Dissertation Index

Author: Schuijer, Michiel

Title: Pitch-Class Set Theory and the Construction of Musical Competence

Institution: University of Utrecht

Begun: June 1994

Completed: September 2005


This dissertation studies the evolution of pitch-class set theory, the predominant American theory of post-tonal music. It combines a thorough analysis of concepts (e.g. 'transposition', 'inversion', 'multiplication', 'equivalence', 'similarity') with an investigation of the historical context in which the theory has emerged. Pitch-class set theory is treated as part of the musical and cultural landscape in the United States after 1950, with particular emphasis on its role in the reception of the music of Schoenberg, Stravinsky, and others. The theory's remarkable rise to authority is related to the impact of the computer on the study of music in the 1960s—an impact that most music theory textbooks fail to acknowledge—and to the American university in its double role as protector of high culture and provider of mass education. Particular attention is given to the motives of Milton Babbitt and Allen Forte, the principal pioneers in the field of pitch-class set theory. Babbitt wanted to subject music discourse to the rigorous criteria of logical positivism in order to protect an endangered culture of advanced music. Forte’s concern was music education—not as the guardian of music tradition, but as an instrument in the widest possible dissemination of new knowledge.

Keywords: pitch-class set theory, music analyis, music theory (history of), music education, twelve-tone serialism, computers, mathematics, Forte, Babbitt



1 Pitch-Class Set Theory: An Overture

A Tale of Two Continents
Paradigmatic Pieces
A Short Detour over Schenker
Institutionalization and Criticism
Aim, Scope, and Structure of this Study

2 Objects and Entities

Pitch and Pitch-Class
Pitch Interval and Pitch-Interval Class
Pitch-Class Set
The Interval Content of a Pitch-Class Set

3 Operations

Notes on the term 'Operation'

4 Equivalence

Definitions of Equivalence
Equivalence and Equality
The Study of Interval Content
'Operational' Equivalence
Problems of Representation
Class Types
Canonical Transformation Groups

5 Similarity

Concept and Referent
Gradations of Harmonic Tension
Distributive Patterns
Squaring the Difference
Common Subsets
'Absolute' Measures
An Almost Unreasonable Wish

6 Blurring the Boundaries: Analysis, Performance, History

What Music Analysts Do
Historical Models and Topical Meanings

7 Mise-en-Scène

A: Formalization and Forgetfulness

The Computer as a Role Model
Computer Language and the Structure of Atonal Music

B: Contemporary Music, Science, and Education

Babbitt's Positivism
Anxieties about Musical Discourse
The University as a Refuge?
A Democracy of Learning



Dr. Michiel Schuijer
Conservatorium van Amsterdam
P.O. Box 78022
1070 LP Amsterdam
tel. +31 (0)20 527 7503

Universiteit van Amsterdam
Nieuwe Doelenstraat 16,
Room 1.09
1012 CP Amsterdam
tel. +31 (0)20 525 4667
e-mail: M.C.Schuijer@uva.nl

Weissenbruchstraat 131
2596 GD Den Haag
The Netherlands
tel: +31 (0)70 319 1865
fax: +31 (0)70 324 7241
e-mail: michiel@schuijer.demon.nl

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