I attempt to demonstrate that a substantial aspect of the performing style of the two most important pianists of the Hungarian Liszt school, Bartók and Dohnányi, together with other performers of the era to a certain extent, is the mainly unintentional slowing down at structurally relatively important or surprising moments in terms of musical meaning and, respectively, the speeding up of relatively unimportant or highly predictable moments. Relatively important or surprising moments include the appearance of a new theme, structural boundaries, atypical modulations, and the like; relatively unimportant or highly predictable moments include sequences, transitional passages, and, to a certain extent, cadential formulae. Computer-assisted analysis of microtiming patterns of representative recording samples as well as their comparison with preliminary results of a listening experiment suggests a tight connection of Bartók’s and Dohnányi’s rubato patterns with structural importance and predictability.
By an invariant set in a metric space we mean a non-empty compact set K such that K = ⋃i=1nTi(K) for some contractions T1, …, Tn of the space. We prove that, under not too restrictive conditions, the union of finitely many invariant sets is an invariant
set. Hence we establish collage theorems for non-affine invariant sets in terms of Lipschitzian retracts. We show that any
rectifiable curve is an invariant set though there is a simple arc which is not an invariant set.