Harmonic Perception and Voice Leading Spaces of Set Classes Related by Unordered Interval Classes

Abstract

We call PCORD the prime form the interval string of Forte’s set classes. Analysis based on PCORD relations can yield a structural similarity between two different set classes, besides some possible perceptual likeness, measured by trichordal content. However different, the PCORD relation is analog to Forte’s Z-relation, but more embracing. This study provides the table of all set classes related by PCORD to be used as an analytical and compositional tool. The paper points out a precursor analytical use of the PCORD relation by Richard Parks in Debussy’s music. To demonstrate the analytical application of PCORD-relations, we analyzed four excerpts: from Hans Otte’s Das Buch der Klänge (1982), Villa-Lobos’ Rudepoema (1920) and from Coelho de Souza’s Metropolis (1990) and Dialogues (1987). We also analyzed the harmonic content of set classes using trichords or PCORDs of cardinality 3 and the PCORD connections in the voice-leading space of set classes with cardinality 3 to 9. Finally, we proposed that PCORD theory can be used as a compositional tool to engender harmonic directionality in atonal progressions.

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