Generating Rhythms with Genetic Algorithms

My system uses an interactive genetic algorithm to learn a user’s criteria for the task of generating musical rhythms. Interactive genetic algorithms (Smith 91) are well suited to solving this problem because they allow for a user to simply execute fitness functions (that is, to choose which rhythms or features of rhythms he likes), without necessarily understanding the details or parameters of these functions. As the system learns (develops an increasingly accurate model of the function which represents the user’s criteria), the quality of the rhythms it produces improves to suit the user’s taste. This approach is largely motivated by Richard Dawkins, who succinctly summarizes the attraction of IGAs for artistic endeavors in stating: “Effective searching procedures become, when the search space is sufficiently large, indistinguishable from true creativity” (Dawkins 86). In the context of this project, rhythms are one measure long sequences of notes and rests occurring on natural pulse subdivisions of a beat; I only deal with a specific subset of the enormous class of rhythms, in order to provide a well-defined domain for the application of the learning algorithm. The benefit of this reduction of the domain is that a rhythm phenotype can now be viewed as a simple vector. Thus, the set of rhythms satisfying the user’s criteria could be represented by a Boolean formula. I actually use a slightly more complex representation for the rhythm genotype, motivated by the benefits of using a diploid genetic structure, consisting of several short array templates; the order of the layering of these templates in creating the phenotype effectively determines the dominance hierarchy between the genes. The simplest mode of interaction is for the user to playback each of the rhythms in a randomly generated population, and then subjectively assign them fitness values based upon their satisfaction of his criteria. The system then uses standard GA selection (with fitness scaling), reproduction (with crossover monitors), and mutation operators. In order to deal with the difficulties resultant from the subjectivity and variability of the user’s criteria, there are also several objective functions with which the system can automatically evolve generations of rhythms: syncopation, density, downbeat, beat repetition, cross rhythm, and cluster functions are currently included. Each of these functions represents an axis in a feature space which is useful for distinguishing rhythms. While these are only a few of the many possible objective functions that could be implemented, they provide a richset of possibilities with which to begin exploring. The user can specify the ideal target value for each of these fitness functions, and also their relative importance (weighting of coefficients) in determining the overall fitness of a rhythm. The system then automatically evolves the indicated number of successive generations, using the objective fitness values to determine selection. The system also makes use of a meta-level genetic algorithm designed to evolve populations of parameters (target values and weights) to the objective fitness functions defined above. This is motivated by the research done in the application of genetic algorithms to the k-nearest-neighbor technique of classification (Punch et al. 93); each meta-level individual represents a warping of K-NN space, such that the fitness of each individual is determined by how well its warping of the feature-space helps to discriminate useful features, and thus correctly perform classifications. Evolving populations of metaindividuals allows a user to quickly reduce the search space by subjective evaluation of the rhythms generated by the meta-individuals, without having to directly specify values for the objective functions. This combination of methods proves to be a powerful hybrid approach to the subjectivity problem, one which allows for greater coverage of the search space than would have been possible ordinarily using a small population (which is necessitated by most IGA’s, and is particularly important when dealing with sequential acoustic data), and more efficient convergence on a satisficing solution. The system is able to converge on near-optimal solutions (acceptable to test users) after about fifty user-evaluations of rhythms. While the GA itself is mechanically quite simple, it is important to note that the implementation of appropriate fitness functions is difficult, and largely determines the musicality of the output. The major future improvement will involve adding the capacity for the system to learn to design its own fitness functions to represent features characteristic of rhythms selected by users in past sessions.