Pitch-class Function, Centricity, And Symmetry As Transposition Relations In Two Works Of Stravinsky.

Abstract

Stravinsky has long been known to use small pitch-class collections, particularly four-note symmetrical sets; what has not been systematically examined is the intervallic constitution of such sets, their roles as centric structures, and their relationship to the functional pitch successions within a musical work. Concepts of pitch-class function (temporal and conceptual ordering), centricity (referentiality), and symmetry are necessary to understand pitch-succession in twentieth century works. These concepts are clarified and applied, in particular, to characterize transposition relationships within and among small pitch-class sets. Examples of the treatment of such sets are offered for two diverse works, the Three Pieces for String Quartet (1914) and the second movement of the Octet for Wind Instruments (1923, revised in 1952). The first two chapters examine the ideas of pitch-class function and centricity, their meanings for various writers, and their relationships to various temporal and conceptual frameworks. A brief sketch of a conventional tonal system follows along with a discussion of methods of altering a common-practice model. The properties of symmetrical sets and of four-note sets in particular are discussed in the third chapter. These sets are categorized by their internal interval-class relationships. This study considers small symmetrical pitch-class sets as products of Stravinsky's broader compositional practice of functionally pairing identical interval structures at particular transposition levels. His pairing of identical structures often results in the position complementation of pitch-class, a relationship of pitch-classes, often invariant, in complementary positions within inversionally- or transpositionally-related sets. The relationships of transposition pairing and position complementation effect an opposition of paired structures that is resolved in various ways within the context of each work; moreover, these relationships indicate ways in which Stravinsky's metaphor of polarity may be associated with consistent theoretical descriptions of musical relationships in each work. An alternative to the axial treatment of symmetrical pitch-class relationships associated with Schoenberg, Berg and Bartok, Stravinsky's treatment is non-axial in nature because it references conventional tonal transposition relations associated with the (tonal) diatonic set. A change in transposition pairing relationships is associated with functional processes of progression and closure in each piece. Identical interval structures exhibiting transportation pairing and position complementation are positioned in specific formal positions within a piece conveying the drawing together and separation of poles of attraction, Stravinsky's metaphor for musical form. This study employs theoretical models, such as interval-cycle models, viewed from the perspective of referentially-centric pc structures to describe relationships within and between small pitch-class collections and small and large temporal spans of each work.Ph.D.Communication and the ArtsMusicUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/127572/2/8116269.pd