Tonal prisms: iterated quantization in chromatic tonality and Ravel's 'Ondine'
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Citation (published version)Jason Yust. 2013. "Tonal prisms: iterated quantization in chromatic tonality and Ravel's 'Ondine'." Journal Of Mathematics And Music, Volume 7, Issue 2, pp. 145 - 165 (21). https://doi.org/10.1080/17459737.2013.821634
The mathematics of second-order maximal evenness has far-reaching potential for application in music analysis. One of its assets is its foundation in an inherently continuous conception of pitch, a feature it shares with voice-leading geometries. This paper reformulates second-order maximal evenness as iterated quantization in voice-leading spaces, discusses the implications of viewing diatonic triads as second-order maximally even sets for the understanding of nineteenth-century modulatory schemes, and applies a second-order maximally even derivation of acoustic collections in an in-depth analysis of Ravel's ‘Ondine’. In the interaction between these two very different applications, the paper generalizes the concepts and analytical methods associated with iterated quantization and also pursues a broader argument about the mutual dependence of mathematical music theory and music analysis.