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 considering track that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 easy musical positive factors that together give a contribution to the experience of tonality, and exhibits how those positive aspects recur during the background of Western tune. within the approach he sheds new mild on an age-old query: what makes track sound good?
A Geometry of tune presents an available creation to Tymoczko's progressive geometrical method of track thought. The publication indicates the right way to build basic diagrams representing relationships between favourite chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing staggering levels of constitution in in a different way hard-to-understand items.
Tymoczko makes use of this theoretical starting place to retell the background 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 a substitute that Western track includes a longer universal perform stretching from the overdue center a long time to the current. He discusses a number of commonplace items via a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of tune is offered to quite a number readers, from undergraduate track majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the way in which, it presupposes no designated mathematical history and just a uncomplicated familiarity with Western song concept. The ebook additionally includes routines designed to enhance and expand readers' realizing, in addition to a sequence of appendices that discover the technical information of this fascinating new conception.
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Extra resources for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)
These questions make good homework assignments when the book is used in a classroom. 28 Babbitt 1958. 29 Avant-garde techniques have been used in consonant contexts by composers like Conlon Nancarrow, Paul Lansky, Steve Reich (Cohn 1992), and “totalists” such as Mikel Rouse (Gann 2006). Five Components of Tonality The second part uses these ideas to reinterpret the history of Western music. Chapter 6 proposes that there is an “extended common practice” stretching from the beginning of Western counterpoint to the tonal music of the twentieth century.
2, labels for familiar equal-tempered pitches 1 Transposition preserves these distances, since f/g = cf/cg. McDermott and Hauser (2005) suggest that this measure of musical distance is innate and that it is common to at least some nonhuman animals. Dowling and Harwood (1986) suggest it is a musical universal. 2 Linear pitch space is a continuous line, containing a point for every conceivable pitch. can be determined by counting keys on an ordinary piano, so that the Cs above middle C is 61, the D above that is 62, and so on.
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. This space contains all possible three-note chords in any conceivable scale and any conceivable tuning system. 14 (a) Onesemitone voice leading and (b) two-semitone voice leading among triads. 15 This three-dimensional graph represents single-semitone voice leading between major, minor, augmented, and diminished triads—represented by dark spheres, light spheres, dark cubes, and light cubes respectively.
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko