The expression and production of piano timbre : gestural control and technique, perception and verbalisation in the context of piano performance and practice

La version intégrale de cette thèse est disponible uniquement pour consultation individuelle à la Bibliothèque de musique de l’Université de Montréal (http://www.bib.umontreal.ca/MU).Cette thèse a pour objet l’étude interdisciplinaire et systématique de l’expression du timbre au piano par les pianistes de haut niveau, dans le contexte de l’interprétation et la pratique musicales. En premier lieu sont exposées la problématique générale et les différentes définitions et perspectives sur le timbre au piano, selon les points de vue scientifiques et musicaux. Suite à la présentation de la conception du timbre au piano telle qu’établie par les pianistes dans les traités pédagogiques, la perception et la verbalisation du timbre au piano sont examinées à l’aide de méthodes scientifiques expérimentales et quantitatives. Les mots dont usent les pianistes pour décrire et parler de différentes nuances de timbre sont étudiés de façon quantitative, en fonction de leurs relations sémantiques, et une carte sémantique des descripteurs de timbre communs est dressée. Dans deux différentes études, la perception du timbre au piano par les pianistes de haut niveau est examinée. Les résultats suggèrent que les pianistes peuvent identifier et nommer les nuances de timbre contrôlées par l’interprète dans des enregistrements audio, de façon consistante et convergente entre production et perception. Enfin, la production et le contrôle gestuel du timbre au piano en interprétation musicale est explorée à l’aide du système d’enregistrement d’interprétation Bösendorfer CEUS. La PianoTouch toolbox, développée spécialement sous MATLAB afin d’extraire des descripteurs d’interprétation à partir de données de clavier et pédales à haute résolution, est présentée puis mise en œuvre pour étudier la production expressive du timbre au piano par le toucher et le geste au sein d’interprétations par quatre pianistes exprimant cinq nuances de timbre et enregistrées avec le système CEUS. Les espaces et portraits gestuels des nuances de timbre ainsi obtenus présentent différents degrés d’intensité, attaque, équilibre entre les mains, articulation et usage des pédales. Ces résultats représentent des stratégies communément employées pour l’expression de chaque nuance de timbre en interprétation au piano.This dissertation presents an interdisciplinary, systematic study of the expression of piano timbre by advanced-level pianists in the context of musical performance and practice. To begin, general issues and aims are introduced, as well as differing definitions and perspectives on piano timbre from scientific and musical points of view. After the conception of piano timbre is presented as documented by pianists in pedagogical treatises, the perception and verbalisation of piano timbre is investigated with experimental and quantitative scientific methods. The words that pianists use to describe and talk about different timbral nuances are studied quantitatively, according to their semantic relationships, and a semantic map of common piano timbre descriptors is drawn out. In two separate studies, the perception of piano timbre by highly skilled pianists is investigated. Results suggest that advanced pianists can identify and label performer-controlled timbral nuances in audio recordings with consistency and agreement from production to perception. Finally, the production and gestural control of piano timbre in musical performance is explored using the Bösendorfer CEUS piano performance recording system. The PianoTouch toolbox, specifically developed in MATLAB for extracting performance features from high-resolution keyboard and pedalling data, is presented and used to study the expressive production of piano timbre through touch and gesture in CEUS-recorded performances by four pianists in five timbral nuances. Gestural spaces and portraits of the timbral nuances are obtained with differing patterns in intensity, attack, balance between hands, articulation and pedalling. The data represents common strategies used for the expression of each timbral nuance in piano performance

A system of axiomatic set theory. Part III. Infinity and enumerability. Analysis

The foundation of analysis does not require the full generality of set theory but can be accomplished within a more restricted frame. Just as for number theory we need not introduce a set of all finite ordinals but only a class of all finite ordinals, all sets which occur being finite, so likewise for analysis we need not have a set of all real numbers but only a class of them, and the sets with which we have to deal are either finite or enumerable. We begin with the definitions of infinity and enumerability and with some consideration of these concepts on the basis of the axioms I—III, IV, V a, V b, which, as we shall see later, are sufficient for general set theory. Let us recall that the axioms I—III and V a suffice for establishing number theory, in particular for the iteration theorem, and for the theorems on finitenes

A system of axiomatic set theory. Part IV. General set theory

Our task in the treatment of general set theory will be to give a survey for the purpose of characterizing the different stages and the principal theorems with respect to their axiomatic requirements from the point of view of our system of axioms. The delimitation of "general set theory” which we have in view differs from that of Fraenkel's general set theory, and also from that of "standard logic” as understood by most logicians. It is adapted rather to the tendency of von Neumann's system of set theory—the von Neumann system having been the first in which the possibility appeared of separating the assumptions which are required for the conceptual formations from those which lead to the Cantor hierarchy of powers. Thus our intention is to obtain general set theory without use of the axioms V d, V c, VI. It will also be desirable to separate those proofs which can be made without the axiom of choice, and in doing this we shall have to use the axiom V*—i.e., the theorem of replacement taken as an axiom. From V*, as we saw in §4, we can immediately derive V a and V b as theorems, and also the theorem that a function whose domain is represented by a set is itself represented by a functional set; and on the other hand V* was found to be derivable from V a and V b in combination with the axiom of choice. (These statements on deducibility are of course all on the basis of the axioms I-III.

A system of axiomatic set theory. Part V. General set theory (continued)

We have still to consider the extension of the methods of number theory to infinite ordinals—or to transfinite numbers as they may also, as usual, be called. The means for establishing number theory are, as we know, recursive definition, complete induction, and the "principle of the least number.” The last of these applies to arbitrary ordinals as well as to finite ordinals, since every nonempty class of ordinals has a lowest element. Hence immediately results also the following generalization of complete induction, called transfinite induction: If A is a class of ordinals such that (1) ΟηA, and (2) αηA → α′ηA, and (3) for every limiting number l, (x)(xεl → xηA) → lηA, then every ordinal belongs to

A system of axiomatic set theory - Part VII

The reader of Part VI will have noticed that among the set-theoretic models considered there some models were missing which were announced in Part II for certain proofs of independence. These models will be supplied now. Mainly two models have to be constructed: one with the property that there exists a set which is its own only element, and another in which the axioms I-III and VII, but not Va, are satisfied. In either case we need not satisfy the axiom of infinity. Thereby it becomes possible to set up the models on the basis of only I-III, and either VII or Va, a basis from which number theory can be obtained as we saw in Part II. On both these bases the Π0-system of Part VI, which satisfies the axioms I-V and VII, but not VI, can be constructed, as we stated there. An isomorphic model can also be obtained on that basis, by first setting up number theory as in Part II, and then proceeding as Ackermann did. Let us recall the main points of this procedure. For the sake of clarity in the discussion of this and the subsequent models, it will be necessary to distinguish precisely between the concepts which are relative to the basic set-theoretic system, and those which are relative to the model to be define

Public Relations—A Contemporary Concept

Public relations and public opinion have been my vocation and avocation since 1912. I shall hope to share with you what I have learned over these fifty years. I hope, too, to give you suggestions out of my experience to help you deal with problems all of you face in what has aptly been called the age of public relations