By Dmitri Tymoczko

ISBN-10: 0195336674

ISBN-13: 9780195336672

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 brooding about 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 indicates how those beneficial properties recur through the historical past of Western song. within the technique he sheds new gentle on an age-old query: what makes tune sound good?
A Geometry of tune presents an available advent to Tymoczko's progressive geometrical method of tune concept. The publication exhibits find out how to build uncomplicated diagrams representing relationships between commonly used chords and scales, giving readers the instruments to translate among the musical and visible nation-states and revealing stunning levels of constitution in in a different way hard-to-understand items.
Tymoczko makes use of this theoretical beginning to retell the historical past of Western tune 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 track includes a longer universal perform stretching from the overdue heart a while to the current. He discusses a number of prevalent items by means of a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of song is on the market to quite a number readers, from undergraduate song majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the best way, it presupposes no detailed mathematical heritage and just a simple familiarity with Western song idea. The ebook additionally includes workouts designed to enhance and expand readers' realizing, in addition to a sequence of appendices that discover the technical info of this fascinating new idea.

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

Example text

Voice-leading relations among four-note chords, five-note chords, and so on. We will use them throughout this book, both for modeling chords and scales and for analyzing specific pieces. 15, is significantly more complicated than the simple circle representing diatonic triads. Because of this complexity, the fundamental logic animating nineteenth-century music has not always been clearly understood: theorists have sometimes depicted chromaticism as involving whimsical aberrations, departures from compositional good sense, rather than as the systematic exploration of a complex but coherent terrain.

When a chord’s notes are relatively spread out, it is not possible to create conjunct melodies by using only the notes of the chord, but it is possible to create scales with a nice arrangement of chord and non-chord tones. Now consider a more sophisticated problem. Suppose Lyrico decides to write a C major chord followed by an F major chord, its transposition by ascending perfect fourth. 3 (a) Every note of the tones from both F and A. This means that C major triad is near some note of Lyrico can write a sequence of C and F major the F major triad.

8 shows a passage of “polytonal” music in which the upper staff moves systematically along the C diatonic scale, while the lower staff moves along Gf pentatonic. To explain how this music works, we need to postulate two different scales, one for each staff. ) Here, then, is a passage of music that uses pentatonic and diatonic scales to create a chromatic macroharmony. The concept of “scale” allows us to describe the structure within each voice, while the concept “macroharmony” allows us to describe the global harmony they produce.

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A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko


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