A Geometry of Music: Harmony and Counterpoint in the Extended Common PracticeHow is the Beatles' "Help!" similar to Stravinsky's "Dance of the Adolescents?" How does Radiohead's "Just" relate to the improvisations of Bill Evans? And how do Chopin's works exploit the non-Euclidean geometry of musical chords? In this groundbreaking work, author Dmitri Tymoczko describes a new framework for thinking about music that emphasizes the commonalities among styles from medieval polyphony to contemporary rock. Tymoczko identifies five basic musical features that jointly contribute to the sense of tonality, and shows how these features recur throughout the history of Western music. In the process he sheds new light on an age-old question: what makes music sound good? A Geometry of Music provides an accessible introduction to Tymoczko's revolutionary geometrical approach to music theory. The book shows how to construct simple diagrams representing relationships among familiar chords and scales, giving readers the tools to translate between the musical and visual realms and revealing surprising degrees of structure in otherwise hard-to-understand pieces. Tymoczko uses this theoretical foundation to retell the history of Western music from the eleventh century to the present day. Arguing that traditional histories focus too narrowly on the "common practice" period from 1680-1850, he proposes instead that Western music comprises an extended common practice stretching from the late middle ages to the present. He discusses a host of familiar pieces by a wide range of composers, from Bach to the Beatles, Mozart to Miles Davis, and many in between. A Geometry of Music is accessible to a range of readers, from undergraduate music majors to scientists and mathematicians with an interest in music. Defining its terms along the way, it presupposes no special mathematical background and only a basic familiarity with Western music theory. The book also contains exercises designed to reinforce and extend readers' understanding, along with a series of appendices that explore the technical details of this exciting new theory. |
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LibraryThing Review
User Review - ztutz - LibraryThingI had huge hopes for this book, but sadly, I found it quite lacking. Tymoczko's theories are not well supported - because of this, the book winds up being a collection of interesting mathematical factoids about encoding music, rather than the exposition of a new tool for taming music theory. Read full review
Contents
HISTORY AND ANALYSIS | 193 |
Measuring VoiceLeading Size | 397 |
Chord Geometry A More Technical Look | 401 |
Discrete VoiceLeading Lattices | 412 |
The Interscalar Interval Matrix | 418 |
Scale Macroharmony and Lerdahls Basic Space | 424 |
Some Study Questions Problems and Activities | 428 |
| 435 | |
| 445 | |
Other editions - View all
A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice Dmitri Tymoczko No preview available - 2011 |
Common terms and phrases
acoustic scale ascending atonal Bach’s basic bass centricity Chapter Chopin chord progressions chord space chord types chromatic voice leading chromaticism circle of fifths classes composers connected contains contrapuntal counterpoint cross section crossing-free Debussy Debussy’s descending diatonic scale distance divide the octave dominant seventh chord efficient voice leading equal-tempered example F major F minor familiar four-voice fourth geometrical graph half-diminished harmonic consistency harmonic minor hexatonic scale interscalar transposition intervals inversion jazz lattice line segments macroharmony major triad Möbius strip modulation Mozart’s musicians nineteenth-century notes octatonic scale œ œ œ passages pentatonic perfect fifth piano piece pitch space pitch-class pitch-class space prelude pure contrary relatively represent root scalar transposition scale degree Schoenberg semitones sequence seven-note Shostakovich similar single-semitone sonorities stepwise structure symmetry techniques theorists three-note chord tonal music tone tonic traditional transposed transpositionally Tristan tritone substitution twentieth-century Tymoczko voice crossings voice-leading voices move whole-tone
Bibliographic information
| Title | A Geometry of Music: Harmony and Counterpoint in the Extended Common Practice Oxford Studies in Music Theory |
| Author | Dmitri Tymoczko |
| Publisher | Oxford University Press, 2010 |
| ISBN | 0199714355, 9780199714353 |
| Length | 480 pages |
| Subjects | › › Mathematics / Geometry / Analytic Music / History & Criticism Music / Instruction & Study / Composition Music / Instruction & Study / Theory Science / General |
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