1. Guerino Mazzola (Spring 2016 © ): Performance Theory IV RUBATO IV.2 (Wed Apr 06) Inverse Performance Theory

2. Guerino Mazzola (Spring 2016 © ): Performance Theory What is inverse performance theory? Direct performance theory deals with the construction of performances from determined rationales. Inverse performance theory deals with the reconstruction of adequate rationales from a given performance. Neutral Niveau Neutral NiveauPoiesis   -1

3. Guerino Mazzola (Spring 2016 © ): Performance Theory Inverse performance theory first needs to retrieve the performance information necessary for further analysis, e.g. Direct measurements of tempo curves as made by Bruno Repp from 28 audio recordings of Schumann‘s dream op. 15/7 Repp B: Diversity and Commonality in Music Performance: An Analysis of Timing Microstructure in Schumann’s “Träumerei”. J. Acoustic Soc. Am. 92, 1992Direct measurements of tempo curves as made by Bruno Repp from 28 audio recordings of Schumann‘s dream op. 15/7 Repp B: Diversity and Commonality in Music Performance: An Analysis of Timing Microstructure in Schumann’s “Träumerei”. J. Acoustic Soc. Am. 92, 1992 Direct measurements of tempo curves as made by Robert Goswitz from 30 audio recordings of Chopin‘s Prélude op. 28 No. 4. Beran J, Goswitz R, Mazzola G, Mazzola P: On the relationship between tempo and quantitative metric, melodic, and harmonic information in Chopin‘s Prélude op. 28 No. 4: a statistical analysis of 30 performances. J. Math & Music, Vol 8, No. 3, 2014Direct measurements of tempo curves as made by Robert Goswitz from 30 audio recordings of Chopin‘s Prélude op. 28 No. 4. Beran J, Goswitz R, Mazzola G, Mazzola P: On the relationship between tempo and quantitative metric, melodic, and harmonic information in Chopin‘s Prélude op. 28 No. 4: a statistical analysis of 30 performances. J. Math & Music, Vol 8, No. 3, 2014

4. Guerino Mazzola (Spring 2016 © ): Performance Theory Software-generated performance fields from given MIDI files from MIDI piano recordings, as realized with the Espresso Rubette.Software-generated performance fields from given MIDI files from MIDI piano recordings, as realized with the Espresso Rubette. Performance fields calculated with the Espresso Rubette from MIDI files that were generated via Melodyne editor software from audio recordings.Performance fields calculated with the Espresso Rubette from MIDI files that were generated via Melodyne editor software from audio recordings. The tempo curve data in Repp‘s analysis were generated by direct inspection of audio data.The tempo curve data in Repp‘s analysis were generated by direct inspection of audio data. The tempo curve data in Goswitz‘s analysis were generated using Audiosculpt software.The tempo curve data in Goswitz‘s analysis were generated using Audiosculpt software.

5. Guerino Mazzola (Spring 2016 © ): Performance Theory Stefan Göller, Stefan Müller

6. Guerino Mazzola (Spring 2016 © ): Performance Theory Melodyne editor audio file MIDI file

7. Guerino Mazzola (Spring 2016 © ): Performance Theory Effective Calcuations: see 2003 Computer Music Journal Paper with Stefan Mueller

8. Guerino Mazzola (Spring 2016 © ): Performance Theory

10. Bruno Repp: Diversity and Commonality inMusic Performance: An Analysis of Timing Microstructure in Schumann‘s „Träumerei“ Haskins Laboratories Status Report on Speech Research 1992.

11. Guerino Mazzola (Spring 2016 © ): Performance Theory Bruno Repp‘s measurements Our results are closely related to Repp's work. (Repp applied principal component analysis to the 28 tempo curves.) One of his main results is that Cortot and Horowitz appear to represent two extreme types of performances. One of his main results is that Cortot and Horowitz appear to represent two extreme types of performances. Thus, in a heuristic way, Repp suggested classifying the performances according to their factor loadings into a Cortot and a Horowitz cluster respectively. Thus, in a heuristic way, Repp suggested classifying the performances according to their factor loadings into a Cortot and a Horowitz cluster respectively. Our regression analysis confirms the basic findings. Our regression analysis confirms the basic findings.

12. Guerino Mazzola (Spring 2016 © ): Performance Theory The Beran-Mazzola approach (see The Topos of Music, ch. 44) Hierarchical smoothing: make successively refined average curves from metrical, melodic, harmonic weights as well as from their first and second derivatives. Get a total of 58 such curves X(E) =(X 1 (E), X 2 (E), X 3 (E),... X 58 (E)) onset time E

13. Guerino Mazzola (Spring 2016 © ): Performance Theory onset time E slope of metric slope of slope of metric

14. Guerino Mazzola (Spring 2016 © ): Performance Theory The Beran-Mazzola Operator Statistical linear regression method, but has a very geometric interpretation: How do we get the tempo curves of the 28 performers? 1.For each perfomer p, we take the logarithm of tempo curves log(T p (E)). This is similar to pitch = log(frequency), loudness = log(Amplitude)! 2.Take the analytical curve X(E) =(X 1 (E), X 2 (E), X 3 (E),... X 58 (E)) 3.Find a vector w p = (w p,1, w p,2, w p,3,... w p,58 ) for each perfomer p such that we have log(T p (E)) = X(E). w p + const. log(T p (E)) = X(E). w p + const. X(E). w p = |X(E)||w p | cos(  ) X(E) wpwpwpwp  This works!

15. Guerino Mazzola (Spring 2016 © ): Performance Theory https://www.youtube.com/watch?v=Tovh6JjaQ1A

16. Guerino Mazzola (Spring 2016 © ): Performance Theory Gottfried Wilhelm Leibniz: musica est exercitium arithmeticae occultum nescientis se numerare animi music is a hidden arithmetic exercise of the soul which does not know that it is counting Gottfried Wilhelm Leibniz: musica est exercitium arithmeticae occultum nescientis se numerare animi music is a hidden arithmetic exercise of the soul which does not know that it is counting Relating emotions to structure? performance Sloboda A S & Lehmann A C: Tracking Performance Correlates of Changes in Perceived Intensity of Emotion During Different Interpretations of a Chopin Piano Prelude. Music Perception, 2001 Beran J, Goswitz R, Mazzola G, Mazzola P: On the relationship between tempo and quantitative metric, melodic, and harmonic information in Chopin‘s Prélude op. 28 No. 4: a statistical analysis of 30 performances. J. Math & Music, Vol 8, No. 3, 2014 emotions structure

17. Guerino Mazzola (Spring 2016 © ): Performance Theory

18. log-tempo curves

19. Guerino Mazzola (Spring 2016 © ): Performance Theory 1 9 12 16 17 18 mean tempo curve

20. Guerino Mazzola (Spring 2016 © ): Performance Theory original metrical, melodic, and harmonic weights

21. Guerino Mazzola (Spring 2016 © ): Performance Theory

24. Lie type restriction Inverse performance theory = Mathematical theory of music criticism? Inverse performance theory = Mathematical theory of music criticism? given output unknown shaping forces affine transport

25. Guerino Mazzola (Spring 2016 © ): Performance Theory ij i j flying carpets defined by 4 parameters influence of daughter i on daughter j Influnce(i ⇒ j) = Influence(n-j ⇒ n-i) Influnce(i ⇒ i ) =1

26. Guerino Mazzola (Spring 2016 © ): Performance Theory

27. Lie type restriction restriction sum affine transport

28. Guerino Mazzola (Spring 2016 © ): Performance Theory parameters of affine transport parameters of Lie operators: weights,directions field output Z. fiber(Z.) Roberto Ferretti

29. Guerino Mazzola (Spring 2016 © ): Performance Theory AA’BA’’ Träumerei 8 measures 5 flying carpets ~ 20 parameters + initial tempo ~ 21 parameters melodic weight for tempo operator

30. Guerino Mazzola (Spring 2016 © ): Performance Theory Roberto Ferretti Jan Beran This approach reveals a more global coherence in Argerich's performance than in Horowitz's performance

31. Guerino Mazzola (Spring 2016 © ): Performance Theory Period level: In the inter-period coherence, Argerich is more final than Horowitz, whereas the causal level is more pronounced by Horowitz. Measure level: Horowitz: He plays the first period with pronounced causal and final coherence, whereas the causal coherence decreases to a very low level towards the end of the piece. The repetition A’ of the first period A shows a ‘relaxation of coherence’ which may be justified by the repetitive situation. The development section B slightly increases the final character. The recapitulation seems to be quite ‘tired’: the causal character is very low, the final character is decreased. Argerich: The first period has a less coherent ambitus than with Horowitz. In contrast to Horowitz, the final coherence of Argerich increases as the piece goes on. The development and the recapitulation are pronouncedly final. The development and the recapitulation shows a consciousness of the end of the piece which is absent with Horowitz. In other words, Argerich's recapitulation is ’prospective’ and not ‘retrospective.’