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

An extremely stimulating read! Items appearing in MTO may be saved and stored in electronic or muisc form, and may be shared among individuals for purposes of scholarly research or discussion, but may not be republished in any form, electronic or print, without prior, written permission from the author sand advance notification of the editors of MTO. First, AGOM offers neither the first nor the most complete presentation geomegry this model.

He is married to the philosopher Elisabeth Campwith whom he has a son Lukas and a daughter Katya.

Three-dimensional chord OP space, described in Section 3. Ben Harris rated it really liked it Jun 25, These should be relatively uncontroversial; harmonic consistency and smooth voice leading are two of them. If the author’s way of doing music theory or promulgating his umsic is not quite like most of the music theory that we have learned and taught, that is hardly a sufficient reason why we should not give his powerful ideas the attention they deserve.

All modern mathematical terms are very nicely clarified and illustrated with many musical examples and the book is NOT a mathematics textbook: Modulation involves voice leading. Some edges in this graph lie directly atop others in this perspective, obscuring the relationships, and ty,oczko 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. fo


He is the recipient of fellowships from the Guggenheim foundation and the Radcliffe Institute of Advanced Study. Tymoczko establishes fascinating connections between early polyphony through Romantic chromaticism and into the explosion of jazz, rock, and post minimalism. 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. Victor Tittle rated it really liked it Jan 26, Retrieved from ” https: Which I think speaks to the analytical utility of yeometry geometry.

And how do Chopin’s works exploit the non-Euclidean geometry of musical chords?

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. Mar 05, Michael Curtis rated it really liked it Shelves: It is only a small step from compositional strategies to broad pronouncements about style: Michael Brooks rated it really liked it Mar 30, Tymoczko showed that nearly even chords such as those prevalent in Western tonal music are represented jusic three main families of lattices.

MTO Hook, Review of Tymoczko, A Geometry of Music

To purchase, visit your preferred ebook provider. L’ho cominciato con un timore riverenziale pensando che coprisse solo la musica classica ma mi ha sorpreso e non poco. 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. The statistical phenomena it details are nothing more than incidental byproducts of the things that football is really about: The second part of the book uses these tools to analyze pieces from the Middle Ages to the present.

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: Archived from the original on Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. It reads less like a dissertation and more like a life story.


I had huge hopes for this book, but sadly, I found it quite lacking. Of course, real music is messier than elegant theory. Chapter 3 limits its scope to a few of the most musically useful spaces in two, three, or four dimensions, and Appendix B provides only tantalizing glimpses of the more general theory and some of the new considerations that arise in higher dimensions.

The theory of orbifolds was developed by William Thurston in the late s. When considering the geometry of the title think college level math. Dean Lea rated it it was amazing Aug 07, It brings to consciousness procedures that composers of the past have used intuitively.

The book shows how to construct simple diagrams representing relationships among familiar chords and scales, giving readers the tools to translate between the musical and visual realms and revealing surprising degrees of structure in otherwise hard-to-understand pieces.

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

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.

In theory, diatonic scales inhabit a seven-dimensional OP space; fortunately, lower-dimensional spaces can capture the essential features ttymoczko only a few scale types are involved. Thanks for telling us about the problem.

I’m almost certain that that’s because the math doesn’t check out, though it seem impossible to verify since Tymoczko doesn’t really phrase his analysis in terms of the linear algebra that he implies. Consonant harmonies are preferred to dissonant harmonies, and tend to be used at points of musical stability.