Colette Depeyre
email: colette.depeyre@dauphine.fr

Jean-Philippe Vergne
email: jvergne@ivey.uwo.ca

Richard Ivey

Explorer le déploiement de capacités dynamiques : le cas de cinq firmes de défense américaines face aux événements du 11 septembre

Keywords: Capacités dynamiques, Processus, Industrie de la défense, Etude de cas enchâssée Unpacking dynamic capability deployment: U.S. defense systems integrators' response to 9/11

Le papier vise à développer une contribution à la fois théorique et méthodologique au sein du courant des capacités dynamiques, qui s'intéresse à la façon dont les entreprises modifient leurs ressources et capacités opérationnelles pour répondre à des changements dans leur environnement. Les recherches comportent aujourd'hui un ensemble de propositions clefs mais buttent régulièrement sur d'importants problèmes : la réalisation d'études empiriques approfondies, l'exploration non seulement du contenu mais également des processus à l'oeuvre, la nécessité de distinguer entre différents types de changement. Prêtant attention à ces limites, nous proposons d'explorer le déploiement de capacités dynamiques au travers de trois briques : la reconnaissance que l'environnement a changé (détecter et apprécier), la décision de déployer une capacité dynamique (analyser et décider) et la réorchestration effective d'actifs de l'entreprise (mettre en oeuvre). Pour ce faire, nous présentons une étude de cas longitudinale et enchâssée des principaux intégrateurs de systèmes de défense américains entre 1998 et 2007, étudiant la façon dont ils ont chacun répondu aux événements du 11 septembre. Des séries de données relatives aux discours et à l'orchestration d'actifs interne et externe de cinq entreprises (Boeing, General Dynamics, Lockheed Martin, Northrop Grumman and Raytheon) ont été collectées et organisées. Des outils de mesure sont proposés afin d'analyser, dans le temps et de manière comparative entre les firmes, l'attention des dirigeants aux changements de l'environnement, les changements décidés au niveau de la firme et la façon dont ces changements sont mis en oeuvre à différents niveaux.

INTRODUCTION

The dynamic capability view (DCV) examines how firms alter their resources and operational capabilities when they respond to changes in their environment [START_REF] Eisenhardt | Dynamic Capabilities: What Are They?[END_REF][START_REF] Helfat | Dynamic Capabilities. Understanding Strategic Change in Organizations[END_REF][START_REF] Teece | Dynamic capabilities and strategic management[END_REF][START_REF] Zollo | Deliberate Learning and the Evolution of Dynamic Capabilities[END_REF]. Dynamic capabilities represent "the Holy Grail of strategic management" (Helfat & Peteraf, 2009: 91) as they promise to explain why and how certain firms manage to sustain a competitive advantage despite profound changes in the industries wherein they operate. While still in its infancy [START_REF] Di Stefano | Dynamic capabilities deconstructedz : a bibliographic investigation into the origins, development, and future directions of the research domain[END_REF], DCV research has already converged around a set of core propositions highlighted in recent reviews. Because of imperfect market factor conditions and heterogeneous management skills, firms vary in their ability to control and orchestrate resources and capabilities, especially in dynamic environments. In this context, firms that successfully deploy dynamic capabilities are able to sustain their competitive advantage [START_REF] Teece | Explicating Dynamic Capabilities: the Nature and Microfoundations of (sustainable) enterprise performance[END_REF], understood as the ability to create more value than competition [START_REF] Peteraf | Unraveling the resource-based tangle[END_REF]. How persistent this advantage is depends on barriers to imitation such as time compression diseconomies, asset complementarities, tacit knowledge and causal ambiguity [START_REF] Leiblein | What Do Resource-and Capability-Based Theories Propose[END_REF].

Besides agreement on these core ideas, there is also increasing convergence across scholars that the DCV suffers from important limitations. Recent reviews of the DCV literature share three key observations regarding the evolution of the research stream over the last 15 years (Ambrosini & Bowman, 2009;[START_REF] Arend | Assessing the dynamic capabilities view: spare change, everyone?[END_REF][START_REF] Di Stefano | Dynamic capabilities deconstructedz : a bibliographic investigation into the origins, development, and future directions of the research domain[END_REF][START_REF] Easterby-Smith | Dynamic Capabilities: Current Debates and Future Directions[END_REF][START_REF] Leiblein | What Do Resource-and Capability-Based Theories Propose[END_REF]. First, there is wide agreement that more empirical work is needed to operationalize DCV constructs such as 'reconfiguring', 'sensing', or 'leveraging'. This task is challenging methodologically and it is still unclear what type of data researchers need to gather to be able to measure such intangible notions. Second, dynamic capabilities are not synonymous with sustained superior performanceotherwise the DCV would verge on tautology. This acknowledgment provides scholars with the opportunity to explore two distinct processes: the one that drives firms to deploy DC in the first place and the one that makes deployed DC drive sustained superior performance. While the latter process, which connects DC to performance, has already been studied with some depth [START_REF] Moliterno | Firm performance, rent appropriation, and the strategic resource divestment capability[END_REF][START_REF] Pavlou | Understanding the Elusive Black Box of Dynamic Capabilities[END_REF], the former, which explains why firms would decide to deploy DC in the first place, has received little scholarly attention. Third, DC have been conceptualized as a means to respond to change in firms' environment, yet the very notion of change has remained very vague in the DCV literature. A firm without DC may decide to keep changing in ways consistent with an outdated strategic plan while ignoring recent changes in its environment that would require a new direction [START_REF] Arend | Assessing the dynamic capabilities view: spare change, everyone?[END_REF]. Conversely, a firm with DC may decide not to respond to changes in the environment because it estimates that the cost of doing so would offset the benefits (i.e., that firm has the capability to alter its resource base but has decided not to use it). Alternatively, a firm (with or without DC) may just get lucky and change in ways that coincidentally happen to be consistent with changes in its environment [START_REF] Denrell | Random Walks and Sustained Competitive Advantage[END_REF]. In other words, observing the presence or absence of change outside and inside the firm is not sufficient to provide evidence that dynamic capabilities are or are not at work.

It is this paper's endeavor to contribute to the DCV literature whileand bybeing particularly attentive to its past limitations. To operationalize fine-grained DCV constructs such as 'sensing', one needs to delve deep into how top management envisions a firm's position in its environment [START_REF] Augier | Dynamic Capabilities and the Role of Managers in Business Strategy and Economic Performance[END_REF]. To distinguish between different types of change, one needs to assess them in the light of a firm's recent trajectory and of its top management's intentions. This implies paying particular attention to how top management processes and analyzes new information about the environment before decisions are made to deploy (or not) the firm's dynamic capabilities in response to change. By doing this, scholars would be able to focus their investigation on phenomena that are observable and that meaningfully connect the various components of the DCV. Rather than examining the relationship between DC and (superior) performance, this paper thus proposes to investigate the process of DC deployment, from the recognition that the environment has changed to the decision to deploy DC, and to the implementation of asset re-orchestration.

To achieve this objective, we conduct an in-depth longitudinal case study of the U.S. defense systems integrators industry between 1998 and 2007. Five defense giants, namely Boeing, General Dynamics, Lockheed Martin, Northrop Grumman and Raytheon, compete for the major defense systems integration contracts of the Pentagon. In 2001, the 9/11 attacks triggered a massive overhaul of the U.S. military doctrine that dramatically modified the industry landscape. Immediately after the attacks, the five firms' largest customer, the Pentagon, implemented a new strategy for the U.S. armed forces that puts emphasis on "network-centric warfare" (NCW) and the ability to integrate all national defense capabilities within one single system of systems (Quadrennial Defense Review Report, U.S. Department of Defense, 2001). This profound rethinking of national defense required the five U.S. defense systems integrators to respond to an industry-wide turbulence that can be considered largely exogenous, because it was triggered by the unexpected 9/11 attacks. The goal of our empirical investigation is to answer the following question: What is the process leading to DC deployment in response to a sudden and massive change in the environment?

We do not have any preconceived ideas about which of the five firms did or did not deploy DC. Because past literature has largely overlooked the process leading to DC deployment, this paper does not seek to test logically derived hypotheses, but rather to explore that process in a controlled setting. We expect our first contribution to the DCV literature to be methodological. We will analyze top management discourse over time as well as how firms actually changed at multiple levels to reconnect the 'sensing' and the 'reconfiguring' dimensions of the DCVand we will rely on a set of fine-grained measures to capture these notions. We expect our second contribution to be theoretical, as we will build on our empirical findings to explore the process of DC deployment.

The remainder of the paper is organized as follows. We first review the DCV literature to highlight the main characteristics of DC and how they relate to observable phenomena. We then introduce our empirical setting, describe our data collection routines, and explain how we used the data to track over time, for each of the five firms, a set of observable variables that underlie the DC deployment process (or lack thereof). We then present the main findings and discuss the various trajectories taken by the five defense systems integrators after 9/11 in light of recent performance metrics. Based on these findings, we discuss the process of DC deployment and emphasize our contributions to extant DCV literature as well as some limitations.

UNPACKING AND OBSERVING DYNAMIC CAPABILITIES

DC is defined as "the capacity to renew competences so as to achieve congruence with the changing business environment" (Teece et al., 1997: 515). This definition has had tremendous impact on the scholarly and business communities, yet it remains challenging for researchers when it comes to empirical investigation: how, indeed, can we observe a "capacity"? A capacity may or may not be used, so it may or may not have observable outcomes [START_REF] Easterby-Smith | Dynamic Capabilities: Current Debates and Future Directions[END_REF][START_REF] Godfrey | The Problem of Unobservables in Strategic Management Research[END_REF][START_REF] Loasby | Capabilities and strategy: problems and prospects[END_REF]. What's more, that capacity is defined as being intentional and purposeful, namely, management is aware that they are using the capacity when they do, and they do so for a reason (i.e., to achieve congruence with a changing environment). In a way, inferring the existence of such a capacity from the observation of firms may be as tricky as trying to infer whether an individual is capable of running a marathon without ever seeing her run. If we limit our investigations to observing marathon events, a lot of people that are actually capable of running one (but do not run one) will remain outside our radar. And if we simply assume that all individuals who start running a marathon will pass the finish line, we may wrongly infer that any form of running signals the capacity to run a marathon until the end. Put differently, the question we ask in this section is: How can scholars move from defining DC as a capacity to actually observing DC deployment?

THREE BUILDING BLOCKS TO OBSERVE DC DEPLOYMENT

DC is about changing a firm's existing resources to respond to change in the environment.

However, observing change at the firm level is not enough to infer the existence of DC.

Change can occur for a variety of reasons and managers are not necessarily aware that change is happening. For example, organizational inertia can erode the effectiveness of firm routines without employees noticing it. Perceiving the need for DC deployment requires two conditions. First, the firm must sense that change will be required in the near future. In fact, underlying the DC construct is the idea that firms are not equally capable of monitoring their environment adequately to sense that need for change [START_REF] Schreyögg | How dynamic can organizational capabilities be? Towards a dual-process model of capability dynamization[END_REF].

More specifically, the need for change must be perceived at a high level within the firm (i.e., top management), otherwise the information obtained about the environment will fail to translate into actionable strategic moves [START_REF] Narayanan | Building Organizational and Scientific Platforms in the Pharmaceutical Industry: A Process Perspective on the Development of Dynamic Capabilities[END_REF]. As [START_REF] Teece | Explicating Dynamic Capabilities: the Nature and Microfoundations of (sustainable) enterprise performance[END_REF]Teece ( : 1346) ) puts it, "dynamic capabilities reside in large measure with the enterprise's top management team". At the very beginning of the DC deployment process, we thus expect to see top management devote particular attention to what is going on in the firm's environment.

Sensing change in the environment need not result in making the decision to change the firm.

Managers may decide to stay put if they estimate that the firm's resource base is already in line with what the environment will look like in the future. Alternatively, they may recognize misalignment but still estimate that the cost of aligning firm resources will be higher than the benefits derived from it [START_REF] Zollo | Deliberate Learning and the Evolution of Dynamic Capabilities[END_REF]. Thus, even once top management has sensed change in the environment, they may still decide to not alter the firm's resource base.

Furthermore, even when they decide to do so, they may still fail to implement the proposed change strategies. The organization may be too inert, or a significant portion of its employees may resist change. If the proposed change strategy involves acquiring new resources or capabilities outside the firm, top management is still constrained by the scarcity of such assets [START_REF] Lippman | Uncertain imitability: An analysis of interfirm differences in efficiency under competition[END_REF] if they are unavailable or too expensive on the corporate market, then change will not be implemented as proposed. In other words, to investigate DC deployment empirically, we should gather data on the following sequence.

Figure 1 -The building blocks of DC deployment

The next section will argue that each building block in the sequence can be observed if scholars gather the right data, and we will draw on this discussion to introduce the data collection and measurement section. Importantly, each building block implies a significant dose of intentional behavior, i.e., DC deployment, thus defined, cannot just be a lucky coincidence.

DIFFERENT TYPES OF DYNAMIC FIRM-LEVEL CHANGE

Observing firm-level change may be more difficult than it seems. As understood from a DC perspective, firm-level change entails a purposeful alteration of resources and/or operational capabilities [START_REF] Helfat | Dynamic Capabilities. Understanding Strategic Change in Organizations[END_REF]. Such alteration can be visible at various levels in the firm and can manifest itself in different ways. For example, it can happen within or across strategic business units (SBUs), and it can imply reshuffling firm resources internally (e.g., management) or integrating new external resources (e.g., a recently acquired patent portfolio).

In addition, the alteration can be more or less extensive [START_REF] Ambrosini | Dynamic Capabilities: An Exploration of How Firms Renew Their Resource Base[END_REF]. At the very least, it implies leveraging existing resources or operational capabilities to use them in the context of new activities or in areas of the firm where they were not used previously (e.g., replicating a competitive intelligence capability across SBUs). The alteration can be more significant and involve adjusting existing resources and capabilities (e.g., upgrade of a core proprietary technology). Adjusting is typically driven by management recognition of the existence of a gap between the current effectiveness of a resource and its potential effectiveness. Both leveraging and adjusting, still, imply a continuous form of change, whereby the past and the future states of the organization remain very similar, owing to the fact that no resource or capability previously unknown has been introduced. A more radical form of change occurs when new resources or capabilities are added to the firm, either because they are being developed internally or integrated within the firm following an external acquisition, an alliance or a joint-venture agreement. One can recognize that firms go beyond leveraging and adjusting when change involves the integration of new resources or

Monitoring and sensing

Analyzing and deciding Implementing capabilities that indisputably add something new to what a firm can do, at least at some level (e.g., design, production, advertising, collaborating, customer service, new area of business).

Finally, we should note that firms, especially large ones, typically implement a dose of resource-level change on a continuous basis. For example, some MNCs acquire multiple companies every year as part of their baseline growth strategy, rather than as a response to exogenous change in the environment. Thus, it seems essential to look at variations in rates of resource renewal over time to distinguish between strategy-as-usual and genuine DC deployment. In other words, cross-firm comparison is not enough to tell which firms deploy DC and which do not. A more robust research design will likely include a longitudinal dimension on top of a cross-sectional component [START_REF] Leiblein | What Do Resource-and Capability-Based Theories Propose[END_REF]) so as to analyze data in light of preceding trajectories.

CASE SELECTION AND METHOD

The U.S. defense industry is rarely a matter of study in the area of strategic management.

Interesting exceptions include [START_REF] Dial | Incentives, downsizing, and value creation at General Dynamics[END_REF] on General Dynamics' radical strategic change in the early 90s, [START_REF] Anand | Asset redeployment, acquisitions and corporate strategy in declining industries[END_REF] and [START_REF] Anand | Redeployment of Corporate Resources: A Study of Acquisition Strategies in the US Defense Industries, 1978-1996[END_REF] on acquisition strategies until 1996, or [START_REF] Baum | Outsourcing War: Private Military Companies and Commandand-Control Capabilities after the Cold War[END_REF] on the increasing role of private military companies, but overall our knowledge of this industry remains superficial. With annual defense spending around US$1.5 trillion globally and the U.S. representing half of it, this industry is huge and quite concentrated geographically. Twelve out of the fifteen largest defense contractors worldwide are American firms (SIPRI, 2009).

AN EMBEDDED CASE STUDY OF US DEFENSE SYSTEMS INTEGRATORS' RESPONSE TO 9/11

The U.S. defense industry proved relevant to collect rich and various process data about a few firms, longitudinally, to understand DC deployment in an embedded case study setting [START_REF] Yin | Case Study Research: Design and Methods[END_REF]. The 9/11 attacks represent an opportunity to study the response to a massive exogenous change and examine whether DC were deployed to deal with it.

The Big Five (the subunits of analysis)

In the U.S., five firms have dominated the industry since the mid-1990s: Boeing (BO),

Lockheed Martin (LM), Raytheon (RA), General Dynamics (GD) and Northrop Grumman (NG). These five firms, on which we decided to focus, differ significantly from other industry players because they are systems integrators (also known as prime contractors) for the primary defense systems of the U.S. armed forces, such as bombers, submarines, destroyers, missiles, radars, battle tanks or transport vehicles. By contrast, other defense contractors only act as subcontractors for major programs or as prime contractors for much smaller projects such as aircraft engines and other system parts. In 2009, the average military revenues for the "Big Five" were US$ 29 billion, while the sixth largest U.S. defense contractor, L-3

Communications, was far behind with US$ 13 billion worth of military sales. In 1998, 84% of the 67 main defense programs overviewed by the Government Accountability Office were led by at least one of the Big Five (GAO-08-467SP, 2008). The Big Five are responsible for all the major evolutions of the military equipment used by the U.S. armed forces (Army, Navy, Air Force, Special Forces, Rangers, National Guard, and Marines). They work very closely with their largest customer, the Pentagon, which provides guidelines regarding the future of the armed forces in relation to military doctrine, geopolitics, technology, and desired capabilities. At all levels, the Pentagon's vision has gone through major change, not only with the end of the Cold War but even more so after 9/11.

✦ ✦ ✦ ✦ Unmanned Vehicles ✦ ✦ ✦ ✦ ✦ Space Sytems ✦ ✦ ✦ ✦ ✦ Artillery & Missiles ✦ ✦ ✦ ✦ ✦ Surface Ships & Submarines ✦ ✦ ✦ ✦ Military Vehicles ✦ Defense Electronics ✦ ✦ ✦ ✦ ✦

From the Cold War to 9/11 and the rise of NCW (the context)

The fall of the Soviet bloc led to a rethinking of U.S. military strategy. U.S. forces had from now on to be able to fight simultaneously two major regional conflicts in the world. Communications, Intelligence, Surveillance and Reconnaissance) were also starting to be mentioned as a way to redirect the field of defense electronics. At the end of the 90s, doctrine renewal was on the way but with no clear picture of how the "integrated system of systems" that the 1997 report was envisioning would actually translate into new military equipment.

There was a controversy among defense firms about what this techno-organizational change meant. Did the design and production of these systems of systems involve a shift in the way they were running their business? If such a shift should take place, what would it imply? This period of doubts will be the focus of the first sequence of our case study.

Then, the events of 9/11 sadly gave substance to the new threats that the U.S. were facing and shed light on several gaps in national defense capabilities. 9/11 acted as a trigger in the RMA. in 2001 and by 7,9% and 5,7% in 2002. This period of growth will be the focus of the second sequence of our case study. The rise to prominence of the NCW concept is visible in Figure 3 below, which shows on the right-hand scale the increase in the proportion of books citing the NCW concept as registered in the Google Ngram search engine. In other words, while the NCW revolution was discussed prior to 9/11, the terrorist attacks represented an exogenous shock that suddenly made NCW highly salient to all defense industry stakeholders. For the Big Five, the change was too massive and important to miss, and appropriate strategic responses were required.

A cross-sectional, longitudinal case study design and a quasi-natural experiment

Our embedded case study is thus designed with a longitudinal perspective, so as to focus on the process of DC deployment (or absence thereof) in a controlled, quasi-experimental setting, where 9/11 represents an exogenous shock that permits before/after comparison of firm behavior. The temporal bracketing [START_REF] Langley | Strategies for theorizing from process data[END_REF] is neither theoretical nor arbitrary. The first sequence starts in 1998, a pivotal year when the post Cold War consolidation wave eventually reached an end with the cancellation of the planned merger between LM and NG.

The timeframe allows focusing on the period before 9/11, with some changes that were starting to emerge, and the period after, when these changes crystallized. 9/11 both builds on trends that were going on and acts as a trigger for change. Each firm's trajectory will be studied in detail while keeping in mind this industry-wide pace.

The design also allows for cross-case comparison [START_REF] Eisenhardt | Building theories from case study research[END_REF] between the five firms while holding constant their environment, as they compete against one another in the same industry and have to face similar changes in market conditions. The five firms are both similar and dissimilar enough to allow for a meaningful and rich comparison (see Table 1 above) and the fact that it is an embedded case studynot a multiple-case oneprovides us with many insights regarding how the evolution of competitive conditions interacts with the evolution of each firm's capabilities.

DATA COLLECTION

Several sources of information were identified as consistent sets of data across firms and over time. Our goal was to collect rich data to design measures that capture the three building blocks of DC deployment outlined above in Figure 1.

First, we gathered 50 letters to shareholders to analyze the strategic discourse of top management (in the firms' annual reports from 1998 to 2007). Such letters are a meaningful way to capture managerial attention, particularly for comparison across companies and in longitudinal designs [START_REF] Kaplan | Cognition, capabilities, and incentives: Assessing firm response to the fiber-optic revolution[END_REF][START_REF] Pollach | Taming Textual Data: The Contribution of Corpus Linguistics to Computer-Aided Text Analysis[END_REF]. The letters include thematic emphases and descriptions by firms of their surrounding environment and of their strategic orientation and actions. We also gathered additional statements of top managers as reported in press releases and newspaper articles, collected in relation to punctual actions such as a new strategic plan, an acquisition, a reorganization or a winning bid.

Then, to put these discourses into perspectiveshould they be decoupled from actionsand study the firms' actions in more detail, we gathered extensive data on internal and external asset re-orchestration (e.g., reorganization of business units, renewal of product lines, acquisitions and divestitures, alliances). These data were obtained from annual reports, industry reviews by external stakeholders, two specialized databases (Mergent Database and Infobase, a private competitive intelligence provider based in Washington, D.C.). In addition,

we collected commentaries on corporate activity by external actors such as financial analysts, defense experts and government officials, to look for potentially diverging interpretations of firm strategies. These data come from business newspapers and specialized press outlets such as Defense Daily, Jane's Defence, and Defense News.

Finally, all these archival data were complemented with 21 semi-structured interviews, which were conducted in the U.S. and in Europe with company officials, defense industry experts and government representatives. We transcribed the interview material and used it to validate our interpretation of the findings. Table 2 summarizes the main sources and their use to trace the discourses and assets orchestration of the five firms. Table 2 distinguishes between main and complementary sources of data, because several sources were often combined to gather as much information as possible. For example, financial statements or messages to shareholders allowed detecting reorganizations of business units, but to better grasp the content and context of these reorganizations, complementary information was then collected from press releases, newspapers' articles, analysts' reports and sometimes interviews. In the same way, data on mergers and acquisitions were compiled from specialized databases and complementary data were found in annual reports and newspapers. The combination of several sources also allowed for triangulation.

Table 2 -Series of data and sources of information

DATA REDUCTION AND MEASURES

Our goal was not only to gather rich data but also to restitute them with richness [START_REF] Weick | The generative properties of richness[END_REF] and rigor [START_REF] Gibbert | What passes as a rigorous case study?[END_REF]. To examine the process of DC deployment over time and across firms, we constructed a series of measures that capture the most important dimensions of DC identified in the literature review above. Since we are primarily interested in firm response (or lack thereof) to industry-wide change following 9/11, our research design emphasizes the observation of cross-firm differences in behavior over time. Put differently, we are looking for variance in the way firms alter their behavior as a reaction to the changes triggered by the 9/11 attacks. Thus, our case study design is not unlike a "differences-in-differences" model wherein firm-specific unobserved heterogeneity is controlled for by looking at the first differences of the model's independent variables, which is made possible by a quasi-natural experiment setting wherein 9/11 represents an exogenous shock.

Top management attention to change in the environment

The first stage of the DC deployment process involves attentional mechanisms (Figure 1). To capture the extent of top management "sensing" [START_REF] Teece | Explicating Dynamic Capabilities: the Nature and Microfoundations of (sustainable) enterprise performance[END_REF] and "monitoring" [START_REF] Schreyögg | How dynamic can organizational capabilities be? Towards a dual-process model of capability dynamization[END_REF], we content-analyzed all the letters to shareholders opening the five firms' annual reports over the period of study (n=50). Such data have been used in prior works on managerial attention as they readily express what top management deem important and which issues they decide to attend to [START_REF] Barr | Adapting to unfamiliar environmental events: a look at the evolution of interpretation and its role in strategic change[END_REF][START_REF] Eggers | Cognition and renewal: comparing CEO and organizational effects on incumbent adaptation to technical change[END_REF][START_REF] Fiol | Explaining strategic alliance in the chemical industry[END_REF]. In each letter, we calculated the proportion of text devoted to discussing how the defense industry is changing. By looking at proportions, we control for heterogeneity in letters' length and are able to observe how much attention top management devotes to various topics in relative terms. We paid particular attention to the context surrounding the occurrence of words describing the new industry trend, such as "revolution in military affairs (RMA)", "integrated systems", "systems of systems", "network-centric warfare (NCW)", or "cyberspace revolution" (e.g., "I expect each of our sectors to play a key role in this cyberspace revolution -a revolution in which wars will be won not only by the fastest and most capable aircraft, but also by the fastest computer chip an the smartest, most robust software." -NG 1999).

Top management discourse on firm-level change

Using a similar coding procedure, we calculated the proportion of text devoted to firm-level change, while distinguishing between four dimensions consistent with the literature review above. This measure corresponds to the second stage of the DC deployment process (Figure 1) and captures purposeful decision-making seeking to "renew competences" (Teece et al., 1997: 515). The first dimension includes discourse indicating management decision to leverage existing resources and operational capabilities across the firm (e.g., "By creating a new business area, Integrated Systems & Solutions, we are leveraging technical expertise across the breadth of Lockheed Martin to address our customers' requirements for highly integrated, networked solutions" -LM 2003). The second dimension includes discourse on adjusting existing resources and operational capabilities to improve their effectiveness (e.g., "We have flattened the organizational structure to improve controls and increase organizational simplicity" -RA 1999). The third dimension is about adding new resources or capabilities to the firm through external acquisitions, alliances or joint-venture agreements (e.g., "We have made acquisitions that broadened our product lines and increased our portfolio of programs and technologies -all in anticipation of our customers' evolving requirements" -GD 1998). The fourth dimension is also about adding new resources and capabilities, but this time by developing them internally (e.g., "We created two brand-new businesses in 2000. (…) 'Markets' is an active concept. The best companies do more than respond to market conditions. They shape the markets of tomorrow" -BO 2000).

Resource and capability renewal

The third stage of the DC deployment process consists in renewing firm resources and operational capabilities "to achieve congruence with the changing business environment" (Teece et al., 1997: 515). Asset renewal includes a variety of components, such as asset acquisition and integration, internal reorganization (e.g., a SBU is dismantled and its assets are spread across other SBUs), scale or scope adjustments (e.g., non-profitable units within an existing SBU are divested), or asset recombination (e.g., a new SBU is created from a combination of assets previously spread across other SBUs). To examine asset renewal, we decided to present the most significant changes implemented by firms over the period of study in a visual way. Figure 2

INTER-FIRM AND LONGITUDINAL COMPARATIVE FINDINGS

Findings can be looked at in complementary ways. This section first reports, for each of the three building blocks, the main similarities and differences over time and across firms and spots some potential gaps between them. We then propose a grouping of firms in relation to DC deployment.

Observing the three building blocks, over time and across firms

First, regarding top management attention as captured in letters to shareholders (Figure 3), comparative findings show that GD and NG are the two firms that start referring early on to ongoing changes in military doctrine (i.e., before 9/11). For example, in its 1998 annual report Northrop Grumman states: "We recognized early this decade that we may be entering a period of revolutionary change in military affairs, propelled by the doctrinal implications of technologies ranging from stealth and precision targeting to advanced situation awareness and battle management capabilities. Should such a 'revolution in military affairs' become a central tenet of U.S. defense planning, our business focus on sensors, electronic warfare

" # $ # # # $ $ $ $ $ $ $ # # # # # # $ $ $ " # # # #
systems, space, and information technologies will reinforce Northrop Grumman's competitive position well into the next century." Or General Dynamics emphasizes in 1998 the importance of "battlefield digitization skills" and in 1999 its "growing expertise in total battlespace information management systems that are key to military superiority in the 21st century". In 1998, no other firm makes reference to these types of changes in their letters to shareholders.

There is then a peak in 2001 for all firms in their attention to change in the industry as well as increasing references in the second sequence compared to the pre-9/11 period. As shown by our proxy for societal attention, from 2002 NCW becomes a popular term.

NCW books BO GD LM NG RA 0 0,1 0,2 0,3 0,4 BO1 BO2 GD1 GD2 LM1 LM2 NG1 NG2 RA1 RA2 Managerial attention
Discourse on firm-level change befor e (1) and after (2) 9/1 1 developing ext developing int leveraging adjusting (e.g. "We began 2000 with firm commitments to serve customers better, improve financial performance, manage for cash, drive operational improvements, and improve planning quality" -LM 2000; "Our businesses still must improve processes and reduce complexity; we are on the right track, but it will take time" -RA 1999). Also, while BO and RA always talk more about developing new capabilities internally rather than externally, it is the reverse for GD, LM and NG, which more extensively report about mergers and acquisitions.

Third, regarding assets renewal (Figure 2), the evolution of GD departs from the other ones in that it is strikingly stable over the period. Two SBUs (Information Systems and Technologies, Aerospace) are set up in 1998 and 1999 through a series of acquisitions, without impacting the organization of the two other SBUs (Marine Systems, Combat Systems), and from then on the four SBUs remain stable until the end of the period. It does not mean that the content of each SBU does not evolveconversely, two of them are deeply reinforced through acquisitionsbut there is no asset re-orchestration between SBUs over the period of study.

The evolution of NG is similar to the one of GD in that: new SBUs are created through external assets, in 2001 and 2002; other SBUs are maintained through the whole period (the only divested SBU comes from side assets acquired with Litton Industries and that were rapidly spotted as outside of the range of the firm's activities); and there are no reorchestration between SBUs (only some activities that are redirected from one unit to another but without shaking the overall organization of SBUs). In sum, GD and NG have the most stable trajectories.

The evolution of NG is still slightly different from that of GD: because a central simulation lab appears from 2002, because a new SBU is internally set up in 2006 (for Technical Services) and because some SBUs are grouped under the same heading also in 2006.

However, these changes remain minor when compared to the trajectories of BO, LM and RA. The latter indeed have a higher degree of internal asset re-orchestration in that they each engage at least twice in a major overhaul of their SBUs' breakdown with an adjustment of the changes overtime (the evolution of BO and LM even show some backward moveswith for example the failure of Lockheed Martin Global Telecommunications or the re-gathering of Network and Space Systems at Boeingwhile RA, after a massive SBUs overhaul in 2002, remained more stable).

In relation to the exogenous shock under study, it can be noticed that 2002 is the year with the largest amount of re-orchestrations between SBUs. The figures also show the progressive highlighting of central simulation laboratories for almost all the firms, except GD. BO starts in 2000, NG follows in 2002, LM in 2003and RA in 2005. Regarding external asset re-orchestration, divestitures are globally more frequent during the first sequence, while mergers and acquisitions are increasingly present during the second sequence. However there are some discrepancies between firms: until 2002, while BO, LM and RA are majorly divesting assets, GD and NG are busy acquiring businesses. Moreover NG, after missing major bids in the 90s, is the only firm that gets here involved into major acquisitions that fundamentally reshape its portfolio (adding naval and space assets) when Litton, Newport News Shipbuilding and TRW are bought in 2001 and 2002. As for more minor acquisitions, LM and RA are the two firms that significantly increase their number after 2002.

To finish with this first exploration of our findings, we can note that it is striking that GD is among the firms that talks the most about change in the environment and at the firm-level, while showing very few changes in terms of internal asset re-orchestration. Over the period many assets are bought and new lines of business appear (aircraft, space), but without shaking the overall SBUs' organization and with no mention of any central simulation lab (while it is a key asset that is put forward by the four other firms for the design of network-centric systems). To a lesser extent but still significantly, NG is also early in talking about change but does not show as much change at the level of SBUs when compared to BO, LM and RA.

Proposition of an induced typology

If we now go one step further in our analysis, we can spot from these findings different types in DC deployment. Regarding the first building block of DC deployment (sensing and monitoring), GD and NG stand as the two actors that somehow anticipate the industry-wide change while BO, LM and RA adopt a more reactive behavior. Regarding the second building block (analyzing and deciding), GD and NG also stand out in that, during the first sequence, they talk more about developing their business through external assets, when the three other firms insist on adjusting their assets, by comparison with the second sequence. As for the third building block (implementation of asset re-orchestration), the two sets of firms can also be opposed in that GD and NG are more active during the first sequence, making use of external renewal of assets, while BO, LM and RA are more intensive in their actions during the second sequence, and with more internal overhaul (during the first sequence, there are some adjustments in their assets but they do not seem to be well adapted yet as they are followed by new changes after 2001, or to put it another way, the change at work during the first sequence stand more as a consequence of the past than as an anticipation of new patterns). We can also note that LM shows more delay in its post-9/11 reaction and is more fumbling.

Considering the overall process of DC deployment, we could thus infer that GD and NG deployed DC by anticipation, BO and RA by reaction, and that LM belatedly attempted to deploy DC but failed to some extent to do so. However, given the noticed discrepancies between top management attention to change and the subsequent nature of asset reorchestration (especially for GD), we can wonder whether an anticipated deployment leads to more continuous and perhaps less extensive change in a firm's capabilities.

ROBUSTNESS OF THE FINDINGS

Performance outcomes

Our case study led us to infer the existence of three distinct groups in our sample when it comes to DC deployment (or lack thereof). Because the DC literature is premised on a causal relationship between DC and performance, we checked whether a similar grouping of firms emerged from performance data. We chose to look at yearly operational margin, which is the best indicator of performance in our context. There have been several sudden variations across firms, at different points in time, in the way asset values are recorded in the companies' balance sheets, which makes ROA a poor candidate to compare firms over time. ROE is sensitive the capital structure of firms, which in the defense industry depends on multiple factors, including the type of segments and customers served by each firm. ROI (return on operating investment) was consistently available in databases, yet the nature of the contractual relationships between the U.S. government and defense contractors makes it difficult to track which part of fixed defense program cost is supported by the State and with which time horizon. Operating margins, on the other hand, readily capture the capacity of firms to earn a living given all the contractual conditions that are fixed in advance by the customer. In addition, it is the best measure to track over time the firms' capacity to contain coststhe primary source of competitive advantage in the industry since the fall of the USSR. In fact, the five firms discuss at length the evolution of operating margins in their annual reports, as most industry experts and stakeholders use it as the most informative indicator of firm performance. Figure 4 As visible on the graph above, NG and GD stand out over the whole period. They consistently outperform competition and their operating margins have a lower variance. While patterns emerge less clearly from the three other curves, LM's operating margin hits a minimum in 2002, consistent with the fact that the firm was the least prepared to face a changing environment. On the other hand, RA and BO are able to maintain a high operating margin in 2002, as they respond to change by deploying a DC, yet their lack of anticipation in the previous period seems to have consequences later on as operating margins decrease significantly for both firms in 2003. Even if the nature of the data presented here does not allow us to infer any causal relationship between DC deployment and performance, the performance patterns are partly consistent with the typology of DC deployment proposed above. At the very least, nothing in the performance patterns seems to be at odds with the paper's findingsand they appear consistent with the broader DC literature.

Cluster analysis

Based on our case study, we inferred inductively a typology of DC deployment strategies. It adds to prior developments in the DC literature by unpacking the process of DC deployment and by shedding new light on the trade-offs between deployment and non-deployment, and between deployment of an "anticipation" versus a "response" DC. However, despite our important efforts aimed at triangulating our data and validating our interpretation across multiple sources at three levels of the DC deployment process, our typology is still a product of our own interpretive schemes. To assess the extent to which the latter influence the structure of the typology, we decided to compile a table summarizing all the quantified data pertaining to DC deployment for the five firms. For both periods (i.e., before and after 9/11), 1998-2000 (before), 2001-2002 (during), and 2003-2006 (after). Finally, we included the mean operating margins before and after 9/11 in the table. We then run a hierarchical cluster analysis on the 17 variables to obtain a typology of the five firms using the Ward's distance method. The Figure 5 below displays the results as a dendrogram.

Figure 5 -Dendrogram using Ward Linkage

The firms are grouped in three categories that are consistent with our inductively derived typology: BO and RA are grouped together, and so are NG and GD, while LM is isolated until the cluster analysis forces the existence of exactly two categories of firms, in which case LM appears closer to (BO, RA) than to (NG, GD). This is consistent with the idea that LM, BO and RA adopted a "wait and see" strategy, while NG and GD anticipated change in their environment early on.

CONCLUDING DISCUSSION

As outlined in the introduction, we can discuss our case-study analysis at two levels.

Our first contribution is methodological. We analyzed, over time and across firms, top management discourse on the environment and on firm-level change, as well as how firms actually changed at multiple levels, to reconnect the different dimensions of DC deployment.

We relied on a set of fine-grained measures to capture these three building blocks that we identified from the literature. The collection of data on discourses and actions, their translation into three constructs and their visual representation in Figures 2 and 3 allowed us to track down the process of DC deployment (or lack thereof) for each firm. The longitudinal and comparative perspective was essential to interpret our data and assess the presence of change for every firm.

It is interesting to notice that the observed data does not always show a systematic process whereby every deployment would imply first, sensing change in the environment, second, deciding of the type of change that is needed and third, implementing it. The firms' trajectories can be much more fumbling: we mentioned in our literature review that a firm can sense change in the environment but decide not to change, or it can decide to change but fail to do so; also, assets can be re-orchestrated without any explicit discourse preceding it and top management can retroactively relate it to change in the environment and at the firm-level. The analysis of these vacillations was beyond the scope of our analysis. We focused on the definition of appropriate measures to track the three building blocks of DC deployment.

Further analysis would then be required to explore within-firm autocorrelation across the three building blocks. We could also explore some patterns in how DC can unfold: in our case, when a new SBU is created it is most of time supported (even sometime triggered) by the acquisition of external assets; the creation of non-reporting SBUs (signaling uncertainty) can pave the way for divestitures or on the contrary catalyze the development of new initiatives; discourse on leveraging can refer to a circulation of assets between SBUs or to a deeper re-orchestration of SBUs; it can also follow a major merger or acquisition that requires a reorganization of assets within the firm, etc.

Our second contribution is theoretical. We proposed to explore the process of DC deployment by tracking three building blocks. Our model follows [START_REF] Teece | Explicating Dynamic Capabilities: the Nature and Microfoundations of (sustainable) enterprise performance[END_REF] and [START_REF] Loasby | Capabilities and strategy: problems and prospects[END_REF] 1 in that it insists on the conjectures that are formulated by the firms. When top managers talk about change in the environment and at the firm level and undertake assets re-orchestration, they formulate and re-formulate conjectures about their firm's capabilities. Thereby DC progressively deploy. Our empirical findings allowed us to distinguish between two types of deployment: by anticipation or as a response to change in the environment. Our findings also distinguished between change at different levels (internal and external asset orchestration, reorchestration between SBUs and addition/removal of a product line, etc.) and suggested that an anticipated deployment of DC does not equate with the most extensive change, even the contrary. Further research could explore this link between timing and extensiveness of change (in particular, our robustness check focused on rates of change, not on the detailed content of change). Based on Ambrosini et al. (2009), we distinguished between leveraging and adjusting as more continuous types of change and internal and external developments as more extensive change. However, the use of longitudinal data also proved essential to go beyond this initial typology and evaluate, for each firm, the extensiveness of change.

RÉFÉRENCES



  Main data sources (series)  Complementary data sources

  displays the results. A visual presentation of asset renewal seemed the best option to summarize the collected data, as it allowed a rich and refined comparison of renewal patterns across firms and over time without reducing a vast amount of heterogeneous data to a couple of rough proxies.

Figure 2 -

 2 Figure 2 -Assets re-orchestration

Figure 3 -

 3 Figure 3 -Comparative discourses in letters to shareholders

  below displays yearly operating margins for the five firms between 1997 and 2006.

Figure 4 -

 4 Figure 4 -Comparative EBIDTA margins

  proportions, averaged on a yearly basis, of top management attention devoted to sensing change and to firm stakeholders. It also includes similar proportions regarding decisions to leverage, adjust, and add (internally and externally) resources or operational capabilities. Furthermore, it includes measures of asset renewal for three different periods:

Table 1 -Introducing the Big Five

 1

		BOEING	GENERAL DYNAMICS	LOCKHEED MARTIN	NORTHROP GRUMMAN	RAYTHEON
	GENERAL INFORMATION
	Company creation	1916	1899	1912	1929	1922
		(Boeing/McDD		(Lockheed/	(Northrop/
		merger in 1997)		Martin Marietta	Grumman
				merger in 1995)	merger in 1994)
	Corporate headquarters (2007)	Chicago, IL	Falls Church,	Bethesda, MD	Los Angeles,	Waltham, MA
			VA		VA
	BUSINESSES
	Military Aircraft

  Then, given the rising asymmetric threats and smaller conflicts, the 1997 Quadrennial Defense Review Report (U.S. Department of Defense, 1997) added the need for more global presence.

	The report called for information technologies to transform warfighting "by taking advantage
	of the Revolution in Business Affairs that [had] occurred in the commercial world" -with a
	symmetric "Revolution in Military Affairs" (RMA). But what this "revolution" was precisely
	about was not clear. A nebula of concepts were being discussed like the "full spectrum
	dominance" concept of the Joint Vision 2010 (U.S. Department of Defense, 1996) or the
	Navy concept of "Network-Centric Warfare" (Cebrowksi & Garstka, 1998) -ships were to be

conceived as swarms and be smaller, lighter, faster; complexity was moving from the nodes (i.e. the ships) to the network. C4ISR systems

(Computerized Command, Control,

"Because of uncertainty, entrepreneurs/managers must make informed conjectures about the path ahead. These conjectures become working hypotheses that can be updated as evidence emerges"(Teece,

2007: 1323). "Since the set of possible combinations and applications can never be knownremember the fundamental assumption of uncertainty -the potential value of any element depends on future imaginings"[START_REF] Loasby | Capabilities and strategy: problems and prospects[END_REF](Loasby, : 1308)).


Jean-Loic Le Carrou

Sandie Le Conte

Joel Dugot

Jean-Loïc Le Carrou

Joël Dugot

8 th and 19 th French harp classification using vibration analysis

Keywords:

come

1-Introduction

The study of historical musical instruments can be done from many different approaches.

Wood scientists are interested in accessing to aged wood to understand the ageing of some species [START_REF] Noguchi | Effects of aging on the vibrational properties of wood[END_REF]. With this understanding, they hope to develop an accelerated ageing process to offer aged wood to makers. Some authors are studied the surface layers [START_REF] Echard | Review on the characterisation of ancient stringed musical instruments varnishes and implementation of an analytical strategy[END_REF][START_REF] Ryhl-Svendsen | Corrosivity measurements of indoor museum environments using lead coupons as dosimeters[END_REF] of the musical instruments and their conservation within cases. Some others consider the static deformation of the mechanical structure due to hygrometric variations or string tension [START_REF] Fioravanti | Structural assessment and measurement of the elastic deformation of historical violins: The case study of the Guarneri 'del Gesù' violin (1743) known as the 'Cannone[END_REF][START_REF] Saft | Kaliske Computational approach towards structural investigations for the restoration of historical keyboard instruments[END_REF].

Most of these studies on historical string instruments [START_REF] Noguchi | Effects of aging on the vibrational properties of wood[END_REF][START_REF] Echard | Review on the characterisation of ancient stringed musical instruments varnishes and implementation of an analytical strategy[END_REF][START_REF] Fioravanti | Structural assessment and measurement of the elastic deformation of historical violins: The case study of the Guarneri 'del Gesù' violin (1743) known as the 'Cannone[END_REF] deal with the violin and very few deal with several instruments which allow comparisons. In these studies, the instrument is generally considered in its static state whereas musical instruments were designed to radiate sound and therefore to vibrate. However, one study uses real historical violins to compare their spectrum in a playing configuration [START_REF] Saft | Kaliske Computational approach towards structural investigations for the restoration of historical keyboard instruments[END_REF] but this kind of study requires that instruments are kept in playable conditions, which is not always the case. The pressure of cultural heritage requires replacing the playing of the instrument with alternative measurements. How is it possible to characterise the acoustic properties of instruments, which are muted because of conservation rules? Nowadays when a musical instrument joins a museum collection, it becomes a cultural heritage object that is loaded with a new cultural value in relation to its connection to history, music and culture. However this implies changes in the criteria that attribute value and interest to the instrument: its historic role and connections, its rarity, its peculiarity of shape and material. These criteria may become more relevant than the quality and power of its sound or its usability for concert repertoire. In this context it becomes essential to think about methodology and tools of study which exclude putting those instruments under a mechanical stress such as string tension (typically more than 4500 N for a 41 strings harp) [START_REF] Fith | Harp strings of the eighteenth and twentieth centuries: an acoustical comparison[END_REF], and, of course, any destructive analysis. Le Conte & al. [START_REF] Conte | Using mechanical modelling and experimentation for the conservation of musical instruments[END_REF] applied near-field acoustical holography to track the restoration process of a famous XVIth century harpsichord by following modal frequencies. This technique allows the capturing of operating deflection shapes close to resonance frequencies. While this technique is quick in comparison to other modal analysis methods, it is still time consuming and not always easy to set-up when a whole corpus has to be studied. In this context, a comparison of historical instruments requires developping methods which have to be repeatable, reproducible, quick and independent of the acoustical environment. Mobility measurements, defined as the ratio between the velocity to a force applied on the structure at a given point [START_REF] Dj Ewins | Modal Testing: theory and practice[END_REF], could be good candidates. By using criteria based on these mobility measurements, classifications linked to the structural modification of a set of musical instruments were recently successfully performed [START_REF] Jl Le Carrou | Vibratory study of harp's soundboxes[END_REF][START_REF] Elie | Analysis of bridge admittance of plucked string instruments in the high frequency range[END_REF][START_REF] Elie | Macro parameters describing the mechanical behavior of classical guitares[END_REF][START_REF] Elie | Analysis of bridge mobility of violins[END_REF]. The aim of this study is therefore to apply such vibratory measurements to a historical harp corpus and to interpret the data in relation to the structural evolution of the harps.

The Musée de la Musique in Paris preserves 31 pedal harps built in France between the 18th and the 20th centuries (figure 1). This interesting collection allows a deep comparative study between two famous makers of this period: Erard and Cousineau. In the first section, the studied corpus, i.e. harps built by Erard and Cousineau, and their role in the historical evolution of the harp is presented. In the second section, a multidisciplinary method used to compare the instruments of the corpus is described: it is based on the method usually carried out by curators added with a method based on the mobility measurement classically performed by researchers. Finally, we present results obtained from these complementary approaches in order to characterise the two makers (Erard and Cousineau) and their know-how.

2-Instrument's corpus

2.1-Cousineau and Erard, famous French harp makers: the historical context

The pedal harp such as we know it today made its appearance during the first 30 years of the 18th century in South Germany. With regard to the harps which had preceded it, the novelty of the pedal harp consisted of the integration of a system to shorten the strings with "hooks", activated by 7 pedals (each pedal corresponding to a note of the scale, for example if the D pedal is pushed then all the D notes of the instrument are raised by one semi-tone). This mechanism allowed changing the key of the diatonic tuning giving a semi-chromatic instrument. The role of Queen Marie-Antoinette was important in the process of introducing this fashionable instrument, first to Paris and then to the whole country. Not only did she play the harp (as it can be seen on the painting by Gautier Dagoty, kept in the Palace of Versailles's collection), she also encouraged the establishment of German artists and craftsmen such as J.-H. Naderman in Paris. French makers, such as Cousineau, Saunier, Renault and Chatelain etc., quickly followed in their footsteps. They were keen to compete, as they were attracted by the mechanical complexity and the delicacy of design of this new instrument, coupled with the promise of a beautiful future and corresponding economic stakes.

For the manufacturers, this complexity implied the need for a chain of different specialties: cabinetmakers, woodcarvers, mechanics, gilders and painters. Their works were coordinated by the instrument maker, who finally assembled and produced a musical instrument often brilliantly decorated.

Under the pressure of more and more virtuosos, the harp makers quickly tried to increase the possibilities of the instrument regarding its range, its chromatic capacities, its specific sound and its dynamic. The competition, which raged between makers, was also the source of numerous inventions such as the chromatic system, which contributed to the instrument the characteristics that we know today.

In this context and during the focus period (18 th to 19 th ), two personalities seem to dominate harp making in Paris with regard to the quality and the quantity of constructed harps and especially with regard to their inventiveness of these makers: Georges Cousineau (1733-prosperous shops where the public could find harps and other instruments alongside manuscripts and printed music. For the purpose of this study, which is mainly dedicated to the acoustic potential of instruments, it is pertinent to mention the training of these men.

Thanks to his apprenticeship in Paris (with François Lejeune), Georges Cousineau comes from the Parisian environment of the stringed-instrument makers, holders of knowledge solidly anchored in a tradition of several centuries. During his career, he invented several mechanical systems for the harp. He was believed to be the first one to conceive and present to the Royal Academy of Sciences, in 1782, the first completely chromatic harp on which each string could produce three sounds (flat, natural, sharp), thanks to its complicated mechanism which used 14 pedals [START_REF] Adelson | Fourteen pedal harp Cousineau's Rediscovering[END_REF].

The second personality who had a profound impact within his own time is Sébastien Erard.

He was not only a harp maker but also a maker of pianoforte and a brilliant inventor.

Contrary to Cousineau, he does not come from the luthiers1 circle but from harpsichord makers. He had been trained in drawing and geometry, which was appreciably different from the average Parisian craftsmen of the time. In 1812, Erard patented an ultimate improvement: the addition of a double movement producing fully chromatic harps (each pedal giving three positions: flat, natural, sharp).

From an organological point of view, the instruments made by Cousineau and Erard at the same time present both similarities and striking differences, bearing in mind that Cousineau was the elder by about twenty years.

The Musée de la Musique keeps in its collection 31 European harps. Among them, seven have been attributed to the Cousineau family (four to the father Georges, two to the father and his son Jacques Georges, and one to the son) and at least nine have been made by Erard (Sebastien, Company or Frères). The organological description is given in table 1. The harps are ordered by chronological order for each maker.

2.2-Corpus dating

The harps made by Cousineau in this corpus are difficult to date because Cousineau never put any date or reliable number on his instruments and, at the moment, we do not know if any documents such as registers or archives ever existed. Nevertheless, it is possible to evaluate the period of each harp with the help of different elements such as the mechanical system, the number of strings which tend to increase along the period, and the decorative style. By comparing all these elements, it is possible to establish a chronology in this corpus.

For Erard, even with the help of information written on the instruments as well as surviving documents such as workshop registers, dating the harps is not so easy either. The date is only certain for a few harps, when the description made in the register matches the real instrument. Nevertheless, the numbering (made by the maker) remains a reliable method to classify the instruments. Only the harp E.2100 presents a real uncertainty. No inscription has been found outside or inside the instrument except the signature and address of the firm.

The making process of the body, which seems to be recycled from an older instrument (body made of ribs), the mechanical system (single action with forks) and the number of strings could correspond to an instrument built before 1798, which is the year of his first dated and numbered instruments.

3-Method

From an acoustical point of view, the concert harp is composed of a set of strings connected to a flat panel, called the soundboard. Like most plucked instruments, a cavity is added at the back of the instrument to avoid any acoustical short-circuit, allowing the soundboard to radiate the sound efficiently. When the cavity has sound-holes, the air inside the cavity interacts with the soundboard vibrations to amplify the sound radiated in low frequencies [START_REF] Jl Le Carrou | Experimental study of A0 and T1 modes of the concert harp[END_REF]. In order to build instruments that radiate sound in all its tessitura, the maker has to design a soundboard as thin as possible and that can stand the string tension. Since string tension has been increased (notably by the addition of strings, as shown in Table 1), harp makers have to adapt the manufacturing of the instrument, not only the soundboard but also the sound-box. Two complementary ways to study this evolution in the harp corpus is to measure geometrical descriptors classically used by curators as well as vibratory descriptors used by musical acoustics researchers.

3-1 Classical descriptors

In order to compare instruments, geometrical information such as the vibrating length of each string, the soundboard area and thickness a well as the weight of the instrument and the number of strings were collected. In practice, the string length was only measured for every C string (from C0 to C6) when the string colour was still present or when the tuning mechanical system worked. That is unfortunately not the case for harp 1. The shape of the soundboard was approximated as a trapezoid allowing us to obtain the area with the measurement of the length, the width at the top and at the bottom of the soundboard. The soundboard's thickness was measured by using a Hacklinger gauge when the harp had open soundbox holes to allow the magnet to be placed on the back of the soundboard. The measurements were done at the top (extreme top), in the middle and at the bottom of the soundboard along the line of string connections. Across the plane of the strings, the measurements were done between the bridge and the soundboard rib. However, for the harps with no hole in the box or with a blocked reinforcement system (harp 1, 2, 3, 5, A, C and F), the thickness measurement was impossible.

3-2 Vibratory descriptors

In addition to geometrical measurements, vibrational measurements could be done on each instrument for taking into account its dynamical behaviour.

Experimental setup

In order to analyse the vibrational behaviour, without playing the instrument, the mobilities of the soundboard and of the sound-box were measured. The mobility is the frequency domain ratio between the velocity of a structure and the applied force, which caused that movement.

The velocity and the force can be separately measured at the same point or at two different points. The mobility characterises the capability of the soundboard or the sound-box to vibrate under an excitation imposed on the soundboard. This quantity obviously depends on the instrument and on the pair points where the velocity and the force are measured.

Figure 2: Experimental setup of the vibrational measurements

To measure the mobility on the 16 harps, the impact testing method was used. This method is well adapted to our corpus because it is a non-intrusive method. With this method, a hammer with an appropriate sensor was used to apply a known force by impacting the soundboard at the base of the C2-string (found by activating the appropriate pedal) and on

Data Acquisition Hardware

Muffling system Accelerometer Impacts on the soundbox two points at equal distance between the middle of the lower sound-box hole and the soundboard (see Figure 2). The frequency range of the measurement produced by this method depends on the hammer impact. We found that the cut-off frequency of the impact hammer [START_REF] Dj Ewins | Modal Testing: theory and practice[END_REF] was about 2000Hz, which defines the high-frequency limit of the measurements.

For the response, an accelerometer was glued with wax on the soundboard close to the impact point between the C2-string and the D2-string as shown on Figure 3. To avoid any parasitic vibration due to the strings, a particular muffling system consisting of two pieces of foam attached together was used as shown on Figure 2.

The MVM descriptor

A typical mobility measurement is shown on Figure 3. In the low frequency range (before 300Hz), we can distinguish peaks, which are representative of the soundboard resonances.

With other mobility measurements on the soundboard and by using a mathematical algorithm, it can be possible to identify the soundboard modes. In the middle frequency range (after 300Hz to the hammer cut-off frequency around 2000Hz), it is no longer possible to identify modes and we have to extract an indicator that can characterise the response of the soundboard (or the soundbox) and which is easy to use for the whole corpus. In a preliminary study, we used the Mean-Value of the Mobility (MVM) modulus to categorize instruments [START_REF] Jl Le Carrou | Vibratory study of harp's soundboxes[END_REF]. This MVM is computed from the beginning of the middle frequency range to the hammer cut-off frequency. On Figure 3, the MVM is shown for a typical mobility. This value does not represent the complexity of the mobility but extracts a global value of the capability of the soundboard (or the soundbox) to respond to an applied force (by the string for instance). Note that the MVM of the soundbox is calculated as the mean value of the two MVMs computed from mobilities measured on each side of the soundbox (see Figure 2 and explanations provided in subsection 3.2.1). For conservation reasons, no harp was tuned in the same way: some had tuned strings, some had strings at just minimum tension and some had no strings at all. Unfortunately, it was not possible to change this without running the risk of damaging the instruments. However, the influence of the string tension on the MVM descriptor should not have any significant effect. Indeed, as shown for the piano, only the first modes shapes and the frequencies are impacted by the down bearing exerted by the strings. Above these modes (in the middle frequency range), the mobility remains essentially uninfluenced [START_REF] Wogram | The string and the soundboard, Five lectures on the Acoustics of the piano[END_REF][START_REF] Mamou-Mani | Numerical simulation of a piano soundboard under downbearing[END_REF][START_REF] Mamou-Mani | Prestress effects on the eigenfrequencies of the soundboards: experimental results on a simplified string instrument[END_REF].

4-Results

4-1 Analysis of classical descriptors

All classical descriptors, defined in Sec. 3.1, are gathered on Figure 4. They show some trends but do not clearly discriminate between the two makers. and area (E) for each concert harp of the corpus. Each harp is labelled according to Table 1.

The vibrating length is defined for each C from C0 to C6. The number of strings is in average higher for Erard's harps (from 39 to 47) than for Cousineau's (from 34 to 40), showing an evolution between the two corpora (see Figure 4-A). In the same way, all harp models made by Cousineau are appreciably lighter than those made by Erard (except for harp B with 41 strings, see Figure 4-C). This observation may have two explanations: first the structure of the mechanical part situated on the console is bigger for Erard's harps, which made it stiffer and more stable for tuning, and secondly the whole forged steel pedal set is heavier than those of Cousineau. Another considerable difference is the soundbox construction: Cousineau assembled seven thin wood ribs (generally made of maple) whereas Erard introduced plywood backs with the first numbered harps (from 1799, harps B-I).

For the vibrating length (shown on Figure 2-B), only a few differences can be noticed:

Cousineau's harps seem to present slightly longer strings than Erard's for the same note. At the same time, Cousineau made soundboards thinner (based on 3 harps measured) than Erard. More surprising is that Erard did -or tried-different thickness profiles (which was not the case for Cousineau) all the more that he did not change the soundboard area, as for harps C, D, E, F and G. We can believe that Erard may have used a gauge. For harps H and I, which are the latest ones in the corpus, the soundboard size is very different, larger than the other ones. At this time (late XIXth) the makers were looking for a more powerful instrument and increasing the soundboard size is a plausible strategy to achieve that. Note that for harp 2 (Cousineau E.2000.26.1), which is supposed to be a children's harp, the soundboard area is found to have a value close to the average. The soundboard area could be useful for observing a probable evolution in the acoustical power for Erard's harps but is useless for Cousineau's harps. A kind of "standardization" can be noticed for Erard's harps, independ of the workshop location (Paris or London) since every harp made at the beginning of the 19th century has the same size. These results show the need to improve the knowledge of the instruments from the acoustical point of view. (as defined in Table 1). In black are Cousineau's harps and in grey, Erard's. Mobility measurements of harps 1, 3, 4, 6, B, G, F, H, I were repeated. These results are found to be very close showing that the methodology is reproducible. This gives us confidence in our results and allows us to compare the two harp makers. Likewise, the opening or the closing of the soundbox holes, by the reinforcement system, affects very slightly the MVMs (as shown for harp 6 on Figure 5). This result was expected since the effect of the soundholes on the mobility is principally localised in the low frequency range [START_REF] Jl Le Carrou | Experimental study of A0 and T1 modes of the concert harp[END_REF]. Note that for harp 2, the conservation state may be different than a normally ageing one due to water damage before belonging to the collection. The instrument was totally disassembled and reassembled for a presentation state in the permanent exhibition in the museum [START_REF] Dugot | La harpe, instrument des lumières -l'aventure d'une mise en présentation au Musée de la musique[END_REF].

Analysis of vibrational descriptors

On Figure 5, the two harp makers are found to be well separated except for harps 7 and A.

Cousineau's harps have higher sound-box and soundboard mobilities than Erard's harps.

This particular result can be linked to the design of the instrument. For Cousineau, most of the sound-boxes are coopered in various wood species whereas Erard's soundboxes are made of rounded plywood backs reinforced by internal ribs and with face veneer in wood.

Erard's design reinforces the rigidity of the sound-box and decreases the mobility. The case of harps A and 7 confirms this link between mobilities and construction. Indeed, these two harps are built differently from other harps of the same maker. For harp 7 (of Cousineau G), the sound-box is made of a rounded plywood back reinforced by internal ribs whereas for harp A (of Erard Frères), it is coopered. Harp 7 is the most recent of Cousineau's harps in the Musée de la Musique (around 1820) and Harp A is probably one of the first harps constructed by Erard (before 1799). For the soundboard, the MVM values for Erard's or Cousineau's harps are certainly due to the increased number of strings, involving more strain on the soundboard. A complementary explanation would be that the maker increased the string tension to make the instrument more powerful. These results were found in a comparison of two harps: one built at the end of the eighteenth century with silk strings, and the other one in the twentieth century with gut strings [START_REF] Fith | Harp strings of the eighteenth and twentieth centuries: an acoustical comparison[END_REF]. For our corpus, this cannot be verified because we lack information about the linear mass density (diameter and material) of the original strings. Nevertheless, for both cases, the maker has to increase the thickness of the soundboard (as shown on Figure 4) and of the sound-box to stand the strain, which leads to lower mobilities [START_REF] Elie | Analysis of bridge admittance of plucked string instruments in the high frequency range[END_REF][START_REF] Skudrzyk | The mean value method of predicting the dynamic response of complex vibrators[END_REF].

According to Figure 5, the two harp makers are found to be reproducible in their manufacturing in terms of MVMs (both the soundboard and soundbox) and thus on the harps vibratory behaviour. Indeed, for Cousineau, The MVMs of harps 4 to 6 are close even though their soundboard areas (see Figure 2-E

5.Conclusion

The Musée de la Musique owns a beautiful harp collection revealing the technical evolutions of the instrument over a period of about 250 years. Studying more particularly two makers who are known to be famous allows us to have a better understanding of the harp evolution.

The advantage of studying instruments preserved in the museum is that we could be sure that they are evidence of know-how. The drawback is that in most cases, it is not possible to record its sound. The present study shows that adding vibratory analysis to geometric measurements brings complementary information about the vibratory behaviour resulting from the manufacturing process choices of Erard and Cousineau. The MVM is a simple measurement but is robust enough to understand the makers' strategy. Over the years, Erard's strategy was to rigidify both the soundboard and the soundbox, which resulted in decreasing both the sounboard and soundbox mobilities. This evolution is clearly linked to the increase in the number of strings and of their tension in order to make more powerful instruments. For Cousineau, our measurements showed the same tendency but with a higher mobility. Beyond the distinction between the makers, the important result of our work is that the construction techniques used for the sound box (plywood versus ribs) significantly affects the acoustical behaviour of the instrument, which can be characterised by a straightforward experimental method presented in the paper. We also found that both Cousineau's and Erard's manufacturing have incredible reproducibility in terms of vibrational characteristics. Thanks to this study, we collected a lot of data about historical harps.

Beyond the comparison between two manufacturers, a vibrational signature for each instrument is now known. This data could be used in the future to develop a monitoring method. From an acoustical point of view, the knowledge of this data would be useful to synthesise the sound of each historical instrument. Obviously, research on the material and diameter of the strings originally mounted on these harps has to be done.

Figure 1 :

 1 Figure 1: Harp exhibition in Musée de la musique

Figure 3 :

 3 Figure 3: Soundboard mobility at the base of the C2-string with mean-value of the mobility in dashed line. Ref 1 dB: 10 -3 m/s/N

Frequency

Figure 4 :

 4 Figure 4: Number of strings (A), vibrating lengths (B), mass (C), soundboard thickness (D)

Figure 5 :

 5 Figure 5: MVM of the soundbox versus MVM of the soundboard for the harp corpus. The

Figure 5

 5 Figure5shows the MVM of the soundbox versus the MVM of the soundboard. Each

  ) are different. For Erard, two harps built in the interval of one month with serial numbers 1271 (Harp F, September 1835) and 1273 (Harp G, October 1835) have similar vibrational characteristics: the MVM of their soundboards are equal while for the soundbox the MVM differ slightly. It could be explained by a small difference in the plywood's thickness or in the internal ribs. This seems to reveal two different approaches to achieve the same goal (i.e. keeping the vibratory response relatively constant): the Cousineau family could use very different shapes while Erard favoured geometrically similar instruments (same area of Harp F and G soundboard on

Figure 2 -

 2 Figure 2-E), confirming that the manufacturing of Erard's harps resulted in a more

Table 1 :

 1 organologic description of the corpus

	N°	Maker	Date	Diatonic tuning	String number	Soundbox	Soundbox hole	Reinforc-ment system	Sound hole	Mechanical system for tuning	Range	Museum number	Max Length (cm)	Min Length (cm)
	1	Cousineau G	< 1770	simple action	34	9 ribs	-	N	6 roses made of 7 holes	crochets		E.275	152.9	116.4
	2	Cousineau G	1770	simple action	36	7 ribs	-	N	6 roses made of 7 holes	crochets		E2000.26.1	154.6	120.3
	3	Cousineau G	1770-80	simple action	36	9 ribs	-	N	6 roses made of 7 holes	crochets	E0-E5	D.A.D.40297	161.3	119.6
	4	Cousineau G	1782-85	simple action	37	7 ribs	-	N	N	bequilles	F0-G5	E.985.2.1
	5	Cousineau G et J-G	1785-90	simple action	37	7 ribs	5 trapez	O	N	bequilles	A0-A5	E.970.3.1	163.6	123.5
	6	Cousineau G et J-G	1790-95	simple action	39	7 ribs	5 trapez	O	N	crochets	F0-B5	D.A.D.2592	163	119
	7	Cousineau J-G	vers 1820	simple action	40	plywood	5 trapez	N	N	rotation peg	B0-F6	E.991.11.1	167	124.8
	A	Erard Frères	< 1799	simple action	39	7 ribs	4 olive	N	N	fork	E0-A5	E.2100	171	129.5
	B	Erard & Cie	1799	simple action	41	plywood	5 trapez	O	N	fork	F0-D6	E.981.6.1	166.9	123.3
	C	Erard Londres	1820 Patent 3006	double action	43	plywood	5 trapez	O	N	fork	E0-E6	E.991.14.1	169.1	132.9
	D	Erard Londres	1821 Patent 3070	double action	43	plywood	5 trapez	O	N	fork	E0-E6	E.0997	169.5	132.2
	E	Erard Londres	1826 Patent 3830	double action	43	plywood	5 ellipse	N	N	fork	E0-E6	E.2003.5.8
	F	Erard Sebastien	1835 N°1271	double action	43	plywood	5 trapez	O	N	fork	E0-E6	x	168.9	134.2
	G Erard Sebastien	1835 N°1273	double action	43	plywood	5 trapez	O	N	fork	E0-E6	E.0998	170	133.4
	H	Erard & Cie	1873 N°1752	double action	47	plywood	5 trapez	O	N	fork	C1-F7	D.OAR.240	183.2	135.9
	I	Erard Frères	1890 N°2099	double action	47	plywood	5 trapez	O	N	fork	C0-G6	E.998.3.1

Luthiers refer to builders or repairers of stringed instruments such as the violin or the classical guitar.

Acknowledgment

The authors would like to thank Francois Gautier for fruitful discussions. The authors are very grateful to Timothy Wofford for his careful proofreading and corrections and to the assistant guest editor for their valuable comments.