Dissertation Index

Author: Poudrier, Ève

Title: Toward a general theory of polymeter: Polymetric potential and realization in Elliott Carter's solo and chamber instrumental works after 1980

Institution: City University of New York

Begun: August 2003

Completed: September 2008


This dissertation proposes a conceptual framework and tools for the analysis of polymeter in contemporary musical practices applied to the short instrumental works of Elliott Carter, where multiple temporalities have been identified as an essential aesthetic component. Three works are discussed in more detail: Changes for guitar (1983), Esprit rude/Esprit doux I for flute and clarinet (1985), and 90 + for piano (1994). The composer's use of metrical modulations and structural polyrhythms is re-evaluated in the context of a theory of polymeter. Structural polyrhythms are represented by means of proximity charts, and Carter's compositional strategies are explored, including rhetorical use of background pulsations on the musical surface.

In contrast to current theories of meter, this study does not assume that hierarchical rhythmic structures necessarily imply recursiveness or rely on accentual structure. In Carter's music, polymetric potential stems from the systematic partitioning of pulses of different speeds. Textural streaming is contrasted with multileveled polyrhythmic design, and polymetric structures are defined as contrasting rhythmic strands that are built on competing pulse streams or non-isochronous beat structures and give rise to non-synchronous metrical projections. In a balanced polymetric structure, the rhythmic strands are nearly equal in metrical strength; polarized structures either involve shifting dominance or one pulse stream that is dominant while the other(s) provide periodic syncopation; when the two streams are fused, the polymetric structure is integrated . The realization of polymetric potential is an interactive process involving the composer, performer(s), and the listener. From a music-analytical perspective, polymetric realization can be assessed by an investigation of the metrical properties of each pulse stream as well as the interaction of pulse streams at different structural levels ( foreground, middleground, background ).

The first part introduces various analytical tools that measure the relative mensural determinacy of competing rhythmic strands, including pulse stream reductions and density and nestedness analyses. Issues of perception and performance are briefly discussed in relation to specific interpretations. The second part explores the topic of polymeter from a psychological perspective. The results of a listening experiment based on an example from 90 + for piano are presented and possible avenues for future research are discussed.

Keywords: polyrhythm and polymeter, Elliott Carter, twentieth-century music, music theory, 90+, Changes, Esprit rude/doux I, music perception and cognition, chamber music


CHAPTER 1 Introduction: Elliott Carter and Multiple Temporalities
1.1 Composing with Simultaneous Speeds
1.1.1 Structural Polyrhythms and Metrical Modulation
1.1.2 Character-Patterns and Referential Pitch Collections
1.2 Purpose of Study
1.2.1 Interdisciplinary Considerations
1.2.2 Repertoire
1.2.3 Dissertation Plan

CHAPTER 2 Structural Levels and the Mapping of Polyrhythmic
2.1 Preliminary Remarks
2.1.1 Defining Meter
2.1.2 Carter’s Notational Practice
2.2 Structural Levels
2.2.1 Background
2.2.2 Foreground
2.2.3 Middleground
2.3 Compositional Strategies and Interaction of Structural Levels
2.3.1 Metrical Modulation Re-visited Background Continuity Surface Discontinuities Perceptual Issues
2.3.2 Long-Range Polyrhythms in Action Background Irregularities: Polycyclic Spectrum and
Proximity Charts Analytical Details

CHAPTER 3 Polymetric Potential and Realization
3.1 Streaming and Multileveled Polyrhythmic Design: Esprit rude/Esprit doux I (1985)
3.1.1 Polymetric Structures Defined
3.1.2 Abstract Models
3.2 Local Conditions: Mensural Determinacy and Pulse Stream Reductions
3.2.1 Middleground Level: Quarter Pulse Stream
3.2.2 Foreground Level: Elementary Pulse Streams
3.3 Global Conditions: Density and Nestedness Analyses
3.3.1 Case Study No. 1: The Opening of Mozart’s Symphony in G minor, K. 550
3.3.2 Case Study No. 2: Changes for Guitar (1983) Musical Surface and Pulse Activity: Sectional Density Analyses Polarity and Integration at Work: Nestedness Analyses
3.4 Polymetric Potential and Realization in 90+ for Piano (1994)
3.4.1 Integrated Polymeter
3.4.2 Polarized Polymeter
3.4.3 Balanced Polymeter

CHAPTER 4 The Realization of Polymetric Potential from a Psychological Perspective
4.1 Methodological Issues
4.1.1 Previous Research
4.1.2 Experimental Design Participants Source Materials Stimuli Apparatus and Experimental Procedure Data Collection and Measures Data Analysis
4.2 Results
4.1.1 Overall Tapping Consistency and Tapping Contour Graphs
4.2.2 Block 1 Preliminary Analysis: Order of Presentation and Phase Discrimination Main Analysis: The Effect of Layer and Accent Exploratory Analyses: Selected Between-Subjects Factors
4.2.3 Block 2 Preliminary Analysis: Order of Presentation and Phase Discrimination Main Analysis: The Effect of Layer and Articulation Exploratory Analyses: Selected Between-Subjects Factors Across-Blocks Analysis: Blocks 1&2 (Timbre)
4.2.4 Block 3 Preliminary Analysis: Order of Presentation and Phase Discrimination Main Analysis: Layer-Specific Accentuation (Laccent and Raccent) Exploratory Analyses: Selected Between-Subjects Factors Across-Blocks Analysis: Blocks 1&3 (Version)
4.2.5 Block 4 Preliminary Analysis: Order of Presentation and Phase Discrimination Main Analysis: The Effect of Attention and Condition Exploratory Analyses: Selected Between-Subjects Factors Across-Blocks Analyses: Blocks 2&4 (Version) and 3&4 (Timbre)
4.3 Final Discussion: Assessing Polymetric Realization

CHAPTER 5 Concluding Remarks: Toward a General Theory of Polymeter



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