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Download The Music of the Spherical Quotients - Dmitri Tymoczko
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http://dmitri.tymoczko.com MUSIC THEORY 2.0 Dmitri Tymoczko Princeton University [email protected] http://dmitri.tymoczko.com THREE THINGS ABOUT ME 1. 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 2. I am mostly interested in symbolic musical data (scores) rather than audio. 3. 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. http://dmitri.tymoczko.com TWO ANALYSES? 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.” 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 0, 1, 2the fifth up by two (C, E, G) (C, F, A) semitones.” http://dmitri.tymoczko.com FIFTH IDEA http://dmitri.tymoczko.com FIFTH IDEA 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. 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!
