Harmonic qualities in Debussy's "Les sons et les parfums tournent dans l'air du soir". Issue 2 (2nd September 2017)

• Record Type: Journal Article
• Authors: Yust, Jason
• Is Part Of: Journal of mathematics and music. Volume 11:Issue 2/3(2017)
• Page Start: 155
• Page End: 173
• Publication Date: 2017-09-02
• Subjects: discrete Fourier transform -- Debussy -- harmonic qualities -- diatonicity -- octatonicity -- whole-tone collection -- perfect balance -- harmonic function; 00A65 -- 20B35 -- 18B25; Music theory -- Periodicals; Music -- Mathematical models -- Periodicals; Music -- Mathematics -- Periodicals; 781.2
• DOI: 10.1080/17459737.2018.1450457
• Languages: English
• ISSNs: 1745-9737

Abstract

Abstract : This analysis of the fourth piece from Debussy's Préludes Book I illustrates typical harmonic techniques of Debussy as manipulations of harmonic qualities. We quantify harmonic qualities via the magnitudes and squared-magnitudes of the coefficients of the discrete Fourier transform (DFT) of pitch class sets, following Ian Quinn. The principal activity of the piece occurs in the fourth and fifth coefficients, the octatonic and diatonic qualities, respectively. The development of harmonic ideas can therefore be mapped out in a two-dimensional octatonic/diatonic phase space. Whole-tone material, representative of the sixth coefficient of the DFT, also plays an important role. I discuss Debussy's motivic work, how features of tonality – diatonicity and harmonic function – relate to his musical language, and the significance of perfectly balanced set classes, which are a special case of nil DFT coefficients.