Abstract
One of the reasons for the widely felt influence of Schenker’s theory is his idea of long-range voice-leading structure. However, an implicit premise, that voice leading is necessarily a relationship between chords, leads Schenker to a reductive method that undermines the structural status of keys. This leads to analytical mistakes as demonstrated by Schenker’s analysis of Brahms’s Second Cello Sonata. Using a spatial concept of harmony based on DFT phase space, this paper shows that Schenker’s implicit premise is in fact incorrect: it is possible to model long-range voice-leading relationships between objects other than chords. The concept of voice leading derived from DFT phases is explained by means of triadic orbits. Triadic orbits are then applied in an analysis of Beethoven’s Heiliger Dankgesang, giving a way to understand the ostensibly “Lydian” tonality and the tonal relationship between the chorale sections and “Neue Kraft” sections.
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Notes
- 1.
Korsyn’s [5] motivic analysis highlights motives of the chorale tune involving D, including C–C–D and D–E–F, the latter representative of D’s resistance to downward resolution.
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Yust, J. (2017). Restoring the Structural Status of Keys Through DFT Phase Space. In: Pareyon, G., Pina-Romero, S., Agustín-Aquino, O., Lluis-Puebla, E. (eds) The Musical-Mathematical Mind. Computational Music Science. Springer, Cham. https://doi.org/10.1007/978-3-319-47337-6_32
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DOI: https://doi.org/10.1007/978-3-319-47337-6_32
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