Geometry

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?
during this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for puzzling over track 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 feel of tonality, and indicates how those beneficial properties recur in the course of the heritage of Western track. within the procedure he sheds new gentle 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 track conception. The ebook indicates the best way to build uncomplicated diagrams representing relationships between well-known chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing fabulous levels of constitution in differently hard-to-understand items.
Tymoczko makes use of this theoretical origin 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 contains a longer universal perform stretching from the overdue center a while to the current. He discusses a number of usual items via quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of tune is offered to a number of readers, from undergraduate tune majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the best way, it presupposes no specified mathematical history and just a simple familiarity with Western song thought. The e-book additionally includes routines designed to augment and expand readers' knowing, in addition to a chain of appendices that discover the technical info of this interesting new thought.

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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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26 These differences no doubt reflect the fact that music largely lacks semantic content. A listener who does not understand “be quiet, there’s a tiger nearby” is a serious danger to himself and others; consequently, there is tremendous pressure for speakers and listeners to converge on the same interpretation of sentences. By contrast, a listener who does not follow the detailed syntax of a Beethoven symphony, but who nevertheless enjoys it, creates no problems whatsoever. In some important sense it 25 See Babbitt 1958, Lerdahl 1988, Raffman 2003, and Temperley 2007.

Does the piece use consonant or dissonant harmonies? Does it restrict itself, over moderate spans of musical time, to a small set of notes, and do these notes themselves change over larger time spans? Do melodies in general move by short distances? The answers to these questions tell us an enormous amount about how untrained listeners will respond to a piece. Hence my five features might be compared to a set of basic tools which composers can use to perform their musical magic. Fourth, musical heterogeneity poses special problems for composers, who confront an audience of widely varying interests and abilities.

The second type of distance-preserving transformation, inversion, turns musical space upside-down. 2 depicts inversion as it operates on the theme of Bach’s A minor prelude from Book II of the Well-Tempered Clavier. Where the left hand of (a) begins with an ascending octave leap, followed by a series of descending semitones, the left hand of (b) begins with a descending octave leap followed by a series of ascending semitones. In other words, the direction of motion has changed while the distances remain the same.

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