Jeff Bilmes's Masters Thesis

Timing is of the Essence: Perceptual and Computational Techniques for Representing, Learning, and Reproducing Expressive Timing in Percussive Rhythm

Jeff A. Bilmes
MIT Masters Thesis, 1993


This thesis has one main goal: design algorithms that computers can use to produce expressive sounding rhythmic phrases. First, I describe four elements that can characterize musical rhythm: metric structure, tempo variation, deviations, and ametric phrases. The first three elements can be used successfully to model percussive rhythm.

Second, I describe two algorithms: one, an automatic transcription algorithm, extracts stroke attack times and automatically constructs unique stroke types from a percussive performance. The other takes a percussive performance and factors out the metric structure, tempo variation, and deviations.

Third, I apply these algorithms to a performance given by the percussion group Los Munequitos de Matanzas. Using both a synthesis of the performance and statistical analysis, I demonstrate that timing data represented in this form is not random and is in fact meaningful. In a synthesis with tempo variation removed but deviations retained, the original performance's expressive feel is preserved. Therefore, I claim that rhythmic analysis requires the study of both tempo variation and deviations.

Finally, because similar quantized rhythmic phrases have similar corresponding deviations, the smoothness assumption necessary for a function approximation approach to learning is satisfied. I describe a multi-stage clustering algorithm that locates sets of similar quantized phrases in a performance. I then describe a machine learning algorithm that can build a mapping between quantized phrases and deviations. This algorithm can be used to apply deviations to new phrases.

I claim that deviations are most important for the expressive feel of percussive music. Therefore, I have developed a new drum machine interface, a deviation experimentation program, with which deviations can be explored.

Here is the entire thesis in PDF format.