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This textbook is a first introduction to mathematics for music theorists, covering basic topics such as sets and functions, universal properties, numbers and recursion, graphs, groups, rings, matrices and modules, continuity, calculus, and gestures.

This book explains music's comprehensive ontology, its way of existence and processing, as specified in its compact characterization: music embodies meaningful communication and mediates physically between its emotional and mental layers.

This book presents a deep spectrum of musical, mathematical, physical, and philosophical perspectives that have emerged in this field at the intersection of music and mathematics.

This is an introduction to basic music technology, including acoustics for sound production and analysis, Fourier, frequency modulation, wavelets, and physical modeling and a classification of musical instruments and sound spaces for tuning and counterpoint.

This book is a first sketch of what the overall field of performance could look like as a modern scientific field but not its stylistically differentiated practice, pedagogy, and history.

This book offers a new approach to musical creativity, dealing with software and the semiotics and mathematical principles of creativity. The text is supported with musical score examples, and the authors' sound and video examples are freely available online.

In particular the author explains the DFT of pitch-class distributions, homometry and the phase retrieval problem, nil Fourier coefficients and tilings, saliency, extrapolation to the continuous Fourier transform and continuous spaces, and the meaning of the phases of Fourier coefficients.

In the third and final book of his iconic piano etudes György Ligeti charts a new path relative to the rest of his musical output, representing a significant arrival in a composer¿s oeuvre known for its stylistic transformations. This monograph is the first dedicated study of these capstone works, investigating them through a novel lens of statistical-graphical analysis that illuminates their compositional uniqueness as well as broader questions regarding the perception of stability in musical texture.With nearly 200 graphical illustrations and a detailed commentary, this examination reveals the unique manner in which Ligeti treads between tonality and atonality¿a key idea in his late style¿and the centrality of processes related to broader scale areas (or ¿macroharmony¿) in articulating structures and narratives. The analytical techniques developed here are a powerful tool for investigating macroharmonic stability that can be applied to a wide range of repertoire beyond these works.This book is intended for graduate-level and professional music theorists, musicologists, performers and mathematicians.

This book presents and discusses the fundamental topic of classification of musical objects, such as chords, motifs, and gestures. Their classification deals with the exhibition of isomorphism classes. Our structure types include local and global constructions, the latter being similar to global structures in geometry, such as differentiable manifolds.The discussion extends to the role, which classification plays for the creative construction of musical compositions. Our examples include references to classical compositions, such as Beethoven¿s sonatas, and some of the author¿s own compositions of classical and jazz styles.We also discuss software that enables the application of classification to musical creativity.The volume is addressed to an audience that would apply classification to programming and creative musical construction.