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Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 9780521009355
Category : Mathematics
Languages : en
Pages : 158
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Book Description
Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on - overtones, scales, and tuning systems - the musical dice game attributed to Mozart and Haydn - the several-hundred-year-old style of bell-playing known as ringing the changes - the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 9780521009355
Category : Mathematics
Languages : en
Pages : 158
Get Book
Book Description
Mathematics has been used for centuries to describe, analyze, and create music. In this book, Leon Harkleroad explores the math related aspects of music from its acoustical bases to compositional techniques to music criticism, touching on - overtones, scales, and tuning systems - the musical dice game attributed to Mozart and Haydn - the several-hundred-year-old style of bell-playing known as ringing the changes - the twelve-tone school of composition that strongly influenced music throughout the 20th century and many other topics involving mathematical ideas from probability theory to Fourier series to group theory. He also relates some cautionary tales of misguided attempts to mix music and mathematics. Both the mathematical and the musical concepts are described in an elementary way, making the book accessible to general readers as well as to mathematicians and musicians of all levels. The book is accompanied by an audio CD of musical examples.
Author: Leon Harkleroad
Publisher: Cambridge University Press
ISBN: 0521810957
Category : Mathematics
Languages : en
Pages : 7
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Book Description
Accompanying CD-ROM includes musical selections.
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Category : Mathematics
Languages : en
Pages : 84
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Book Description
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Category : Mathematics
Languages : en
Pages : 100
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Book Description
Author: Guerino Mazzola
Publisher: Springer Science & Business Media
ISBN: 9783764357313
Category : Mathematics
Languages : en
Pages : 1372
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Book Description
The Topos of Music is the upgraded and vastly deepened English extension of the seminal German Geometrie der Töne. It reflects the dramatic progress of mathematical music theory and its operationalization by information technology since the publication of Geometrie der Töne in 1990. The conceptual basis has been vastly generalized to topos-theoretic foundations, including a corresponding thoroughly geometric musical logic. The theoretical models and results now include topologies for rhythm, melody, and harmony, as well as a classification theory of musical objects that comprises the topos-theoretic concept framework. Classification also implies techniques of algebraic moduli theory. The classical models of modulation and counterpoint have been extended to exotic scales and counterpoint interval dichotomies. The probably most exciting new field of research deals with musical performance and its implementation on advanced object-oriented software environments. This subject not only uses extensively the existing mathematical music theory, it also opens the language to differential equations and tools of differential geometry, such as Lie derivatives. Mathematical performance theory is the key to inverse performance theory, an advanced new research field which deals with the calculation of varieties of parameters which give rise to a determined performance. This field uses techniques of algebraic geometry and statistics, approaches which have already produced significant results in the understanding of highest-ranked human performances. The book's formal language and models are currently being used by leading researchers in Europe and Northern America and have become a foundation of music software design. This is also testified by the book's nineteen collaborators and the included CD-ROM containing software and music examples.
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Category : Trademarks
Languages : en
Pages : 1368
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Category : Education
Languages : en
Pages : 106
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Book Description
Author: Jan Haluska
Publisher: CRC Press
ISBN: 1482276380
Category : Mathematics
Languages : en
Pages : 380
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Book Description
The Mathematical Theory of Tone Systems patterns a unified theory defining the tone system in functional terms based on the principles and forms of uncertainty theory. This title uses geometrical nets and other measures to study all classes of used and theoretical tone systems, from Pythagorean tuning to superparticular pentatonics. Hundreds of exa
Author: Terese M. Volk
Publisher: Oxford University Press
ISBN: 0195179757
Category : Education
Languages : en
Pages : 283
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Book Description
Beginning with a discussion of the philosophical underpinnings of multiculturalism in education and in music education, this book traces the growth and development of multicultural music education.
Author: Laura Lohman
Publisher: Routledge
ISBN: 1000388956
Category : Music
Languages : en
Pages : 170
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Book Description
This book provides a practical introduction to researching and performing early Anglo-American secular music and dance with attention to their place in society. Supporting growing interest among scholars and performers spanning numerous disciplines, this book contributes quality new scholarship to spur further research on this overshadowed period of American music and dance. Organized in three parts, the chapters offer methodological and interpretative guidance and model varied approaches to contemporary scholarship. The first part introduces important bibliographic tools and models their use in focused examinations of individual objects of material musical culture. The second part illustrates methods of situating dance and its music in early American society as relevant to scholars working in multiple disciplines. The third part examines contemporary performance of early American music and dance from three distinct perspectives ranging from ethnomusicological fieldwork and phenomenology to the theatrical stage. Dedicated to scholar Kate Van Winkle Keller, this volume builds on her legacy of foundational contributions to the study of early American secular music, dance, and society. It provides an essential resource for all those researching and performing music and dance from the revolutionary era through the early nineteenth century.
