KEYWORDS: Tymoczko, geometry, chords, voice leading, scales, tonality, some brute facts in Tymoczko’s new book A Geometry of Music (henceforth AGOM). A Geometry of Music has 69 ratings and 6 reviews. Peter said: Tymoczko is an intriguing composer and adept mathematician, so his mix of math and (lots of. Dmitri Tymoczko: A Geometry of Music: Harmony and. Counterpoint in the Extended. Common Practice. Hardcover, , ISBN , pages.

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A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice by Dmitri Tymoczko

Augmented triads, equal divisions of the octave into four-semitone intervals, lie on the central axis of this prism, and major and minor triads, which divide the octave nearly equally, are grouped near this central axis see Figure 1. Laitz and Ian Sewell. Fortunately, most of the errors I spotted are of the sorts that many readers will likely pass over without notice or will correct with little difficulty: One can skim the terminology of the early theoretical writing tymocczko still comprehend the latter analysis and application.

Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music.

An Essay in the Philosophy of Language.

Reich’s “New York Counterpoint” Sean Mckinney rated it did not like it Jan 03, Thanks for telling us about the problem. Scales in Twentieth-Century Music 9. The geometric model that takes pride of place in the title is a monumental achievement in its own right, and is brought to bear revealingly on fundamental aspects lf harmony, voice leading, consonance, tonality, and style, aptly illustrated through hundreds tymozcko figures and musical examples in a wide range of styles.


A Geometry of Music – Dmitri Tymoczko – Oxford University Press

Tymoczko argues that there is an “extended common practice” linking superficially distinct styles, with jazz being much closer to classical music than many have tymoczio. All modern mathematical terms are very nicely clarified and illustrated with many musical examples and the book is NOT a mathematics textbook: The idea that music should consist of rapidly changing chords is a deeply Western idea, in a double sense: Tymoczko is an excellent composer and all of this must make sense in his head to the degree that he uses his own methodology.

The second part of the book uses these tools to analyze pieces from the Middle Ages to the present. Audacious Euphony Richard Cohn.

Quotes from A Geometry of Mus Dmitri Tymoczko is a composer and music theorist. Retrieved from ” https: It’s good for composers, though, and I enjoyed the intelligent coverage of such a broad range of music. Just a moment while we sign you in to your Goodreads account. Views Read Edit View history. Tymoczko has produced an outstandingly original synthesis of new music theory that unifies quite a large number of separate subfields and realizes the theorist’s dream of finding the rational basis for tonality and tonal-compositional practices in music.

His article “The Geometry of Musical Chords,” was the first music-theory article ever published by the journal Science. David Longo rated it it was amazing Oct 26, How is the Beatles’ “Help! Selected pages Table of Contents. The book also contains exercises designed to reinforce and extend readers’ understanding, along with a series of appendices that explore the technical details of this exciting new theory. Secondly, A Geometry of Music is not a book about gemetry it is a book about music.


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Dmitri Tymoczko

A passage in the enchanting Prelude, op. A Geometry of Music provides an accessible introduction to Tymoczko’s revolutionary geometrical approach to music theory. In contrast, a chord that divides the octave less evenly, musid as the trichord E— G —A, lies far from the central axis and far from all other chords of the same set class Harmony and Voice Leading 2.

The Extended Common Practice musc. He makes available a custom-designed software tool enabling visualization of chords in several geometric spaces; one can easily display the chords shown in Figure 1, for example, and rotate the picture in three dimensions to view it from tumoczko angles. A Geometry tymiczko Music is accessible to a range of readers, from undergraduate music majors to scientists and mathematicians with an interest in music. As such, the OPTIC spaces use sophisticated techniques from contemporary mathematics to pull together many threads from musical scholarship of the last half-century, including set theory, scale theory, neo-Riemannian theory, and an assortment of work on voice leading and geometric representations.

Luis Formiga rated it it was amazing Jul 14, Readers looking for coverage of the OPTIC spaces in their full generality still have no alternative to the technical presentation in Science.