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The idea of this monograph is to present an overview of decisive
theoretical, computational, technological, aesthetical, artistic,
economical, and sociological directions to create future music. It
features a unique insight into dominant scientific and artistic new
directions, which are guaranteed by the authors' prominent
publications in books, software, musical, and dance productions.
Applying recent research results from mathematical and
computational music theory and software as well as new ideas of
embodiment approaches and non-Western music cultures, this book
presents new composition methods and technologies. Mathematical,
computational, and semiotic models of artistic presence (imaginary
time, gestural creativity) as well as strategies are also covered.
This book will be of interest to composers, music technicians, and
organizers in the internet-based music industry, who are offered
concrete conceptual architectures and tools for their future
strategies in musical creativity and production.
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.
The acoustical theory is applied to its implementation in analogue
and digital technology, including a detailed discussion of Fast
Fourier Transform and MP3 compression. Beyond acoustics, the book
discusses important symbolic sound event representation and
software as typically realized by MIDI and denotator formalisms.
The concluding chapters deal with globalization of music on the
Internet, referring to iTunes, Spotify and similar environments.
The book will be valuable for students of music, music informatics,
and sound engineering.
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. The
book unfolds in a basic discourse in everyday language that is
accessible to everybody who wants to understand what this topic is
about. Musical ontology is delayed in its fundamental dimensions:
its realities, its meaningful communication, and its embodied
utterance from musical creators to an interested audience. The
authors' approach is applicable to every musical genre and is
scientific, the book is suitable for non-musicians and
non-scientists alike.
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. It
approaches these abstract themes in a new way: Every concept or
theorem is motivated and illustrated by examples from music theory
(such as harmony, counterpoint, tuning), composition (e.g.,
classical combinatorics, dodecaphonic composition), and gestural
performance. The book includes many illustrations, and exercises
with solutions.
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. The
book unfolds in a basic discourse in everyday language that is
accessible to everybody who wants to understand what this topic is
about. Musical ontology is delayed in its fundamental dimensions:
its realities, its meaningful communication, and its embodied
utterance from musical creators to an interested audience. The
authors' approach is applicable to every musical genre and is
scientific, the book is suitable for non-musicians and
non-scientists alike.
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. It
approaches these abstract themes in a new way: Every concept or
theorem is motivated and illustrated by examples from music theory
(such as harmony, counterpoint, tuning), composition (e.g.,
classical combinatorics, dodecaphonic composition), and gestural
performance. The book includes many illustrations, and exercises
with solutions.
This book presents a new semiotic theory based upon category theory
and applying to a classification of creativity in music and
mathematics. It is the first functorial approach to mathematical
semiotics that can be applied to AI implementations for creativity
by using topos theory and its applications to music theory. Of
particular interest is the generalized Yoneda embedding in the
bidual of the category of categories (Lawvere) - parametrizing
semiotic units - enabling a Čech cohomology of manifolds of
semiotic entities. It opens up a conceptual mathematics as
initiated by Grothendieck and Galois and allows a precise
description of musical and mathematical creativity, including a
classification thereof in three types. This approach is new, as it
connects topos theory, semiotics, creativity theory, and AI
objectives for a missing link to HI (Human Intelligence). The
reader can apply creativity research using our classification,
cohomology theory, generalized Yoneda embedding, and Java
implementation of the presented functorial display of semiotics,
especially generalizing the Hjelmslev architecture. The intended
audience are academic, industrial, and artistic researchers in
creativity.
This book is a comprehensive examination of the conception,
perception, performance, and composition of time in music across
time and culture. It surveys the literature of time in mathematics,
philosophy, psychology, music theory, and somatic studies (medicine
and disability studies) and looks ahead through original research
in performance, composition, psychology, and education. It is the
first monograph solely devoted to the theory of construction of
musical time since Kramer in 1988, with new insights, mathematical
precision, and an expansive global and historical context. The
mathematical methods applied for the construction of musical time
are totally new. They relate to category theory (projective limits)
and the mathematical theory of gestures. These methods and results
extend the music theory of time but also apply to the applied
performative understanding of making music. In addition, it is the
very first approach to a constructive theory of time, deduced from
the recent theory of musical gestures and their categories. Making
Musical Time is intended for a wide audience of scholars with
interest in music. These include mathematicians, music theorists,
(ethno)musicologists, music psychologists / educators / therapists,
music performers, philosophers of music, audiologists, and
acousticians.
This book is a comprehensive examination of the conception,
perception, performance, and composition of time in music across
time and culture. It surveys the literature of time in mathematics,
philosophy, psychology, music theory, and somatic studies (medicine
and disability studies) and looks ahead through original research
in performance, composition, psychology, and education. It is the
first monograph solely devoted to the theory of construction of
musical time since Kramer in 1988, with new insights, mathematical
precision, and an expansive global and historical context. The
mathematical methods applied for the construction of musical time
are totally new. They relate to category theory (projective limits)
and the mathematical theory of gestures. These methods and results
extend the music theory of time but also apply to the applied
performative understanding of making music. In addition, it is the
very first approach to a constructive theory of time, deduced from
the recent theory of musical gestures and their categories. Making
Musical Time is intended for a wide audience of scholars with
interest in music. These include mathematicians, music theorists,
(ethno)musicologists, music psychologists / educators / therapists,
music performers, philosophers of music, audiologists, and
acousticians.
The idea of this monograph is to present an overview of decisive
theoretical, computational, technological, aesthetical, artistic,
economical, and sociological directions to create future music. It
features a unique insight into dominant scientific and artistic new
directions, which are guaranteed by the authors' prominent
publications in books, software, musical, and dance productions.
Applying recent research results from mathematical and
computational music theory and software as well as new ideas of
embodiment approaches and non-Western music cultures, this book
presents new composition methods and technologies. Mathematical,
computational, and semiotic models of artistic presence (imaginary
time, gestural creativity) as well as strategies are also covered.
This book will be of interest to composers, music technicians, and
organizers in the internet-based music industry, who are offered
concrete conceptual architectures and tools for their future
strategies in musical creativity and production.
This book presents a new semiotic theory based upon category theory
and applying to a classification of creativity in music and
mathematics. It is the first functorial approach to mathematical
semiotics that can be applied to AI implementations for creativity
by using topos theory and its applications to music theory. Of
particular interest is the generalized Yoneda embedding in the
bidual of the category of categories (Lawvere) - parametrizing
semiotic units - enabling a Cech cohomology of manifolds of
semiotic entities. It opens up a conceptual mathematics as
initiated by Grothendieck and Galois and allows a precise
description of musical and mathematical creativity, including a
classification thereof in three types. This approach is new, as it
connects topos theory, semiotics, creativity theory, and AI
objectives for a missing link to HI (Human Intelligence). The
reader can apply creativity research using our classification,
cohomology theory, generalized Yoneda embedding, and Java
implementation of the presented functorial display of semiotics,
especially generalizing the Hjelmslev architecture. The intended
audience are academic, industrial, and artistic researchers in
creativity.
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