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 song that emphasizes the commonalities between kinds from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical good points that together give a contribution to the experience of tonality, and indicates how those good points recur through the background of Western tune. within the strategy he sheds new mild on an age-old query: what makes track sound good?
A Geometry of tune offers an available advent to Tymoczko's progressive geometrical method of song conception. The ebook exhibits the right way to build basic diagrams representing relationships between wide-spread chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing miraculous levels of constitution in another way hard-to-understand items.
Tymoczko makes use of this theoretical starting place to retell the historical past 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 track contains a longer universal perform stretching from the past due center a while to the current. He discusses a number of accepted items via quite a lot of composers, from Bach to the Beatles, Mozart to Miles Davis, and lots of in between.
A Geometry of song is available to quite a number readers, from undergraduate track majors to scientists and mathematicians with an curiosity in song. Defining its phrases alongside the best way, it presupposes no unique mathematical historical past and just a easy familiarity with Western track idea. The publication additionally includes routines designed to enhance and expand readers' figuring out, besides a sequence of appendices that discover the technical information of this interesting new conception.
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Additional info for A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory)
This creates a linear pitch space in which the unit of distance is the semitone and middle C is (arbitrarily) assigned the number 60. 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.
17 Schoenberg (1975, p. 215) observed that “composing [using twelve-tone techniques] does not become easier, but rather ten times more difﬁcult” (see also Dubiel 1997). 1 Harmony and Counterpoint Constrain One Another Imagine a composer, Lyrico, who would like to combine conjunct melodic motion with harmonic consistency; that is, he would like to write melodies that move by short distances while using harmonies that are structurally similar to one another. Intuitively, it might seem that there are innumerable ways to satisfy these two constraints—that there is an entire universe of syntaxes consistent with these fundamental principles.
10 Two levels of voice leading in Clementi’s Op. 25 No. 6. single efﬁcient voice leading between D major and A major scales, occurring somewhere near the seventh measure of the example. 11 shows that similar processes occur in twentieth-century music. The top system depicts the main theme of Debussy’s prelude “Le vent dans la plaine,” which uses the pitches of Ef natural minor. When the theme returns, Bf moves by semitone to Bff, producing a collection that is enharmonically equivalent to Fs melodic minor ascending.