38 Computer Music Journal Evolutionary computation (De Jong et al. 1993) is being considered with growing interest in musical applications. One of the music domains in which evolutionary computation has made the most impact is music composition. A number of evolu- tionary systems for composing musical material have been proposed (e.g., Horner and Goldberg 1991 Dahlstedt and Nordhal 2001). In addition to music composition, evolutionary computing has been considered in music improvisation applications where an evolutionary algorithm typically models a musician���s improvising (e.g., Biles 1994). Neverthe- less, little research focusing on the use of evolution- ary computation for expressive- performance analysis has been reported. Traditionally, expressive performance has been studied using empirical approaches based on statis- tical analysis (e.g., Repp 1992), mathematical model- ing (e.g., Todd 1992), and analysis- by- synthesis (e.g., Friberg et al. 1998). In these approaches, humans are responsible for devising a theory or a mathematical model that captures different aspects of musical expressive performance. The theory or model is later tested on real performance data to determine its accuracy. In this article, we describe an approach to investi- gating musical expressive performance based on evolutionary computation. Instead of manually modeling expressive performance and testing the model on real musical data, we let a computer execute a sequential- covering genetic algorithm to automatically discover regularities and performance principles from real performance data, consisting of audio recordings of jazz standards. The algorithm combines sequential covering (Michalski 1969) and genetic algorithms (Holland 1975). The sequential- covering component of the algorithm incrementally constructs a set of rules by learning new rules one at a time, removing the positive examples covered by the latest rule before attempting to learn the next rule. The genetic component of the algorithm learns each of the new rules by applying a genetic algorithm. The algorithm provides an interpretable specifi - cation of the expressive principles applied to an interpretation of piece of music and, at the same time, it provides a generative model of expressive performance, namely, a model capable of generating a computer- music performance with the timing and energy expressiveness that characterizes human- generated music. The use of evolutionary techniques for modeling expressive music performance provides a number of potential advantages over other supervised- learning algorithms. By applying our evolutionary algorithm, it is possible to explore and analyze the induced expressive model as it ���evolves,��� to guide and interact with the evolution of the model, and to obtain different models resulting from different executions of the algorithm. This last point is very relevant to the task of modeling expressive music performance, because it is desirable to obtain a non- deterministic model capturing the different possible interpretations a performer may produce for a given piece. The rest of this article is organized as follows. First, we report on related work and describe how we extract a set of acoustic features from the audio recordings. We then describe our evolutionary ap- proach for inducing an expressive music- performance computational model. Finally, we present some con- clusions and indicate some areas of future research. Related Work Evolutionary computation has been considered with growing interest in musical applications (Miranda 2004). A large number of experimental Rafael Ramirez, Amaury Hazan, Esteban Maestre, and Xavier Serra Music Technology Group Universitat Pompeu Fabra Ocata 1, 08003 Barcelona, Spain {rafael, ahazan, emaestre, xserra}@iua.upf.edu A Genetic Rule- Based Model of Expressive Performance for Jazz Saxophone Computer Music Journal, 32:1, pp. 38���50, Spring 2008 �� 2008 Massachusetts Institute of Technology. MIT CMJ321 03Ramirez 38-50.indd 38 MIT CMJ321 03Ramirez 38-50.indd 38 1/17/08 12:53:56 PM 1/17/08 12:53:56 PM

Ramirez et al. 39 number of errors in automatic- performance annota- tion, they use an evolutionary approach to optimize the parameter values of cost functions of the edit distance. In another study, Hazan et al. (2006) pro- posed an evolutionary generative regression- tree model for expressive rendering of MIDI perfor- mances. Madsen and Widmer (2005) present an approach exploring similarities in classical piano performances based on simple measurements of timing and intensity in 12 recordings of a Schubert piano piece. The work presented in this article is an extension of our previous work (Ramirez and Hazan 2005), where we induce expressive- performance classifi cation rules using a genetic algorithm. Here, in addition to considering classifi cation rules, we consider regression rules, and whereas in Ramirez and Hazan, rules are independently induced by the genetic algorithm, here we apply a sequential- covering algorithm to cover the whole example space. Other Machine- Learning Techniques Several approaches have addressed expressive music performance using machine- learning techniques other than evolutionary techniques. The work most relevant to that presented in this article is described in Lopez de Mantaras and Arcos (2002) and Ramirez et al. (2005, 2006). Lopez de Mantaras and Arcos (2002) describe SaxEx, a performance system capable of generating expressive solo performances of jazz. Their system is based on case- based reasoning, a type of analogi- cal reasoning in which problems are solved by reusing the solutions of similar, previously solved problems. To generate expressive solo performances, the case- based reasoning system retrieves, from a memory containing expressive interpretations, those notes that are similar to the input inexpres- sive notes. The case memory contains information about metrical strength, note duration, and so on, and uses this information to retrieve the appropriate notes. However, their system does not allow one to examine or understand the way it makes predictions. Ramirez et al. (2007) explore and compare differ- ent machine- learning techniques for inducing both systems using evolutionary techniques to generate musical compositions have been proposed, includ- ing Cellular Automata Music (Millen 1990), a Cellular Automata Music Workstation (Hunt, Kirk, and Orton 1991), CAMUS (Miranda 1993), MOE (Degazio 1999), GenDash (Waschka 1999), CAMUS 3D (McAlpine, Miranda, and Hogar 1999), Vox Populi (Manzolli et al. 1999), Synthetic Harmonies (Bilotta, Pantano, and Talarico 2000), Living Melo- dies (Dahlstedt and Nordhal 2001), and Genophone (Mandelis 2001). Composition systems based on genetic algorithms generally follow the standard genetic- algorithm approach for evolving musical materials such as melodies, rhythms, and chords. As a result, such compositional systems share the core approach with the one presented in this article. For example, Vox Populi (Manzolli et al. 1999) evolves populations of chords of four notes, each of which is represented as a seven- bit string. The genotype of a chord therefore consists of a string of 28 bits, and the genetic operations of crossover and mutation are applied to these strings to produce new generations of the population. The fi tness func- tion is based on three criteria: melodic fi tness, har- monic fi tness, and voice- range fi tness. The melodic fi tness is evaluated by comparing the notes of the chord to a reference value provided by the user the harmonic fi tness takes into account the consonance of the chord and the voice- range fi tness measures whether the notes of the chord are within a range also specifi ed by the user. Evolutionary computa- tion has also been considered for improvisation applications (Biles 1994), where a genetic algorithm- based model of a novice jazz musician learning to improvise was developed. The system evolves a set of melodic ideas that are mapped into notes consid- ering the chord progression being played. The fi t- ness function can be altered by the feedback of the human playing with the system. Nevertheless, few works focusing on the use of evolutionary computation for expressive- performance analysis exist. In the context of the ProMusic project, Grachten et al. (2004) optimized the weights of edit- distance operations by a genetic algorithm to annotate a human jazz performance. They present an enhancement of edit- distance- based music- performance annotation. To reduce the MIT CMJ321 03Ramirez 38-50.indd 39 MIT CMJ321 03Ramirez 38-50.indd 39 1/17/08 12:53:56 PM 1/17/08 12:53:56 PM