Generation of Two-Voice Imitative Counterpoint from Statistical Models

Generating new music based on rules of counterpoint has been deeply studied in music informatics. In this article, we try to go further, exploring a method for generating new music based on the style of Palestrina, based on combining statistical generation and pattern discovery. A template piece is used for pattern discovery, and the patterns are selected and organized according to a probabilistic distribution, using horizontal viewpoints to describe melodic properties of events. Once the template is covered with patterns, two-voice counterpoint in a florid style is generated into those patterns using a first-order Markov model. The template method solves the problem of coherence and imitation never addressed before in previous research in counterpoint music generation. For constructing the Markov model, vertical slices of pitch and rhythm are compiled over a large corpus of dyads from Palestrina masses. The template enforces different restrictions that filter the possible paths through the generation process. A double backtracking algorithm is implemented to handle cases where no solutions are found at some point within a generation path. Results are evaluated by both information content and listener evaluation, and the paper concludes with a proposed relationship between musical quality and information content. Part of this research has been presented at SMC 2016 in Hamburg, Germany

Composición Musical a Través del Uso de Algoritmos Genéticos

Este trabajo se enfocará en el uso de los algoritmos genéticos (AAGG) con el fin de mezclar armonías y melodías de forma que se genere una composición musical de buen sonido para el oído, lo que significa que el contexto de cada nota respaldará la sonoridad de la misma provocando que no se genere un efecto disonante de forma permanente, que se genere una disonancia momentánea es permisible ya que es parte de la misma música generar tensión a través de pequeños intervalos poco agradables al oído

Complexity and heuristics in ruled-based algorithmic music composition

Successful algorithmic music composition requires the efficient creation of works that reflect human preferences. In examining this key issue, we make two main contributions in this dissertation: analysis of the computational complexity of algorithmic music composition, and methods to produce music that approximates a commendable human effort. We use species counterpoint as our compositional model, wherein a set of stylistic and grammatical rules governs the search for suitable countermelodies to match a given melody. Our analysis of the complexity of rule-based music composition considers four different types of computational problems: decision, enumeration, number, and optimization. For restricted versions of the decision problem, we devise a polynomial algorithm by constructing a non-deterministic finite state transducer. This transducer can also solve corresponding restricted versions of the enumeration and number problems. The general forms of the four types of problems, however, are respectively NP-complete, #P-complete, NP-complete in the strong sense, and NP-equivalent. We prove this by first reducing from the well known Three-Dimensional Matching problem to the music composition decision problem, and then by reducing among the music problems themselves. In order to compose music both correct and human-like, we formulate new “artistry” rules to supplement traditional rules of musical style and grammar. We also propose the fuzzy application of these artistry rules, to complement the crisp application of the traditional rules. We then suggest two methods to model human preferences: (1) distinguish an expert’s compositions from alternative compositions by determining rule weights; (2) train an artificial neural network to reflect an expert’s musical preferences through the latter’s evaluations of a set of compositions. We were able to approximate that elusive factor of human preference with better than 75% accuracy. To solve the optimization problem, we adapt two different search algorithms: best-first search with branch-and-bound pruning (for m ≥ 1 optimal solutions), and a genetic algorithm (for m ≥ 1 near-optimal solutions). Through these algorithms, we test the techniques of rule weightings and of trained neural networks as evaluation functions. Our adaptation of the genetic algorithm produced optimal countermelodies in execution time favorably comparable to that taken by the best-first algorithm