We show that it is possible to extend hidden Markov models to have a countably infinite number of hidden states. By using the theory of Dirichlet processes we can implicitly integrate out the infinitely many transition parameters, leaving only three hyperparameters which can be learned from data. These three hyperparameters define a hierarchical Dirichlet process capable of capturing a rich set of transition dynamics. The three hyperparameters control the time scale of the dynamics, the sparsity of the underlying state-transition matrix, and the expected number of distinct hidden states in a finite sequence. In this framework it is also natural to allow the alphabet of emitted symbols to be infinite---consider, for example, symbols being possible words appearing in English text.

We propose a system, the Continuator, that bridges the gap between two classes of traditionally incompatible musical systems: 1) interactive musical systems, limited in their ability to generate stylistically consistent material, and 2) music imitation systems, which are fundamentally not interactive. Our purpose is to allow musicians to extend their technical ability with stylistically consistent, automatically learnt material. This goal requires the ability for the system to build operational representations of musical styles in a real time context. Our approach is based on a Markov model of musical styles augmented to account for musical issues such as management of rhythm, beat, harmony, and imprecision. The resulting system is able to learn and generate music in any style, either in standalone mode, as continuations of musician's input, or as interactive improvisation back up. Lastly, the very design of the system makes possible new modes of musical collaborative playing. We describe the architecture, implementation issues and experimentations conducted with the system in several real world contexts.

An important problem in computational music analysis is the representation and automated discovery of recurrent patterns. In this paper we present a new method for pattern representation and discovery in a large corpus of music. Using the formalism of multiple viewpoints, music is viewed as multiple streams of description derived from the basic surface representation. Patterns are discovered within viewpoint sequences derived from the corpus for selected viewpoints. A statistical method is used to restrict attention to only those patterns which occur much more frequently than expected, where expectation is based on a Markov model of viewpoint elements. The concept of the longest significant patterns in a corpus is introduced. The method presented in this paper is designed to rapidly enumerate all longest significant patterns within a large corpus. An application of the method to the Bach chorales is presented.

In this paper we survey the use of different AI methods for algorithmic composition, present their advantages and disadvantages, discuss some important general issues and propose desirable future prospects.

We explore the application of statistical techniques, borrowed from natural language processing, to music. A probabilistic method is used to capture and generalise from the local harmonic movement of a corpus of seventeenth-century dance music. The probabilistic grammars so generated are then used for experiments in generation (composition). The corpus

The automated discovery of recurrent patterns in music is a fundamental task in computational music analysis. This paper describes a new method for discovering patterns in the vertical and horizontal dimensions of polyphonic music. A formal representation of music objects is used to structure the musical surface, and several ideas for viewing pieces as successions of vertical structures are examined. A knowledge representation method is used to view pieces as sequences of relationships between music objects, and a pattern discovery algorithm is applied using this view of the Bach chorale harmonizations to find significant recurrent patterns. The method finds a small set of vertical patterns that occur in a large number of pieces in the corpus. Most of these patterns represent specific voice leading formulae within cadences.

This paper discusses the use of statistical models for the problem of musical style imitation. Statistical models are created from extant pieces in a stylistic corpus, and have an objective goal which is to accurately classify new pieces. The process of music generation is equated with the problem of sampling from a statistical model. In principle there is no need to make the classical distinction between analytic and synthetic models of music. This paper presents several methods for sampling from an analytic statistical model, and proposes a new approach that maintains the intra opus pattern repetition within an extant piece. A major component of creativity is the adaptation of extant art works, and this is also an efficient way to sample pieces from complex statistical models.

This paper presents a representation for melodic segment classes and applies it to music data mining. Melody is modeled as a sequence of segments, each segment being a sequence of notes. These segments are assigned to classes through a knowledge representation scheme which allows the flexible construction of abstract views of the music surface. The representation is applied to sequential pattern discovery and to the statistical modeling of musical style.

The Continuator system is an attempt to bridge the gap between two classes of traditionally incompatible musical systems: 1) interactive musical systems, limited in their ability to generate stylistically consistent material, and 2) music composition systems, which are fundamentally not interactive. The purpose of Continuator is to extend the technical ability of musicians with stylistically consistent, automatically learnt musical material. This requires the ability for the system to build operational representations of musical styles in real time, and to adapt quickly to external musical information. The Continuator is based on a Markov model of musical styles augmented to account for efficient real time learning of musical styles and to arbitrary external bias. The paper describes the main technical issues at stake concerning the integration of an agnostic learning scheme in an interactive instrument, and reports on real-world experiments performed with various musicians.

We outline a framework within which machine compositions may be evaluated objectively. In particular, the framework allows statements about those compositions to be refuted on the basis of empirical experimentation. We consider this to be fundamental if we wish to evaluate the degree to which our programs achieve their compositional aims. Furthermore, a review of the literature reveals that this is a largely ignored aspect of research into algorithmic composition. Our framework involves four components: specifying the compositional aims; inducing a critic from a set of example musical phrases; composing music that satisfies the critic; and evaluating specific claims about the compositions in experiments using human subjects. We describe a system which exemplifies these four stages and which demonstrates the practicality of the framework. Finally, the application of the framework to the evaluation of musical creativity is discussed and directions for future research are suggested.