SchenkerGUIDE: research
Tom Pankhurst: Paper read at HuMAC 2003

Diatonic dramas and choleric cadences: A semiotic approach to tonal structure in Beethoven and Nielsen
(read by Tom Pankhurst at HuMAC 2003)

Part I - Schenker and Greimasian Semiotics
My research into Carl Nielsen's powerful and idiosyncratic take on tonality has led me to draw on the theories of both Heinrich Schenker and the French-Lithuanian semiotician A.J. Greimas. In this paper, I want to speculate on how shining a Greimasian light onto Schenker's understanding of tonal forces and structures might show up at least some shadows of musical narrative.

Figure 1: Schenkerian and Greimasian models

Figure 1 outlines what I believe to be one of the most interesting correspondences between these two theorists: both outline a process of elaboration or generation from deep to surface level, as shown by the arrows. Schenker's prolongational model, with which I am sure you are familiar, essentially shows how tonal music is, on multiple levels, the elaboration of a perfect cadence.

Probably less familiar will be Greimas's narrative model, which shows how discourse is, among other things, an elaboration of conjunctions and disjunctions between subjects and objects. Working up from the bottom line of the diagram, these junctions, or states of being, are realized (or performed) by subjects in an act of doing, and these two basic modalities - the "being" of conjunction and disjunction, and the "doing" of their performance - form the basis of Greimas's semiotics of narrative action. The doing of a particular conjunction is modalised by their competence in respect of performing the junction. This involves four further modalities shown below the main diagram. Two of these, wanting and having-to are virtualizing modalities - they raise the prospect of a particular conjunction. The other two, being-able and knowing, are actualizing modalities - the conjunction becomes a genuine possibility, even if it has not yet been realized. By exploring various types of discourse in these terms, Greimas develops some interesting models of how they are understood as narrative. In extending this exploration to tonal music, I am building on a small but crucial part of Eero Tarasti's framework for musical semiotics, adding and adapting where necessary.

In his discussion of Greimas, Tarasti discusses the difficulty of distinguishing subjects in a musical discourse. He suggests that when music is consonant it might be equated with the modality of 'being' and goes onto say that:

It is rather in dissonance, 'doing' that we feel music lacking something and that its energy leaves us unsatisfied ... Would it thus not be more appropriate to speak of the way a subject appears in the music's kinetic energy, which from dissonance strives for a state of rest? (Tarasti 1994: 104)

Tarasti's suggestion that the resolution of tension is analogous to conjunction is suggestive for a Schenkerian view of tonal space. For Schenker the Urlinie is not only a conceptual tension that binds passages into musically coherent wholes but also a palpable one, in that scale-degree embodies 'striving toward a goal' (Schenker 1935: 4) and arrival on scale-degree over the tonic means that 'all tensions in a musical work cease' (1935: 13). It is this second sort of tension that particularly lends itself to narrative interpretation, as Schenker himself suggests when he writes: 'In the art of music, as in life, motion towards the goal encounters obstacles, reversals, disappointments [etc.] ... Thus we hear in the middleground and foreground an almost dramatic course of events' (1979: 5).

Returning to Greimas, the reduction of texts to a series of canonical or representative sequences is the narrative aspect of his semiotics and is complemented by a cognitive dimension of achronic oppositional structures that underpin discourses. Schenker's understanding of tonal space in terms of tension and resolution, dissonance and consonance are just the sort of oppositions through which Greimas tries to illuminate the deep structure of narratives. He uses a tool called the semiotic square, which opens out oppositions into four terms as shown in Figure 2.

Figure 2: semiotic square of tonal forces and basic modalities

Example 1: Schenkerian interruption structure (& initial ascent)

Musical tension and resolution (or dissonance and consonance) can be mapped, as Tarasti suggests, onto the basic opposition of "being" and "doing". Progressions that effect resolution thus project the modality of "being" whilst those that introduce tension project "doing". The Urlinie (a middleground elaboration of which is shown in Example 1) represents a move from scale-degree 3, which is a relative tension (or 'doing'), towards the 'being' of resolution on scale-degree 1. Schenker's metaphor of striving suggests that the Urlinie does not represent resolution and stability per se, but the desire for resolution - "want-to-be". By analogy, the initial ascent on Example 1 can be understood as a striving for tension (want-to-do). As relatively abstract representations of a deep level of only one parameter of the music it makes sense to describe such progressions in terms of the virtualizing modality of "wanting".

Schenker's subordination of structure to the norms of strict counterpoint introduces another virtualizing modality that of "must". Here we also bring another position on the semiotic square of tensions into play. The obligation to resolve suspensions, for example, is a move away from tension - a negation of doing on the semiotic square at Figure 2 - so the modal description of this obligation on suspended notes would be "must-not-do". Schenkerian tonal space adds another obligation - the eventual structural resolution of all tensions to scale-degree 1 over the tonic - and this can be described in terms of "must- be". This obligation is in force all the time but becomes particularly pertinent when it is denied as in the first half of an interruption structure.

Rather than continue to discuss this in the abstract, I want to move to the first analytical example, the exposition from the first movement of Beethoven IV.

Part I Part II Part III
Example 2
Example 3
Example 4
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