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 make the most the non-Euclidean geometry of musical chords?
during this groundbreaking paintings, writer Dmitri Tymoczko describes a brand new framework for wondering track that emphasizes the commonalities between types 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 beneficial properties recur in the course of the heritage of Western track. within the technique he sheds new mild on an age-old query: what makes track sound good?
A Geometry of track presents an available creation to Tymoczko's progressive geometrical method of song idea. The ebook indicates how you can build basic diagrams representing relationships between widely used chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing remarkable levels of constitution in another way hard-to-understand items.
Tymoczko makes use of this theoretical starting place to retell the heritage of Western song 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 in its place that Western song includes a longer universal perform stretching from the past due center a long time to the current. He discusses a number of widespread items by way of quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of song is obtainable to more than a few readers, from undergraduate tune majors to scientists and mathematicians with an curiosity in tune. Defining its phrases alongside the best way, it presupposes no exact mathematical historical past and just a uncomplicated familiarity with Western track idea. The ebook additionally comprises workouts designed to augment and expand readers' knowing, in addition to a chain of appendices that discover the technical information of this intriguing new idea.

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

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The terms “above” and “below” also inherit their meaning from pitch space: the phrase “the pitch class a quarter tone above pitch class D” simply refers to the chroma possessed by any pitch a quarter tone above any pitch with chroma D. ) Finally, the distance between two pitch classes can be defined as the shortest distance between any two pitches belonging to those pitch classes. Thus, when a musician says “pitch class E is four semitones away from C,” this means that for every pitch with chroma C, the nearest pitch with chroma E is precisely four semitones away.

How can she depict the voice-leading possibilities between all the triads in the chromatic scale? 15. This figure provides a map of all the contrapuntal possibilities available to a composer who wants to use traditional triads, but is willing to step outside the confines of a single diatonic scale. This complex-looking construction provides the first hint that ordinary musical questions might sometimes lead to nontrivial geometrical answers. In fact, Chapter 3 shows that Avanta’s lattice lives in what mathematicians would call “the interior of a twisted triangular two-torus,” otherwise known as a triangular doughnut.

Or that the twentieth-century quest for alternatives to traditional tonality is fruitless? 17 And while twelve-tone music is just one twentiethcentury musical system, similar comments might be made about other approaches. To my mind, this suggests that the five features are unusually powerful tools for creating musical coherence. To say this is not to deny that alternative tools may in principle exist, but simply to reiterate the basic point that tonality constitutes a fairly unique solution to some elementary compositional problems.

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