Timing microstructure in Schumann's “Träumerei” as an expression of harmony, rhythm, and motivic structure in music performance

Abstract

We give statistical evidence that specific rhythmic, melodic, and harmonic analyses are dominating shaping structures for the agogical streams from 28 performances of Schumann's “Träumerei”, as measured by Repp [1]. These analyses are provided by the Rubato analysis and performance workstation. The statistical model is based on regression analysis and realizes shaping of agogics by a second-order linear differential operator. More precisely, the logarithm of the tempo function T(E) at onset time E can be expressed as a linear function of a sequence of particular smooth “weight” functions Wi(E) and their first and second derivatives. These numerical functions are generated by Rubato's harmonic, melodic, and rhythmical analyses and include an averaging process over a natural grouping hierarchy defined by Schumann's score.