Dissertation Index

Author: Coenen, Alcedo, E.

Title: Meta-Plus: Stockhausen's Plus-Minus computerized and analyzed

Institution: University of Amsterdam

Begun: September 1993

Completed: November 1995


Stockhausen's piece "Plus-Minus", composed in 1963, is analyzed and implemented into a computer program, called "Meta-Plus". Stockhausen's piece is an example of abstract composition, which has to be worked out first by the musician before she can play it.

The hypothesis is twofold: (1) that formalisation and implementation is an appropriate way of analysing "Plus-Minus" and comparable meta-musical pieces; (2) that Stockhausen's "Plus-Minus" is a piece which examplifies a specific method of composition which can be formalised.

The purpose of the computer program is twofold: (1) to provide musicians, who want to make a version of Plus-Minus, with a user-friendly tool to manage this task; the program asks for the input of parameters, and calculates a structure according to the rules of Stockhausen; its output can be either a MIDI-file, a score or a sound-file; (2) to provide the musicologist, who wants to analyze Plus-Minus, with a tool with which she can study its formal description, as well as create as many versions as possible with different parameter settings.

The research focusses on two questions: (1) - a musicological issue - what is the musical identity of Plus-Minus; (2) - an AI issue - what kind of composition is modelled in Plus-Minus, and what can be learned from this (Stockhausen's) method for more generalized composition models.

Keywords: Composition Theory, Music Representation, AI, Stockhausen, Serialism


1. Meta-Plus: Plus-Minus as a computer program
1.1 design - general considerations
1.2 design - data structures
1.3 design - rule structures
1.4 design - user interface
1.5 implementation
1.6 future features

2. Plus-Minus as a work of Stockhausen
2.1 Stockhausen's oeuvre
2.2 Stockhausen's process music
2.3 The computerability of Plus-Minus
2.4 Evaluation of outputs results from Meta-Plus

3. Plus-Minus as a method of composition
3.1 Formalisation as an analysis method for meta-music
3.2 Plus-Minus as a blue print for composition
3.3 Meta-Plus as an expert system for composition

4. Conclusions and future possibilities
4.1 About the formalisability of Plus-Minus
4.2 About the analysis of Plus-Minus
4.3 Towards a cognitive model of composition
4.4 Towards an aesthetic of meta-music


Alcedo E. Coenen
Argonautenstraat 59-1
NL-1076-KM Amsterdam
The Netherlands
Voice: +31 20 6731348
Fax: +31 20 6731348
E-mail: alcedo@mars.let.uva.nl

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