Topology of Sound Forms & Music

By Mihai Brediceanu
October 2002
Editura Academiei Romane
ISBN: 973-27-0855-7
430 pages, Illustrated, 6 " x 9 "
$130.00 Paper Original



This book represents the culmination of a life in which two major passions have joined: the passion for music and the passion for mathematics. The author is one of the major Romanian conductors of the second half of the twentieth century. The aim of this work has two distinct aspects: (1) the creation of an instrument of investigation allowing an adequate generalization, so that a number of seemingly dissimilar sound organizations may be included in a system, much being considered a sound organization belonging to that system; (2) the endowment of the musical composition act with new tools, by proving that the traditional methods are but particular cases of a much more general group of principles for sound organizations, out of which only a small part is used by composers.

Contents include: Elements of a Theory of Sound Forms, Sound events, forms and spaces, Sound forms and topological transformations, From the general sound event to spoken languages and musical structures, the Role of sound forms in the musical language, the Role of semiography in the development of European music, Musical Concepts and Composition Methods Interpreted in Real Sound Space R^2 and in Virtual Sound Space R^3, Musical sounds and modes in sound space R^3, Topology of modes in real sound space R^2, Musical transformations in sound space R^2 endowed with topological, vectorial and projective structures, Transformations in sound space R^2 endowed with affine structure, Transformations in sound space R^2 endowed with Euclidean structure, Transformations in virtual sound space R^3, Behavior of Sound Forms Under the Generalized Action of Topological Transformations which Exhibit Particular Cases in Musical Composition Methods, the Composer and the topological transformations, Behavior of sound forms under the action of homology transformation, Behavior of sound forms under the action of transformations through homothety, Behavior of sound forms under the action of transformations through rotation, Behavior of sound forms under the action of transformations through inversion, Transformations in sound space R^3, Continuous Topological Transformations and Generative Mechanisms, Dynamic aspects in studying and generating sound forms, Generating mechanism, Musical structures generated by the discontinuous survey of a sound form in motion in R^2, the Concept of "function of time" as reflected in the thinking of preclassical composers, Generative mechanisms making use of continuous composed topological transformations, Generative mechanisms in virtual sound space R^3, Two aspects of time in generative mechanisms: chronological time, musical time, Role of Computers in Generating Musical Sound Structures by Means of Topological Transformations and of Generative Mechanisms, General remarks, Brief description of some programs, Programs operating with compound transformation, Program translating in score symbols musical sound forms represented numerically in sound space R^2, Music and Polymodular Time, Laws of distribution of virtual and real pulsations in a polymodular time structure, Polymodular time and chronological time, Topological aspects of the polymodular time, the Polymodular time structure of music, and Polytimer.

Music Theory

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