In this paper we give an overview of four algorithms that we have developed for pattern matching, pattern discovery and data compression in multidimensional datasets. We show that these algorithms can fruitfully be used for processing musical data. In particular, we show that our algorithms can discover instances of perceptually significant musical repetition that cannot be found using previous approaches. We also describe results that suggest the possibility of using our datacompression algorithm for modelling expert motivicthematic music analysis.

Throughout this paper, (R, m) denotes a (noetherian) local ring R with maximal ideal m.In [5], Monsky and Washnitzer define weakly complete R-algebras with respect to m. In brief, an R-algebra A† is weakly complete if

and Other Multidimensional Datasets 1. We're going to be talking to you about pattern discovery and matching in polyphonic music and in multidimensional datasets in general.

The fields of music, health, and technology have seen significant interactions in recent years in developing music technology for health care and well-being. In an effort to strengthen the collaboration between the involved disciplines, the workshop “Music, Computing, and Health” was held to discuss best practices and state-of-the-art at the intersection of these areas with researchers from music psychology and neuroscience, music therapy, music information retrieval, music technology, medical technology (medtech), and robotics. Following the discussions at the workshop, this article provides an overview of the different methods of the involved disciplines and their potential contributions to developing music technology for health and well-being. Furthermore, the article summarizes the state of the art in music technology that can be applied in various health scenarios and provides a perspective on challenges and opportunities for developing music technology that (1) supports person-centered care and evidence-based treatments, and (2) contributes to developing standardized, large-scale research on music-based interventions in an interdisciplinary manner. The article provides a resource for those seeking to engage in interdisciplinary research using music-based computational methods to develop technology for health care, and aims to inspire future research directions by evaluating the state of the art with respect to the challenges facing each field.

Our aim in this paper is to clarify the range of motivations that have inspired the development of computer programs for the composition of music. We consider this to be important since different methodologies are appropriate for different motivations and goals. We argue that a widespread failure to specify the motivations and goals involved has lead to a methodological malaise in music related research. A brief consideration of some of the earliest attempts to produce computational systems for the composition of music leads us to identify four activities involving the development of computer programs which compose music each of which is inspired by different practical or theoretical motivations. These activities are algorithmic composition, the design of compositional tools, the computational modelling of musical styles and the computational modelling of music cognition. We consider these four motivations in turn, illustrating the problems that have arisen from failing to distinguish between them. We propose a terminology that clearly differentiates the activities defined by the four motivations and present methodological suggestions for research in each domain. While it is clearly important for researchers to embrace developments in related disciplines, we argue that research in the four domains will continue to stagnate unless the motivations and aims of research projects are clearly stated and appropriate methodologies are adopted for developing and evaluating systems that compose music.