Listening with Two Ears: Conflicting Perceptions of Space in Tonal Music
The Tonnetz is a spatial model of tonal pitch, constructed by placing fifths along the horizontal axis of a coordinate plane and thirds along the vertical axis. This dissertation examines the ways in which different conceptions of interval, including just-intonation ratios, diatonic scalar intervals, and pitch-class intervals, result in different Tonnetz geometries, representing different, and sometimes conflicting, modes of musical perception, and argues for treating conflicts between these often unexamined conceptions of interval as an explicit part of musical analysis. Chapter One considers relationships between a number of Tonnetz spaces, as well as the groups of intervals they model, using harmonic function theory. Chapter Two examines ways in which pitches may project multiple functions in Tonnetz spaces and uses these spaces to model some aspects of the harmonic theory of Jean-Philippe Rameau. Chapter Three considers the ways in which neo-Riemannian transformations, as ways of relating triads and seventh chords to one another, might be associated with changes of harmonic function in different Tonnetz spaces, and culminates in an analysis of Chopin's E Minor Prelude. Chapter Four explores primary triads with chromatically altered roots and fifths and, in this context, analyzes an unusual modulation from A-flat major to E major in Hugo Wolf's song "An den Schlaf." Finally, Chapter Five considers harmonic function in nontriadic music, examining the beginning of the final movement of Bartók's Fourth String Quartet.
Music, Tonality, Musical intervals and scales
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