Abstract:
Expressive performance of music is realized with local and global variations in dynamics, timing, intonation, timbre, etc., where particular profiles of these ``expressive elements'' depend on the players' performance practices based on their musical thoughts. This paper presents a method to study the correspondence between the physical nature and the subjective effect of expressive elements in piano performances. Let f(s) be a function in musical time, where s represents the temporal profile of physical correlates with either dynamics, agogics, or pedaling in a piano performance, and let n be the number of these performances for the same music score. The dissimilarity d[inf ij] between two performances i and j is defined as the root mean square of f[inf i](s)-f[inf j](s) over the prescribed time span S of the concerned music passage. The discussion focuses on: (1) the construction of f(s) for each of the above-mentioned expressive elements, and (2) the mapping of n performances in a geometrical space with the dissimilarity matrix D=[d[inf ij]], which is then related to the rating data of subjective impression obtained from a suitably designed listening session. As an example, the maps of dynamics, agogics, and pedaling are given for 24 performances for Chopin's Waltz No. 9 rendered by eight pianists with three kinds of intended musical expressions, and the rating data from a listening session are associated with the maps.