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

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 take advantage of the non-Euclidean geometry of musical chords?

In this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for brooding about song that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 easy musical gains that together give a contribution to the experience of tonality, and exhibits how those positive factors recur during the background of Western track. within the strategy he sheds new gentle on an age-old query: what makes track sound good?

A Geometry of Music presents an available advent to Tymoczko's innovative geometrical method of song idea. The e-book exhibits the way to build easy diagrams representing relationships between favourite chords and scales, giving readers the instruments to translate among the musical and visible nation-states and revealing dazzling levels of constitution in another way hard-to-understand pieces.

Tymoczko makes use of this theoretical beginning to retell the heritage of Western track from the 11th century to the current day. Arguing that conventional histories concentration too narrowly at the "common perform" interval from 1680-1850, he proposes as a substitute that Western song contains a longer universal perform stretching from the overdue center a while to the current. He discusses a bunch of popular items by means of a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.

A Geometry of Music is offered to a number of readers, from undergraduate track majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the best way, it presupposes no distinct mathematical historical past and just a easy familiarity with Western track thought. The e-book additionally includes workouts designed to enhance and expand readers' knowing, in addition to a sequence of appendices that discover the technical information of this fascinating new theory.

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