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 puzzling over song that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical beneficial properties that together give a contribution to the experience of tonality, and indicates how those gains recur during the heritage of Western track. within the approach he sheds new mild on an age-old query: what makes song sound good?
A Geometry of song offers an obtainable advent to Tymoczko's progressive geometrical method of tune conception. The e-book indicates the way to build basic diagrams representing relationships between established chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing unbelievable levels of constitution in in a different way hard-to-understand items.
Tymoczko makes use of this theoretical starting place 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 practice" interval from 1680-1850, he proposes as an alternative that Western track includes a longer universal perform stretching from the past due heart a while to the current. He discusses a bunch of customary items by way of quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of song is offered to a number of readers, from undergraduate song majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the best way, it presupposes no targeted mathematical history and just a simple familiarity with Western tune thought. The publication additionally comprises routines designed to enhance and expand readers' figuring out, in addition to a sequence of appendices that discover the technical information of this intriguing new idea.

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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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Finally, Chapter 10 treats what I call the “modern jazz synthesis,” a contemporary common practice that unites impressionist chords and scales, chromatic voice leading, and the functional harmony of the classical era. The design of the book means that readers will need to absorb a considerable amount of theoretical material before reaching the analytical payoff in the second half. Readers who are less interested in theory for its own sake may therefore want to read the book out of order. 8–10. Chapter 9 can be read directly after Chapter 4.

Because measure are inversionally related, they are direction reversing, inversions change the and sound more similar to each other than to either of the chords character of musical passages more dramatically in the other measure. than transpositions: nobody would ever mistake the inverted form of Bach’s theme for the original. ”8 For this reason, many twentieth-century composers consider inversionally related chords to be similar. 2c, then every pitch would be sent to the place where its reflection 8 Major and minor triads are of course importantly different, even though they are related by inversion; nevertheless, they are more similar to one another than to three-note chromatic clusters.

When composing, I make various choices about chords, scales, rhythm, and instrumentation to create feelings of tension, relaxation, terror, and ecstasy, to recall earlier moments in the piece or anticipate later events. But I do not in general expect listeners to be consciously tracking these choices. ”) are like professional magicians watching each others’ routines—at best, engaged in a different 24 Cook 1987, Marvin and Brinkman 1999. Five Components of Tonality sort of appreciation, and, at worst too intellectually engaged to enjoy the music as deeply as they might.

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