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 pondering tune that emphasizes the commonalities between types from medieval polyphony to modern rock. Tymoczko identifies 5 simple musical positive factors that together give a contribution to the feel of tonality, and exhibits how those beneficial properties recur during the background of Western track. within the method he sheds new mild on an age-old query: what makes song sound good?
A Geometry of song offers an available advent to Tymoczko's progressive geometrical method of song concept. The ebook exhibits the way to build uncomplicated diagrams representing relationships between wide-spread chords and scales, giving readers the instruments to translate among the musical and visible geographical regions and revealing excellent 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 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 as a substitute that Western song includes a longer universal perform stretching from the overdue heart a while to the current. He discusses a bunch of established items by means of a variety of composers, from Bach to the Beatles, Mozart to Miles Davis, and plenty of in between.
A Geometry of song is obtainable to quite a number readers, from undergraduate tune majors to scientists and mathematicians with an curiosity in track. Defining its phrases alongside the best way, it presupposes no designated mathematical historical past and just a easy familiarity with Western track concept. The publication additionally includes routines designed to enhance and expand readers' knowing, besides a sequence of appendices that discover the technical info 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)
26 Of course, musical signals are in some respects more complex than spoken sentences: listening to a Bach fugue is like listening to four people speak at the same time. But this should make us wonder why we tolerate higher information content in music. 23 24 theory simply does not matter whether you follow all the details of a piece’s syntax; what matters is that you follow the piece well enough to enjoy what you hear. For in the end, the composer’s well-being depends on your willingness to listen, not on whether you interpret music in the same way that he or she does.
In this book, I will always choose c1 = 69 and c2 = 12. 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.
24 This means that theorists should not assume that the cognitive structures involved in making music are the same as those involved in perceiving it: ideas that are central to the composer’s craft, such as the principle that a classical sonata should recapitulate the second theme in the tonic key, may have only a glancing relevance to ordinary listeners. I ﬁnd it useful here to consider the analogy with magic. A stage magician uses various tricks to cause the audience to have extraordinary experiences—bunnies seem to disappear, beautiful assistants seem to be sawed in half, and so on.
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice (Oxford Studies in Music Theory) by Dmitri Tymoczko