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

By Dmitri Tymoczko

How is the Beatles' "Help!" just like Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of invoice Evans? and the way do Chopin's works make the most the non-Euclidean geometry of musical chords?
during this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for wondering song that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 uncomplicated musical gains that together give a contribution to the experience of tonality, and exhibits how those positive factors recur during the heritage of Western song. within the strategy he sheds new mild on an age-old query: what makes tune sound good?
A Geometry of song presents an obtainable advent to Tymoczko's progressive geometrical method of song thought. The ebook indicates tips on how to build basic diagrams representing relationships between widespread chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing fabulous levels of constitution in another way hard-to-understand items.
Tymoczko makes use of this theoretical origin to retell the historical past of Western track from the 11th century to the current day. Arguing that conventional histories concentration too narrowly at the "common practice" interval from 1680-1850, he proposes as a substitute that Western song includes a longer universal perform stretching from the overdue heart a while to the current. He discusses a bunch of customary items through quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of track is on the market to quite a number readers, from undergraduate song majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the best way, it presupposes no distinct mathematical historical past and just a easy familiarity with Western tune idea. The publication additionally includes routines designed to augment and expand readers' realizing, besides a sequence of appendices that discover the technical information of this intriguing new conception.

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Additional info for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)

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I find it fascinating that so many twentieth-century musicians chose to abandon this strategy. Composers such as Schoenberg, Webern, Berg, and Varèse—and later Babbitt, Boulez, Cage, Xenakis, and Stockhausen—wrote music that listeners often found quite unpleasant. In many cases, this was because these composers rejected not just acoustic consonance, but also harmonic consistency, conjunct melodic motion, limited macroharmony, and centricity. Some early modernist composers may have hoped that ordinary listeners would adapt to this new musical style, adjusting their ears to the absence of familiar musical structures and coming to enjoy atonality as deeply and directly as traditional music.

Mazzola 2002 contains related ideas. 3 transposition and inversion as distance-preserving functions Since musicians are primarily sensitive to the distances between notes, we have reason to be interested in the distance-preserving transformations of musical space. It turns out that there are only two of these—transposition and inversion, corresponding to the geometrical operations of translation and reflection. These transformations play an important role in many different musical styles, and are central to contemporary music theory.

This abbreviated path hits the main theoretical highlights (new tools for understanding voice leading and scales), as well as the most important analytical applications: to the chromatic tonality of Schubert, Chopin and Wagner, and to the twentieth-century scale-based tonality of Debussy, Stravinsky and Reich. When using the book in an advanced undergraduate theory class, I have assigned pieces from Chapters 8–9 as homework assignments early in the semester, while students are still reading the introductory chapters.

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