A Functional Taxonomy of Music Generation Systems

Digital advances have transformed the face of automatic music generation since its beginnings at the dawn of computing. Despite the many breakthroughs, issues such as the musical tasks targeted by different machines and the degree to which they succeed remain open questions. We present a functional taxonomy for music generation systems with reference to existing systems. The taxonomy organizes systems according to the purposes for which they were designed. It also reveals the inter-relatedness amongst the systems. This design-centered approach contrasts with predominant methods-based surveys and facilitates the identification of grand challenges to set the stage for new breakthroughs.Comment: survey, music generation, taxonomy, functional survey, survey, automatic composition, algorithmic compositio

Composing first species counterpoint with a variable neighbourhood search algorithm

In this article, a variable neighbourhood search (VNS) algorithm is developed that can generate musical fragments consisting of a melody for the cantus firmus and the first species counterpoint. The objective function of the algorithm is based on a quantification of existing rules for counterpoint. The VNS algorithm developed in this article is a local search algorithm that starts from a randomly generated melody and improves it by changing one or two notes at a time. A thorough parametric analysis of the VNS reveals the significance of the algorithm's parameters on the quality of the composed fragment, as well as their optimal settings. A comparison of the VNS algorithm with a developed genetic algorithm shows that the VNS is more efficient. The VNS algorithm has been implemented in a user-friendly software environment for composition, called Optimuse. Optimuse allows a user to specify a number of characteristics such as length, key and mode. Based on this information, Optimuse 'composes' both cantus firmus and first species counterpoint. Alternatively, the user may specify a cantus firmus, and let Optimuse compose the accompanying first species counterpoint. © 2012 Taylor & Francis

SODES: Solving ordinary differential equations step by step

In this paper, we introduce SODES (Stepwise Ordinary Differential Equations Solver) a new solver for Ordinary Differential Equations (ODE). SODES can optionally provide the solution displaying all the steps needed to obtain it. This way, SODES is an important tool not only for researchers who need solving ODE but also constitutes an important tool for the teaching and learning process of ODE. SODES has been developed using programming with a Computer Algebra System (CAS). Specifically, we use the CAS Derive but it can be easily adapted to any other CAS supporting programming. SODES provides, step by step, the solution of the following types of ODE: separable, homogeneous, exact, integrating factors, linear, Bernoulli, Riccati, first order ODE of nth degree, Cauchy’s problems of first order ODE, higher order linear homogeneous equations with constant coefficients, Lagrange’s method for particular solutions of higher order linear equations with constant coefficients, higher order linear equations with constant coefficients and Cauchy’s problems of higher order linear equations with constant coefficients. SODES also deals with two generic programs which determine the type or types of a given ODE and provides the solution. In this paper we will also introduce a draft of a Graphical User Interface (GUI) for SODES in a local web application using programming in Python (using its CAS module SymPy) which is a more portable and free CAS. This draft can be used in English, French and Spanish, and can be easily extended to other languages. The code of SODES and the GUI are freely available so that it can be used by users who also will be able to adapt it to their needsFunding for open access charge: Universidad de Málaga / CBU

Perception based approach on pattern discovery and organisation of point-set data

The general topic of the thesis is computer aided music analysis on point-set data utilising theories outlined in Timo Laiho’s Analytic-Generative Methodology (AGM) [19]. The topic is in the field of music information retrieval, and is related to previous work on both pattern discovery and computational models of music. The thesis aims to provide analysis results that can be compared to existing studies. AGM introduces two concepts based on perception, sensation and cognitive processing: interval–time complex (IntiC) and musical vectors (muV). These provide a mathematical framework for the analysis of music. IntiC is a value associated with the velocity, or rate of change, between musical notes. Musical vectors are the vector representations of these rates of change. Laiho explains these attributes as meaningful for both music analysis and as tools for music generation. Both of these attributes can be computed from a point-set representation of music data. The concepts in AGM can be viewed as being related to geometric methods for pattern discovery algorithmsof Meredith, Lemström et al.[24] whointroduce afamily of ‘Structure Induction Algorithms’. These algorithms are used to find repeating patterns in multidimensional point-set data. Algorithmic implementations of intiC and muV were made for this thesis and examined in the use of rating and selecting patterns output by the pattern discovery algorithms. In addition software tools for using these concepts of AGM were created. The concepts of AGM and pattern discovery were further related to existing work in computer aided musicology

Hearing the Tonality in Microtonality

In the late 1970s and 1980s, composer-pianist Easley Blackwood wrote a series of microtonal compositions exploring the tonal and modal behavior of a dozen non–twelve-tone equal temperaments, ranging from 13 to 24 tones per octave. This dissertation investigates a central paradox of Blackwood’s microtonal music: that despite being full of intervals most Western listeners have never heard before, it still seems to “make sense” in nontrivial ways. Much of this has to do with the music’s idiosyncratic approach to tonality, which I define as a regime of culturally conditioned expectations that guides one’s attentional processing of music’s gravitational qualities over time. More specifically, Blackwood configures each tuning’s unfamiliar elements in ways that correspond to certain schematic expectations Western listeners tend to have about how tonal music “works.” This is why it is still possible to hear the forest of tonality in this music, so to speak, despite the odd-sounding trees that comprise it. Because of its paradoxical blend of expectational conformance and expectational noncompliance, Blackwood’s microtonal music makes for a useful tool to snap most Western-enculturated listeners out of their ingrained modes of musical processing and reveal certain things about tonality that are often taken for granted. Accordingly, just as Blackwood writes conventional-sounding music in unconventional tunings, this dissertation rethinks several familiar music-theoretic terms and concepts through the defamiliarizing lens of microtonality. I use Blackwood’s microtonal music as a prism to shine a light on traditional theories of tonality, scale degrees, consonance and dissonance, and harmonic function, arguing that many of these theories rely on assumptions that are tacitly tied to twelve-tone equal temperament and common-practice major/minor music. By unhooking these terms and concepts from any one specific tuning or historical period, I build up a set of analytical tools that can allow one to engage more productively with the many modalities of tonality typically heard on a daily basis today. This dissertation proceeds in six chapters. The four interior chapters each center on one of the terms and concepts mentioned above: scale degrees (Chapter 2), consonance and dissonance (Chapter 3), harmonic function (Chapter 4), and tonality (Chapter 5). In Chapter 2, I propose a system for labeling scale degrees that can provide more nuance and flexibility when reckoning with music in any diatonic mode (and in any tuning). In Chapter 3, I advance an account of consonance and dissonance as expectational phenomena (rather than purely psychoacoustic ones), and I consider the ways that non-pitched elements such as meter and notation can act as “consonating” and/or “dissonating” forces. In Chapter 4, I characterize harmonic function as arising from the interaction of generic scalar position and metrical position, and I devise a system for labeling harmonic functions that is better attuned to affective differences across the diatonic modes. In Chapter 5, I synthesize these building blocks into a conception of fuzzy heptatonic diatonic tonality that links together not only all of Blackwood’s microtonal compositions but also more familiar musics that use a twelve-tone octave, from Euroclassical to popular styles. The outer chapters are less explicitly music-analytical in focus. Chapter 1 introduces readers to Blackwood’s compositional approach and notational system, considers the question of his intended audience, and discusses the ways that enculturation mediates the cognition of microtonality (and of unfamiliar music more generally). Chapter 6 draws upon archival documents to paint a more detailed picture of who Blackwood was as a person and how his idiosyncratic worldview colors his approach to composition, scholarship, and interpersonal interaction. While my nominal focus in these six chapters is Blackwood’s microtonal music, the repertorial purview of my project is far broader. One of my guiding claims throughout is that attending more closely to the paradoxes and contradictions of Blackwood’s microtonality can help one better understand the musics they are accustomed to hearing. For this reason, I frequently compare moments in Blackwood’s microtonal music to ones in more familiar styles to highlight unexpected analogies and point up common concerns. Sharing space with Blackwood in the pages that follow are Anita Baker, Ornette Coleman, Claude Debussy, and Richard Rodgers, among others—not to mention music from Curb Your Enthusiasm, Fortnite, Sesame Street, and Star Wars. Ultimately, this project is a testament to the value of stepping outside of one’s musical comfort zone. For not only can this reveal certain things about that comfort zone that would not be apparent otherwise, but it can also help one think with greater nuance, precision, and (self-)awareness when “stepping back in” to reflect upon the music they know and love