operation, the user goes to the second level, at which she/he will get the contact's address (content of the RoME 2 ) as well as the contacts' names and phones, which is the content of the RoME 1 . Considering the limited display size common to cellphones, the information of the RoME 1 that remains when presenting the RoME 2 can be seen as useless, since the user has already seen it. In this case, it is more interesting to present to the user only the content of the current level, hiding the elements from the previous one.

mask(RoME i )=RoME i-1 ,
Therefore, we propose here two extra operations that can apply in mobile environments. These operations, next and previous, intend to allow the transition from a RoME to another one within a given stratification. Unlike unmask and mask operations, next and previous present the information of each level separately. These new operations do not preserve the information of the previous levels when presenting the next or previous one. These operations are defined as follow:

• first of all, let us define a basic operation called proper(i), which isolate the elements included at a level i: Therefore, the Progressive Access Model (PAM) is defined as a generic UML class diagram (see Fig. 4) which allows the description of well-formed stratifications for maskable entities. Fig. 4 shows all the definitions mentioned before, notably the stratification, represented by the class "Stratification", which is seen as an aggregation of, at least, two ordered instances of the class "Representation of Maskable Entity". An instance of this class is linked by the association adds to one or more instance(s) of the class "Element of Maskable Entity" which are the elements of the ME added by the RoME i at the level of detail i. The dependency relation ({subset}) ensures that the added elements belong to the set of elements corresponding to the ME. An important characteristic of the PAM is the ternary association called definition which links the classes "Stratification" (S), "Maskable Entity" (ME) and "User Category" (U). The class "User Category" is an abstract class which allows the connection with any user model so that each described user can benefit from a personalized progressive access to a given maskable entity. In this work, we consider as maskable entities the informational content delivered by a groupware system, which is represented through a superclass event (cf. section 2.3).

proper(RoME i ) = RoME i if i=1, otherwise proper(RoME i ) = RoME i - RoME i-1 ,

Modelling the Informational Content and the User's Preferences

In order to simplify the filtering process, we have modelled the informational content that can be delivered to the user through a superclass named event. An event may contain any useful information (for the group's members) about a specific topic related to the collaborative process. The idea is to describe events that are interesting for users in a mobile situation, such as the presence of a member of the group in a given location. In this work, we are particularly interested by the awareness information. Awareness in groupware systems refers to cooperating actors taking heed of the context of their joint effort [START_REF] Schmidt | The problem with 'awareness': introductory remarks on 'Awareness in CSCW[END_REF]. It refers to the knowledge and the understanding a user has about the group itself and her/his colleagues' activities, providing a shared context for individual activities in the group [START_REF] Dourish | Awareness and Coordination in Shared Workspaces[END_REF]. Awareness information is pointed out by CSCW community as crucial for the success of a cooperative work [START_REF] Schmidt | The problem with 'awareness': introductory remarks on 'Awareness in CSCW[END_REF], since it helps in forming a common ground for individual and cooperative actions. However, active groups tend to produce large amounts of awareness information, and users may feel overloaded by it. This is particularly true when considering mobile users, who are subject to multiple constraints (physical and environmental constraints), such as devices with limited capacities (a cellphone, for instance), or inadequate environments (like working in a rail station). Thus, mobile users need awareness information that is adapted to their current situation, i.e., adapted to their current context. In this work, each event represents a piece of awareness information.

The set of events is defined by the system designer, which should define them according to the interests the users may have when working in the groupware system. The event class should be specialized by the system designer when developing the groupware system. This class contains some attributes that we consider as essential when describing awareness information (see Fig. 5): an event name (for instance, "Alice's presence"), a description (e.g. "Alice is online from the office D322"), some details about it (i.e. a more detailed description, like "Alice is online since 8h30am from the office D322, 3 rd floor"), a time interval in which it occurs (for instance, "from 8h30am until now"), and some media describing its content (e.g., a photo of Alice). We also consider the event as referring to one or more elements of the context model (see concerns association in Fig. 5), since it may carry information related to these elements (for instance, the event referring to the Alice's presence is linked to the object of the Member class that refers Alice). Additionally, each event instance is associated with a context description instance, representing the context in which the event is or has been produced (for instance, the location object related to the office D322).

We consider the event class (and its subclasses) as a maskable entity when applying the progressive access model. In other words, stratifications can be defined for the event class and its instances. We may define intensional stratifications, associating the attributes of the event class (its intension) with the levels of detail (for instance, a stratification S 1 intensional = {{name, description}, {interval, details}, {medias}} may be defined), as well as extensional stratifications, selecting the instances of the event class according the value of their attributes (e.g. The user's preferences are represented through the notion of profiles. A profile represents the preferences and the constraints the system should satisfy for a given element (a group member, a role, a device…). It includes the description of a potential context that may characterize a user's situation (called the application context), and defines filtering rules that should apply when this situation happens (i.e. when the user's current context matches the application context, cf. section 3.1). The filtering rules are based on a set of stratifications and reflect the user's preferences considering the context associated with the profile. In other words, a profile describes what information the user wants to be informed of when in this situation and how this information is organized. Each profile can be seen as a set composed by: 1. an owner, for who/what the profile is defined. The owner is represented by a context element object (association describe in Fig. 5), allowing the definition of a profile either for users or for any element of the context model; 2. at least one application context to be considered, which represents the potential contexts in which this profile can be applied, i.e. the situations in which the profile is valid (association apply in Fig. 5) and should be selected by the filtering mechanism (cf. Section 3); 3. a list of event subclasses whose instances can be selected (association sign up in Fig. 6), representing the informational content considered as relevant for the owner; 4. a set of stratifications defined for the owner (see Fig. 6). The stratifications as well as the list of events define the filtering rules related to the profile.

The basic idea behind the profiles is to allow users, system designers and administrators to define the profiles and the application context objects related to them. In other words, each user may determine what information she/he considers as relevant and in which circumstances, as well as how this information is organized in levels of detail. A system designer may create profiles for the supported devices according to the capabilities of each device type, and a system administrator may also define profiles for some particular roles, like the coordinator role, which have special needs considering the informational content. This last case is particularly interesting for groupware systems, in which the roles represent the rights and the responsibilities of each team member. Indeed, we have observed that often mobile users do access groupware systems from a limited number of well known situations: from the rail station, from the airport, from home, using a particular PDA, a laptop, etc. By describing these potential situations (the corresponding application context) and defining particular profiles for them, each user (or the team manager) may express her/his needs and preferences for the most common situations, allowing the system to better adapt the delivered content in these situations. For instance, considering a cooperative editor (as the one proposed in [START_REF] Guerrero | Mobile support for collaborative work[END_REF]), the system designer may pre-define some event subclasses such as a "document changed" class, whose objects describe the changes performed in a document, or a "new comment" class, whose objects include the comments made by the group members about a document. In such case, the user "Alice" may define a profile signing up the "comment" events. This profile could be related to the situations in which she is using her PDA (i.e. a profile that is valid when she is using this device) and organize the "comment" events according to the stratification S 1 int = {{name, description}, {interval, details}, {medias}}. Additionally, it is worth to note that the multiplicity of the association sign up allows the definition of many stratifications for a given event class, by assigning it to different stratifications or to different profiles (and, consequently, to different application context). In the other hand, it is important to observe that a profile may concern any given context element (user, group, role, device…). We believe that, for groupware systems, it is particularly interesting for roles, defining the role's needs considering the delivered awareness information (e.g. a team coordinator needs a global view of the team performance, which may be unnecessary for a simple participant). It is equally interesting to define profiles for devices, describing the characteristics and limitations of a given device. Thus, as we can see in the Fig. 5, we specialize the profile class in preferences, describing the preferences of the user or her/his role, and in characteristics, describing the capabilities of the referred.

A Personalized and Context-Based Filtering Process

The adaptation approach we propose here is based on a filtering process in two steps. The first step selects the profiles the system should apply in order to filter the available information, according the user's current context. The second step consists in applying the filtering rules defined by the selected profiles. These rules are based on a set of pre-defined stratifications, which filters and organizes the set of available events that represent the available informational content. We assume that each user (or the system designer or its administrator) may define several profiles and the situations in which they are valid (i.e. the description of each application context). Thus, the first step selects, among the available profiles, those the system should apply, and the second step applies the stratifications defined in the selected profiles.

Step 1: Selecting Profiles According the User's Context

The first step of the proposed filtering process consists in selecting the profiles that are valid with regard to the user's current context. This selection is performed by comparing the application context related to the available user's profiles with the user's current context. Please note that these two kinds of context are both instances of the class context description of the context model. For each profile, we test if one of its application contexts has the same content or is a subset of the user's current context description. In other words, we verify if the situation described by the application profile occurs in the user's current context. If it is the case, then the profile is selected to be applied.

In order to identify this subset relationship, we consider that each context description instance and the context element instances associated with it define a graph, where the nodes represent the instances and the edges between them represent the tuples of associations involving these instances. Thus, a context C is a sub-context of a context C' whenever the graph corresponding to C is a subgraph of the graph corresponding to C'. The subgraph relationship is established using a pattern matching algorithm, which is based on two operations (equals and contains), defined as follow:

• Equals: (i) a node N is considered as equal to a node N' if the object O represented by N belongs to the same class and defines the same values for the same variables that the object O' represented by N'. (ii) an edge E is equal to an edge E' if the associations they represent belong to the same type (tuples of the same association) and connect equal objects.

• Contains: a graph C contains a graph C' if: (i) for each node N' that belongs to C' (called N' C' ), there is a node N belonging to C (N C ) for which N' C' equals N C ; (ii) for each edge E' in C' (called E' C' ), there is an edge E in C (E C ) for which E' C' equals E C .
Thus, we consider that a context description C' is a subset of a context description C if the graph defined by C contains the graph defined by C'. For instance, considering the user Alice that is consulting the notes about a report, as in Fig. 2. Let us suppose that Alice has defined two profiles: (i) a first one that is applicable only when she is involved in an activity which concerns a given report and when she is working on her desktop device. This means that the application context related to this profile includes the context elements corresponding to the shared object report2005 and to the device desktop. (ii) And a second profile that includes in its application context an instance referring to her PDA (i.e. a profile for the situations in which she is using this device). When Alice finds herself in the situation described by the Fig. 2, only the second profile is selected. The first one is rejected since the context description object representing the application context of this profile does not match the user's context description (the latter does not include a node referring to the desktop device that is present in the former, so it does not contains application context of this profile). The Fig. 7 represents the graphs defined by context description objects related to Alice's current context (Fig. 7a) and her profiles (Fig. 7b and Fig. 7c respectively). In this figure, we observe that the graph defined by the application context of the first profile is not a subgraph of the graph defined by the Alice's context, while the graph defined by the application context of the second profile is a subgraph of the one defined by Alice's context.

Step 2: Applying the Progressive Access Model

Once the profiles have been selected, the second step of the filtering process applies the stratifications defined in the selected profiles. These stratifications filter and organize the available set of events. It is worth noting that, in order to respect the stratification definition, we apply one profile at time by ordering the profiles. This is achieved by an algorithm in four steps: (i) it orders, by priority, the selected profiles; (ii) for each profile, it selects, among the set of available events, all events whose class corresponds to a class signed up by the profile; (iii) it performs the stratifications associated with this profile, by applying the extensional stratifications before the intensional ones; (iv) it delivers the content of the first level of these stratifications.

The priority of a profile is defined by a similarity measure between the application context of the profile and the user's current context. This measure evaluates the matching degree of the application context with the user's context. In other words, it estimates the proportion of elements of the graph defined by the user's context that have equals elements in the graph defined by the application context. Therefore, more specific profiles (i.e. profiles whose application context is composed by several context elements) will have a higher priority than more general profiles, which have fewer context elements instances composing their application context. This similarity measure is defined as:

• Sim (C u , C p ) = x, x ∈ [0, 1], where: x = 1 if each element of C u has an equal element in C p ; otherwise x = | X | / | C u | with X = { x | x equals y, x ∈ C u , y ∈ C p }
As an illustration, let us consider once again the example of a collaborative editor. The designer of such a system may have defined three event classes: user session, document changed and new comment. Let us consider now that a user (Alice) has two selected profiles. The first profile signs up the first event class, defining one stratification S 1 int = {{name, description}, {interval, details}, {medias}}. The second profile signs up the second and the third event classes, defining two stratifications, S 2 int = {{name, interval}, {description}} and S 3 ext = {{event.interval during DAY}, {event.interval during WEEK}}. Considering that the first profile has 0.2 as priority order, and the second has 0.8, the filtering process will apply first the stratifications S 2 and S 3 to the document changed and new comment instances, and then it will apply S 1 to the user session instances. As a result, the filtering process will make available for the user Alice, at the first level, the document changed and new comment events instances whose interval corresponds to a period of the current day, presenting only their attributes name and interval.

At the end of the proposed filtering process, an organized (in levels of details) set of events will be available for delivering to the mobile user. This set will probably better suit the current mobile user's context since it accords the user's preferences defined for this context.

Preliminary Results and Discussion

We have implemented the proposed filtering process using the AROM system [START_REF] Page | A New Approach in Object-Based Knowledge Representation: the AROM System[END_REF] and a framework for awareness support called BW-M [START_REF] Kirsch-Pinheiro | BW-M: A Framework for Awareness Support in Web-Based Groupware Systems[END_REF]. AROM is an object-based knowledge representation system, which adopts classes/objects and associations/tuples as main representation entities. Using AROM, we have created a knowledge base (KB) in which we keep the instances of the context model as well as the profiles and the events. Using the BW-M framework, we have implemented the filtering process using the algorithms presented in Section 3.

Using these algorithms, we have performed some tests simulating situations that represent the use of a collaborative web system which provides shared repository and synchronous/asynchronous communication features. The simulation uses five users and fifteen profile definitions, and we have evaluated different types of pattern matching algorithm acting on the equals and contains operations, and on the similarity measure Sim. We have evaluated two versions of the equals operator (one that considers only perfect match -objects must be exactly equal -and another that allows to define a minimum set of similar attributes in the objects) and analyzed the effects of these versions on the contains operator and on the Sim measure. We have also tested two versions of the contains operator (one that compares only equal instances, and another that compares the graph from two instances, even if they are not equal).

These tests have showed the validity of our filtering process with regard to a user's current context, the profiles being applied as expected in most cases and the total amount of delivered information being reduced in all cases. These tests have also pointed out some critical aspects. First, using distinct versions of the equals and contains operators leads to different results: the most satisfactory ones are those obtained with the most flexible versions (equals with predefined limit, and contains with the comparison of different instances). Then, the definition of the application context related to a profile is more or less critical given the version of the operator. In fact, defining a detailed application context causes the non selection of the profile (or the attribution of a lower priority to the profile with the Sim measure) in most cases when using the first version of the operators. On the other hand, defining a minimal application context causes its selection in almost all cases, especially when using the second version of the operators. However, the use of the most flexible versions of the equal operator does not affect the priority of these profiles, as those with detailed application context are always better ranked than those with a reduced application context.

Conclusions

In this paper, we have presented a context-based filtering process that proposes to adapt the information delivered to mobile user by filtering it according to the current user's context and to the user's preferences for this context. This approach differs from other approaches in context-aware systems, such as [START_REF] Burrell | Context-aware computing: a text case[END_REF][10] [START_REF] Lemlouma | Context-Aware Adaptation for Mobile Devices[END_REF] [START_REF] Schilit | Context-aware computing applications[END_REF], by the use of these preferences, and it differs from traditional approaches on groupware systems, such as [8][19], by the use of context knowledge. We believe that, by allowing a direct participation of the user into the adaptation process, this process may provide results that are more adequate to the user's expectations. We also differ from other works, such as [2][15], by a largest vision of what is context, as our approach takes into account both the user's physical context and the user's collaborative context. Moreover, our context model is mainly concerned by representing context information, instead of concerning its acquisition process, such as in [START_REF] Dey | Understanding and using context[END_REF].

Additionally, we have also proposed two new operations (next and previous) for navigation purposes in the Progressive Access Model. These operations are particularly interesting for a mobile use, since they limit the information presented to the user in a given moment. By using these new operations and the Progressive Access Model, we not only filter the awareness information (such as in [START_REF] Kirsch-Pinheiro | BW-M: A Framework for Awareness Support in Web-Based Groupware Systems[END_REF]), but we also organize it according to its relevance for the user. This represents a clear improvement, since mobile users usually do not dispose of enough time to analyze all information. Organizing the delivered information by relevance becomes then necessary, as pointed out by Billsus et al. [START_REF] Billsus | Adaptative interfaces for ubiquitous web access[END_REF] and by Coppola et al. [START_REF] Coppola | The concept of relevance in mobile and ubiquitous information access[END_REF].

Fig. 1 .

 1 Fig. 1. A context description is seen as a composition of context elements.

Fig. 2 .

 2 Fig. 2. Example of a context description for a given user (Alice).

Fig. 3 .

 3 Fig. 3. A Maskable Entity with three RoMEs.

Fig. 4 .

 4 Fig. 4. The Progressive Access Model described using UML stereotypes.

S 2 extensional

 2 = {{event.interval during DAY}, {event.interval during (WEEK)}}).

Fig. 5 .

 5 Fig. 5. UML class diagram describing the event and the profile class.

Fig. 6 .

 6 Fig. 6. The association concerning the profiles and the stratifications.

Fig. 7 .

 7 Fig. 7. The graphs defined by a user's current context (a), and the application context of two profiles (b and c).

  where 2≤i≤max • from a RoME i , at level of detail i, the unmask operation gives access to the

	RoME i+1 at level of detail i+1:
	unmask(RoME i )=RoME i+1, where 1≤i≤max-1
	A Maskable Entity and its	RoME1 defines the detail level 1	RoME2 defines the detail level 2 (composed of RoME1 elements + 1 new element)
	elements
			RoME3 defines the
			detail level 3 (composed
			of RoME 2 elements + 2
			new elements)

At detail level 1, the mask hides the following elements ………………. At detail level 2, the mask hides the following elements …………… At detail level 3, the mask hides no element

  where 2≤i≤max.• then, from a RoME i , at level of detail i, the previous operation gives access only to the elements of the RoME i-1 at level of detail i-1: previous(RoMEi)= proper(i-1), where 2≤i≤max. • and from a RoME i , at level of detail i, the next operation gives only access to the elements of the RoME i+1 at level of detail i+1: next(RoMEi)= proper(i+1), where 1≤i≤max-1.

We expect to extend the proposed filtering process by refining the pattern matching algorithm used to compare instances of the context description class. We are interested in calculating an acceptable semantic distance between the objects, in order to check if they are sufficiently similar (and not necessarily equal) to establish a subgraph relationship. We are also interested in studying how to simplify the profile definition in order to reduce problems that may be caused by an incorrect definition.


Pour une filiation Xenakis-Grisey ?

Makis Solomos *

Abstract.

Cette article construit une filiation entre Xenakis et Grisye, à partir de quatre axes qui souligneront quelques points de convergence (et de divergence) entre les deux compositeurs : la question de la " présence ", c'est-à-dire le fait que Xenakis comme Grisey peuvent, à un certain degré, être caractérisés comme des musiciens de la plénitude sonore ; le problème du temps ensuite, problème que nos deux compositeurs ont théorisé d'une manière relativement proche ; le recentrement sur le son, en troisième lieu ; enfin, l'idée à la fois très technique et très générale du processus.

POUR UNE FILIATION XENAKIS-GRISEY

Il est plus que probable que Grisey et Xenakis ne se sont pratiquement pas connus, ni humainement, ni à travers leur musique. Cette constatation ne devrait pourtant pas nous empêcher de tenter le rapprochement entre leurs deux univers musico-théoriques, car tous deux s'inscrivent dans cette extraordinaire tradition musicale propre au 20 e siècle où il est question d'un recentrement sur le son, une chaîne historique qui inclut Debussy, Varèse, certains aspects de Webern et des sériels des années 1950-60, la musique concrète et celle électronique historiques, des compositeurs comme Feldman, ou encore, le premier Ligetipour s'arrêter aux années 1970, où Xenakis a déjà composé une partie essentielle de son oeuvre et où Grisey entre en scène.

En somme, je m'efforce ici de construire une filiation, où l'enjeu n'est rien moins qu'une réécriture de l'histoire de la musique récente. Le besoin de cette réécriture surgit d'une compréhension intrinsèque des phénomènes musicaux qui conduit à insister sur l'importance de la tradition en question, car nous assistons actuellement à un devenir musical menant de la musique au " son ", une évolution dont je ne discuterai pas ici des implications -positives et, certainement, négatives également. Une évolution où, du pur point de vue musical, le " son " constitue une catégorie très générale qui inclut, comme phénomènes partiels, le timbre, le bruit, la focalisation sur l'écoute, etc. 1 .

Ce besoin découle tout autant de la constatation que nous assistons également à une alliance guère paradoxale entre globalisation et nationalisme, où chaque pays se livre au néolibéralisme et, simultanément, conserve de son héritage national (au sens historique de ce terme) les choses les moins intéressantes. Ainsi, que, sur le sol français, Xenakis n'a pas eu de descendants -si l'on excepte des descendants occasionnels tels que Pascal Dusapin-et, inversement, que Grisey s'inscrit exclusivement dans la réaction de certains jeunes musiciens français des années 1970 au sérialisme et post-sérialisme (boulezien) constituent, certes, des faits exacts. Mais l'existence de la tradition mentionnée précédemment s'avère, avec le recul, un fait tout autant exact. Que l'on s'arrête aux faits soulignant l'absence de filiation constitue simplement un choix impliquant que Grisey devrait entrer au Panthéon et que Xenakis devrait rester un produit de l'immigration généreuse des Trente glorieuses… Pour construire la filiation en question, j'ai choisi quatre axes qui souligneront quelques points de convergence (et de divergence) entre les deux compositeurs : la question de la " présence ", c'est-à-dire le fait que Xenakis comme Grisey peuvent, à un certain degré, être caractérisés comme des musiciens de la plénitude sonore ; le problème du temps ensuite, problème que nos deux compositeurs ont théorisé d'une manière relativement proche ; le recentrement sur le son, en troisième lieu ; enfin, l'idée à la fois très technique et très générale du processus.

UN ART DE LA PRÉSENCE

Comme il a été dit, Xenakis et Grisey peuvent être appréhendés, avec le recul, comme deux maillons d'une chaîne musicale très importante, caractérisée par le recentrement sur le son. Cette tradition couvre tout le 20 e siècle et comprend plusieurs générations. Elle se centre sur le son, sur la plénitude sonore : avec elle, la composition du son se substitue progressivement à la composition avec des sons. Si l'on se limite à la France, qui a été un des vecteurs privilégiés de cette chaîne, on dira qu'elle fut inaugurée par Debussy, l'initiateur français de la modernité. Elle s'est ensuite radicalisée avec Varèse qui, comme on le sait, devra attendre les années 1950 pour obtenir un début de reconnaissance en France. Elle s'instaure durablement à partir des années 1950 avec la naissance de la musique concrète et avec Xenakis. Elle se prolonge avec des compositeurs comme Ferrari, Bayle ou Mâche. Elle prend un nouvel élan avec les recherches sur la synthèse du son menées par Risset. Enfin, cette tradition -qui a bénéficié des apports extrêmes-orientaux d'un Eloy ou d'un Taïraaboutit logiquement à la musique spectrale, donc, en premier lieu, à Grisey. La musique spectrale s'inscrit clairement dans la tendance centrée sur le son, même si, parce que la chaîne s'est essoufflée, elle semble l'avoir conduite vers un autre sentier -j'ai développé ailleurs l'idée que la musique spectrale a joué, en quelque sorte, un rôle historique similaire au rôle qu'a joué le minimalisme américain2 .

A un niveau général, le recentrement, la focalisation sur le son signifie la quête d'une plénitude (sonore), plus exactement : la recherche d'une présence intégrale. L'enjeu de l'oeuvre devient l'ici et le maintenant. Chez Xenakis, comme chez Grisey, plus encore peutêtre que dans les autres maillons de la chaîne, la capacité à évoquer, à symboliser, à faire rêver, etc., ne disparaît certes pas ; néanmoins, elle se joue dans la présence quasi physique, une présence dont le son sans trous est le modèle. C'est pourquoi Xenakis a horreur des silences, du moins des silences qui ne sont pas les simples ingrédients d'une pâte sonore, mais qui sont chargés de connotations méta-physiques (au sens littéral) -par exemple, les silences d'un Nono3 . Chez Grisey, cela est moins évident, mais il ne serait sans doute pas inexact de dire que sa musique s'inscrit dans le plein et non dans le vide. C'est en ce sens que, tous deux, sont aux antipodes d'une certaine musique sérielle, par exemple celle de Boulez qui, au contraire, constitue une revendication de l'absence. Comme l'écrit Hugues Dufourt, chez Boulez, la forme musicale " ne se présente pas comme une totalité articulée, elle ne consiste pas non plus en un processus de récapitulation ou d'intégration complète. La forme musicale résulte de la différenciation de ses moments constitutifs, qui entretiennent entre eux des rapports d'exclusion mutuelle. […] Alors que le travail sur les figures sonores consistait à composer des résultantes, l'élaboration de la forme, chez Boulez, conjugue en quelque sorte la négativité de la structuration "4 . Chez Grisey et Xenakis, au contraire, la forme est bien la somme de ses constituants : l'oeuvre rejette l'absence -même si, celle-ci, fort heureusement, subsiste, ne serait-ce qu'à travers la capacité à symboliser, à faire rêver, etc., dont il était question précédemment.

La conséquence de ce travail sur le plein, de ce rejet du vide -ou de l'utilisation du vide uniquement pour créer du plein-est la redéfinition de la notion d'écriture au profit de son adéquation avec l'écoute, la perception. Ce fait constitue un lieu commun et c'est pourquoi il ne sera pas développé ici, sinon pour rapprocher Xenakis et Grisey. On sait que l'une des critiques du sérialisme par Xenakis dans les années 19505 fut précisément la constatation qu'il mettait en oeuvre une contradiction entre le mode d'écriture, centré sur les notes et les intervalles, et le résultat perceptif qui était global. Quant à Grisey, il rechercha, du moins à ses débuts, " une adéquation optimale entre le Conceptuel et le Perceptuel ", pour reprendre ses propres termes6 . Pour ces deux compositeurs, la notion d'écriture est donc à redéfinir. Les critiques à l'encontre de Xenakis et des spectraux -ainsi qu'à l'encontre du Ligeti des années 1960-ont pu dire que, chez eux, l'écriture devient simple tablature. C'est inexact. Grisey fut un musicien tout ce qu'il y a de plus traditionnel sur ce point : c'est par l'écriture (la notation solfégique) qu'il pensa sa musique. De même chez Xenakis, l'écriture est loin d'avoir perdu son rôle premier de conceptualisation, de mode privilégié de la pensée ; simplement, il ne s'agit plus de notation solfégique, mais d'autres types de représentation (algébrique graphique et/ou géométrique)7 . Par contre, chez tous les deux, le fossé entre chose écrite et chose perçue, qui était allé en s'agrandissant, est promis à la disparition -même si, encore une fois, la disparition n'est pas atteinte, puisque si l'on entend clairement par exemple les processus mis en oeuvre par Xenakis ou Grisey, on n'en saisit pas toute la complexité, seule l'analyse de la partition (donc : de l'écriture au sens le plus général du terme) permettant de le faire.

DU TEMPS

Pour commencer à présent à entrer dans la substance musicale, voici un autre trait commun : la conceptualisation de la question du temps. Le point de départ de nos deux compositeurs est identique. Xenakis appréhende le temps comme un " tableau noir " : " Le temps pourrait être considéré comme un tableau noir (vide) sur lequel on inscrit des symboles et des relations, des architectures, des organismes abstraits ", écrit-il8 ; ou encore : " le Temps primaire apparaît comme une matière cireuse, une glaise dans laquelle les opérations et les relations viennent s'inscrire, se graver "9 . Le temps comme " tableau noir ", comme " matière cireuse " : ces expressions formulent de la manière la plus concise possible la recherche d'un temps a priori, qui permet d'échapper à la trichotomie temporelle classique (pulsationmétrique-rythme), et qui pose la question du temps en des termes plus généraux. De la même manière, Grisey, dans son célèbre essai " Tempus ex machina ", emploie les expressions " squelette du temps " et " chair du temps " : " Par squelette du temps, nous entendons le découpage temporel qu'opère le compositeur pour mettre en forme les sons. Sans aucune immédiateté pour la perception, tout au plus devinée sous la "chair du temps", cette infrastructure reste cependant le lieu de prédilection des compositeurs du 20 e siècle, sans doute parce que dans sa relative simplicité, elle nous donne l'illusion de l'efficacité opératoire. L'unité de mesure en est le temps chronométrique, disons la seconde "10 . Comme chez Xenakis, le temps évoqué ici n'est nullement un temps " premier " -quoiqu'il existe, chez Grisey, une certaine ambiguïté, dans d'autres passages du même article-, mais un temps purement théorique, une extraordinaire abstraction, dont l'utilité première est d'autoriser le compositeur à poser la question du temps en termes de construction -calcul, mais aussi unification de niveaux temporels hétérogènes.

Précisément, à partir de cette définition similaire du temps, les deux compositeurs théoriseront d'une manière très voisine des temporalités hétérogènes, mais unifiables. Aussi bien Xenakis que Grisey ont défini pour l'oeuvre musicale des niveaux de temps différents. Dans les deux cas, le nombre de ces niveaux temporels est identique : trois. On connaît la très belle distinction de Grisey entre temps des baleines, temps des hommes et temps des oiseaux : " Pensez aux baleines, aux hommes et aux oiseaux. Si l'on écoute les chants des baleines, ils sont tellement étalés que ce qui paraît être un gigantesque gémissement étiré et sans fin n'est peut-être pour elles qu'une consonne. C'est-à-dire qu'il est impossible avec notre constante de temps de percevoir leur discours. Parallèlement, à l'audition d'un chant d'oiseaux, on a l'impression qu'il est très aigu et agité. Car il a une constante de temps beaucoup plus courte que la nôtre. Difficile pour nous de percevoir ses subtiles variations de timbre, alors que lui nous perçoit, peut-être comme nous percevons les baleines "11 .

Xenakis pose sa distinction en termes de structures, mais nous pouvons la rapporter au temps. Ainsi, il distingue entre trois niveaux : " La musique a toutes sortes de formes, au niveau microscopique, au niveau macroscopique, au niveau de l'échantillon " 12 . Ailleurs, il ajoute une quatrième temporalité : " micro-structure ( = timbre), mini-structure ( = note), mésostructure ( = polyrythmie, échelles mélodiques, intensités), macro-structure ( = évolution globale de l'ordre de dizaines de minutes) " 13 .

Quant à l'unification de ces différentes temporalités, Grisey l'atteint dans certaines oeuvres par le calcul, par l'élaboration de proportions qui restent invariables indépendamment de l'échelle temporelle. Ainsi, avec Le Temps et l'Ecume, " la partition est une application directe du concept d'échelles relatives de temps. Un geste fondamental est constitué de deux objets antinomiques : un objet "bruit" (rythme, pulsation, discontinuité), suivi d'un objet "son" (temps étale, sans sentiment pulsatoire, continuité). L'organisation formelle consiste en la projection successive du geste dans les trois temporalités chères à Grisey […]. Après le temps des hommes, temps normal où le geste, aisément perceptible, est entendu plusieurs fois de suite, le temps des oiseaux contracte cette succession en quelques secondes. Puis un seul geste occupe toute la durée du temps des baleines, tellement sa dilatation est importante " 14 . Xenakis, quant à lui, n'a envisagé l'unification des niveaux temporels que dans un seul cas, celui du programme informatique GENDYN, élaboré vers la fin des années 1980, avec lequel il a composé deux oeuvres, Gendy3 et S.709. Comme Grisey, il postule une unification sans médiations, car réalisée automatiquement. Mais, à la différence de ce dernier, il ne travaille pas avec un modèle projeté dans plusieurs temporalités : les niveaux temporels sont immédiatement déduits les uns des autres. Avec le programme GENDYN, le compositeur introduit quelques données, puis la machine calcule des courbes de pression stochastiques (aléatoires) qui évoluent également stochastiquement, le long du temps. On obtient ainsi directement une oeuvre -bien sûr, le compositeur peut intervenir pour préciser le nombre de pistes, éliminer telle ou telle courbe, etc. Est alors réalisée l'unité des deux niveaux temporels extrêmes : le microscopique et le macroscopique, puisque l'oeuvre est automatiquement générée à partir du niveau le plus bas, celui de l'onde sonore. C'est peut-être le rêve de tout musicien, même si l'absence totale de médiation entre les niveaux temporels peut poser des problèmes quant au résultat sonore -d'ailleurs, Xenakis n'a écrit que deux pièces de ce genre et, en outre, Peter Hoffmann montre que, pour l'une des deux au moins, Xenakis est intervenu après le calcul d'une manière importante 15 … Pour conclure sur la question du temps, ajoutons que la distinction de niveaux temporels ainsi que la recherche de leur unification relative, même si elle fut une question que Xenakis et Grisey ont théorisé d'une manière relativement ample, reste une question générale, qui a occupé également d'autres compositeurs : pensons à la mode des fractals dans les années 1980-90, ou bien aux travaux compositionnels et théoriques d'Horacio Vaggione 16 .

12 Iannis Xenakis, " Condition du musicien " (1985), repris in Kéleütha, op. cit., p. 127. 13 Iannis Xenakis, " Sur le temps " (1988), repris in Kéleütha, op. cit., p. 104. 14 Jérôme Baillet, op. cit., p. 71. 15 Cf. Peter Hoffmann, Music out of Nothing? Dynamic Stochastic Synthesis : A Rigorous Approach to Algorithmic Composition by Iannis Xenakis, thèse de doctorat, Université de Berlin, travail en cours. 16 Cf. Horacio Vaggione, " Son, temps, objet, syntaxe. Vers une approche multi-échelle dans la composition assistée par ordinateur ", in Musique, rationalité, langage. L'harmonie : du monde au matériau = Cahiers de philosophie du langage n°3, 1998, p. 169-202.

L'ÉMERGENCE DU SON

Le troisième thème de comparaison est à la fois le plus facile et le plus difficile. On peut le nommer de manières multiples : l'émergence du son, la convergence vers le timbre, la fusion dans une totalité sensible, le modèle du son, etc. Il est étroitement relié à la question de la présence mentionnée précédemment, à la qualité quasi charnelle qui se dégage des musiques de Xenakis et de Grisey. Sur ce point, ceux-ci sont très proches et, en outre, Grisey y est beaucoup plus proche de Xenakis que les autres spectraux, notamment Murail, dont le travail sur le son est nettement plus ravélien. Mais c'est aussi sur ce point que nos deux compositeurs divergent.

Chez Xenakis comme chez Grisey, l'émergence du son s'obtient en premier lieu par la fusion de la forme et du matériau ou, du moins, leur tendance à la fusion. Dans les deux cas, la composition ne part pas d'un matériau qu'elle développe. Nous sommes aux antipodes de la tradition classique où l'on peut clairement isoler un matériau premier (thème, motif, cellule) et analyser les procédés de développement (répétition, variation, transformations diverses, etc.). Nous sommes également très loin de la tradition sérielle qui, pour employer une expression d'Henri-Louis Matter à propos de Webern, emploie un matériau " chromosomique " 17 , la série ou l'intervalle. Ce qui signifie également que, malgré les apparences, les formes xenakiennes ou griseyennes ne tendent pas vers des formes organiques -je pense ici à la phrase célèbre de Goethe, citée par Webern, qui conçoit l'oeuvre musicale comme la croissance d'une plante 18 . Le matériau chez Grisey et Xenakis existe, cela va de soi, mais il ne se développe pas, il ne croît pas non plus : il se déploie. On pourrait comparer ce déploiement au tracé d'un geste : l'évolution du matériau ressemble au mouvement d'une main qui se lève doucement ou qui tape violemment du poing. De ce fait, la forme n'est pas le produit de l'évolution d'un matériau premier, la cellule ou l'intervalle. Elle se définit par le tracé de ce geste. C'est peut-être cela qui fait que nos deux musiciens se caractérisent par la présence, la plénitude. En tant que simple résultat du tracé du geste, leurs formes musicales ne laissent rien en suspens, elles ne dévoilent aucune faille, elles ne laissent deviner aucune piste qui, volontairement ou involontairement, n'aurait pas été développée. D'un thème mozartien, on pourrait imaginer mille développements, mille formes. Dans la fusion forme-matériau, au contraire, chaque déploiement de matériau détermine sa propre forme.

En second lieu, l'émergence du son s'opère par la dissolution des dimensions du son et leur convergence. A l'encontre des sériels -rejoignant en cela Varèse-, Xenakis, tout en reconnaissant les vertus de la décomposition paramétrique, s'orienta dès le début vers la resynthèse, c'est-à-dire vers la convergence des dimensions du son. Chez les sériels, la totalité sonore est finement découpée en paramètres ; ceux-ci évoluent souvent d'une manière totalement indépendante, volontairement asynchrone ; il n'arrive que rarement, lorsqu'on désire créer des " enveloppes " (terme de Boulez), d'assister à leur convergence. Par contre, 17 Cf. Henri-Louis Matter, Webern, Lausanne, L'Age d'Homme, 1981, p. 78. 18 Webern, citant Goethe, aimait employer la métaphore de la plante : " L'organisation de la plante est la chose la plus simple que l'on puisse penser ; tout y est identique : racine, tige, fleur. Et, selon Goethe, il en est de même du corps humain. […] L'idée de Goethe est que l'on pourrait inventer des plantes à l'infini. Et c'est aussi le sens de notre style de composition " (Anton Webern, Chemins vers la nouvelle musique, traduction A. Servant, D. Alluard et C. Huvé, Paris, Jean-Claude Lattès, 1980, p.106). chez Xenakis, faire une analyse paramétrique de sa musique n'aurait aucun sens. On peut étudier séparément le traitement des hauteurs, des intensités, des modes de jeu, des transformations spatiales, etc., mais, en règle générale, l'important est leur association en vue d'un résultat global. La même démonstration a souvent été faite pour Grisey, et, d'une manière plus générale, pour les spectraux, qui se sont caractérisés à leurs débuts par cette quête d'une fusion des paramètres. Il faudrait cependant insister sur une différence fondamentale entre le travail de Grisey et celui de Xenakis quant à cet aspect de leur musique. Xenakis recherche une fusion totale qui, sur ce point, reste classique. Chez lui, la fusionpourvu qu'on cherche à l'entendre ou qu'elle soit réussie-est sans ambiguïtés. Sa musique ne se distingue pas, en ce sens, des développements d'un Beethoven qui, tout en maintenant la distinction matériau-forme, parachevait une totalité dramatique univoque. Chez Grisey, par contre, la quête de la fusion est aussi synonyme de recherche des ambiguïtés, notamment au niveau de la perception -sur ce point, Grisey a bénéficié des travaux de Risset et des psychoacousticiens. Cette quête est orientée vers le tâtonnement en vue de découvrir des seuils, des moments très particuliers à partir desquels la fusion s'opère -le rêve de l'alchimie est omniprésent chez Grisey, car il est revitalisé par la découverte que l'oreille est beaucoup plus fluctuante que la réalité physique des sons. C'est en ce sens que Grisey a toujours préféré, pour définir sa musique, l'adjectif " liminal " à celui " spectral ". Ecoutons-le : " La musique des Espaces Acoustiques peut apparaître comme la négation de la mélodie, de la polyphonie, du timbre et du rythme comme catégories exclusives du son, au profit de l'ambiguïté et de la fusion. Les paramètres n'y sont qu'une grille de lecture et la réalité musicale réside au-delà, dans les seuils où s'opère une tentative de fusion. Liminal est l'adjectif que je donnerais volontiers à ce type d'écriture : plus volontiers en tout cas que celui de spectral, entendu souvent aujourd'hui et qui me semble trop limitatif ", écrit-il 19 .

En troisième et dernier lieu, posons la question : vers quoi tendent la fusion formematériau ainsi que la convergence des dimensions du son ? Sur ce point, nos deux musiciens divergent considérablement. Et peut-être qu'ici Grisey s'avérera plus conservateur, alors que Xenakis l'était par rapport à la fusion des dimensions où, d'une manière classique, il n'a pas posé la question de notre écoute et donc des ambiguïtés délicieuses que l'on peut explorer lors de cette fusion. Chez Grisey, les fusions, les convergences tendent vers le point d'où elles partent. Je veux dire par là que l'exposé habituel du spectralisme consiste à énoncer en premier l'idée, la métaphore qui l'a incité à créer les outils pour opérer ces fusions, à savoir : le modèle du son ou, dit autrement, l'idée d'un son ausculté comme au microscope. Ce désir a mené Grisey vers deux idées imbriquées. Tout d'abord, il a constaté -comme l'avaient déjà fait Stockhausen, puis Risset-que timbre et harmonie étaient deux aspects d'un seul phénomène, qu'on peut composer un timbre comme on compose un accord 20 . Parce qu'il a 19 Gérard Grisey, " Structuration des timbres dans la musique instrumentale ", in J.-B. Barrière (éd.), Le timbre, métaphore pour la composition, Paris, Christian Bourgois, 1991, p. 377. 20 Stockhausen écrit à propos de l'Etude électronique I : " Je retournais à l'élément qui constitue la base de toute la multiplicité sonore : à la pure vibration, qui peut être produite électroniquement et qui se nomme une onde sinusoïdale. Tout son existant, tout bruit est un mélange de telles ondes sinusoïdales -un spectre. Les proportions numériques, intervalliques et des dynamiques de ces ondes déterminent les caractéristiques de chaque spectre. Elles déterminent le timbre. Et ainsi, pour la première fois, il était possible en musique de composer, dans le sens véritable de ce mot, les timbres, c'est-à-dire de les synthétiser à partir d'éléments et, en faisant cela, de laisser agir le principe structurel d'une musique également dans les proportions sonores " voulu faire de la musique instrumentale, Grisey a réalisé l'inverse : il a composé des agrégats -les fameux " spectres "-comme s'il s'agissait de sons, postulant ainsi l'équivalence entre hauteur et partiel (ou harmonique), se situant bien ainsi dans la lignée d'un Debussy qui composait déjà des agrégats sonnant plus comme des timbres composés que comme des accords 21 . Dans un deuxième temps, Grisey a étendu ce principe à toute l'oeuvre musicale : puisque l'on compose un accord comme s'il s'agissait de la superposition des harmoniques d'un son, on peut très bien envisager une forme, une oeuvre musicale, comme l'agrandissement à l'échelle macroscopique de l'évolution d'un son (échelle microscopique) -d'où, bien entendu, la question des temporalités hétérogènes à unifier. Bien évidemment, on ne peut pas réduire l'oeuvre de Grisey à ce projet. Jérôme Baillet insiste fortement sur le fait que Grisey n'a employé des " transcriptions ", des simulations de sonagrammes à l'échelle instrumentale que dans trois et seulement trois passages de toute son oeuvre. En outre, il ajoute : " Il n'est pas question de nier l'importance de la physique du son dans l'art de Grisey, mais d'être conscient du rôle qu'elle y joue. Prépondérant dans les manifestes et les motivations créatrices, l'acoustique ne tient guère plus de place dans les oeuvres de Grisey qu'elle n'en tient dans d'autres musiques qu'on ne songerait à qualifier de spectrales. Insister sur cet élément serait tristement réducteur " 22 . C'est certain. Mais cela n'empêche pas que ce projet, même s'il ne concerne qu'une petite partie de l'oeuvre de Grisey, restera, encore plus que chez les autres spectraux -car il l'a développé de manière plus claire-son apport original dans l'histoire des techniques compositionnelles, c'est-à-dire de ce qui nous intéresse ici. Pour aller donc un peu plus loin dans la discussion de ce projet, il faudrait constater que c'est sur ce point que se situe le conservatisme (relatif) de Grisey. L'idée, avons-nous dit, est nouvelle. Mais, d'une part, elle a précisément été une manière de revenir à la musique instrumentale -c'est pourquoi justement l'oeuvre de Grisey ne se limite pas à ce projet !-, c'est-à-dire, en quelque sorte, une manière de fermer la porte au monde sonore nouveau, de l'électronique, de l'électroacoustique. D'autre part, comme l'a montré Anne Sédès 23 , la physique du son qui préside à son projet, reste la physique helmholzienne, c'est-à-dire la physique acoustique du 19 e siècle qui postule que le " son musical " est un phénomène périodique, en quelque sorte atemporel. Certes, Grisey, qui a étudié l'acoustique avec Emile Leipp, a eu connaissance du fait que le son est aussi caractérisé par les transitoires d'attaque et d'extinction et a même " transcrit " instrumentalement ces transitoires avec les fameux (Karlheinz Stockhausen, " Arbeitsbericht 1953 : Die Enstehung der Elektronischen Musik ", in Karlheinz Stockhausen, Texte zur Elektronischen und Instrumentalen Musik, volume 1, Cologne, Dumont Schauberg, 1963, p. 42). Quant à Risset, c'est dès 1971 (cf. " Synthèse des sons à l'aide de l'ordinateur ", Musique et technologie = La Revue Musicale n°268-269, 1971, p. 113-123) qu'il parle, dans le cadre de la synthèse du son par ordinateur, de " composer le son ". De même que Stockhausen, il se réfère au fait que la synthèse additive du son permet en quelque sorte de " composer " (synthétiser) un son comme on compose un accord. 21 Un critique averti, Edward Dent, écrivait déjà en 1916, se référant à Debussy (mais également à Satie et à Ravel) : " Les dissonances de l'harmonie moderne proviennent […] du fait que l'on accepte les accords dissonants, aussi bien que consonants, comme des effets de timbre […]. Nous savons que toute note particulière peut se fragmenter en ses composantes harmoniques, et que le timbre dépend de la relative intensité de celles-ci ; dans ce cas, pourquoi ne créérions-nous pas synthétiquement de nouveaux timbres, en faisant résonner ensemble plusieurs notes ? " (cité par Edward Lockspeiser, Claude Debussy, Paris, Fayard, 1980, p. 311-312). 22 Jérôme Baillet, op. cit., p. 93. 23 Cf. Anne Sédès, Les modèles acoustiques et leurs applications en musique : le cas du courant spectral français, thèse de doctorat, Université Paris 8, 1999. sonagrammes de son de trombone. Mais, de même que Leipp et Helmholtz [START_REF]Helmholtz les qualifie de " particularités du son[END_REF] , il a considéré ces transitoires comme des phénomènes particuliers, l'essentiel du son restant la répétition, la non-évolution dans le temps. Enfin, comme il vient d'être dit, la fusion des dimensions du son ou de la forme et du matériau s'opère pour Grisey grâce à la métaphore du son, c'est-à-dire selon un phénomène supposé organique. C'est dire que la totalité qui en résulte doit avoir une apparence de vivant ou alors, elle n'existe pas. A partir de ce point débute le credo organiciste et peut-être mystique, le credo qui, précisément, nous fait replonger dans l'alchimie [START_REF] Cf | L'identité du son (notes croisées sur Jonathan Harvey et Gérard Grisey)[END_REF] . Voilà rapidement quel est le résultat des fusions obtenues dans l'oeuvre de Grisey ainsi que les raisons qui expliquent ses divergences avec Xenakis. Car, avec Xenakis, la fusion ne prend pas pour modèle le son au sens physique du terme -à quelques exceptions près, qui mériteraient d'être détaillées si l'on s'intéresse à prolonger le parallélisme qui est tenté ici. L'origine, le modèle, la métaphore qui ont conduit Xenakis à travailler sur des idées acoustiques globales, ce sont les cris de manifestations, les sons désordonnés de mitrailleuses, les polyphonies complexes de cigales, etc. Le résultat global obtenu a les allures d'un son, mais il est toujours composé sur un modèle qui, d'une part, n'est pas le son physique luimême, c'est pourquoi je l'appelle sonorité 26 ; d'autre part, Xenakis prend pour appui les probabilités et la thermodynamique, c'est-à-dire la science qui, la première, a introduit la notion de temps comme l'élément décisif pour toute notre description du réel. Ce qui fait également que, lorsque Xenakis compose des sons réels, à l'échelle microscopique, c'est-àdire lorsqu'il compose des oeuvres électroacoustiques, il s'intéresse aux bruits, aux phénomènes non-périodiques, évoluant dans le temps. C'est pourquoi enfin, le naturalisme xenakien, s'il existe, n'est pas d'essence organiciste -le modèle organiciste qui a prévalu en musique étant finalement issu d'une science centrée sur la notion d'harmonie et non sur le désordre.

L'oeuvre entière est un modèle des diverses techniques de transformations progressives, continues ou discontinues, de registre, de densité, de mouvement spatial, de " filtrage ", etc., appliquées à des sections particulières. Par manque de place, concentrons-nous sur deux sections, les mesures 172-179 et les mesures 208-237. Pour commenter les premières, il nous suffit d'une transcription graphique (exemple 1 33 ). Le procédé mis en jeu est évident : partant d'un registre entièrement écarté, les 46 cordes en col legno frappé s'orientent d'une manière très continue vers un cluster très compact d'un ambitus d'une neuvième majeure. Pourtant, chaque instrument possède son propre dessin mélodique. En effet, la vue de la transcription graphique peut tromper : on pourrait penser qu'il se réaliserait à l'orchestre avec chaque instrument jouant une ligne droite partant d'une note du registre éclaté de la mesure 172 pour aboutir à une note du cluster de la mesure 180. La lecture de la partition montre au contraire que chaque instrument possède un parcours riche 34 . Une analyse plus approfondie montre que Xenakis a réalisé les 46 courbes mélodiques selon trois schémas de base : une ligne globalement descendante, une globalement ascendante et un trajet qui procède par tassements. L'exemple 2 présente trois courbes exemplaires (respectivement par rapport aux trois schémas, celles du vl .I.3, de la C.B. 6 et du vl. I.1). Les mesures 208-237, quant à elles, présentent également une transformation globale de registre, que permet de visualiser la transcription que je propose dans l'exemple 3 35 . On notera que l'évolution est inverse de celle des mesures 172-179, mais non linéaire (ne sont pas notées les fins des glissandi qui, souvent, excèdent ce registre). En outre, Pithoprakta constitue l'une des rares oeuvres de Xenakis qui semble épouser le modèle du son : il s'agit de passer globalement du bruit (coups sur la caisse des cordes) au son pur (harmoniques finales). Mais le résultat n'est pas immédiatement perceptible, car Xenakis le réalise par interpolations, avec de fréquents retours vers des états déjà passés quant au degré de bruit. L'exemple 4, où les caractères gras indiquent l'unique section qui n'est pas en transformation progressive, résume tout Pithoprakta.

Mesures Description

33 On remarquera une " erreur " : une note, dans l'aigu (un ré# qui, dans la partition, est joué par le vl. II.2), à la mesure 177. Il ne s'agit pas d'une erreur de transcription : on la retrouve dans le graphique de Xenakis lui-même, qui lui servit pour composer ce passage, publié récemment in F.-B. Mâche (éd.), op. cit., p. 54-55. 34

Exemple 1 .

 1 Transcription graphique des mesures 172-179 de Pithoprakta. Exemple 2. Transcription graphique de trois courbes mélodiques des mesures 172-179 de Pithoprakta. Exemple 3. Transcription graphiques des mesures 208-237 de Pithoprakta.

  avec transformation continue de la densité et de la spatialisation ; puis, émergence progressive de pizzicati et d'arcos 52-59 Transformation globale par " filtrage " d'un " nuage de sons " 60-104 Tenues avec émergence progressive de pizzicati puis de glissandi 105-121 Transformations discontinues d'un champ de glissandi 122-171 Superposition bruiteuse de 6 groupes de timbre avec " vues au microscope " ponctuelles 172-179 Transformation continue du registre de sons en battuto col legno 180-207 Transformations discontinues par " filtrage " d'un cluster 208-231 Champs de glissandi avec transformation irrégulière, puis linéaire de registre 231-250 Large cluster qui " s'évapore " progressivement dans l'aigu 250-268 Harmoniques en transformations spatiales discontinues DU BRUIT AU SON PUR Exemple 4. Pithoprakta : description globale des transformations progressives *** Intense présence sonore, définition du temps musical, de ses échelles et de leur unification, recentrement sur le son, technique du processus : voilà certains traits qui permettent de fonder une comparaison entre Xenakis et Grisey. Dans la mesure où les convergences de positions sont nombreuses, l'hypothèse de la filiation au sens mentionné (filiation construite) peut, dans une certaine mesure, tenir.

  Notons cependant deux redondances : le vl. I.6 double le vl. I.3 aux mesures 172-174 ; le vl. I.12 et le vl. II.12 jouent pratiquement les mêmes notes aux mesures 175-179.

35

Le graphique original avec lequel Xenakis composa ce passage est publié in Edit Walter, " Xenakis et la naissance d'un langage ", Harmonie n°33, 1968, p. 18-19. On soulignera que le graphique global fait penser à l'enveloppe d'un son.

Cf. Makis Solomos, " Néoclassicisme et postmodernisme : deux antimodernismes ", Musurgia vol. V n°3-4, Paris, 1998, p. 91-107.

Cf. Makis Solomos, " Le silence chez Boulez et Xenakis dans les années 1950-60 ", Les Cahiers du CIREM n°32-34, Tours, 1994, p. 127-136.

Hugues Dufourt, Musique, pouvoir, écriture, Paris, Christian Bourgois, 1991, p. 157.

Cf. Iannis Xenakis, " La crise de la musique sérielle " (1955), repris in Kéleütha, Paris, L'Arche, 1994, p. 39-43.

6 Gérard Grisey, " Le devenir des sons "(1982), repris in Danielle Cohen-Levinas (éd.), Vingt cinq ans de création musicale contemporaine. L'Itinéraire en temps réel, Paris, l'Harmattan, 1998, p. 291

.7 Cf. Iannis Xenakis, " Vers une philosophie de la musique " (1966), repris in Musique. Architecture, Tournai,Casterman, 1971

, p. 88-92 : Xenakis parle de " trois codes " de représentation du son : a) par la notation traditionnelle ; b) " algébriquement par une collection de nombres " ; c) " géométriquement (ou graphiquement par des dessins) ".

Iannis Xenakis, " Vers une métamusique " (1967), repris in Musique. Architecture, op. cit., p. 58.

Iannis Xenakis, Musiques formelles = Revue Musicale n°253-254, 1963 ; réédition : Paris, Stock, 1981, p. 17.

Gérard Grisey, " Tempus ex machina. Réflexions d'un compositeur sur le temps musical ", Entretemps n°8, 1989, p. 83.

Gérard Grisey, entretien avec Ivanka Stoïanova, plaquette éditions Ricordi, Paris, 1990, p. 22-23 ; cité par Jérôme Baillet, Gérard Grisey. Fondements d'une écriture, Paris, l'Harmattan, 2001, p. 25.


Sculptor

Makis Solomos

XENAKIS AS A SOUND

One of the main revolutions -and maybe the most important one-of twentieth century music is the emergence of sound. From Debussy to recent contemporary music, from rock'n'roll to electronica, the history of music has progressively and to some extent focused on the very foundation of music: sound. During this history -when, in some way, composition of sound takes the place of composition with sounds-, Xenakis plays a major role. Already from the 1950s, with orchestral pieces like Metastaseis (1953-54) or Pithoprakta (1955-56) and with electronic pieces like Diamorphoses (1957) or Concret PH (1958), he develops the idea of composition as composition-of-sound to such an extent that, if the expression was not already used for designating a new interdisciplinary artistic activity, we could characterize him as a "sound sculptor".

SOUND AS THE FOUNDATION OF MUSIC

Xenakis did not develop a theory for characterising this new idea of composition; at least, he did not treat it in his writings in a direct and systematic way-as it is well known, his theoretical work is mostly devoted to the question of formalizing music. But some important paragraphs of his writings refer to this focus on sound. One of his first articles, "Problems of Greek musical composition" (1955, written in 1954) 1 , which is very important for his early evolution, has such a paragraph. Xenakis wrote this article in a decisive moment of transition, that between the early works, like Procession to clear waters (Procession aux eaux claires, 1953), which belong to his Bartókian period 2 , and the first recognized pieces (such as Metastaseis), works that introduce the new musical questions and that place him in the centre of the musical scene. In the midst of this moment of transition, he is not sure which path to take. Although he is living now in France for six years, he is still torn between traditional Greek music (that he refers to as demotic music, i.e. rural traditions) and western music. But he also has to face the gap between past western music and avant-garde music. In addition, the avant-garde is now divided between the serialist school (Xenakis continues to speak about "dodecaphonism") and concrète or electronic music. Finally, he seems fascinated by jazz music. In simple and direct words, he wonders: "Which then is the best path? What is real music? Traditional European music, dodecaphony, electronic jazz, demotic music?"3 .

For a young self-taught (or almost) composer and, moreover, in exile, the choice seems impossible. There is no reason to choose one kind of music over another, to join this tradition rather another. This is why, to answer such a question, Xenakis asks another question: "Is there any link between these different sorts of music or are they, in fact, incompatible to the point that some should be condemned as being outdated or as being monstrous creations from abnormal periods?" 4 . His answer puts the question of sound in the foreground:

COMPOSING SOUND

To assert that sound is the foundation of music means, in a way, that the traditional way of thinking about music is reversed. Sound, henceforth, according to Xenakis, is not treated as the starting point of composition, but as its outcome. We could draw a parallel between twentieth century research of the musical avant-garde and the so-called "crisis of foundations", which happened in mathematics at the same time 6 . While mathematicians tried to found mathematics, musicians tested several ways to found music on sound. From Schönberg's Klangfarbenmelodie to Scelsi's mysticism, composers who focused on sound phenomenon have been countless. Using an epistemologist's terminology, we could define two ways to focus on sound: "intuitive" and "axiomatic". In the first case, the question is to "let sounds be", to paraphrase one of Cage's famous maxims; in the second case, the question is to compose sound.

Xenakis belongs to the most representative group of composers who choose the second way. An important part of his music, both instrumental and electronic, can by analysed and listened to as composed sound, as sound synthesis transposed into the temporal scale of a work. Some of his compositions are very explicit. Such is the case with his two last electronic pieces, composed with the program GENDYN, Gendy3 (1991) and S.709 (1994) [START_REF] Hoffmann | Analysis through Resynthesis. Gendy3 by Iannis Xenakis[END_REF] . The program GENDYN, based on stochastic dynamic synthesis, completes the project initiated thirty years earlier with Achorripsis (1956-57) and the ST-program of 1962, a project whose main idea was to create a mechanism that, after introducing some data, could produce a whole composition. An algorithm synthesizes sound as stochastic changes on the time-pressure curve. Consequently, there is no difference between synthesis (of sound) and composition (in the traditional sense): in theory, composition is a direct outcome of synthesis -in Xenakis' words, "macrocomposition" results from "microcomposition" [START_REF]This terminology is common in Xenakis' writings, even if it not developed; cf. for instance "Les chemins de la composition musicale[END_REF] . Another example is the granular conception of sound that Xenakis developed in the late 1950s, in reference to Gabor [START_REF]Cf. Formalized Music[END_REF] . At that time, he could only have the intuition of granular sound synthesis (which was implemented in the 1970s). So, he put forward the hypothesis that we could create a "sonority of second order" 10 and composed Analogique A and B (1958-59) to test it: the nine strings (Analogique A) play very short sounds (short arco, pizzicati or battuto col legno) and the tape (Analogique B) is made with clouds of very short sine waves; these short sounds are like "granular sounds" and Xenakis hopes that, for the listener's ear, they will merge into a global sound [START_REF] Di | For an analysis of Xenakis' hypothesis of a "sonority of second order[END_REF] . With this hypothesis, composition is supposed to be like sound synthesis in a metalevel.

In Xenakis' whole production, the above-mentioned compositions are exceptions. The general case is not one where macrocomposition is directly deduced from microcomposition, the first being a transposed sound synthesis [START_REF]Another exception of this kind is the "Brownian movement" technique that Xenakis uses in his instrumental music of the 1970s: it is a transposition of curves he calculated in the late 1960s while trying for the first time to implement stochastic synthesis (cf. Makis Solomos, "The unity of Xenakis' instrumental and electroacoustic music . The case of 'Brownian movements[END_REF] . Nevertheless, an important part of his music is like composed sound. To analyze his music in this perspective, we have to replace the word "sound" with the word "sonority", in order to suggest that the composed objects are not exactly sounds (in the physical sense), but more complex entities, for instance whole parts of an orchestral work.

Let's take as example the first section (bars 10-62) of Jonchaies (1977), where the strings (and some percussion) are playing. This is a very long part, almost monolithic, with a clear, inner, progressive evolution, which unravels like the evolution of a single sound. The strings are divided into 18 parts, sometimes playing in partial unisons and sometimes completely independently. It begins with a single high-pitched unison line, which follows a sinuous route to descend in an irregular way. Then other lines enter progressively, following the same route and constructing thus a broad heterophony. In bars 24-29, this heterophony reaches the low register and then begins to climb, always following a sinuous route. In bar 43, one of the lines reaches the highest pitch and is progressively followed by the others. Then the melodic route stays in the high register. Finally, some lines again descend. Despite the fact that the global route stretches over a long period, it is continuous and schematic enough that the listener's ear can follow it throughout as the eye would do with a graph 13 . In addition, this part of Jonchaies is based on one single sieve (scale), illustrated in figure 1 (a sieve that, according to Xenakis, is near to the pelog scale 14 ). But Xenakis is not using this sieve for itself, as a succession of pitches. Pitch here is not a main feature: the sieve is maintained over a long period, and is explored throughout its whole register in a linear manner (irregular ascending-descending lines) and, finally, it is treated, thanks to heterophony, and constructs a giant sound aura. The sieve is used then to produce a sound color. In a way, this part can be heard as a single sound, which progressively spreads and can be explored, as though with a microscope and in slow motion, its inner composition and its temporal evolution.

Figure 1. Jonchaies: sieve of bars10-62

Many of Xenakis' compositions can be analysed as successions of sonorities, i.e. successions of sections that can be heard, metaphorically, as composed sound. Within the limits of this article, it is impossible to give other examples and to develop this type of analysis and of listening 15 . Let's only add that such an analytical method is not exclusive. To listen to one of Xenakis' compositions as a succession of composed sounds, of sonorities, does not prevent us from hear its dramatic qualities, for instance.

SCULPTING SOUND

13 For a graphic transcription of this part of Jonchaies, cf. James Harley, "Formal Analysis of the Music of Iannis Xenakis by Means of Sonic Events: Recent Orchestral Works", in Présences de / Presences of Iannis Xenakis, op. cit., p. 41. 14 Cf. Bálint A. Varga, Conversations with Iannis Xenakis, London, Faber and Faber, 1996, p. 162. 15 Cf. Makis Solomos: A propos des premières oeuvres (1953-1969) de I. Xenakis. Pour une approche historique du phénomène de l'émergence du son, Ph.D., Paris, Université Paris 4, 1993; Iannis Xenakis, Mercuès, PO Editions, 1996, chapter 5. This study develops the concept of "sonority" and establishes a typology of Xenakis' sonorities.

Within the "axiomatic" tradition, which leans towards seeing a musical piece as composed sound, Xenakis plays not only a major role, but also a specific one. With him, to compose sound means to work it like a sculptor. Let's examine the graph with which he composed bars 52-59 of Pithoprakta 16 (figure 2). Xenakis first calculated, with the help of a Gaussian distribution, around one thousand glissandi 17 . But their distribution in time was made thanks to the graph. Thus, the global result -the sonority-is, according to Xenakis himself, a "plastic configuration of the sonic material" 18 . Now, let's observe more carefully the graph. We see "holes", empty regions of a whole portion of the register. We could compare this to filtering in electronic music. But we could also think to the work of a sculptor who carves a statue in a piece of stone. Xenakis often composed with graphs, at least until the end of the 1970s. Many of the sonorities, with which he was the first to experiment and which make his music so original, have been conceived thanks to graphs. One may think of glissandi, a typical Xenakis signature. In Xenakis' theories, a glissando is the general case of sounds with defined pitch. But it is important to notice that what allowed him to invent massive glissandi is the possibility to draw straight transversal lines in a graph where the two coordinates represent pitch and time. Syrmos (1959), a piece that is a kind of glissandi étude, was entirely composed with graphs. These graphs (see figure 3 for an example) reveal the visual imagination of Xenakis (and thus, his sonic imagination!), who defines different categories of glissandi (ascending, descending, crossed, convergent, divergent, in skewed surfaces). In the 1970s, it is also thanks to graphs that Xenakis invented a new kind of glissandi, the "Brownian movements", which are characterized by non-linearity. The technique of "arborescences" is also the result of graphs (see an example in figure 4). It means also that, while analyzing a Xenakis composition, we can use _ graphical transcriptions as a tool for analyzing its sonorities. Figure 5 presents my transcription of bars 291-303 of Terretektorh (1965-66), which shows the extraordinary "braids" that characterise important parts of this piece. 16 Xenakis drew two graphs for this part of Pithoprakta: cf. Benoît Gibson, "La théorie et l'oeuvre chez Xenakis : éléments pour une réflexion", Circuits vol. 5 n°2, 1994, p. 42-46. The one reproduced here is the final version. 17 1142 glissandi according to the historical article published in the Gravesaner Blätter ("Wahrscheinlichkeitstheorie und Musik", Gravesaner Blätter n°6, 1956, p. 31). According to Formalized Music, op. cit., p. 15, they are 1148. My analysis counted 1146. 18 Formalized Music, op. cit., p. 15.

Figure 2 .

 2 Figure 2. Pithoprakta: Xenakis' graph for bars 52-59 (Bibliothèque Nationale de France, Département Musique, Archives Xenakis)

Figure 3 .

 3 Figure 3. Syrmos: Xenakis' graph for bars 255-259 (Bibliothèque Nationale de France, Département Musique, Archives Xenakis) Figure 4. Erikhthon: Xenakis' graph (Bibliothèque Nationale de France, Département Musique, Archives Xenakis) Figure 5. Terretektorh: graphical transcription of bars 291-303 (Makis Solomos)

"The link does exist. It is the basis, the contents of sound and of the musical art that uses it. Music is made up of sound messages, of sound signals. Acoustic sounds are analysed in physico-mathematical equations (being that they are elastic vibrations of matter) that are measurable: intensity, colour, time (duration). When we say colour, we include pitch, harmonics, additive and subtractive sounds, undulations, etc. Consequently, sound is a quantitative entity But when sound goes into the ear, it becomes impression, sense, thus a qualitative entity. The psychophysics of music is not yet a science. The good composer could express the senses he wishes" 5 . This statement could seem to be a commonplace, but such is not the case. Xenakis does not give a traditional definition based on the idea that music is a "language" and, that therefore, sound is defined as raw material and music as the "art of sounds". He does not oppose a first level of articulation (sound) to a second one (music). Rather, he replaces this dichotomy with another one: quantitative/qualitative. The qualitative aspect of music is not totally defined -Xenakis talks about "impression, sense, thus a qualitative entity". On the other hand, his definition of the quantitative aspect is very clear: it is sound. Thus, sound is not defined as a first level of articulation, as raw material. Upheld as the link between all different musical traditions, it constitutes "the basis" of music: we could say then that sound is asserted as the foundation of music.

Iannis Xenakis, "Προβληµατα ελληνικης µουσικης συνθεσης", op. cit., p.

 4 Idem.5 Ibid., p. 44-45. 6 I am borrowing the comparison between the "crisis of foundations" in mathematic and the focus on sound in music from Jean-François Lyotard "L'obédience", InHarmoniques n°1, 1986, p. 112-115.