This dissertation is concerned with the use of a computer to analyze and understand rhythm in music. The research focuses on the development of a program that automatically transcribes percussive music, investigating issues of timing and rhythmic complexity in a rich musical setting. Beginning with a recording of an improvised performance, the intent is to be able to produce a score of the performance, to be able to resynthesize the performance in various ways, and also to make inferencesabout rhythmic structure and style.|
In order to segment percussive sound from the given acoustic waveform, automatic slope-detection algorithms have been developed and implemented. Initially, a simple amplitude envelope is found by tracing the peaks of the waveform. This provides a data reduction of about 200:1 and is useful for obtaining an overview of the musical material. The data are then segmented by repeatedly performing a linear regression over a small moving window of the envelope data, moving the window one point at a time over the envelope. The linear regressions create a sequence of line segments that "float" over the data and allow segmentation by carefully set slope thresholds.
The slope threshold determines the attacks. Once the attacks are determined, the decay time-constant, tau, is determined by fitting a one-pole model to the amplitude envelope. From the value of tau, a decision can be made as to whether a given stroke is damped or undamped. This corresponds to the method of striking the drum. Once the damped/undamped decision is made, a portion of the original time waveform is sent to a "stroke-detector" that determines how the drum was struck in greater detail.
At this point, enough information about the performance has been obtained to begin a higher-level analysis. Given the timing information and the patterns of strokes, it is possible to track tempo automatically, and to try to make inferences about the meter. These two issues are in fact quite deep, and are the focus of a body of work that involves detection of "macro-periodicity", that is a repetition rate over longer periods of time than signal processing would normally yield. Also included in this thesis is an historical and theoretical overview of research on rhythm, from several perspectives.