Guerino Mazzola U & ETH Zürich Internet Institute for Music Science Manifolds and Stemmata in Musical Time Manifolds and Stemmata in Musical Time

The Performance Transformation Normative vs. Immanent Analysis Local and Global Meters Nerves and Weights MetroRubette ® : Examples Czerny‘s Tempi and Stemmata Analytical Performance on Rubato ® The Performance Transformation Normative vs. Immanent Analysis Local and Global Meters Nerves and Weights MetroRubette ® : Examples Czerny‘s Tempi and Stemmata Analytical Performance on Rubato ® program

√ H E h e Ee √E√E T(E) = (d √ E /dE) -1 [ q /sec] transformations

analysis ? (symbolic) time maximal local meter no local meter local meter

meters n/16 a b c d e

nerves b nerve of the covering {a,b,c,d,e} x dominates y iff simplex(y)  simplex(x) e c a d

nerves weight(x) =  z Œ simplex(x), m £ length(z) length(z) p m = p =

Os X  RUBATO ®    Java Classes for Modules, Forms, and Denotators examples

stemmata         bar 1bar 2bar 3bar 4

stemmata presto ® mamma curva 1 curva 2 curvetta 4curvetta 3

stemmata Chopin: Impromptu op. 29 tr

T dTdT TT Z( d T,  ) Mother Daughter Granddaughter  performance

X x = √ (X) √  = (1,1,…,1) = Const. x 0 = √ I (X 0 ) initial performance x = x 0  t.  Z(X)= J( √ )(X) -1  performance field performance field, defined on F frame cube F = the frame of Z I = initial set X 0 Œ I = initial set X 0 = Ú X Z(t) Ú X Z = integral curve through X X0X0 x0x0 F performance

RUBATO ® software: Calculations via Runge-Kutta-Fehlberg methods for numerical ODE solutions Performnce

Emotions, Gestures, Analyses Big Problem: Describe Typology of shaping operators! w(E,H,…) H E Performnce

performance J.S. Bach: Die Kunst der Fuge — Contrapunctus III Joachim Stange-Elbe Metrical and Motivic Weights act on agogics, dynamics, and articulation sopran alt tenor bass score sum of all

The Topos of Music Geometric Logic of Concepts, Theory, and Performance in collaboration with Moreno Andreatta, Jan Beran, Chantal Buteau, Karlheinz Essl, Roberto Ferretti, Anja Fleischer, Harald Fripertinger, Jörg Garbers, Stefan Göller, Werner Hemmert, Mariana Montiel, Andreas Nestke, Thomas Noll, Joachim Stange-Elbe, Oliver Zahorka