Dmitri Tymoczko is a composer and music theorist. His music, which draws on rock, jazz, and romanticism, has been performed by ensembles such as the Amernet String Quartet, the Brentano Quartet, Janus, Newspeak, the San Francisco Contemporary Players, the Pacifica Quartet, and the pianist Ursula Oppens. As a theorist, he has published more than two dozen articles dealing with topics related to contemporary tonality, including scales, voice leading, and functional harmonic norms. His article "The Geometry of Musical Chords," was the first music-theory article ever published by the journal Science.
Tymoczko's album Beat Therapy, combines jazz instrumentation with classical ideas of development. The critic Frank Oteri describes it as "far reaching and utterly entertaining." In Crackpot Hymnal, he presents expressly composed chamber pieces inspired and mixed from a number of traditional styles. Jazz, popular, blues and rock styles interact with folk and contemporary classical music. A third CD, Rube Goldberg Variations was released in 2018. Joshua Kosman, writing at SFGate, called it "whimsical," "ingenious," and with a "rich emotional arc" produced by a "warmth of personality that is distinctive."
Theoretical work
In A Geometry of Music, Tymoczko proposes a general framework for thinking about tonality, arguing that there are five basic features that jointly contribute to the sense of tonality:
conjunct melodic motion
harmonic consistency
acoustic consonance
limited macroharmony
centricity
The first part of the book explores theoretical questions about how these properties can be combined. In particular, Tymoczko uses orbifolds to develop "maps" of musical chords, showing that the first two properties can be combined only in special circumstances. The second part of the book uses these tools to analyze pieces from the Middle Ages to the present. Tymoczko argues that there is an "extended common practice" linking superficially distinct styles, with jazz being much closer to classical music than many have thought. Tymoczko showed that nearly even chords are represented by three main families of lattices. Two of these :
a circle of n-dimensional cubes linked by shared vertices
a circle of n-dimensional cubes linked by shared facets
are particularly useful in analysis. What results is a systematic perspective on the full family of chord-based graphs. Tymoczko has also written a free software program, "ChordGeometries," allowing users to visualize the orbifolds representing musical chords.