Timmers, R., Desain, P., Honing, H., & Trilsbeek, P. (2002). Introducing a model of grace note timing. In Proceedings of the Workshop on Music, Motor Behavior and the Mind. Ascona, 32.
Abstract
In an empirical study, it was found that certain specific principles underlie the onsettiming of grace notes: (a) The duration of a grace note scales linearly with bar duration. (b) The insertion of a grace note only affects the timing of the preceding and following melody notes. (c) The timing of these notes is affected by stealing time from them. (d) The time stolen is a proportion of the grace note duration, irrespective of tempo. From these principles, a model of grace note timing was designed that predicts a performance with grace note from a performance without a grace note. The model first predicts the grace duration as a function of grace duration at tempo 60, global tempo and scaling behaviour of the grace note with tempo and then predicts the grace note position as a function of the proportion of the grace duration stolen from the previous note and from the main note. To validate the model, it was fitted to a large collection of performance of the theme of Beethoven’s Paissiello Variations without grace notes. The result was compared to the original performances with grace notes in similar tempi and by the same pianists. This comparison showed a high correspondence between predicted and observed durations. An extension of the model to a generalized grace note generator can be used as an exploratory and explanatory device. A grace note web demo was therefore designed that makes possible the exploration of different ways of grace note timing. By changing the settings of the model parameters, the position and duration of the grace note can be changes and a grace note can be put to have a constant or flexible duration over tempi. Exploration of the different settings showed remarkable interdependencies between duration and position of the grace note, and between uninvestigated aspects of grace note performance such as the loudness, position with respect to the bass note and articulation of the grace note.