Dissertation Index

Author: Kallis, Vasilis, C

Title: Modes of Cross-collectional Interaction: A Study of Four Collections in Music by Debussy, Ravel and Scriabin

Institution: University of Nottingham

Begun: October 1997

Completed: October 2003


Cross-collectional interaction is a primary means of pitch organisation in twentieth-century music. This enquiry examines two broad interactive categories: one based on the genetics of symmetrical collections through certain transpositional schemes, the other promoting the direct, one-to-one juxtaposition of pitch fields: collections and constituent substructures. The focus is on four collections (chosen specifically for their special inherent properties) that show consistency of usage in the early twentieth century: octatonic (8-28), whole-tone (6-35), hexatonic (6-20) and acoustic (7-34).

Inspection reveals that the above entities exhibit peculiar and intriguing ways of interacting with one another as well as with diatonic/tonal determinacy. A central aim of this study is to substantiate that the proposed modus operandi of cross-collectional interaction — which precisely reflects this intriguing interactive pluralism — receives extensive realisation in Debussy’s Nuages, Ravel’s Jeux d’eau and Scriabin’s Tenth Sonata, Opus 70.

Keywords: Non-diatonic collections, cross-collectional interaction, octatonic scale, acoustic scale, hexatonic scale, whole-tone scale, set theory, symmetry, Scriabin, Debussy, Ravel


1. The Octatonic Collection
i. Intervallic Properties
ii. History of Usage
iii. Octatonicism in France
iv. Alexander Scriabin: 8-28/7-34 Interpenetration
within 9-10
v. Igor Stravinsky: Inheritance and Contrivance
vi. Bartók and other Octatonic Exponents in Europe
and the United States

2. The Whole-Tone Collection
i. Whole-Tone Harmonic Resourcefulness 98
ii. Historical Awareness: the Whole-Tone Scale in
Eastern Europe
iii. The Whole-Tone Scale and Late Nineteenth-
Century Chromatic Tonality
iv. The Whole-Tone Collection in Post-tonal Music;
Whole-Tone Tonality
v. Issues concerning Whole-Tone Harmonic
Resourcefulness in Post-tonal
vi. The Whole-Tone Collection: an Alternative
Harmonic System?

3. The Hexatonic Collection
i. Symmetrical Partitioning: Hexatonic Derivation
and Cross-collectional Interpenetration
ii. Historical Route

4. Modes of Cross-collectional Interaction
i. Intervallic Properties; the Medium to
Interpenetration Procedures
ii. The First Mode of Cross-collectional
Interaction; Synthetically Modelled
iii. The Second Mode of Cross-collectional

5. Debussy: Nuages
i. Levels of Structure: 8-28, 7-34 and the Striving
for Priority
ii. A Dramatic Opposition: B versus G Priority
iii. Hermeneutical Issues: from Orientation to
iv. The Musical Surface
v. Structural Coherence through Motivic Unity

6. Ravel: Jeux d’eau
i. Exposition
ii. Development
iii. Recapitulation

7. Scriabin: Tenth Sonata, Opus 70
i. Scriabin and the Hexatonic Universe: 6-20
and 9-12
ii. Opus 70 and Beyond; Models of Pitch
Organisation: 9-10 and 9-12
iii. Tenth Sonata, Opus 70: Sets and Structure




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