MUSIC THEORY 2.0 Dmitri Tymoczko Princeton University http://dmitri.tymoczko.com MUSIC THEORY 2.0 Dmitri Tymoczko Princeton University dmitri@princeton.edu 1

http://dmitri.tymoczko.com THREE THINGS ABOUT ME I am most interested in modern and broadly tonal music: Debussy Stravinsky 1940s Messiaen Shostakovich Jazz (especially after WWII) Rock Minimalism and postminimalism World music But, many of the things I say will be applicable to atonal music as well.

http://dmitri.tymoczko.com THREE THINGS ABOUT ME I am mostly interested in symbolic musical data (scores) rather than audio. I am interested in composer or analyst cognition rather than listener perception. Ideas we might have to work to hear Many great composers are intellectual Discovering new ways for music to be I like understanding what other composers are doing, and discovering new ideas for writing music.

TWO ANALYSES? http://dmitri.tymoczko.com Future versions of this talk may begin with two brief analyses: the analysis of Des pas sur la neige from Debussy’s Preludes and Chopin Prelude in E minor. These can be found in Chapters 8 and 9 of “A Geometry of Music.”

SOME IDEAS A fast tour through a lot of material. http://dmitri.tymoczko.com SOME IDEAS A fast tour through a lot of material. The main point: our most general way of thinking about musical objects (set theory) is incomplete: Scales Voice leading. More generally, to suggest that there is room for new ideas in music!

http://dmitri.tymoczko.com FIRST IDEA Two-leveled hierarchy, with progressions happening at the level of the chord and the scale.

http://dmitri.tymoczko.com SECOND IDEA At each level of the hierarchy, we can identify two different kinds of structure.

http://dmitri.tymoczko.com THIRD IDEA The best way to test a theoretical idea is to experiment on yourself.

http://dmitri.tymoczko.com FOURTH IDEA We can formalize the motion between objects using the concept of a voice leading: A voice leading is a collection of paths in pitch class space. It shows how the notes of one chord move to the notes of another (ignoring octaves). “C major moves to F major by keeping the root constant, moving the third up by semitone, and moving the fifth up by two semitones.”

http://dmitri.tymoczko.com FIFTH IDEA

http://dmitri.tymoczko.com FIFTH IDEA

SIXTH IDEA Scales serve two different functions: http://dmitri.tymoczko.com SIXTH IDEA Scales serve two different functions: They act as large or macro harmonies that control the pitches we hear. They provide a measure of musical distance, the scale step.

SEVENTH IDEA Evenness is a fundamental attribute of musical objects. http://dmitri.tymoczko.com SEVENTH IDEA Evenness is a fundamental attribute of musical objects. At the level of the chord: it allows chords to be connected to their transpositions by small voice leadings. At the level of the scale: it ensures that the scalar measure of musical distance is roughly equal to the log-frequency measure. Very uneven objects are also interesting.

http://dmitri.tymoczko.com EIGHTH IDEA Approximateness: if you can do something with a chord, then you can do something like it with a nearby chord.

http://dmitri.tymoczko.com EIGHTH IDEA Approximateness: if you can do something with a chord, then you can do something like it with a nearby chord.

http://dmitri.tymoczko.com NINTH IDEA If you can do something in one scale, you can do something similar in other scales.

http://dmitri.tymoczko.com TENTH IDEA Consider voice leadings to be related when they differ only by a transpositional factor. the center-of-mass coordinate system

http://dmitri.tymoczko.com TENTH IDEA

http://dmitri.tymoczko.com ELEVENTH IDEA

http://dmitri.tymoczko.com Thank you! 20