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Let us now look at the general procedure for defining performance. We write P: for a sequence P1P2 … Pn. [ABSTRACT FROM AUTHOR]

We have learned in previous chapters that performance conveys a doubly infinite message: the infinity of interpretative perspectives as they are realized in music analysis, gesturality, and emotive expressivity, and the variety of performative shaping expressed in the infinitesimal vocabulary of performance fields. [ABSTRACT FROM AUTHOR]

After having introduced the three basic performance maps for onset, pitch, and loudness, we have to put these components together and ask for a better understanding of the combined situation. This means that we have to look for the simultaneous performance of all these parameters. [ABSTRACT FROM AUTHOR]

In this chapter, we want to make the idea explained in chapter 24 more precise in an explicit technical sense. Of course, this must rely on a concrete model of performance, one which is much more explicit than the generic setup for statistics, although statistics are a very strong argument for the construction of analytical rationales built upon weights and operators. We refer to figure 25.1 for the following discussion. [ABSTRACT FROM AUTHOR]

Inverse Performance Theory is the study of the reconstruction of the performance process from a given performance. This is a completely natural situation, since we usually perceive music as listeners and have to imagine what the performance could express, what it conveys in its complex signification process. [ABSTRACT FROM AUTHOR]

This chapter deals with a special type of experiment in performance theory, since experiments are necessary to test the relevance of a theoretical approach to real performance. How can we know that such an approach is explaining what we are experiencing in performance? The question is quite hard, because it is dificult in music to distinguish the creative subjective aspect from the scientific objective one. [ABSTRACT FROM AUTHOR]

Our first longer performance was constructed in 1995 with Robert Schumann΄s famous Träumerei, the seventh Kinderszene in his collection op.15. It was an experiment conducted in the context of a performance conference at the KTH, where different approaches to performance were compared [82], and from where we take the following presentation. The performance was played on a MIDI Boesendorfer Imperial grand piano at the School of Music in Karlsruhe. [ABSTRACT FROM AUTHOR]

The Rubato methodology was opened towards a variation of performance rules and their rationales, and although only the analytical rationale has so far been implemented, there is no obstruction against enrichments with emotional or gestural expressivity. This is due to the modularity of the Rubato architecture. Performance rules are by no means encoded in the analytical components. [ABSTRACT FROM AUTHOR]

Why are we including this topic in a book on performance theory? Couldn΄t one include any other topic relating to a specific musical genre as well? Solo piano music, operas, what not? The reason for the special role of the string quartet is that this genre has a theory, a re ection about why these four instruments–the two violins, the viola and the violoncello–merge to such a perfect harmony or collaborative music, a theory that is not only relevant sociologically, but also with respect to the intrinsic messaging of musical contents. [ABSTRACT FROM AUTHOR]

Besides partial models with emotional, gestural, or analytical rationales, there are two models that comprise all these approaches. We want to briefly present them for completeness, and less because they offer a deeper insight into the complex of problems related to expressive performance. [ABSTRACT FROM AUTHOR]

Performance operators are those instances of our theory that shape a performance transformation. We have defined the relevant structures, namely performance cells, in chapter 10. [ABSTRACT FROM AUTHOR]

Analytical weights did not come up from empty space. In fact, our idea was taken from Hugo Riemann΄s definition of metrical weights: Meter relates to weights. So it was decided to generate an output in the form of numerical weights for any analytical engine. [ABSTRACT FROM AUTHOR]

This last chapter dealing with expressive performance focuses on analytical rationales of performance, which means that the shaping of performance is grounded in analytical facts, as opposed to gestural or emotional ones. This means that we have to analyze the given score΄s structure and then define performance by use of such facts. [ABSTRACT FROM AUTHOR]

Gestural expression is a diffcult topic, not because the concept of a gesture is so diffcult, but because it looks so obvious that everybody believes to know what it means. This first impression is, however, misleading and it is there that the diffculty arises. The word ˵gesture″ is like ˵time″: If your are not asked, what it means, you know, but if you are asked you cannot tell. [ABSTRACT FROM AUTHOR]

Before we discuss prominent approaches to emotional expressivity in performance, we should introduce the very concept of emotion as it is understood in psychology, together with some remarks on neurological correlates to emotion. [ABSTRACT FROM AUTHOR]

Expressive theory has been sketched in sections 4.6, 4.7, 4.8 of chapter 4 dealing with (oni)ontology of performance. We have seen that expression splits into semantics and rhetorics: What is expressed, and how this is performed. Performance theory as it stands now partitions this complex of expressivity into three big themes: emotion, gesture, and analysis. These refer not to the rhetoric aspect, but to the variety of contents that are transferred to the audience, i.e. to the two axes of realities and embodiments on which these contents are distributed. [ABSTRACT FROM AUTHOR]

This chapter completes our study of the structure of performance. Recall from chapter 5 that we had four local-global dichotomies for performance theory: instrumental, parts, dimensions, and evolution. We are not going to discuss the first two, but dimensions and evolution will be dealt with. Dimensions are what we want to discuss now, and evolution will be discussed in chapter 21. [ABSTRACT FROM AUTHOR]

Tuning and intonation deal with the transformation of pitch symbols to frequency, while dynamics does so with the symbols of loudness that are transformed to sound pressure. Mathematically speaking, both transformations behave similarly to the situation with tempo. However, the conditions for tuning and intonation are much more complex than for tempo with regard to the semantics of pitch symbols. The dynamical situation is by far more simple, and we therefore have included this topic in the present chapter. [ABSTRACT FROM AUTHOR]

Tempo deals with the performance of time. There is a symbolic time, as used in the score notation, and the physical time of acoustical sounds, into which the symbolic time is transformed; for example, quarter note time units are transformed into seconds. [ABSTRACT FROM AUTHOR]

The previous, however sketchy, discussion of the history of performance theory has exhibited a split development between philosophical and empirical perspectives. Uniting such categorically different aspects not only is a question of finding a common language, but also requires a unifying epistemological approach. The present state of the art lacks unity on a deeper ontological level. It is, in fact, not even clear which dimensions of musical ontology are involved when dealing with the totality of performance. Evidently, we cannot neglect its deeper semantics, neither can we reduce the topic to purely quantitative, positivistic positions. It turns out that performance is above all complex through its ramified ontological richness. [ABSTRACT FROM AUTHOR]

A first look at the history of performance research seems to confirm Reinhard Kopiez΄s thesis [62] that there are two unrelated threads: on the one hand the empirical research as typically represented by Carl Seashore΄s measurements of agogics [62], and on the other the philosophical research as typically represented by Theodor Wiesengrund Adorno΄s writings [2]. It is true that these threads can be recognized, and we shall give their short history below, but it is erroneous to consider them as being in any contradictory position. [ABSTRACT FROM AUTHOR]

Transformation from symbolic reality of a score to physical reality of sounds [ABSTRACT FROM AUTHOR]

The oniontological topography developed in the last chapter specifies a communication from the poietic to the neutral position, yielding the performed music as a sounding expression. The delicate point is the technical way of connecting the score information and the surrounding CSI to the sounding output. The solution we have chosen is historically justified in that the score has evolved from the neumatic notation, meaning that the score is a ˵dance floor of gestures″ and therefore relates to real physical events in an abstracted way. This implies that the score coordinates of onset and pitch are an abstraction from real physical coordinates. [ABSTRACT FROM AUTHOR]

Musical performance deals with the transformation of a (typically classical Western) score into a physical entity composed of acoustical events and the embodiment of the score΄s symbols in the musicians΄ bodies. This is already a strong restriction of musical activities, since it excludes musical utterances that are not generated by scores. For example, oral traditions from different ethnicities and the standard practice of jazz are excluded. Jazz, when based on lead sheet notation, uses strongly reduced information requiring a significant interpretational work in order to represent the concretely played sounds. This means that we conceive a score as containing exhaustive data concerning the sounds to be played. [ABSTRACT FROM AUTHOR]

Performance theory is a part of music theory in its larger understanding. It is not classical music theory, which unfortunately and implicitly focuses on harmony, a miniature part of theoretical topics in music (comprising theory of motives, of rhythms, of tunings, of physical modeling of sound, orchestration, composition, algorithmic composition, representation, etc.). [ABSTRACT FROM AUTHOR]

Articulation adds a completely different phenomenon to performance. While we had seen that a priori onset, pitch, and dynamics can be performed independently from each other, articulation introduces performance of duration as a situation where this new parameter is intrinsically connected to the other time parameter, namely onset. [ABSTRACT FROM AUTHOR]

We want to apply the inverse theory described in chapter 25 to a concrete case: The agogical tempo fields as measured by Bruno Repp [111] from recordings by Marta Argerich (ARG in Repp΄s List, example ♫ 25) and Vladimir Horowitz (HO1 in Repp΄s List, example ♫ 26) of Schumann΄s Träumerei. [ABSTRACT FROM AUTHOR]

We have described the Rubato concept in section 15.3. The software Rubato was first implemented in Objevtice C on NEXTSTEP from 1992 to 1996 by Oliver Zahorka and the author. Later, the software was ported in 2001 to Mac OSX by Jörg Garbers in a research project at the TU Berlin. This version is available from [118]. [ABSTRACT FROM AUTHOR]

The prospects of future developments in performance theory are many. They are mainly split into two main threads: theory and experiment. Perhaps one should rename performance theory and call it Performance Science, splitting into theory and experiments. [ABSTRACT FROM AUTHOR]