Tatar – Measur ing Time MTSMA: Lexington, KY ( March 20, 2020 ) 1 Measuring Time in Morton Feldman’s Late Music Jeremy Tatar, McGill University (jeremy.tatar@mail.mcgill.ca ) Figure 1 . Morton Feldman, For Christian Wolff (1986), mm. 1 – 8 annotated with beat - class sets (mod 9) in {curly braces} and their prime forms in [square braces] under Tn/TnI. Note the shared rhythmic set - classes of mm. 4 and 5 (in bold), whose surface rhythms are related by t 3 Figure 2. For Christian Wolff , m m . 48 – 56. N ew set - classes accompanying the change in registration at m. 51 marked in bold, with i 5 connecting mm. 51 and 52. M. 54 brings the first appearance of [0134]. i 5 t 3 Tatar – Measur ing Time MTSMA: Lexington, KY ( March 20, 2020 ) 2 Figure 3. For Christian Wolff , mm. 1 – 8, abstracted as bc sets (compare with Figure 1). Beat - class voice - leading uniformity shown between measures after Straus (2003), where transpositions marked “*” are fuzzy, with their offsets indicated beneath. Arrows beneath the example indicate the cumulative voice - leading shifts from mm. 1 – 4 ( - 1 +1 - 1 = - 1) and 5 – 8 (0+2 - 1 = +1) Selected Bibliography Boutwell, Brett. 2014. “ ‘The Breathing of Sound Itself ’ : Notation and Temporality in Feldman ’ s Music to 1970 .” Contemporary Music Review 32: 531 – 570. Cline, David. 2016. The Graph Music of Morton Feldman . Cambridge: Cambridge University Press. Cohn, Richard. 1992. “ Transpositional Combination of Beat - Class Sets in Steve Reich’s Phase - Shifting Music.” Perspectives of New Music 30: 146 – 77. Hall, Tom. 2007. “Notational Image, Transformation and the Grid in the Late Music of Morton Feldman.” Current Issues in Music 1: 7 – 24. Hanninen, Dora. 2004. “Feldman, Analysis, Experience.” Twentieth - Century Music 1: 225 – 251. Kane, Brian. 2004. “Of Repetition, Habit and Involuntary Memory: An Analysis and Speculation upon Morton Feldman’s Final Composition.” Self - published: http://www .cnvill.net/mfkane.pdf. Accessed March 11, 2019. Lewin, David. 1987. Generalized Musical Intervals and Transformations . New Haven: Yale University Press. Noble, Alistair. 2013 Composing Ambiguity: The Early Music of Morton Feldman . Burlington, Vermont: Ashgate. Roeder, John. 2003 “Beat - Class Modulation in Steve Reich’s Music,” Music Theory Spectrum 25: 275 – 304. Straus, Joseph. 2003. “Uniformity, Balance, and Smoothness in Atonal Voice Leading.” Music Theory Spectrum 25: 305 – 352. *t 0 ( - 1) *t 0 (1) *t 0 ( - 1) t 3 (0) t 0 (0) *t 0 (2) *t 0 ( - 1) m. 1 2 3 4 5 6 7 8 - 1 +1