Music is temporal in nature, and each music piece has its own way of building expectations and surprises while the piece unfolds itself in time. Musical expectations are created by regularities of series of musical events while surprises are created by either the variation or breaking of such regularities. In that sense, identifying repeated sequences and distinguishing between variations is an essential task for either human listening to music, or modeling music algorithmically.
In this dissertation, a model is proposed to have the capabilities modeling both the temporal and expectation/surprise nature of music signals. The proposed model is named the Variable Markov Oracle since it is derived from a string matching method called Factor Oracle, that is capable of detecting arbitrarily long repetitions and could emulate variable-order Markov chain behavior. The Variable Markov Oracle, in short, is a compressed suffix tree indexing each time instance in a music piece, while in the same time tracing the repeated sub-sequences in the piece. The model selection for the Variable Markov Oracle allows detection of inexact repetitions and utilizes information theoretic measurements which corresponds to the concept of expectation and surprises.
Motif identification and structural segmentation are two of the music research problems that are closely related to the concept of repeated sub-sequences
in music, and in this dissertation the Variable Markov Oracle is used to solve these two problems and proved to be effective. The Variable Markov Oracle is also used in the context of machine improvisation to improve previously Factor Oracle based systems by providing query-guided and structural improvisation. Besides being applied to music signals, the uses of Variable Markov Oracle for retrieval and creative use on other time series data, such as human gesture, are also presented.