Musical timbre is a complex and multidimensional entity which provides information regarding the properties of a sound source (size, material, etc.). When it comes to music, however, timbre does not merely carry environmental information, but it also conveys aesthetic meaning. In this sense, semantic description of musical tones is used to express perceptual concepts related to artistic intention. Recent advances in sound processing and synthesis technology have enabled the production of unique timbral qualities which cannot be easily associated with a familiar musical instrument. Therefore, verbal description of these qualities facilitates communication between musicians, composers, producers, audio engineers etc. The development of a common semantic framework for musical timbre description could be exploited by intuitive sound synthesis and processing systems and could even influence the way in which music is being consumed. This work investigates the relationship between musical timbre perception and its semantics. A set of listening experiments in which participants from two different language groups (Greek and English) rated isolated musical tones on semantic scales has tested semantic universality of musical timbre. The results suggested that the salient semantic dimensions of timbre, namely: luminance, texture and mass, are indeed largely common between these two languages. The relationship between semantics and perception was further examined by comparing the previously identified semantic space with a perceptual timbre space (resulting from pairwise dissimilarity rating of the same stimuli). The two spaces featured a substantial amount of common variance suggesting that semantic description can largely capture timbre perception. Additionally, the acoustic correlates of the semantic and perceptual dimensions were investigated. This work concludes by introducing the concept of partial timbre through a listening experiment that demonstrates the influence of background white noise on the perception of musical tones. The results show that timbre is a relative percept which is influenced by the auditory environment.

This thesis describes research in the computational analysis of harmony in western art music, focussing particularly on improving the accuracy and information-richness of key and chord extraction from digital score data. It is argued that a greater sophistication in automatic harmony analysis is an important contribution to the field of computational musicology. Initial experiments use hidden Markov models to predict key and modulation from automatically labelled chord sequences. Model parameters are based on heuristically formulated chord and key weightings derived from Sch¨onberg’s harmonic theory and the key and chord ratings resulting from perceptual experiments with listeners. The music theory models are shown to outperform the perceptual models both in terms of key accuracy and modelling the precise moment of key change. All of the models perform well enough to generate descriptive data about modulatory frequency, modulatory type and key distance. A robust method of classifying underlying chord types from elaborated keyboard music is then detailed. The method successfully distinguishes between essential and inessential notes, for example, passing notes and neighbour notes, and combines note classification information with tertian chord potential to measure the harmonic importance of a note. Existing approaches to automatic chord classification are unsuitable for use with complex textures and are restricted to triads and simple sevenths. An important goal is therefore to recognise a much broader set of chords, including complex chord types such as 9ths, 11ths and 13ths. This level of detail is necessary if the methods are to supply sophisticated information about the harmonic techniques of composers. Testing on the first twenty-four preludes of J. S. Bach’s Well Tempered Clavier, hand annotated by the author, a state of the art approach achieves 22.1% accuracy; our method achieves 55% accuracy.

This dissertation features methods of analyzing symbolic music, focused on n-gram-based approaches, as this representation resembles the most text and natural languages. The analysis of similarities between several text and music corpora is accompanied with implementation of text-based methods for problems of composer classification and symbolic music similarity definition. Both problems contain thorough evaluation of performance of the systems with comparisons to other approaches on existing testbeds. It is also described how one can use this symbolic representation in conjunction with genetic algorithms to tackle problems like melody generation. The proposed method is fully automated, and the process utilizes n-gram statistics from a sample corpus to achieve it. A method of visualization of complex symbolic music pieces is also presented. It consist of creating a self similarity matrix of a piece in question, revealing dependencies between voices, themes and sections, as well as music structure. A fully automatic technique of inferring music structure from these similarity matrices is also presented The proposed structure analysis system is compared against similar approaches that operate on audio data. The evaluation shows that the presented structure analysis system outperformed significantly all audio-based algorithms available for comparison in both precision and recall.

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A la frontière entre musique et mathématiques, cette étude présente un espace musical géométrique original utilisé pour l'analyse et la pédagogie.En utilisant différentes méthodes, les mathématiciens et théoriciens de la musique ont démontré que notre espace des hauteurs tempéré à douze notes peut être considéré comme une combinaison de tierces mineurs et majeures. Nous utilisons le produit cartésien de deux graphes circulaires C3□C4 pour construire le graphe Planet qui répond à ce concept. Comme la décomposition implique deux ensembles et que chaque classe de hauteur est la combinaison unique de ces deux sous-groupes, nous utilisons une coloration en termes de graphes par des nombres complexes et introduisons le concept d'idéogrammes à deux dimensions. Nous effectuons une analyse spectrale du graphe Planet pour déterminer ses espaces propres et obtenir des coordonnées géométriques. Le modèle qui en résulte est appelé Planet-4D, il offre à chaque symbole une position physiquement équivalente. Il comporte plus de symétries que tout modèle discret 3D. A partir de ce modèle, nous construisons une représentation en quatre dimensions où les accords parfaits se trouvent en surface d'une hypersphère. Nous étendons enfin le concept principal pour afficher n'importe quel agrégat de notes sur l'hypersphère dans un cadre atonal. Dans une seconde partie, nous modélisons sous forme de graphes des objets musicaux existants : claviers, réseaux de notes (Tonnetze) ou d'accords ainsi que des schémas de modulation. Nous appliquons des projections spectrales afin de visualiser les symétries inhérentes à ces objets et terminons par des études d'œuvres tonales et atonales, effectuées avec le système de visualisation inventé. / At the frontier between music and mathematics, this study presents an original geometrical musical space used for musical analysis and pedagogy.Using different schemes, mathematicians and music theorists have demonstrated that the tempered twelve tones pitch space can be considered as a combination of minor and major thirds. We use the Cartesian product of two circular graphs C3□C4 to build the Planet graph that matches this concept. Since the decomposition involves two sets and each pitch class being a unique combination of these two sub-groups, we use a graph coloration based on complex numbers and introduce the concept of bi-dimensional ideograms. We perform a spectral analysis of the Planet graph to determine its Eigen spaces and obtain geometrical coordinates. The resulting model, called Planet-4D, grants each symbol and equivalent physical position, and involves more symmetries than any discrete 3D model. From there, we build a four dimensional chordal space where perfect chords lie on a hypersphere. We finally extend this concept to display any set of pitches in an atonal context. In the second section we construct the graphs of some existing musical objects such as keyboards, tone networks (Tonnetze), chordal spaces or modulation schemes. We apply spectral projections to visualize the symmetries that are inherent to these objects. This work concludes with musical studies of tonal and atonal pieces, performed with the help of the visualization tolls designed in this study.

A partir d'une interprétation musicologique de la notion scientifique de "modélisation et simulation'', cette thèse présente une approche d'analyse assistée par ordinateur où les partitions musicales sont reconstruites à partir de processus algorithmiques et simulées avec différents paramètres à partir desquels des variantes, appelés instances, sont générés. L'étude d'une pièce musicale par modélisation et simulation signifie comprendre l'oeuvre en la (re) composant de nouveau, en brouillant les limites entre le travail analytique et créatif. Cette approche est appliquée à trois études de cas: 1. une technique isolée, la "multiplication d'accords'', utilisé par Pierre Boulez (1925- 2016), qui a été explorée à travers le prisme formé par les théories de H. Hanson, S. Heinemann et L. Koblyakov; 2. La pièce "Spectral Canon pour Conlon Nancarrow" (1974) du compositeur américain James Tenney (1934-2006) à laquelle la simulation computationnelle à partir de différents paramètres a été prise à ses conséquences ultimes quand un "espace d'instances" est explorée a partir de stratégies de visualisation graphique; 3. Et enfin "Désordre" (1985), le première étude pour piano de l'austro-hongrois György Ligeti (1923-2006) dans laquelle les concepts de "tonalité combinatoire" et "décomposition en nombres premiers'', appliqué aux durées, ont été utilisés pour maximiser le potentiel de production d'instances. / From a musicological interpretation of the scientific notion of “modeling and simulation”, this thesis presents an approach for computer-aided analysis where musical scores are reconstructed from algorithmic processes and then simulated with different sets of parameters from which neighbouring variants, called instances, are generated. Studying a musical piece by modelling and simulation means to understand the work by (re)composing it again, blurring boundaries between analytical and creative work. This approach is applied to three case studies: an isolated technique, Pierre Boulez Chord Multiplication, which is explored through the prism formed by the theories of H. Hanson, S. Heinemann and L. Koblyakov; the piece Spectral Canon for Conlon Nancarrow (1974) by the american James Tenney (1934-2006) to which the computational simulation from different sets of parameters was taken to its ultimate consequences when a “space of instances” is created and strategies of visualisation and exploration are devised; and finally “Disorder”, the first piano study written by austro-hungarian György Ligeti in which the concepts of “combinatorial tonality” and “decomposition prime numbers”, applied to durations, are used to maximize the potential that a model has to produce different variations of the original piece.

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