Oriented Networks
Steven Rings · Oxford University Press eBooks · 2011
Chapter 3 introduces the concept of tonal intention—the directedness of a listener's awareness toward a tonic—and defines a species of transformational networks designed to model such intentional structures. Correspondences with the phenomenological idea of intentionality are touched on, as are precedents for the idea of tonal intention in the history of music theory. Oriented networks are defined formally and used to model both abstract theoretical structures—such as Riemann's system of tonal functions—and specific musical passages. A distinction is drawn between oriented networks whose nodes and arrows are arranged from left to right on the page to reflect temporal order (event networks) and networks that instead exhibit a more abstract spatial structuring that does not reflect musical chronology (spatial networks). A special type of event network is defined to model intentional structures implicit in Schenkerian theory. The chapter includes analytical discussions of music by Mozart, Beethoven, Chopin, Brahms, Wagner, and Strauss.