1. Guerino Mazzola U & ETH Zürich Internet Institute for Music Science guerino@mazzola.ch www.encyclospace.org/talks Manifolds and Stemmata in Musical Time Manifolds and Stemmata in Musical Time

2. 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

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

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

5. meters n/16 a b c d e 0234681012

6. 0 6 4 2 nerves b nerve of the covering {a,b,c,d,e} x dominates y iff simplex(y)  simplex(x) e c a d 12 10 3

7. nerves weight(x) =  z Œ simplex(x), m £ length(z) length(z) p m = p = 2 4 6 8 10 12 14 16 18 20 22

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

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

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

12. stemmata Chopin: Impromptu op. 29 tr

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

14. 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

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

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

17. 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

18. The Topos of Music Geometric Logic of Concepts, Theory, and Performance www.encyclospace.org 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