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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Parts 2 and 3.

Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. But the substance of the book is harmony, counterpoint, tonality, scales—the stuff of music theory—and it is music theorists who stand to benefit the most from it. A Geometry of Music provides an accessible introduction to Tymoczko’s revolutionary geometrical approach to music theory. In heometry groundbreaking work, author Dmitri Tymoczko describes a new framework It brings to consciousness procedures that composers of the past have used intuitively.

In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Spatially proximate chords often function in similar ways, and in many musical contexts a chord may often be substituted for one of its near neighbors.

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

Joshua Kosman, writing at SFGate, called it “whimsical,” “ingenious,” and with a “rich emotional arc” produced by a “warmth of personality that is distinctive. The upshot of it all is a book that occasionally vexes but more often illuminates, inspires, and exhilarates: A Geometry of Music: Goodreads helps you keep track of books you want to read.

First, AGOM offers neither the first nor the most complete presentation of this model. In theory, diatonic scales inhabit a seven-dimensional OP space; fortunately, lower-dimensional spaces can capture the essential features when only a few scale types are involved.


The role of a chord in the above examples may be played instead by a scaleor more generally by what Tymoczko calls a macroharmonya collection of notes controlling the pitch content of music over a period of time. Tymoczko is an intriguing composer and adept mathematician, so his mix of math and lots of theory can be extremely thought-provoking for readers familiar with both.

A Geometry of Music – Dmitri Tymoczko – Oxford University Press

Nov 17, Steto Scopius rated it it was amazing. They may help composers and musicians to ‘see’ new possibilities within that intricate labyrinth, as well as to bring the old ones to life anew. How is the Beatles’ “Help! Nov 15, Peter rated it it was amazing.

Selected pages Table of Contents.

The book also contains exercises designed to reinforce and extend readers’ understanding, along with hymoczko series of appendices that explore the technical details of this exciting new theory. More exactly, it is about the ways in which geometry can shape and inform our understanding of music—ways that are many and varied indeed. Kevin Newman rated it liked it Dec 27, Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory.

He discusses a host of goemetry pieces by a wide range of composers, from Bach to the Beatles, Mozart to Miles Davis, and many in between.

A Geometry of Music

The significant work on voice leading and musical geometry includes, among others, RoederMorrisDouthett and SteinbachStrausCohnand notable contributions by the O portion of the CQT triumvirate, such as Callender and Quinn and Three-dimensional chord OP space, described in Section 3.

And how do Chopin’s works exploit the non-Euclidean geometry of musical chords? Stravinsky’s “Dance of the Adolescents” The mathematical understanding is by no means necessary, however.


Jason Quackenbush rated it it was amazing Mar 27, University of Pennsylvania Press. Secondly, A Geometry of Music is not a book about geometry; it is a book about music.

Two pages later, Figure 9. Music by Stravinsky, Glass, and Bill Evans, for example, falls comfortably within this compass, thus addressing geometryy Tymoczko perceives as a failing of his own musical education, in which these composers were marginalized. Tymodzko from the original on Lists with This Book. Check date values in: L’ho cominciato con un timore riverenziale pensando che coprisse solo la musica classica ma mi ha sorpreso e non poco.

Tymoczko, geometry, chords, voice leading, scales, tonality, chromaticism, style, common practice, jazz. 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. In the process he sheds new light on an age-old question: Anyone who finds diagrams like the pitch-class circle, the circle of fifths, or the neo-Riemannian Tonnetz useful for visualizing aspects of musical structure should, upon learning to navigate the OPTIC spaces, come to appreciate the varied perspectives and novel musical insights that these spaces provide.

Quotes from A Geometry of Mus Appendix F provides some pedagogically valuable exercises, most of them pertaining to the most technical material in Chapters 2—4. If you like books and love to build cool products, we may be looking for you. The Geometry of Chords 3.

Nathan rated it it was amazing Jul 29, Modulation involves voice leading.