Syntax Square (MIT, Dpt. of Linguistics & Philosophy), April 4, 2016
A fundamental aspect of Western music is tonal harmony, or tonality, a complex rule system for specifying a) acceptable combinations of notes and chords within a key through reference to the tonic, its tonal center, and b) relationships between different keys. This is usually called harmonic function. Implicit knowledge of harmonic functions enables listeners to form strong expectations about the harmonic structure of musical pieces. To account for this phenomenon, previous research points to hierarchical grammatical models similar to those used to account for linguistic structure. The harmonic structure in music of the common practice period (Bach to Beethoven) is well described by grammars which define harmonic functions as recursive, tonic-headed patterns. In extended tonality, the language of the romantic period (Schubert to Mahler), harmonic patterns can be formalized in terms of finite state automata or as finite cyclic groups of transformations acting on notes or chords. However, the relationship to hierarchical descriptions and thus the integration into cognitive models that account for the building of harmonic expectations faces several challenges:
- How to deal with cyclic patterns?
- Are local dependencies enough?
- How to determine head(s) of phrases?
This talk will outline the conceptual framework for dealing with musical instances of extended tonality in order to draw connections to current cognitive models of tonal harmony. Musical examples that will be discussed include:
- F. Liszt: 5 Klavierstücke S. 192, No. 2 (Lento assai),https://www.youtube.com/watch?v=WoPB1XZs9u8
- L. v. Beethoven: Symphony No. 9 op. 125, mvt. 2 (Scherzo),https://www.youtube.com/watch?v=dvPMXuU35QI
- J. Brahms: Double Concerto in A-minor, op. 102, mvt. 2 (Andante),https://www.youtube.com/watch?v=dco3ms8DNVk
- G. Verdi: Messa da Requiem (Rex Tremendae),https://www.youtube.com/watch?v=tfEBgdYxofI
- A. Dvořák: Symphony No. 9 in E minor, Op. 95 „From The New World“, mvt. 2 “Largo”, https://www.youtube.com/watch?v=ASlch7R1Zvo
- A. Bruckner: “Ecce sacerdos magnus”, WAB 13,https://www.youtube.com/watch?v=OCDZATJvBZg