Anna Nagurney

Elaine Chew

Franck Jedrzejewski

William Sethares

Godfried Toussaint

Robert Peck

Thomas Noll

Rachel Hall

Julian Hook

Ching-Hua Chuan

Operations research (OR) is a field that prides itself in its versatility in the mathematical modeling of complex problems to find optimal or feasible solutions. It should come as no surprise that OR has much to offer in terms of solving problems in music composition, analysis, and performance. Operations researchers have tackled problems in areas ranging from airline yield management and computational finance, to computational biology and radiation oncology, to computational linguistics, and in eclectic applications such as diet formulation, sports strategies and chicken dominance behavior, so why not music?

I am an operations researcher and a musician. Over the past ten years, I have devoted much time to exploring, and building a career at, the interface between music and operations research. At the University of Southern California, I founded the Music Computation and Cognition (MuCoaCo) Laboratory 1 , and direct research in music and computing. To bring music applications to the attention of the OR community, I have organized invited clusters at INFORMS meetings: 'OR in the Arts: Applications in Music 2 ' at the 2003 INFORMS meeting in Atlanta; and, 'Music, Computation and Artificial Intelligence 3 ' at the 2005 INFORMS Computing Society (ICS) meeting in Annapolis. The summer 2006 issue (volume 18, issue 3 4 ) of the INFORMS Journal on Computing (JoC) featured a special cluster of papers on Computation in Music that I edited with Roger Dannenberg, Joel Sokol, and Mark Steedman.

The goal of the present article is to provide a broader perspectives on the growth and maturation of music and computing as a discipline, resources to learn more about the field, and some ways in which operations research impacts, and can influence, this rapidly expanding field. My objective is to show that music -its analysis, composition, and performance -presents rich application areas for OR techniques. Any attempt to give a comprehensive overview of the field in a few pages must necessarily be doomed to failure, due to the vastness of the domain. I shall give selected examples, focusing on a few research projects at the MuCoaCo Laboratory and some related work, of musical problems that can be framed and solved mathematically and computationally. Many of the techniques will be familiar to the OR community, and some will borrow from other computing fields. These examples will feature the modeling of music itself, the analysis and description of its structures, and the manipulation of these structures in composition and performance.

Why Model Music Mathematically or Computationally?

The widespread access to digitally encoded music, from desktop browsers to handheld devices, has given rise to the need for mathematical and computational techniques for generating, manipulating, processing, storing, and retrieving digital music. For example, Shazam 5 provides a service for users to dial a number, hold their cell phones to a music source, and receive a text message with the name of the song and recording for future purchase. Pandora 6 recommendations of songs with music qualities similar to the user's current favorite; much of the technology still depends on human annotation of existing soundtracks. A possible future application could be a musical Google, whereby one could retrieve music files by humming a melody or by providing an audio sample.

Beyond such industrial interests in mathematical and computational modeling of music, such approaches to solving problems in music analysis and in music making have their own scientific and intellectual merit as a natural progression in the evolution of the disciplines of musicology, music theory, performance, composition, and improvisation. Formal models of human capabilities in creating, analyzing, and reproducing music serve to further knowledge in human perception and cognition, and advance the state of the art in psychology and neuroscience. By modeling music making and analysis, we gain a deeper understanding of the levels and kinds of human creativity engaged by these activities.

The rich array of problems in music analysis, generation (composition/improvisation), and rendering (expressive performance) present new and familiar challenges to mathematical and computational modeling and analytical techniques, the bread and butter of operations researchers, in a creative and vast domain.

Publication Venues

While the use of computers in music can be traced back to the beginnings of computers themselves, the use of mathematics and computing to mimic human intelligence and decision-making when appreciating or making music has gathered momentum only in recent years. The escalating activity in mathematical and computational research in music has led to the birth of new societies, conferences and journals. For example, I am a founding member and secretary of the The intensifying activities in mathematics/computation and music are best reflected in the proliferations of conferences founded in only the past few years. A partial listing of some of the main conferences, together with the years they were founded and url of their earliest available websites, is given in the table above. As in other fast moving fields in computing applications, publications in this new field most frequently occur in the peer-reviewed proceedings of the conferences, which are archived in online libraries for ready access.

Open Courseware

One cannot begin research in any field without appropriate contextual knowledge. It can take years to familiarize oneself with the state of the art, even in a relatively new field. To give graduate science and engineering students opportunities to acquaint themselves with mathematical and computational modeling of music, and to try their hand at small-scale projects that could potentially grow into larger-scale or into thesis research projects, I have designed a three-semester course on topics in engineering approaches to music cognition12 . Each course in the sequence focuses on a topic in one of three areas: music analysis, performance, and composition/improvisation.

The course allows students to learn by example, by surveying and presenting literature on current research in the field, and to learn by doing, by creating (designing and implementing) their own research projects in the topic addressed in class. Since the inception of the class in 2003, all course material -week-by-week syllabi, better paper reports, presentations, and student project descriptions, and demonstration software -have been posted online as open courseware, and serve as a resource to the community. In the picture below is an example of a week-by-week syllabus from the 2006 class, which focused on computational modeling of expressive performance.

While the courses provide a broad and structured introduction to topics in music and computing, and the reader is urged to check it out for an overview of research in the field, the next sections provide some concrete examples of mathematical and computational modeling of problems in music.

Mathematical Representation of Music

Music representation and analysis underlie many of the techniques for composition and performance. The mathematical nature of music makes it particularly amenable to effective representation in numerical and digital forms. The mathematical representation of music is a centuries-old puzzle, tackled by luminaries such as mathematician Leonhard Euler, physicist Hermann von Helmholtz, and cognitive scientist Christopher Longuet-Higgins. It remains an important area of research today. Choosing an appropriate music representation can mean the difference between convexity and non-convexity, and make the problem at hand an intractable one, or one that is solvable in reasonable time.

Perhaps more than most time-based or sequential data, music information possesses a high degree of structure, symmetry, and invariance [START_REF] Shepard | Structural Representations of Musical Pitch[END_REF]. Tonal music, which refers to almost all of the music that we hear, consists of collections of sequences, or sequences of collections, of tones, also called pitches. The most common way to represent the fundamental frequencies of these tones is on a logarithmic scale -like on a piano keyboard. However, two pitches next to each other on this logarithmic scale can sound jarring when sounded simultaneously, while pitches farther apart can sound more pleasing. A number of representations have been proposed in which proximity mirrors perceived closeness.

An example of such a model is the spiral array [START_REF] Chew | Towards a Mathematical Model of Tonality[END_REF]. Like Euler's [START_REF] Cohn | Neo Riemannian Operations, Parsimonious Trichords, and Their 'Tonnetz' representations[END_REF] tonnetz and Longuet-Higgins' (1962ab) harmonic network, the spiral array arranges pitch classes, classes of pitches whose frequencies are related by a factor of a power of two, in a lattice so that neighbors along one axis are related by 2:3 frequency ratios, and neighbors along a second axis are related by 4:5 frequency ratios. Unlike planar and network models of musical entities, the spiral array wraps the plane into its three dimensional configuration to exploit its continuous interior space, and uses the convexity of tonal structures, such as chords and keys, to define spatial representations of these objects in the interior.

Automating Music Analysis

A discussion of music representation naturally leads mathematical formulations of problems in music analysis. At a crude level, tonal compositions can be organized into sections, each section consists of regions in particular keys that determine the predominant tones that are sounded in that region, each key region consists of segments of chord sequences, and chord comprises of tone clustered in or over time. Music and computing researchers have sought ways to automatically abstract these structures from music data, using both discrete and probabilistic methods.

In tonal music, the key refers to the predominant pitch set used in the music, and is identified by what is perceived to be the most stable tone. An early key finding algorithm by Longuet-Higgins and [START_REF] Longuet-Higgins | On Interpreting Bach[END_REF] used shape matching on the harmonic network to determine the key. Inspired by Longuet-Higgins and Steedman's method and by interior point approaches to linear optimization, the center of effect generator (CEG) algorithm by [START_REF] Chew | Towards a Mathematical Model of Tonality[END_REF] uses the three-dimensional configuration of the harmonic network, and the interior space to track the evolving tonal context. In the CEG method, a piece of music or its melody generates a sequence of centers of effect that traces a path in the interior of the array of pitches. The key at any given point in time is computed by a nearest neighbor search for the closest major or minor key representation on the respective major/minor key helices. By moving from the lattice to the interior space, the model becomes more robust to noise, and finds the key in fewer note events.

Pitch class (silver), major key (red), and minor key (blue) helices in the spiral array model. The squiggly green line shows a center of effect path produced by a hypothetical segment of music, and the green box indicates the closest key. The translucent blue shape covers the convex hull of the pitches in the closest key, which happens to be a minor key.

The spiral array model and its associated tonal analysis algorithms have been implemented in the MuSA.RT (Music on the Spiral Array . Real-Time) system for interactive tonal analysis and visualization (Chew & François, 2005). Any operations researcher who has implemented a mathematical algorithm for computational use can attest that it is one thing to design an algorithm of low computational complexity, and another to implement it so that it runs in real time. MuSA.RT is built using autocorrelation methods proposed by [START_REF] Dixon | Classification of Dance Music by Periodicity Patterns[END_REF].

Apart from the issues of determining tonal and rhythmic contexts, which can be thought of as finding vertical structures, there are equally interesting and challenging questions with regard to the determining of horizontal structures, such as melody and voice. A number of models have been proposed for finding motivic patterns, an example of a motive is the opening four notes of Beethoven's Fifth, and for separating voices, independent melodic threads superimposed in time. Their sequential nature means that techniques inspired by DNA sequence analysis and tree structure approaches lend themselves readily to solving problems of motivic pattern discovery -see, for example, [START_REF] Conklin | Segmental Pattern Discovery in Music[END_REF] and [START_REF] Lartillot | Multi-Dimensional motivic pattern extraction founded on adaptive redundancy filtering[END_REF]. In the same strain of computational biology-inspired approaches, we proposed a contig mapping approach to voice separation by first fragmenting, then assembling, the voices that make up a polyphonic (multi-voice) composition [START_REF] Chew | Separating Voices in Polyphonic Music: A Contig Mapping Approach[END_REF].

Music Composition and Improvisation

One of the first applications of music and computing that comes to mind is the use of mathematical and computational models for generating music. Music composition and improvisation can often be conceived of, and modeled as, the exploration of a solution space bounded by constraints imposed by the composer or improviser. [START_REF] Truchet | Solving Musical Constraints with Adaptive Search[END_REF] modeled a number of problems in computer-assisted composition as constraint satisfaction problems. A few composers have also discovered operations research techniques: Tom [START_REF] Johnson | Musical Questions for Mathematicians[END_REF] poses composition problems to mathematicians / operations researchers, for example tracing a Hamiltonian circuit through a network of n-note chords connected to other n-note chords that share k pitches, and Daniel [START_REF] Schell | Optimality in musical melodies and harmonic progressions: The travelling musician[END_REF] explores the ideas of optimality in harmonic progressions.

Taking advantage of the fact that music bears similarities with language, [START_REF] Steedman | The Blues and the Abstract Truth: Music and Mentals Models[END_REF] proposed a formal grammar for generating jazz chord sequences. Computational linguistics approaches typically require large corpora of annotated data for learning, which poses numerous challenges for music data. In efforts spearheaded by Ching-Hua Chuan and Reid Swanson, we are seeking ways to generate stylespecific accompaniment given only a few examples [START_REF] Chuan | A Hybrid System for Automatic Generation of Style-Specific Accompaniment[END_REF], and to segment melodies using unsupervised techniques so as to assist in computational creativity projects in music [START_REF] Swanson | Supporting Musical Creativity with Unsupervised Syntactic Parsing[END_REF].

Most systems for generating music originate in some Markov model, as exemplified by Pachet's Continuator (2003), which builds a variable order Markov model from an input sequence for generating new sequences.

An alternate approach, using Factor Oracles, is proposed by [START_REF] Assayag | Using Factor Oracles for Machine Improvisation[END_REF] for their OMax humanmachine improvisation system.

Inspired by OMax, Alexandre François led the development of MIMI -Multimodal Interaction in Musical Improvisation, which centers on a performer-centric interaction environment. MIMI's visual interface [START_REF] François | Visual Feedback in Performer-Machine Interaction for Musical Improvisation[END_REF], achieved through collaborative design, gives the user information about the current state of the system, including the region from which musical material was being sampled for recombination, ten seconds' lead time before the sounding of the new material, and an equal amount of time to review the improvisation, and to plan future strategies during the performance. MIMI received its international debut at the Musical Instrument Museum in Berlin in May, 2007, at the International Conference on Mathematics and Computation in Music.

Expressive Music Performance

While the music score specifies the notes to be played, and to some degree how they should be played, it contains ambiguities the resolution for which can be influenced by a performer. Interpretation in music performance has numerous analogies in speech, where the expression with which a text is spoken, the grouping of words in a sentence, and strategic pauses can affect the meaning of, and add nuance to, the words. The devices by which a performer injects expression into a score include timing deviations, loudness modulations, and articulation (the shortening and lengthening of note durations). A performance can be viewed as a set of decisions regarding the employment of these expressive strategies, constrained by the structure of the notes in the score. Researchers have worked to understand and model the principles of expressive strategies, for example, using machine-learning tools [START_REF] Widmer | Using AI and machine learning to study expressive music performance: project survey and first report[END_REF], or through direct observation of empirical data [START_REF] Palmer | On the assignment of structure in music performance[END_REF][START_REF] Parke | A microcosm of musical expression. I. Quantitative analysis of pianists' timing in the initial measures of Chopin's Etude in E major[END_REF][START_REF] Repp | A microcosm of musical expression: II. Quantitative analysis of pianists' dynamics in the initial measures of Chopin's Etude in E major[END_REF].

In the Expression Synthesis Project (Chew et. al., 2005(Chew et. al., , 2006) ) we employ an analysis-by-synthesis approach to study expressive performance. Taking the cue from motion capture for the generation of realistic animation, ESP uses the metaphor of driving for expressive performance, and a driving (wheel and pedals) interface to map car motion to tempo (speed) and amplitude in the rendering of an expressionless piece. The road is designed to guide expression: bends in the road encourage slowdowns, while straight sections promote speedups. Buttons on the wheel allow the user to change the articulation, by shortening or lengthening the notes. A virtual radius mapping strategy (Liu et. al.) ensures tempo smoothness.

A goal of ESP is to make high level decision making in expressive performance widely accessible to both experts and novices alike. The system was exhibited at the University of Southern California Festival 125 Pavilion over three days in October, 2005. It was showcased again at the National University of Singapore Techno-Arts Festival in March 2007.

One cannot discuss expression without considering its effect on the emotion perceived or experienced by the listener. In Parke, Chew, and Kyriakakis (2007ab), we present quantitative modeling, visualization, and regression analyses of the emotion perceived in film with and without music, showing that perceived emotion in film with music can be reliably predicted by perceived emotion in film alone and in music alone. In Mosst's Masters thesis ( 2006), he models and visualizes individuals' emotion responses to music using features extracted from the music's audio. An interesting finding is that humans' responses to music differ widely, and require individualized models for accurate prediction.

Conclusion

While many examples have been given in the areas of music representation, analysis, composition/improvisation, and expressive performance, we have only begun to scratch the surface with regard to furthering knowledge about these areas of creative human activity through mathematical and computational modeling. I hope I have succeeded in demonstrating the breadth of opportunities that abound for operations researchers significant contributions in this fledgling field.

EC. February 6, 2008.

  Society for Mathematics and Computation in Music 7 , formed in 2006 by an international group of researchers. The society unveiled the inaugural issue of its flagship publication, the Journal of Mathematics and Music 8 at its first meeting in May of 2007. A special issue on Computation will appear in summer 2008, edited by Alfred Cramer, Christopher Raphael, and myself. More traditional archival publication venues include the Journal of New Music Research 9 , the Computer Music Journal 10 , and Computing in Musicology 11 .

  Excerpt from week-byweek syllabus (left) and final project presentation (right) for the Spring 2006 course on Topics in Engineering Approaches to Music Cognition.

  François' Software Architecture for Immersipresence framework (2004), which allows for the efficient processing of multiple concurrent data streams. MuSA.RT has been featured in numerous presentations, including The Mathematics in Music concert-conversation, which made its debut in Los Angeles, in Victoria, B.C., and in Singapore in 2007. Venues in 2008 include North Carolina State University and the Massachusetts Institute of Technology in the Eastern United States.Apart from the pitch structures described in the previous paragraphs, music also possesses time structures. When listening to music, humans are quickly able to pick out the beat, and to tap along with it. The patterns of long and short durations along the grid of the beat produce rhythm. Periodicity in the accent patterns lead to the establishing of meter. Using the mathematical model for metrical analysis, developed at the Multimedia Laboratory headed by Guerino Mazzola (now at the University of Minnesota), and described and advanced by Anja Volk (2002),[START_REF] Chew | Dance Music Classification Using Inner Metric Analysis: a computational approach and case study using 101 Latin American Dances and National Anthems[END_REF] proposed a method for classifying dance music by analyzing their metrical patterns, providing an alternative to the inter-onset-interval distribution andThe Harmonic network and Longuet-Higgins and Steedman's major (red) and minor (blue) key templates for their key finding algorithm.Composer Lisa Bielawa tries out the MuSA.RT music analysis and visualization system following Chew and François' presentation at the Radcliffe Gymnasium, January 16, 2008. Photo by E. Chew. MIMI's international debut at the Musical Instrument Museum, Berlin, with the Seiler piano -the first MIDI grand piano, built in the 50s for TV production, May 2007. Photo by E. Chew.

  ESP at the Festival 125 Pavilion at USC. The pavilion housed exhibits, and was visited by 10,000 visitors over three days, October 6-8, 2005. Photos by E. Chew.

Topics in Engineering Approaches to Music Cognition: www-scf.usc.edu/~ise575

Acknowledgements

This material is based in part upon work supported by the National Science Foundation under Grant No. 0347988, and Cooperative Agreement No. EEC-9529152, and by the Radcliffe Institute for Advanced Study. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author and do not necessarily reflect the views of the National Science Foundation or of the Radcliffe Institute for Advanced Study.


Liang Ma

Pascal Perrier

Jianwu Dang

A study of anticipatory coarticulation for French speakers and for Mandarin Chinese speakers

Keywords: Speech production, Coarticulation, Syllable, Speech planning

Anticipatory coarticulation is studied for two languages, French and Mandarin Chinese, within Vowel 1 -Consonant -Vowel 2 sequences (V 1 CV 2 henceforth). EMMA data and acoustic signals were collected. The influences of V 2 on V 1 and of V 2 on C are more specifically analyzed in this paper. The results showed that, for the French speakers, vowel V 2 influenced the whole sequence V 1 CV 2 , while its influence was limited to the syllable CV 2 for the Chinese speakers. This suggested that speech planning in French is managed beyond the size of a syllable, while the planning is limited within the syllabe for Chinese. The results demonstrated the impact of language based constraints on articulatory planning in speech.

Introduction

Coarticulation is classically considered to be the consequence of two main factors: planning strategies of articulatory movement (cf. [START_REF] Dang | Communication between speech production and speech perception within the brain-Observation and simulation[END_REF], [START_REF] Jordan | Serial order: A parallel distributed processing approach[END_REF], [START_REF] Whalen | Coarticulation is largely planned[END_REF]) and some physical influences. Planning of speech production is more specific than that of other skilled human movements since it is constrained by linguistic factors linked to the phonological structure of the language. Our study focuses on the effects of the phonological structure on speech planning. To do so, we collected consistent kinds of utterances of French and Chinese, and then we analyzed anticipatory coarticulation using the VCV utterances.

Some phonological descriptions in Chinese and in French 2.1 Vowel inventories in Chinese and in French

The description of the vowel system of Chinese is quite controversial. According to a classical phonological description, there are five vowels, /i, y, u, a, ә/ in Mandarin Chinese [START_REF] Chao | A Grammar of Spoken Chinese[END_REF], [START_REF] Deng | Speech Analysis: The Production-Perception Perspective[END_REF]. However, the situation is more complex in real phonetic environments, where a number of allophones emerge in the variant phonetic context. The vowels' variations are associated with 4 places of articulation (front, mid-front, mid-back and back), three degrees of aperture (high, mid, low) and the lip rounding/spreading characteristics.

French vowel inventory is described as including 11 oral vowels and four nasal vowels [START_REF] Calliope | La parole et son traitement automatique[END_REF]. Distinction among the 11 oral vowels are http://www.phonetics.org.cn/phonetic/news/listnews.jsp?newsId=111 realized in a three dimensional space, including three places of articulation along the front/back direction, four degrees of aperture in the vocal tract and the rounded/spreading characteristics of the lips for front vowels.

Status of the syllable in Chinese and in French

In Chinese the syllable is considered as the most important phonological unit. This is a very strong characteristic of the language. Firstly, as a written language, Chinese character corresponds to a syllable systematically. Secondly, as a tone language, each tone always concerns a syllable in its whole and it does not extent across syllable boundaries, although they may affect each other. Thus, the syllable specifies the positioning and the duration of the tones and it appears, thus, as a fundamental element structuring the language. For example, contrary to English or to French, which count many thousands of syllables, Chinese has only 400 monosyllables when tones are not taken in consideration [START_REF] Deng | Speech Analysis: The Production-Perception Perspective[END_REF]. Thus, syllable in Chinese appears to obey very specific rules and to exist in the linguistic structure of the language as a whole.

The status of syllable in French is different than that in Chinese. It is illustrated by the differences between the intonation systems of these two languages. Intonation in French is characterized by rising pitch movements occuring at phrase boundaries. The location of stress is fixed at the word level. A unit of intonation in French contains an average of 3.5~3.9 syllables e.g. [START_REF] Jun | The Realizations of the Accentual Phrase in French Intonation, Pobus 14: a special issue on Intonation in the Romance Languages[END_REF]. Classically French is also considered as a syllable-based language since syllables seem to play a crucial role in speech segmentation [START_REF] Mehler | The syllable's role in speech segmentation[END_REF]. However some recent experiments have softened this hypothesis of the dominance of syllables at the level of the phonological representation of French. Indeed, Content [START_REF] Content | Sequence detection in pseudowords in French: Where is the syllable effect?[END_REF] suggested that the syllable effect in speech segmentation in French could be, at first, due to specific acoustic-phonetic properties existing in the acoustic signal at syllables boundaries and not to a top-down process involving syllabic representations. Although it is not denied that syllable is a fundamental element in French, it can be speculated that the strength of syllable at the phonological level is weaker than it was originally supposed to be, and less dominant than that in Chinese.

Speech material and Data analysis

Speech material consists of 15 VCV nonsense words where the vowel was /a/, /u/ or /i/ and the consonant was /k/ or /t/. The words were uttered at a normal speech rate by three native French speakers (AV, PB, CV) and two native Chinese speakers (SK and JW). Each target word was embedded in a carrier sentence: "C'est VCV ça?" in French and "这是VCV 吗?" in Chinese. Each carrier sentence was repeated 10 times. In order to have consistent sequences in both languages, influence of the tonal structure for Chinese sequences was avoided. All the sequences in Chinese were produced with a high level tone. We also did not include sequences such as /aki/, /iki/ and /uki/ that do not exist in Chinese.

The articulatory data were collected with an electromagnetic midsagittal articulograph (EMMA; AG100 Carstens Electronics). Four sensors glued on the tongue are called T 1 , T 2 , T 3 and T 4 , from the tongue tip to the tongue back. One sensor was also glued on the upper lip, one on the lower lip, and one on the lower incisor. Two reference sensors were located on the upper incisor and on the bridge of the nose.

In a first step, the labeling was carried out manually on the spectrogram. For the consonants, the onset of the burst was measured. For the http://www.phonetics.org.cn/phonetic/news/listnews.jsp?newsId=111 vowels, the point with maximum stability of the first three formants on the spectrogram was labeled. Then, in a second step, in order to achieve a more accurate detection of the most canonical vocal tract configuration, the label for vowels was automatically moved towards the extreme position of the tongue back sensor T 4 in the mid sagittal plane.

For each sequence V 1 CV 2 and for each subject, the influences of V 2 on the articulation of the preceding phonemes were statistically assessed. A variance analysis ANOVA (Repeated Measures) and a post-hoc test were carried out. SPSS for windows was used for this analysis. It is important to mention that the accuracy of the EMMA system AG100 was estimated to be around 0.5 mm. For this reason, we considered differences in tongue positioning to be physically significant only if they were larger than 0.5 mm. In this case, statistical significance threshold was at p<0.05.

Because of hardware problems that happened during the experiment, a large amount of data was missing on sensor T 3 for subject AV and on sensor T 1 for subjects CV and SK. Hence, these sensors were not taken in consideration in the analysis.

Results

Reference tongue shapes for vowels /a, u, i/ in Chinese and in French

Figure 1 shows the tongue sensors positions for each vowel V 1 in the symmetrical /V 1 tV 2 / sequence, in which V 1 =V 2 , for each subject. The dispersion ellipses were calculated from the measurements of all repetitions of sequences. The apical consonantal context was chosen in order to minimize the possible impact of the consonant on the vowel tongue shape. The symmetrical context was selected to avoid any form of anticipatory vowel-to-vowel coarticulation. These articulatory configurations can be considered as the reference patterns for the 3 vowels /a/, /u/ and /i/ in French and in Chinese. Although certain differences exist among speakers, the common features can be extracted as follow: For vowel /a/, the tongue shape is essentially flat for all the subjects. For vowel /u/, sensor T 4 is located in the region of articulation for all the subjects. For vowel /i/, sensors T 2 and T 3 are close to the palate and they correspond for all the subjects to the region of articulation.

These characteristics served as reference to analyze the whole set of data and to interpret them in terms of anticipatory coarticulation. It can be expected that, if the production of V 2 is anticipated during the production of the preceding phonemes (V 1 and C), the sensors positions of these preceding phonemes will be influenced as follows: (1) If the coming phoneme V 2 is vowel /a/, T 3 and T 4 of current phoneme should be lower than if V 2 is vowel /i/ or vowel /u/. (2) If V 2 is vowel /u/, T 4 of current phoneme should be higher and more posterior than if V 2 is vowel /i/ or vowel /a/. (3) If V 2 is vowel /i/; T 2 and T 3 should be higher and more anterior than if V 2 is vowel /a/ or vowel /u/.

Effects of V 2 on V 1

Figure 2 shows tongue sensors positions for V 1 in the various V 2 contexts in /V 1 tV 2 /sequences for each subject (in rows) and for each vowel V 1 (in columns). The tongue position of vowel V 1 was characterized only with the three sensors T 2 , T 3 and T 4 , when they were available. Since the tongue tip is underspecified for vowels, T 1 was not considered. The mean differences of tongue positions for V 1 associated with the changes in V 2 are shown for /V 1 tV 2 / sequences in Table 1. Only the differences that are proved to be statistically http://www.phonetics.org.cn/phonetic/news/listnews.jsp?newsId=111 significant (p<0.05) by a post-hoc test carried out after the ANOVA analysis are presented in these tables. (Table 1.a for three French speakers and table 1.b for two Chinese speakers). At the first sight, one can see that there are much more cases with significant differences of V 1 for the French speakers than for the Chinese speakers. Looking more precisely on the directions of the differences, it can be noted that for the French speakers the significant differences of V 1 are all compatible with the predictions of an anticipatory coarticulation of V 2, which are listed above, except in three unexpected cases (grey shaded in Table 1.a) observed for subject AV when V 1 was vowel /i/. On the contrary, for the Chinese speakers, among the few significant differences that are shown in Table 1.b, less than the half is compatible with predictions based on anticipatory coarticulation.

These results suggest that for the French speakers, vowel V 2 influences the tongue shape during the production of V 1 , while, for the Chinese speakers, this influence of V 2 on V 1 is not only very small, but also the indirect result of an anticipatory strategy. Similar results are obtained for the palatal consonant context sequences /V 1 kV 2 /.

Effects of V 2 on C

Figure 3 shows tongue sensors positions measured for consonant /t/ in the various V 2 contexts for the 5 subjects and for the different vowels V 1 . One can see that the scatters of T 2 , T 3 and T 4 show larger influences of V 2 . The clearest and the most robust influences are in the vertical direction for both French speakers and Chinese speakers, while some variability exists also in the horizontal direction. The average differences in tongue positions for /t/ associated with the changes in V 2 were measured using the same method as for vowel V 1 . For both French speakers and Chinese speakers, we have observed that, in the vertical directions, the significant average differences of T 2 , T 3 and T 4 related to V 2 were numerous and they were almost all in agreement with the predictions of anticipatory strategy. But in the horizontal direction, numbers of the influences were in contradiction with our predictions for both two languages. This can be explained from the point of view of the constraints associated with the production of the alveolar stop consonant, which requires an occlusion in the very front part of the vocal tract. Such a constraint is very crucial and allows little freedom for change by the anticipation.

For the palatal consonnant /k/ sequences, significant influences of the vowel V 2 on the consonant C were also observed for both French speakers and Chinese speakers.

Discussion and conclusions

Our results showed that, for the French speakers, vowel V 2 influences the whole sequence V 1 CV 2 , while its influence is limited to the syllable CV 2 for the Chinese speakers. These findings suggest that French speakers and Chinese speakers use different strategies on speech planning. A possible explanation for the differences in the anticipation of V 2 in V 1 could lie in the vowel inventories of these two languages. Indeed, density of vowel inventory has been suggested to influence vowel variability associated with vowel to vowel coarticulation [START_REF] Manuel | The role of contrast in limiting vowel-to-vowel coarticulation in different languages[END_REF]: the larger the vowel inventory, the smaller the variability. However, in spite of the fact that the description of the vowel system of Chinese is still a controversial issue, it is possible to say that it has fewer vowels than French. From this perspective, the variability of V 1 in Chinese should be larger or equal to that of V 1 in French. But we observed the contrary.

We rather interpret the differences between the anticipatory coarticulation strategies of the French and those of the Chinese speakers as the consequences of the respective status of the syllable in their languages. As mentioned in the phonological description for these two languages, the influences of the CV syllable are stronger in Chinese than in French. For Chinese, the syllable is dominant in linguistic representation. Chinese speakers seem to use the syllable as a basic unit to produce sequence. This explanation is compatible with the syllable model of coarticulation [START_REF] Kozhevnikov | Speech: Articulation and Perception[END_REF] about the major role of the syllable in the organization of speech. On the other hand, French speakers seem to use other longer sequence than syllable on speech planning. Our results for French speakers confirm models of coarticulation like Öhman's model [START_REF] Öhman | Coarticulation in VCV utterance: Spectrographic measurements[END_REF], the MEM model [START_REF] Abry | Modelling lip constriction anticipatory behavior for rounding in French with the MEM (Movement expansion Model)[END_REF], which all take into account phoneme sequences longer than the CV syllable.

Further work using different models of control applied to a biomechanical model of the tongue will aim at testing these different hypotheses. http://www.phonetics.org.cn/phonetic/news/listnews.jsp?newsId=111 To appear in Chinese Journal of Phonetics, 2, 2009, http://www.phonetics.org.cn/phonetic/news/listnews.jsp?newsId=111 Table 1. Mean differences of tongue sensors positions (cm) for V 1 associated with the change of V 2 in /V 1 tV 2 / sequences. Only the statistically significant cases are presented (p<0.05) and only if the difference amplitude is larger than 0.5 mm. Positive differences in the X-axis indicates that the sensor is more posterior, and for the Y-axis it means the sensor is higher. The black shades show the cases that the sensor is not available and the grey shade for the cases that the observation is opposite to the prediction of anticipation.

Figure 1 :

 1 Figure 1: A general view of tongue sensors positions (cm) for three vowels V 1 /a, i, u/ in symmetrical /V 1 tV 2 /sequences with the palate contour as a geometrical reference for 3 French speakers (a) and two Chinese speakers (b) . Sensors T 2 , T 3 and T 4 (from left to right) are presented when they are available. Left panel: V 1 =/a/ in /ata/ sequences, middle panel V 1 =/u/ in /utu/ sequences; right panel: V 1 =/i/ in /iti/ sequences;

Figure 2 :

 2 Figure 2: Tongue sensors positions (cm) for 3 vowels V 1 in /V 1 tV 2 / sequences for 3 French speakers (a) and two Chinese speakers (b). Sensors T 2 , T 3 and T 4 are presented. Left panel: V 1 =/a/; middle panel: V 1 =/u/; right panel: V 1 =/i/. Black line: V 2 =/a/; Gray line: V 2 =/i/; dotted line: V 2 =/u/.

Figure 3 :

 3 Figure 3: Tongue sensors positions (cm) for C= /t/ in /V 1 tV 2 / sequences for 3 French speakers (a) and two Chinese speakers (b). Sensors T 1 , T 2 , T 3 and T 4 are presented when they are available. Left panel: V 1 =/a/; middle panel: V 1 =/u/; right panel: V 1 =/i/. Black line: V 2 =/a/; Gray line: V 2 =/i/; dotted line: V 2 =/u/.

(

  a). Three French speakers PB, CV and AV -/ata/ /ati/-/ata/ /atu/-/ati/ /atu/-/ata/ /ati/-/ata/ /atu/-/ati/ /atu/-/ata/ /ati/-/ata/ /atu/-/ati/

		PB					CV				AV
	/a/ /atu/T2x			0.08						-0.08
	T2y 0.19	0.16						0.21		-0.17	0.24	-0.16
	T3x				0.09
	T3y 0.16	0.18						0.26		-0.20
	T4x		-0.06		0.08						-0.13	0.07
	T4y								0.19		-0.18
	/u/
	T2x										0.14	0,11
	T2y				-0.18				0.33		-0.34	0.13	-0.15
	T3x
	T3y		0.07						0.26		-0.30
	T4x								-0.24		0.15
	/i/	/itu/-/ita/	/iti/-/ita/	/itu/-/iti/	/itu/-/ita/	/iti/-/ita/	/itu/-/iti/	/itu/-/ita/	/iti/ -/ita/	/itu/-/iti/
	T2x										0.22	-0.06	-0.07
	T3x						0.15				0.22
	T3y 0.08
	T4y				0.10						-0.14	-0.20
						(b). two Chinese speakers SK and JW
				SK						JW
			/a /	/atu/-/ata/ /ati/-/ata/	/atu/-/ati/ /atu/-/ata/ /ati/-/ata/ /atu/-/ati/
			T2x								0.32	-0.23
			T3x								0.24	-0.20
			T3y							0.16	0.16
			T4x			0.11					0.17	-0.15
			T4y							0.12
			/i /	/itu/-/ita/	/iti/-/ita/	/itu/-/iti/	/itu/-/ita/	/iti/-/ita/	/itu/-/iti/
			T4x			-0.09		0.14		0.14	0.13

/utu/-/uta/ /uti/-/uta/ /utu/-/uti/ /utu/-/uta/ /uti/-/uta/ /utu/-/uti/ /utu/-/uta/ /uti/-/uta/ /utu/-/uti/