A Survey of Applications of the Discrete Fourier Transform in Music Theory

Abstract

Discrete Fourier Transform may well be the most promising track in recent music theory. Though it dates back to David Lewin’s first paper (Lewin, J. Music Theory (3), 1959) [33], it was but recently revived by Quinn in his PhD dissertation in 2005 (Quinn, Perspectives of New Music 44(2)–45(1), 2006–2007) [35], with a previous mention in (Vuza, Persp. of New Music, nos. 29(2) pp. 22–49; 30(1), pp. 184–207; 30(2), pp. 102–125; 31(1), pp. 270–305, 1991–1992) [40], and numerous further developments by (Andreatta, Agon, (guest eds), JMM 2009, vol. 3(2). Taylor and Francis, Milton Park) [5], (Amiot, Music Theory Online, 2, 2009) [8], (Amiot, Rahn, (eds.), Perspectives of New Music, special issue 49 (2) on Tiling Rhythmic Canons) [9], (Amiot, Proceedings of SMCM, Montreal. Springer, Berlin, 2013) [10], (Amiot, Sethares, JMM 5, vol. 3. Taylor and Francis, Milton Park (2011) [16], (Callender, J. Music Theory 51(2), 2007) [17], (Hoffman, JMT 52(2), 2008) [29] (Tymoczko, JMT 52(2), 251–272, 2008) [38], (Tymoczko, Proceedings of SMCM, Yale, pp. 258–272. Springer, Berlin, 2009) [39], (Yust, J. Music Theory 59(1) (2015) [42]. I chose to broach this subject because I have had a finger in most, or all, of the pies involved (even using Discrete Fourier Transform without consciously knowing it, in the study of rhythmic tilings).