On Linear Algebraic Representation of Time-span and Prolongational Trees

In constructive music theory, such as Schenkerian analysis and the Generative Theory of Tonal Music (GTTM), the hierarchical importance of pitch events is conveniently represented by a tree structure. Although a tree is easy to recognize and has high visibility, such an intuitive representation can hardly be treated in mathematical formalization. Especially in GTTM, the conjunction height of two branches is often arbitrary, contrary to the notion of hierarchy. Since a tree is a kind of graph, and a graph is often represented by a matrix, we show the linear algebraic representation of trees, specifying conjunction heights. Thereafter, we explain the ‘reachability’ between pitch events (corresponding to information about reduction) by the multiplication of matrices. In addition we discuss multiplication with vectors representing a sequence of harmonic functions, and suggest the notion of stability. Finally, we discuss operations between matrices to model compositional processes with simple algebraic operations

Music in Evolution and Evolution in Music

Music in Evolution and Evolution in Music by Steven Jan is a comprehensive account of the relationships between evolutionary theory and music. Examining the ‘evolutionary algorithm’ that drives biological and musical-cultural evolution, the book provides a distinctive commentary on how musicality and music can shed light on our understanding of Darwin’s famous theory, and vice-versa. Comprised of seven chapters, with several musical examples, figures and definitions of terms, this original and accessible book is a valuable resource for anyone interested in the relationships between music and evolutionary thought. Jan guides the reader through key evolutionary ideas and the development of human musicality, before exploring cultural evolution, evolutionary ideas in musical scholarship, animal vocalisations, music generated through technology, and the nature of consciousness as an evolutionary phenomenon. A unique examination of how evolutionary thought intersects with music, Music in Evolution and Evolution in Music is essential to our understanding of how and why music arose in our species and why it is such a significant presence in our lives

AN APPROACH TO MACHINE DEVELOPMENT OF MUSICAL ONTOGENY

This Thesis pursues three main objectives: (i) to use computational modelling to explore how music is perceived, cognitively processed and created by human beings; (ii) to explore interactive musical systems as a method to model and achieve the transmission of musical influence in artificial worlds and between humans and machines; and (iii) to experiment with artificial and alternative developmental musical routes in order to observe the evolution of musical styles. In order to achieve these objectives, this Thesis introduces a new paradigm for the design of computer interactive musical systems called the Ontomemetical Model of Music Evolution - OMME, which includes the fields of musical ontogenesis and memetlcs. OMME-based systems are designed to artificially explore the evolution of music centred on human perceptive and cognitive faculties. The potential of the OMME is illustrated with two interactive musical systems, the Rhythmic Meme Generator (RGeme) and the Interactive Musical Environments (iMe). which have been tested in a series of laboratory experiments and live performances. The introduction to the OMME is preceded by an extensive and critical overview of the state of the art computer models that explore musical creativity and interactivity, in addition to a systematic exposition of the major issues involved in the design and implementation of these systems. This Thesis also proposes innovative solutions for (i) the representation of musical streams based on perceptive features, (ii) music segmentation, (iii) a memory-based music model, (iv) the measure of distance between musical styles, and (v) an impi*ovisation-based creative model