Pitch and Harmony in György Ligeti's Hamburg ConcertoandSyzygy for String Quartet

The analysis component of this dissertation focuses on intricate and complex pitch relationships in György Ligeti's last work, the Hamburg Concerto. This piece uses two distinct tuning systems—twelve tone equal temperament and just intonation—throughout its seven movements. Often, these two systems are used simultaneously, creating complex harmonic relationships. This combination allows Ligeti to exploit the unique features of each system and explore their relationships to each other.Ligeti's just intonation in the Hamburg Concerto comes mainly from the five French horns, who are instructed to keep their hands out of the bell to allow the instrument to sound its exact harmonics. The horns themselves, however, are tuned to varying different fundamentals, creating a constantly changing series of just-intoned pitches anchored above an equal-tempered bass. This method of generating just-intoned intervals adds a second layer to the relationship between equal temperament and just intonation.This paper focuses on creating ways to understand this relationship, and describing the ramifications of these tunings as they unfold throughout the piece. Ligeti very carefully crafts this work in a way that creates a balance between the systems.Research done at the Paul Sacher Stiftung has uncovered a significant collection of errors in the published score. Clearing up these discrepancies allows for a much more accurate and more informed analysis. Throughout this dissertation, mistakes are corrected, and several aspects of the score are clarified. The tuning systems are described, and a likely tuning scheme for the horns is posited. (The analytical component of the dissertation delves into the many varying intervals which all fit into one interval class—a feature that is best explored when two distinct tuning systems are juxtaposed.) A language is created herein to better understand these pitch relationships that fit neither into equal temperament nor just intonation. The analysis clearly shows that very simple musical intervals turn out to be cornerstones of this piece, traceable throughout the entire Hamburg Concerto.The composition, Syzygy for string quartet, is written in just intonation. Through four movements, the relationships evoked by the titles (always groups of homonyms) are examined and illuminated