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The Arithmetic of Listening

Author: Kyle Gann

Publisher: University of Illinois Press

Published: 2019-09-16

Total Pages: 344

ISBN-13: 0252051424

"Tuning is the secret lens through which the history of music falls into focus," says Kyle Gann. Yet in Western circles, no other musical issue is so ignored, so taken for granted, so shoved into the corners of musical discourse. A classroom essential and an invaluable reference, The Arithmetic of Listening offers beginners the grounding in music theory necessary to find their own way into microtonality and the places it may take them. Moving from ancient Greece to the present, Kyle Gann delves into the infinite tunings available to any musician who feels straitjacketed by obedience to standardized Western European tuning. He introduces the concept of the harmonic series and demonstrates its relationship to equal-tempered and well-tempered tuning. He also explores recent experimental tuning models that exploit smaller intervals between pitches to create new sounds and harmonies. Systematic and accessible, The Arithmetic of Listening provides a much-needed primer for the wide range of tuning systems that have informed Western music. Audio examples demonstrating the musical ideas in The Arithmetic of Listening can be found at: https://www.kylegann.com/Arithmetic.html

Listen, Buddy

Author: Helen Lester

Publisher: Houghton Mifflin Harcourt

Published: 2013

Total Pages: 36

ISBN-13: 0544003225

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A lop-eared rabbit named Buddy finds himself in trouble with the Scruffy Varmint because he never listens.

On the Sensations of Tone as a Physiological Basis for the Theory of Music

Author: Hermann von Helmholtz

Publisher:

Published: 1885

Total Pages: 608

ISBN-13:

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Charles Ives's Concord

Author: Kyle Gann

Publisher: University of Illinois Press

Published: 2017-05-16

Total Pages: 488

ISBN-13: 0252099362

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In 1921, insurance executive Charles Ives sent out copies of a piano sonata to two hundred strangers. Laden with dissonant chords, complex rhythm, and a seemingly chaotic structure, the so-called Concord Sonata confounded the recipients, as did the accompanying book, Essays before a Sonata . Kyle Gann merges exhaustive research with his own experience as a composer to reveal the Concord Sonata and the essays in full. Diffracting the twinned works into their essential aspects, Gann lays out the historical context that produced Ives's masterpiece and illuminates the arguments Ives himself explored in the Essays . Gann also provides a movement-by-movement analysis of the work's harmonic structure and compositional technique; connects the sonata to Ives works that share parts of its material; and compares the 1921 version of the Concord with its 1947 revision to reveal important aspects of Ives's creative process. A tour de force of critical, theoretical, and historical thought, Charles Ives's Concord provides nothing less than the first comprehensive consideration of a work at the heart of twentieth century American music.

The Devil's Arithmetic (Puffin Modern Classics)

Author: Jane Yolen

Publisher: Penguin

Published: 2004-04-12

Total Pages: 210

ISBN-13: 0142401099

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30th Anniversary edition with a new introduction from the author Hannah is tired of holiday gatherings−all her family ever talks about is the past. In fact, it seems to her that's what they do every Jewish holiday. But this year's Passover Seder will be different−Hannah will be mysteriously transported into the past . . . and only she knows the unspeakable horrors that await. Winner of the National Jewish Book Award "A triumphantly moving book." --Kirkus Reviews, starred review

Music and the Power of Sound

Author: Alain Daniélou

Publisher: Simon and Schuster

Published: 1995-08-01

Total Pages: 192

ISBN-13: 1620550903

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Music has always been esteemed for its power to speak directly to our higher consciousness, a power founded in the purity of simple harmonic ratios. In this book, Alain Danielou traces the development of musical scales and tuning from their origins in both China and India, through their merging in ancient Greece, and on to the development of the Western traditions of modal and polyphonic music. Understanding these potent harmonic relationships offers a way for today's musicians to transcend the limitations of overly rationalistic music by drawing on its metaphysical roots.

Connecting Arithmetic to Algebra

Author: Susan Jo Russell

Publisher: Heinemann Educational Books

Published: 2011

Total Pages: 0

ISBN-13: 9780325041919

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"To truly engage in mathematics is to become curious and intrigued about regularities and patterns, then describe and explain them. A focus on the behavior of the operations allows students starting in the familiar territory of number and computation to progress to true engagement in the discipline of mathematics." -Susan Jo Russell, Deborah Schifter, and Virginia Bastable Algebra readiness: it's a topic of concern that seems to pervade every school district. How can we better prepare elementary students for algebra? More importantly, how can we help all children, not just those who excel in math, become ready for later instruction? The answer lies not in additional content, but in developing a way of thinking about the mathematics that underlies both arithmetic and algebra. Connecting Arithmetic to Algebra invites readers to learn about a crucial component of algebraic thinking: investigating the behavior of the operations. Nationally-known math educators Susan Jo Russell, Deborah Schifter, and Virginia Bastable and a group of collaborating teachers describe how elementary teachers can shape their instruction so that students learn to: *notice and describe consistencies across problems *articulate generalizations about the behavior of the operations *develop mathematical arguments based on representations to explain why such generalizations are or are not true. Through such work, students become familiar with properties and general rules that underlie computational strategies-including those that form the basis of strategies used in algebra-strengthening their understanding of grade-level content and at the same time preparing them for future studies. Each chapter is illustrated by lively episodes drawn from the classrooms of collaborating teachers in a wide range of settings. These provide examples of posing problems, engaging students in productive discussion, using representations to develop mathematical arguments, and supporting both students with a wide range of learning profiles. Staff Developers: Available online, the Course Facilitator's Guide provides math leaders with tools and resources for implementing a Connecting Arithmetic to Algebra workshop or preservice course. For information on the PD course offered through Mount Holyoke College, download the flyer.

Microtonality and the Tuning Systems of Erv Wilson

Author: Terumi Narushima

Publisher: Routledge

Published: 2017-11-22

Total Pages: 257

ISBN-13: 1317513428

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This book explores the emerging area of microtonality through an examination of the tuning theories of Erv Wilson. It is the first publication to offer a broad discussion of this influential theorist whose innovations have far-reaching ramifications for microtonal tuning systems. This study addresses the breadth and complexity of Wilson’s work by focusing on his microtonal keyboard designs as a means to investigate his tuning concepts and their practical applications. Narushima examines materials ranging from historical and experimental tunings to instrument design, as well as musical applications of mathematical theories and multidimensional geometry. The volume provides an analysis of some of Wilson’s most significant theoretical ideas, including the Scale Tree, Moments of Symmetry, Constant Structures, and Combination-Product Sets. These theories offer ways to conceptualize musical scales as patterns with structural integrity and whose shapes can be altered to produce infinitely varying forms. The book shows how these structural properties can be used to map scales onto a microtonal keyboard by providing step-by-step guidelines and clearly illustrated examples. Most importantly, it brings together theoretical and practical methods of tuning to enable composers, performers, and instrument designers to explore previously uncharted areas of microtonality, making a significant contribution to the fields of music theory, composition and music technology.

The Music of James Tenney

Author: Robert Wannamaker

Publisher: University of Illinois Press

Published: 2021-12-28

Total Pages: 358

ISBN-13: 0252052560

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Parsing the works of the experimental music pioneer Robert Wannamaker's monumental two-volume study explores the influential music and ideas of American composer, theorist, writer, performer, and educator James Tenney. Delving into the whole of Tenney's far-ranging oeuvre, Wannamaker provides in-depth, aurally grounded analyses of works linked to the artist's revolutionary theories of musical form, timbre, and harmonic perception. Volume 1, Contexts and Paradigms, chronologically surveys Tenney's creative development and output. Wannamaker begins each section with biographical, aesthetic, and technical context that illuminates a distinct period in Tenney's career. From there, he analyzes a small number of pieces that illuminate the concerns, characteristics, and techniques that emerged in Tenney's music during that time. Wannamaker supplements the text with musical examples, graphs, and diagrams while also drawing on unpublished material and newly available primary sources to flesh out each work and the ideas that shaped it. A landmark in experimental music scholarship, The Music of James Tenney is a first-of-its-kind consideration of the experimental music titan and his work.

Tuning, Timbre, Spectrum, Scale

Author: William A. Sethares

Publisher: Springer Science & Business Media

Published: 2013-06-05

Total Pages: 346

ISBN-13: 1447141776

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Tuning, Timbre, Spectrum, Scale focuses on perceptions of consonance and dissonance, and how these are dependent on timbre. This also relates to musical scale: certain timbres sound more consonant in some scales than others. Sensory consonance and the ability to measure it have important implications for the design of audio devices and for musical theory and analysis. Applications include methods of adapting sounds for arbitrary scales, ways to specify scales for nonharmonic sounds, and techniques of sound manipulation based on maximizing (or minimizing) consonance. Special consideration is given here to a new method of adaptive tuning that can automatically adjust the tuning of a piece based its timbral character so as to minimize dissonance. Audio examples illustrating the ideas presented are provided on an accompanying CD. This unique analysis of sound and scale will be of interest to physicists and engineers working in acoustics, as well as to musicians and psychologists.