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2017 | Buch

Local and Global Performance Transformations Kapitel lesen Erstes Kapitel lesen

The Topos of Music II: Performance

Theory, Software, and Case Studies

verfasst von: Prof. Dr. Guerino Mazzola

Verlag: Springer International Publishing

Buchreihe : Computational Music Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

This is the second volume of the second edition of the now classic book “The Topos of Music”. The author explains his theory of musical performance, developed in the language of differential geometry, introducing performance vector fields that generalize tempo and intonation. The author also shows how Rubato, a software platform for composition, analysis, and performance, allows an experimental evaluation of principles of expressive performance theories.

Inhaltsverzeichnis

Frontmatter

Structure Theory of Performance

Frontmatter
32. Local and Global Performance Transformations
Summary
Performance includes a non-trivial transformation from the mental reality of a score to the physical reality of acoustic and, in the limit, gestural realization. We discuss a model of local and global transformation structures and present a preliminary discourse on the need to “shape mental reality” in performance. Local performance transformation structures, together with their syntactic combination to global structures, are formally developed. They involve extrapolation from discrete to continuous or differentiable data; the latter are induced by use of spline techniques. We give a justification of such a procedure from the musical and mathematical points of view, in particular with stress on expressive coherence.
Guerino Mazzola
33. Performance Fields
Summary
Performance fields are the core of an in-depth theory of performance structure. They are a distinguished type of vector fields which give an infinitely precise, i.e., infinitesimal, account of the ‘shaping forces’ of a given local performance transformation. Although performance fields are not recognized as such in musicology and traditional performance research, they arise in a completely natural way in the traditional context of tempo, intonation, and dynamics. We give a careful account of this basic fact. A closer look at articulation and further sound parameters (apart from onset, pitch and loudness which are used for tempo, intonation, and dynamics) reveals that performance fields should be viewed within a fairly general approach. We define the formal setup. In order to provide a deeper understanding of the semiotic signification process of performance fields, we review the performance philosophies of Theodor W. Adorno, Benjamin, and Diana Raffman.
Guerino Mazzola
34. Initial Sets and Initial Performances
Summary
Performance has to start somewhere. The theory of this initialization deals with initial sets and initial performance. Naively speaking, initial sets are the first notes of a performance. Semiotically, initial theory describes a turning point from lexicality to reality in music which is supported by shifters; we explain this rationale. Since music deals with many parameters, initialization has to be specified in all dimensions. We first comment on the classical initial sets in onset, pitch, and duration. On an initial set, the performance cannot be calculated from previous performance, an initial performance has to be defined. We discuss ways to do so. On a more technical level, we introduce the hit point theory, a mathematical account for the control of performance field ows as their curves approach initial sets. Strategies of guessing best approaches to initial sets are presented.
Guerino Mazzola
35. Hierarchies and Performance Scores
Summary
As a synthesis of the structural parts described in Chapter 32 through Chapter 34 we establish the overall structure of performance. The objects of performance structure are understood as being an additional score type, called performance score, layered over the given “symbolic” score like a system of optical lenses which ‘deform’ the rigid configuration of note symbols. The performance score is a global object built from an atlas of local performance scores. A local performance score is built from a hierarchy of performance cells, the very core of performance structures. We first describe the category of performance cells. Local performance scores are defined by a hierarchical construction principle: They are particular diagrams in the category of performance cells. The conceptual and musical background of such local hierarchies is evidenced through a series of examples, including the piano and violin hierarchies. We end up with the definition and exemplification of the concept of a (global) performance score.
Guerino Mazzola

Expressive Semantics

Frontmatter
36. Taxonomy of Expressive Performance
Summary
Performance structure describes a semiotic fact: expression of meaning by shaping of score data. These expressive semantics are classified according to the three layers of reality captured by the topographic cube: Psychic, physical, and mental (see Section 2.4). The first one means that performance expresses emotions, the second one deals with expression of gestural contents, and the third one—the musicologically most interesting one—aims at giving one's understanding of the musical text a rhetoric expression. In a realistic performance, all three expressive semantics will participate, however, a theory of expressive semantics must first of all deal with the “pure” types which are, each in its own way, difficult subjects of ongoing research. We will not deal with the psychological, cognitive or neurophysiological esthesic aspect of performance since this is part of music psychology and would exceed our subject.
Guerino Mazzola
37. Performance Grammars
Summary
The idea of basing performance on rules in analogy with linguistic grammar goes back to Mathis Lussy [631]. In modern performance research, this terminology was recovered by Johan Sundberg and his school [1024]. We discuss the principles for a grammar of performance and give an overview of representative approaches to this theory.
Guerino Mazzola
38. Stemma Theory
Summary
The stemma theory is introduced from its musicological and practical motivation. Semiotically speaking, performance is a result of a diachronic process. This is traced on the structure of a genealogical tree, the stemma of a performance. The stemma formalizes the diachronic process of rehearsal and practising. We describe the structure of stemmata as “family trees of performance”, together with the corresponding genetic and environmental principles.
Guerino Mazzola
39. Operator Theory
Summary
Operators are the substance of shaping performance. They refer to mothers, but they are the only instances capable of altering, refining, or ruining what has been achieved. They are also the pipes where exterior information, be it from score predicates, from analytical data, or from general system parameters, can be channeled and transformed into performance structures. We describe and motivate the concept of a weight (function). This is the turning point between “exterior” and “interior” strata to performance. We discuss diffierent exigences for performance operators to cope with `primavista' and `analytical' data. A series of common primavista and analytical weights is discussed. We then expose a taxonomy of operators, followed by some special examples of the existing realizations, regarding tempo and articulation, as well as theoretically founded generalizations which are based upon Lie derivatives. The chapter concludes with a discussion of more “social” types of operators which correspond to “family life” correlations introduced in Section 38.3.4. The final subject is a prospective to `continuous stemmata', i.e., generalized stemmata based upon infinitely small coupled space portions.
Guerino Mazzola

RUBATO®

Frontmatter
40. Architecture
Summary
RUBATO® is a metamachine designed for representation, analysis, and performance of music. It was developed on the NEXTSTEP environment during two SNSF grants from 1992 to 1996 by the author and Oliver Zahorka [690, 689, 692, 699, 1146, 1148]. From 1998 to 2001, the software was ported to Mac OS X by Jöorg Garbers in a grant of the Volkswagen Foundation. RUBATO®’s architecture is that of a frame application which admits loading of an arbitrary number of modules at run-time. Such a module is called RUBETTE®. There are very di_erent types of Rubettes. On the one hand, they may be designed for primavista, compositional, analytical, performance stemma or logical and geometric predication tasks. On the other, they are designed for subsidiary tasks, such as filtering from and to databases, information representation and navigation tasks, or else for more speci_c subtasks for larger “macro” Rubettes. A RUBETTE® of the subtask type is coined OPERATOR and implements, for example, what we have called performance operators in Section 44.7. The RUBATO® concept also includes distributed operability among difierent peers. This software is conceived as a musicological research platform and not a hard-coded device, we describe this approach. Concluding this chapter, we discuss the relation between frame and modules.
Guerino Mazzola
41. The RUBETTE® Family
Summary
We give an overview of the analytical MetroRUBETTE®, MeloRUBETTE®, HarmoRUBETTE®, the PerformanceRUBETTE®, and the PrimavistaRUBETTE®, which have been realized on the NEXTSTEP and then on the Mac OS X environment.
Guerino Mazzola
42. Performance Experiments
Summary
This chapter traces the analyses and syntheses processes which led to the historically first full- edged RUBATO®-driven performance in July 1996 on the MIDI-Boesendorfer at the Staatliche Hochschule für Musik in Karlsruhe, as well as to the qualitatively high performance of contrapunctus III in Bach‘s Kunst der Fuge. We report the technical prerequisites, the analytical background generated by RUBATO®, and the step-by-step realization of the stemma and the overall parametrization.
Guerino Mazzola

Statistics of Analysis and Performance

Frontmatter
43. Analysis of Analysis
Summary
Not unexpectedly, weight analysis turns out to be complex information that cannot always be handled intuitively. This suggests techniques that help analyzing weight analysis. The problem may be tackled by use of statistical methods. We expose the subject and Jan Beran‘s approach based upon hierarchical decompositions of weights, together with an application to comparison of analyses of Bach, Schumann, and Webern.
Guerino Mazzola
44. Differential Operators and Regression
Summary
We give statistical evidence from 28 performances of Schumann’s “Träumerei”, as measured by Bruno Repp [886] that the rhythmic, motivic, and harmonic analyses provided by RUBATO® are shaping structures for the agogical streams. The statistical model is based on regression analysis and realizes shaping of agogics by a second degree linear differential operator as a function of analytical weights which are averaged over a natural grouping hierarchy (as described in Chapter 43) of the score.
Guerino Mazzola
45. Relating Tempo to Metric, Melodic and Harmonic Analyses in Chopin’s Prélude op. 28, No. 4
Summary
We investigate the relationship between analytical information extracted from the score of Chopin’s Prélude op. 28, No. 4 and tempo curves obtained from 30 recordings by well known pianists. The score related information consists of metric, melodic and harmonic weight functions. A hierarchic regression approach is used. The statistical analysis yields strong evidence for the approximate validity of an operator defined in terms of hierarchically decomposed weight functions, as originally introduced in Beran and Mazzola (1997) in the context of Schumann’s Träumerei, see also Chapter 44. Further analysis based on these findings reveals some typical features of the performances. This chapter only summarizes the methods and results and refers to the paper [110]. The reader is asked to consult that paper for a thorough discussion.
Guerino Mazzola

Inverse Performance Theory

Frontmatter
46. Principles of Music Critique
Summary
Inverse performance theory deals with the critic’s problem of how to extract in his critique what is hidden behind a performance output. To initiate this theory, we therefore should question the perspectives which a critic has to envisage. To begin with, we inquire the intriguing task of feuilletonistic critique: why is it a never ending story? Is it substantially necessary—beyond music business? We then position the critic within the sociological context: How do norms intervene in critique? This is exemplified by Glenn Gould’s performative redefinition of classics. The chapter terminates with an ethnomusicological view on historicistic performance as it is typically undertaken by Nicolas Harnoncourt.
Guerino Mazzola
47. Critical Fibers
Summary
Stemma theory offers a model for a critical understanding of performance as a complex process between interpretation and the rhetorics of expressive performance grammar. We make the model and its limitations explicit.
Guerino Mazzola

Operationalization of Poiesis

Frontmatter
48. Unfolding Geometry and Logic in Time
Summary
Musical poiesis in composition (and performance) is intimately related to a projection of abstract objects into time. We discuss the logical and geometric aspects of this mapping process. The subject is crucial to the entire art of music since music is involved in the creation of autonomous time beyond the physical “tyranny” of real time. This enforces a review of Michael Leyton's theory of time as a philosophical category which is derived from spatial symmetry transformations [607]. We also discuss the role of unfolding insight within the syntagmatic discourse of music.
Guerino Mazzola
49. Local and Global Strategies in Composition
Summary
This chapter sketches the compositional process between paradigmatic selection and syntagmatic combination within the musical sign system. Apart from these semiotic perspectives, the process is characterized by a “dialectic” interrelation of local and global criteria. These features—well known from the general structure theory of global compositions—reappear in the special light of poiesis: The construction of a composition resembles the step-by-step completion of a puzzle of logical units, distributed in syntagmatic time, and selected to optimize association to already placed units. This activity is remunerative and fed back by a successive accumulation of poetical semantics.
Guerino Mazzola
50. The Paradigmatic Discourse on presto®
Summary
The presto® composition software was developed as a commercial implementation and operationalization of mathematical music theory. Several large compositions have been successfully realized on this software [101, 103, 680]. One of them will be discussed in chapter 51. We describe the overall architecture and functionality of presto®. This is mainly driven by a local/global paradigmatic perspective. The paradigmata of transformation and deformation are realized on (1) the level of modular affine transformations in the four-dimensional space of onset, pitch, duration, and loudness, and (2) the level of variational deformations. Both paradigmata are discussed and exemplified. We conclude the chapter with a remark on the problem of abstraction in paradigmatic composition, since composers tend to have major difficulties to get familiar with abstract paradigmatic structures.
Guerino Mazzola
51. Case Study I: “Synthesis” by Guerino Mazzola
Summary
“Synthesis” is a composition for piano, percussion and e-bass. Its global and local organization was driven by classification of local compositions and modulation theory on one hand, and by the presto® software tool on the other. We describe the overall organization and the four movements.
Guerino Mazzola
52. Object-Oriented Programming in OpenMusic
Summary
OpenMusic is a visual programming language for music composers. It was designed and implemented by the Musical Representation Team at Ircam-Centre Georges Pompidou. OpenMusic is based and implemented on CLOS (Common Lisp Object System) [1014]. It shows several original features, such as re- flexivity, meta-programming capacities, handling of the duality between musical and computational time, and provides a framework of predefined musical objects for handling sound, MIDI and musical notation. Open- Music combines different technics of programming, e.g., functional programming, constraint programming and object-oriented programming. We will focus in this chapter on the last one. Object-oriented programming is crucially connected with the categorical approach. Category theory helps formalize in an original way concepts like inheritance, methods, classes, etc. More details on this relation can be found in [613] or in Section 9.4.2 of this book.
Guerino Mazzola

String Quartet Theory

Frontmatter
53. Historical and Theoretical Prerequisites
Summary
This chapter introduces the best evolved theoretical part of instrumentation: string quartet theory. It starts with a short historic synopsis and then reviews Ludwig Finscher’s work [320] on string quartet theory. We then focus on the technical core subject: the violin family as an instrumentation paradigm for the string quartet. The chapter concludes with a general discussion of semantics of sound colors.
Guerino Mazzola
54. Estimation of Resolution Parameters
Summary
This chapter is a technical account of the variety of sound parameters which intervene for the family of violins.
Guerino Mazzola
55. The Case of Counterpoint and Harmony
Summary
This final chapter on string quartet theory deals with the analytical conditions on global compositions which are powerful enough to comprehend the structural richness of central European music in the epoch of Boccherini and Haydn. These structures are — essentially— counterpoint and harmony. As a germ for a systematic theory of instrumentation we propose an estimation of maximal necessary chart dimension for Fuxian counterpoint and traditional harmony (including cadence and modulation).
Guerino Mazzola
Backmatter
Metadaten
Titel
The Topos of Music II: Performance
verfasst von
Prof. Dr. Guerino Mazzola
Copyright-Jahr
2017
Electronic ISBN
978-3-319-64444-8
Print ISBN
978-3-319-64443-1
DOI
https://doi.org/10.1007/978-3-319-64444-8

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