"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

"A triumphantly moving book." —Kirkus Reviews, starred review Hannah dreads going to her family's Passover Seder—she's tired of hearing her relatives talk about the past. But when she opens the front door to symbolically welcome the prophet Elijah, she's transported to a Polish village in the year 1942. Why is she there, and who is this "Chaya" that everyone seems to think she is? Just as she begins to unravel the mystery, Nazi soldiers come to take everyone in the village away. And only Hannah knows the unspeakable horrors that await. A critically acclaimed novel from multi-award-winning author Jane Yolen. "[Yolen] adds much to understanding the effects of the Holocaust, which will reverberate throughout history, today and tomorrow." —SLJ, starred review "Readers will come away with a sense of tragic history that both disturbs and compels." —Booklist Winner of the National Jewish Book Award An American Bookseller "Pick of the Lists"

"A fascinating and genuinely accessible guide....Educating, enjoyable, and delightfully unscary."—Classical Music What if Bach and Mozart heard richer, more dramatic chords than we hear in music today? What sonorities and moods have we lost in playing music in "equal temperament"—the equal division of the octave into twelve notes that has become our standard tuning method? Thanks to How Equal Temperament Ruined Harmony, "we may soon be able to hear for ourselves what Beethoven really meant when he called B minor 'black'" (Wall Street Journal).In this "comprehensive plea for more variety in tuning methods" (Kirkus Reviews), Ross W. Duffin presents "a serious and well-argued case" (Goldberg Magazine) that "should make any contemporary musician think differently about tuning" (Saturday Guardian). Some images in the ebook are not displayed owing to permissions issues.

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

This classic chronicle of the longstanding challenges of tuning and temperament devotes a chapter to each principal theory, features a glossary and numerous tables, and requires only minimal background in music theory.

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.

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.

The expatriate American experimentalist composer Conlon Nancarrow is increasingly recognised as having one of the most innovative musical minds of this century. His music, almost all written for player piano, is the most rhythmically complex ever written, couched in intricate contrapuntal systems using up to twelve different tempos at the same time. Yet despite its complexity, Nancarrow's music drew its early influences from the jazz pianism of Art Tatum and Earl Hines and from the rhythms of Indian music; Nancarrow's whirlwinds of notes are joyously physical in their energy. Composed in almost complete isolation from 1940, this music has achieved international fame only in the last few years. Born in 1912, the son of the mayor of Texarkana, Nancarrow fought in the Lincoln Brigade, then fled America to Mexico City to avoid being hounded for his former Communist affiliations. The author travelled to Mexico City to research Nancarrow's music and to discuss it with him. He analyses sixty-five works, virtually the composer's complete output, and includes a biographical chapter containing much information never before published.

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.