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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.
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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