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 brooding about tune that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 uncomplicated musical positive aspects that together give a contribution to the experience of tonality, and indicates how those gains recur through the background of Western tune. within the approach he sheds new mild on an age-old query: what makes tune sound good?
A Geometry of track presents an available advent to Tymoczko's innovative geometrical method of song idea. The publication indicates tips on how to build uncomplicated diagrams representing relationships between ordinary chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing striking levels of constitution in in a different way hard-to-understand items.
Tymoczko makes use of this theoretical starting place 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 past due center a long time to the current. He discusses a number of prevalent items via a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of tune is out there to a number of readers, from undergraduate tune majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the way in which, it presupposes no certain mathematical heritage and just a easy familiarity with Western tune idea. The publication additionally comprises routines designed to enhance and expand readers' knowing, besides a chain of appendices that discover the technical information of this interesting new conception.

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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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2 The passages in (a)−(c) are similar in that they move C to E by four ascending semitones. The passages in (d)−( f ) also move C to E, but differently—by eight descending semitones or by sixteen ascending semitones. We can capture what is similar about (a)−(c) by modeling these progressions as paths in pitch-class space. The progressions in (a)−(c) move C to E clockwise by four semitones along the pitch-class circle; (d) and ( f ) move eight semitones counterclockwise, and (e) moves sixteen clockwise semitones.

The bottom staff shows that we can find a higher-level harmonic motion relating two diatonic collections: the first six measures limit themselves to the seven notes of D major, while the rest of the phrase abandons the Gn in favor of the Gs. As we will see in Chapter 4, this modulation, or motion between macroharmonies, can be represented as a voice leading in which the Gn moves by semitone to Gs. This means that the music exhibits two sorts of efficient voice leading: on the level of the half measure, there is a sequence of eight efficient voice leadings between triads; while on a larger temporal level there is a 22 This is not all that modulation does, of course, but it is typically part of it.

1 (a) Confining a melody to the notes one day in a more ornery mood of the C major chord produces large leaps, so it is and decides to use the dissonant necessary to add “passing tones” (b). chromatic cluster {B, C, Df} as his drone. Here the compositional situation is reversed: where the major chord is consonant, and has its notes spread relatively far apart, this chord is very dissonant and has all its notes close together. 2. 2 (a) Confining a melody to the notes of the cluster {B, C, Df} produces conjunct melodic motion, but changing octaves requires a large number of passing tones (b).

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