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


  • Rodolfo Coelho de Souza USP




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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