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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Some edges in this graph lie directly atop others in this perspective, obscuring the relationships, and unlike most other such graphs, this one is drawn so that a particular voice-leading motion such as E —E is represented, at different places in the graph, by edges that are not parallel.

Tymoczko has also written a free software program, “ChordGeometries,” allowing users to visualize the orbifolds representing musical chords. Oxford University Press is a department of the University of Oxford.

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.

Also, various points are supported by statistical analyses estimating the frequencies gometry which certain characteristics appear in the works of certain composers or eras—a valuable if time-consuming technique that is slowly gaining teometry foothold in music theory scholarship.

Check date values in: The geometry disappears as the book turns more to analysis. 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.

I doubt that it’s worth struggling to comprehend, however, and if it’s composing you’re looking to do, you could spend your time more productively than trying to reduce these fractions of reason to their lowest common denominator.

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

A Geometry of Music is accessible to a range of readers, from undergraduate music majors to scientists tymoczkl mathematicians with an interest in music. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide. 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.


University of Pennsylvania Press. Nov 15, Peter rated it it was amazing. Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory.

The theory of orbifolds was developed by William Thurston in the late s. One reads this book with geometty feeling of witnessing the birth of a classic in musicc theory. Thanks for telling us about the problem. Reich’s “The Desert Music,” movement 1 Ashley Joseph Whitney rated it it muwic ok Jul 21, In Crackpot Hymnal Bridgehe presents expressly composed chamber pieces inspired and mixed from a number of traditional styles.

Dmitri Tymoczko

Occasional oddities in the results betray a lack of discernment in these analyses. All modern mathematical terms are very nicely clarified and illustrated with many musical examples and the book is Muusic a mathematics textbook: 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 of harmony, voice leading, consonance, tonality, and style, aptly illustrated through hundreds of figures and musical examples in a wide range of styles.

If you are interested in tonality in music, you must read it, because it describes by far the most comprehensive theory of what makes tonal music work. This a milestone in music theory and it constitutes an unification of many western practices in composition based in geometry. Tymoczko’s personal history is inspiring and is truly the basis of the book. Shostakovich’s Fs minor Prelude and Fugue, Op. The tymovzko 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.

The audio may be beneficial to those who have difficulty playing or aurally imagining the examples, but the synthesized sound will be off-putting to many listeners, and there are occasional mismatches between printed examples and their audio counterparts. Grieg’s “Klokkeklang,” Bell RingingOp.

Dean Lea rated it it was amazing Aug 07, The middle section of the Fourth Barcarolle, op. 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. Football consists of a statistically tympczko alternation of circular clustering, linear clustering, and random interpenetration.


To form the complete space, the two triangular ends of the prism in Figure 1 must be glued together with a twist, geomeetry that the two corners representing the triple unison CCC are superimposed. Other editions – View all A Geometry of Music: After being asked to leave the philosophy D.

Will Watson rated it it was amazing Apr 12, 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. Harmony and counterpoint constrain each other.

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A Geometry of Music – Dmitri Tymoczko – Oxford University Press

Jun 19, Vladimir rated it it was amazing. It promises nothing less than a rational foundation for tonality; a set of common principles that unify the music of not just one or two centuries but broad swaths of music history spanning the better part of a millennium; new perspectives on among other things scales, modulation, functional harmony, chromaticism, and the place of jazz in music history; and a powerful, overarching geometric model that ties it all together.

Tymoczko argues that there is an “extended common practice” linking superficially distinct styles, with jazz being much closer to classical music than many have thought. The level of originality in this work is remarkable enough already, and hardly needs exaggerating.

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

Lists with This Book. Scales in Twentieth-Century Music 9. What results is a systematic perspective on the fullfamily of chord-based graphs.

Tymoczko’s theories are not well supported – because of this, the book winds up being a collection of interesting mathematical factoids about encoding music, rather than the exposition of a new tool for taming music theory. The interscalar interval matrix.