Using Factor Oracles for Machine Improvisation

Abstract

We describe variable markov models we have used for statistical learning of musical sequences, then we present the factor oracle, a data structure proposed by Crochemore & al for string matching. We show the relation between this structure and the previous models and indicate how it can be adapted for learning musical sequences and generating improvisations in a real-time context. Modeling musical sequencesStatistical modeling of musical sequences has been experimented since the very beginnings of musical informatics (see [Con03] for a review and criticism of most existing models, and [Zic87] for one of the first available real-time interactive system). The idea behind context models, which we are mostly interested in here, is that events in a musical piece can be predicted from the sequence of preceding events. The operational property of such models is to provide the conditional probability distribution over an alphabet given a sequence. For example, if w is musical sequence, r a symbol belonging to the musical alphabet P , P(r|w) is the probability that r will follow w, i.e. the probability of wr given w. This distribution P will be used for generating new sequences or for computing the probability of a given one. First experiments in context based modeling made intensive use of Markov chains.[Ron96] explain that this idea dates back to Shannon : complex sequences do not have obvious underlying source, however, they exhibit a property called short memory property by the authors; there exists a certain memory lengh L such that the conditional probability distribution on the next symbol r does not change significantly if we condition it on suffixes of w longer than L. In the case of Markov chains, L is the order. However, the size of Markov chains is O(| P | L ), so only low order models have been actually experimented.To cope with the model order problem, in earlier works [Dub98, Dub02, Dub03, Ass99] we have proposed a method for building musical style analyzers and generators based on several algorithms for prediction of discrete sequences using Variable Markov Models (VMM). The class of these algorithms is large and we focused mainly on two variants of predictors -universal prediction based on Incremental Parsing (IP) and prediction based on Probabilistic Suffix Trees (PST).The IP method is derived from Information Theory. J. Ziv and A. Lempel [Ziv78] first suggested the core of this method called Incremental Parsing in the context of lossless compression research. IP builds a dictionary of distinct motifs by making a single left to right traversal of a sequence, sequentially adding to a dictionary every new phrase that differs by a single last character from the longest match that already exists in the dictionary. Using a tree representation for the dictionary, every node is associated with a string, whose characters appear as labels on the arcs that lead from the root to that node. Each time the parsing algorithm reaches a longest-match node it means that the node's string has already occurred in the sequen...

On Modeling Affect in Audio with Non-Linear Symbolic Dynamics

“…The Variable Markov Oracle (VMO) [25] is a suffix tree data structure that is derived from Factor Oracle (FO) [27,28] as well as Audio Oracle (AO) [29].…”

“…It has been employed mainly for optimal string matching algorithms, such as biosequence pattern matching. Assayag et al 2004 showed how the FO can be adapted to learn symbolic musical sequences and generate symbolic musical improvisations in real-time [28].…”

Improvisation musicale homme-machine guidée par un scénario temporel

“…Afin de connaître la longueur du contexte commun entre deux évènements musicaux dans une séquence (Assayag, Dubnov, 2004) fait appel à la méthode présentée dans (Lefebvre, Lecroq, 2000) pour le calcul du vecteur lrs, linéaire en temps et en mémoire, en l'intégrant dans l'implémentation de la construction de l'oracle. La longueur de ce contexte correspond au paramètre c p introduit en 2.4.2.…”

Performance Following: Real-Time Prediction of Musical Sequences Without a Score

“…Assayag and Dubnov [18] have suggested using the Factor Oracle structure [19] for musical analysis and generation. The Factor Oracle is a state automata which, for a given sequence of length N, is able to represent the presence and location of repeated sub-sequences of variable length using a linear number of states (N + 1) and transitions (at most 2N − 1).…”