9789026516351

Representing Musical Time: A Temporal-Logic Approach

by
  • ISBN13:

    9789026516351

  • ISBN10:

    9026516355

  • Edition: 1st
  • Format: Hardcover
  • Copyright: 2000-01-01
  • Publisher: Routledge

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Summary

An examination of a crucial issue in processing music by computer and in other abstract and formal approaches to music. The relations of time specified in musical scores and found in bodies of musical performances have a complex and sometimes indeterminate structure, and even the nature of musical time can be in question. Complicating factors such as partially determined ordering of events are found not only in music of the 20th century, when composers explicitly employed such indeterminacy, but also in music where the indeterminacy is only implicit in the interpretation of the notation.;This work analyzes in detail the essential issues of the nature of musical time, possible formulations of musical temporal relations, taking account of indeterminacy, and systems for the measurement of musical time. Representations are classified according to their expressive power and computational complexity. Existing systems of musical representation are related to these formulations, and some generic representations ofmusic are proposed and analyzed. The most expressively powerful representations are shown to be computationally intractable, while those of least computational complexity are shown to be incapable of representing some types of music. A perfect system of representation is therefore impossible, and different representations are appropriate for different purposes.

Table of Contents

Preface vii
Motivation vii
A Note on Logic and Conventions of Notation viii
Acknowledgements ix
Music, Logic, and Time
1(22)
Musical Time
1(4)
Representation
5(4)
Logic
9(4)
Temporal Logic
13(4)
Representations of Musical Time
17(6)
The Ontology of Musical Time
23(32)
Shape
23(8)
Extent
31(2)
Individuals
33(12)
Texture
45(3)
Choice of Ontology
48(3)
Considerations from Psychology
51(4)
Relations of Musical Time
55(36)
Computational Complexity
56(1)
Types of Relation
57(7)
Representing Configurations in Tables
64(5)
Consistency and Inference of Relations
69(9)
Representing Configurations of Events in Graphs
78(3)
Representing Configurations of Events in Sequences
81(6)
Conclusions
87(4)
Measurement of Musical Time
91(18)
Numerical Measurement
91(6)
Metre
97(12)
Representation and Realisation
109(10)
Realisation
109(2)
MIDI
111(1)
Realisation Procedures
112(7)
Music Notation
119(16)
Formal Representation and Realisation
119(10)
Translation to Other Sequence Representations
129(1)
Music Notation in Practice
130(5)
A Structural Representation
135(30)
Features of the Structural Representation
136(3)
Definition
139(4)
Examples
143(11)
Translation and Inference
154(3)
Realisation
157(8)
Conclusion
165(6)
Appendix 1: Algorithms and Formal Definitions 171(66)
Contents
171(2)
Relations
173(7)
Table Representations
180(15)
Graph Representations
195(3)
Sequence Representations
198(7)
Metrical Quantities
205(5)
Realisation of Tables, Graphs and Sequences
210(5)
Symbolic Music-Notation Representation
215(9)
Structural Representation
224(13)
Appendix 2: List of Symbols 237(2)
References 239(6)
Index 245

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