Abstract
Contextual inversion, introduced as an analytical tool by David Lewin, is a concept of wide reach and value in music theory and analysis, at the root of neo-Riemannian theory as well as serial theory, and useful for a range of analytical applications. A shortcoming of contextual inversion as it is currently understood, however, is, as implied by the name, that the transformation has to be defined anew for each application. This is potentially a virtue, requiring the analyst to invest the transformational system with meaning in order to construct it in the first place. However, there are certainly instances where new transformational systems are continually redefined for essentially the same purposes. This paper explores some of the most common theoretical bases for contextual inversion groups and considers possible definitions of inversion operators that can apply across set class types, effectively de-contextualizing contextual inversions.
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Notes
- 1.
The proximity of the triads to these lines can be calculated from the magnitude of the subsets on each Fourier component used to define the phase space, with perfect coincidence where the magnitudes are equal on each. Since all the subsets of major/minor triads are reasonably uniform in their \(|F_3|\) and \(|F_5|\), the triads fall quite close to all of these lines in Ph\(_{3,5}\)-space.
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Yust, J. (2019). Decontextualizing Contextual Inversion. In: Montiel, M., Gomez-Martin, F., AgustÃn-Aquino, O.A. (eds) Mathematics and Computation in Music. MCM 2019. Lecture Notes in Computer Science(), vol 11502. Springer, Cham. https://doi.org/10.1007/978-3-030-21392-3_8
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