composition, music theory, mathematics
Tempo is an important parameter that is varied and analysed in music performance. We argue that it is important to consider both tempo and log(tempo) in score time as well as performance time in the analysis of performances; performance time mirrors listeners’ real time experience, and log(tempo) gauges proportional tempo changes. As demonstration, we revisit Chew’s (2012) score time tempo analysis of performances of Beethoven’s “Moonlight” Sonata, and generate new results using log(tempo) and performance time. We show that extreme differences in score time tempo are ameliorated by considering log(tempo) and performance time, that the performers employed similar log(tempo) ranges and phrase lengths (in performance time), and that long score time phrases do not necessarily map to lengthy performance time spans due to speedier phrase traversal times. The results suggest that log(tempo) range and maximum performance time phrase length may act as perceptual constraints on the shaping of a performance.
Chew, E. and C. Callender (2013). Conceptual and Experiential Representations of Tempo: Effects on Expressive Performance Comparisons. In J. Yust, J. Wild, and A. Burgoyne (eds.): Mathematics and Computation in Music: Fourth International Conference, MCM 2013.