Guerino Mazzola (Spring 2016 © ): Performance Theory III EXPRESSIVE THEORY III.7 (Mo Mar 7) Analytical Expression III

Guerino Mazzola (Spring 2016 © ): Performance Theory Analytical Expression III: Theodor W. AdornoTheodor W. Adorno Anders Friberg and Johan SundbergAnders Friberg and Johan Sundberg Guerino Mazzola et al.Guerino Mazzola et al.

Guerino Mazzola (Spring 2016 © ): Performance Theory     composition performance math. operations analysis sound files

Guerino Mazzola (Spring 2016 © ): Performance Theory Need analytical weights for PerformanceRubette! w(E,H,…) H E

Guerino Mazzola (Spring 2016 © ): Performance Theory Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubettePerformanceRubetteBasic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubettePerformanceRubetteBasic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory ? onset axis maximal local meter M no local meter local meter M length l(M) = 4 GTTM Ray Jackendoff & Fred Lerdahl

Guerino Mazzola (Spring 2016 © ): Performance Theory n/16 a b c d e

b Nerve N max (X) of covering {a, b, c, d, e} e c a d a b c d e „metrical complex“

Guerino Mazzola (Spring 2016 © ): Performance Theory 0 b e c a d Nerve (X) X Sp 6 a b c d e

Guerino Mazzola (Spring 2016 © ): Performance Theory Definition: Global metric is the structure induced by the covering of the onsets by (maximal) local meters. What is rhythm?

Guerino Mazzola (Spring 2016 © ): Performance Theory Need quantification of geometric facts for PerformanceRubette = analytical weights! Especially: metrical weights w(E,H,…) H E

Guerino Mazzola (Spring 2016 © ): Performance Theory Definition: The (metrical) rhythm is the weight function on the onsets, which is deduced from the global metric by the formula w(x) =  x ∈ M, m ≧ l(M) l(M) p w(x) =  x ∈ M, m ≧ l(M) l(M) p M = any motif m = minimal admitted length of local meters p = metrical profile w(x) =  x ∈ M, m ≧ l(M) l(M) p w(x) =  x ∈ M, m ≧ l(M) l(M) p M = any motif m = minimal admitted length of local meters p = metrical profile

Guerino Mazzola (Spring 2016 © ): Performance Theory Quantification of Metrical Semantic Profile = growth number for length contributions Minimum = minimal admitted lengths Elimination of too short local meters lengths < Minimum Onset MetroWeight(E) = x MetroWeight(x) =

Guerino Mazzola (Spring 2016 © ): Performance Theory w(x) =  x ∈ M, m ≧ l(M) l(M) p m = p = a b c d e

Guerino Mazzola (Spring 2016 © ): Performance Theory Have the problem of different types of score objects contributing to the weight functions. How can we take care of this distribution in a precise way? Ideas?

Guerino Mazzola (Spring 2016 © ): Performance Theory four predicates left hand right hand barlines pauses

Guerino Mazzola (Spring 2016 © ): Performance Theory    

Os X MetroRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory J. S. Bach: Kunst der Fuge, Contrapunctus III Joachim Stange-Elbe a b s t Sonification of metrical weights

Guerino Mazzola (Spring 2016 © ): Performance Theory „Träumerei“ right hand, from longest to shortest minima

Guerino Mazzola (Spring 2016 © ): Performance Theory

Anja Volk-Fleischer‘s work (PhD 2002 thesis Die analytische Interpretation) „... lässt sich nun die metrische Kohärenz als Korrespondenz zwischen innerem und äusserem metrischen Gewicht beschreiben.“

Guerino Mazzola (Spring 2016 © ): Performance Theory

Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubettePerformanceRubetteBasic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory Motif Space MOT Give concept of a note „point“: n = sequence of numerical coordinates: n = (o n, p n, l n,...) (onset o, pitch p mandatory, the others may be present but we do not use them here) Definition: A motif M in the given note space (fixed for given context) is a set M = {n 1, n 2,... n k } of notes with o n i ≠ o n j for i ≠ j.

Guerino Mazzola (Spring 2016 © ): Performance Theory Yes!No!Yes!Yes! MOT = space of all motives (of notes of given type)

Guerino Mazzola (Spring 2016 © ): Performance Theory Melodic weights of motives and notes. Take motif M 1.presence(M) ~ # {motives containing a submotif similar to M} 2.content(M) ~ # {motives similar to a submotif contained in M} 3.weight(M) = presence(M) x content(M) presence content weight(note x) =  weights of motives containing note x M

Guerino Mazzola (Spring 2016 © ): Performance Theory Art of Fugue main motif, motives‘ weights

Guerino Mazzola (Spring 2016 © ): Performance Theory R. Schumann Träumerei

Guerino Mazzola (Spring 2016 © ): Performance Theory Chantal Buteau‘s work (PhD 2003 thesis A Topological Model of Motivic Structure and Analysis of Music: Theory and Operationalization. Dissertation, Zürich 2003) Motivic evolution tree

Guerino Mazzola (Spring 2016 © ): Performance Theory Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubettePerformanceRubetteBasic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory HarmoRubette one chord Ch function values tonalities

Guerino Mazzola (Spring 2016 © ): Performance Theory The Harmonic Path

Guerino Mazzola (Spring 2016 © ): Performance Theory Example: Czerny

Guerino Mazzola (Spring 2016 © ): Performance Theory Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubette: just a hint, more later!PerformanceRubette: just a hint, more later!Basic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory Analysis: MetroRubetteMetroRubette MeloRubetteMeloRubette HarmoRubetteHarmoRubettePerformance: PerformanceRubettePerformanceRubetteBasic: PrimavistaRubettePrimavistaRubette

Guerino Mazzola (Spring 2016 © ): Performance Theory PrimavistaRubette