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Organized Time
Organized Time is the first attempt to unite theories of harmony, rhythm and meter, and form under a common idea of structured time. Building off of recent advances in music theory in essential subfields-rhythmic theory, tonal structure, and the theory of musical form--author Jason Yust demonstrates that tonal music exhibits similar hierarchical organization in each of these dimensions. Yust develops a network model for temporal structure with an application of mathematical graph theory, which leads ultimately to musical applications of a multi-dimensional polytope called the associahedron. A wealth of analytical examples includes not only the familiar tonal canon-J.S. Bach, Mozart, Schumann...
Geometry and Topology in Music
This book introduces path-breaking applications of concepts from mathematical topology to music-theory topics including harmony, chord progressions, rhythm, and music classification. Contributions address topics of voice leading, Tonnetze (maps of notes and chords), and automatic music classification. Focusing on some geometrical and topological aspects of the representation and formalisation of musical structures and processes, the book covers topological features of voice-leading geometries in the most recent advances in this mathematical approach to representing how chords are connected through the motion of voices, leading to analytically useful simplified models of high-dimensional spac...
Mathematics and Computation in Music
This book constitutes the thoroughly refereed proceedings of the Fourth International Conference on Mathematics and Computation in Music, MCM 2013, held in Montreal, Canada, in June 2013. The 18 papers presented were carefully reviewed and selected from numerous submissions. They are promoting the collaboration and exchange of ideas among researchers in music theory, mathematics, computer science, musicology, cognition and other related fields.
Audacious Euphony
Music theorists have long believed that 19th-century triadic progressions idiomatically extend the diatonic syntax of 18th-century classical tonality, and have accordingly unified the two repertories under a single mode of representation. Post-structuralist musicologists have challenged this belief, advancing the view that many romantic triadic progressions exceed the reach of classical syntax and are mobilized as the result of a transgressive, anti-syntactic impulse. In Audacious Euphony, author Richard Cohn takes both of these views to task, arguing that romantic harmony operates under syntactic principles distinct from those that underlie classical tonality, but no less susceptible to sys...
Music Through Fourier Space
This book explains the state of the art in the use of the discrete Fourier transform (DFT) of musical structures such as rhythms or scales. 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. This is the first textbook dedicated to this subject, and with supporting examples and exercises this is suitable for researchers and advanced undergraduate and graduate students of music, computer science and engineering. The author has made online supplementary material available, and the book is also suitable for practitioners who want to learn about techniques for understanding musical notions and who want to gain musical insights into mathematical problems.
Mathematics of Musical Rhythm
This book presents original research applying mathematics to musical rhythm, with a focus on computational methods, theoretical approaches, analysis of rhythm in folk and global music traditions, syncopation, and maximal evenness. It honours the legacy of computer scientist and music theorist Godfried Toussaint. In addition to addressing a topic pioneered by Toussaint, application of mathematics to representation of musical rhythms, the volume also builds upon his interest in analysis of music traditions outside the European classical canon and the use of computational methods. Empirical contributions include a study of timing in Scandinavian polska performance showing that timing interacts ...
Mathematics and Computation in Music
This book constitutes the thoroughly refereed proceedings of the 7th International Conference on Mathematics and Computation in Music, MCM 2019, held in Madrid, Spain, in June 2019. The 22 full papers and 10 short papers presented were carefully reviewed and selected from 48 submissions. The papers feature research that combines mathematics or computation with music theory, music analysis, composition, and performance. They are organized in topical sections on algebraic and other abstract mathematical approaches to understanding musical objects; remanaging Riemann: mathematical music theory as “experimental philosophy”?; octave division; computer-based approaches to composition and score structuring; models for music cognition and beat tracking; pedagogy of mathematical music theory. The chapter “Distant Neighbors and Interscalar Contiguities” is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Hypermetric Manipulations in Haydn and Mozart
"This book presents a systematic discussion of hypermeter and phrase structure in eighteenth-century music. It combines perspectives from historical and modern music theory with insights from the cognitive study of music and introduces a dynamic model of hypermeter, which allows the analyst to trace the effect of hypermetric manipulations in real time. This model is applied in analyses of string chamber music by Haydn and Mozart. The analyses shed a new light upon this celebrated musical repertoire, but the aim of this book goes far beyond an analytical survey of specific compositions. Rather, it is to give a comprehensive account of the ways in which phrase structure and hypermeter were described by eighteenth-century music theorists, conceived by eighteenth-century composers, and perceived by eighteenth-century listeners"--
Pattern in Music
This book presents analyses of pattern in music from different computational and mathematical perspectives. A central purpose of music analysis is to represent, discover, and evaluate repeated structures within single pieces or within larger corpora of related pieces. In the chapters of this book, music corpora are structured as monophonic melodies, polyphony, or chord sequences. Patterns are represented either extensionally as locations of pattern occurrences in the music, or intensionally as sequences of pitch or chord features, rhythmic profiles, geometric point sets, and logical expressions. The chapters cover both deductive analysis, where music is queried for occurrences of a known pat...
The Musical-Mathematical Mind
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. In particular the contributed chapters introduce advanced techniques and concepts from modern mathematics and physics, deriving from successes in domains such as Topos theory and physical string theory. The authors include many of the leading researchers in this domain, and the book will be of value to researchers working in computational music, particularly in the areas of counterpoint, gesture, and Topos theory.
