Dissertation Index

Author: Castine, Peter

Title: Set Theory Objects: Abstractions for Computer-Aided Analysis and Composition of Serial and Atonal Music

Institution: Technische Universitaet Berlin

Completed: January 1994


The set theoretical approach to music analysis and composition is an area of research that has spawned numerous computer applications. This paper is concerned with a project in which two goals were pursued: (a) developing a unified collection of computer tools that would support, as far as possible, all methods described in the literature and (b) providing this support in a way which would be accessible to a larger number of musicians than previous software projects.

The Contemporary Music Analysis Package, a collection of programs developed by Craig R. Harris and Alexander R. Brinkman for the Unix operating system, proved an excellent starting point for the first goal. The Macintosh computer system, a widely available computer with many characteristics that, properly employed, support superior human-computer interaction, was chosen as a platform for this project.

The introductory chapter provides a more precise statement of the project goals. This is followed, in the second chapter, by an survey of set theory and the methods it employs. The third chapter reviews currently available software for set theoretic applications. The fourth chapter describes the software designed. Implementation is discussed in the fifth chapter. This is followed, in the final chapter, by a report of the current state of the CMAP for Macintosh project and plans for further development.

Keywords: Set Theory, Computer Programs, Object-Oriented Programming, User Interface Design, Unix, Macintosh, Forte


1. Introduction 1
1.1 An Evaluation 1
1.2 Computers as Music Analysts 2
1.3 Computers as Analytic Aids 3
1.4 The Contemporary Music Analysis Package 5
1.5 So, what is this about? 5
2. The Set Theoretical Approach to Music Analysis and Composition 7
2.1 Pitches, Pitch Equivalence, and Pitch Classes 10
2.2 Intervals, Interval Equivalence, and Interval Class 13
2.3 Ordered Sets, Unordered Sets, Rows, and Cycles 15
2.4 Set Membership and Cardinality 17
2.5 Twelve Tone Operations 18
2.6 Properties of Unordered Sets 27
2.7 Set Equivalence and Set Class 45
2.8 Set Class Relations 52
2.9 Segmentation, and Other Objections 55
3. Computer Tools Available for Set Theory 59
3.1 Survey of Available Computer Tools 60
3.2 The Contemporary Music Analysis Package 67
4. Designing User-Oriented Software for Set Theory 77
4.1 Historical Setting 80
4.2 Target Audience 82
4.3 Task Definition 83
4.4 Basic Design 89
4.5 Further Problems and Solutions 94
5. Implementing Software for Set Theory 105
5.1 Development Hardware and Compatibility Testing 105
5.2 Prototyping Software for Set Theory 107
5.3 Programming Environment 110
5.4 Data Structures for Set Theory 116
6. Current Status and Future Goals 127
6.1 Today 127
6.2 Tomorrow 129
6.3 Further Into the Future 132
Appendix 1QSet Class Tables A-1
Appendix 2QDefinitions and Theorems A-7
Appendix 3QTechnical Documentation A-23


Wildganssteig 28, D-13505 Berlin, Germany
Voice: (x49.30) 431-0850
e-mail: pcastine@mvax.kgw.tu-berlin.de

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