The Mathematics of Rubato: Analyzing Expressivetiming in Sergei Rachmaninoff’s Performances of Hisown Music

The purpose of this paper is to quantitatively investigate the nature of Rachmaninoff’s playing, with a specific focus on his own compositions. The primary source of data for this study is inter-onset intervals, which will be captured through the use of Sonic Visualiser. Inter-onset intervals are calculated by taking the difference between the onset of two adjacent notes, and can be used to calculate an instantaneous tempo. Various statistical methods will be used, including the variance, moving average, Pearson correlation coefficient, and a custom defined metric. The calculation of variance is especially useful in detecting major deviations from the average tempo in certain sections. These tempo fluctuations are either accelerandos or ritardandos whose data can be fit to a curve using a program called MATLAB. The resulting equations can then be compared with other sections of the piece, or with other pianists’ recordings of the same piece. This study will also include a comparison between Rachmaninoff and several other pianists; his playing will be compared to the group average as well as to each individual pianist. The individual comparisons will make use of the Pearson correlation coefficient, which provides a measure of how similar two datasets are to one another.