This paper describes a computational model of loudness variations in expressive ensemble performance. The model predicts and explains the continuous variation of loudness as a function of information extracted automatically from the written score. Although such models have been proposed for expressive performance in solo instruments, this is (to the best of our knowledge) the first attempt to define a model for expressive performance in ensembles. To that end, we extend an existing model that was designed to model expressive piano performances, and describe the additional steps necessary for the model to deal with scores of arbitrary instrumentation, including orchestral scores. We test both linear and non-linear variants of the extended model n a data set of audio recordings of symphonic music, in a leave-one-out setting. The experiments reveal that the most successful model variant is a recurrent, non-linear model. Even if the accuracy of the predicted loudness varies from one recording to another, in several cases the model explains well over 50 of the variance in loudness.
@cite_28: 
@cite_29: Abstract The quest for understanding how pianists interpret notated music to turn it into a lively musical experience, has led to numerous models of musical expression. Several models exist that explain expressive variations over the course of a performance, for example in terms of phrase structure, or musical accent. Often however expressive markings are written explicitly in the score to guide performers. We present a modelling framework for musical expression that is especially suited to model the influence of such markings, along with any other information from the musical score. In two separate experiments, we demonstrate the modelling framework for both predictive and explanatory modelling. Together with the results of these experiments, we discuss our perspective on computational modelling of musical expression in relation to musical creativity.
@cite_32: : A performer can convey different expressive intentions when playing a piece of music. Perceptual and acoustic analysis of expressive music performances attempts to understand the musicians' strategies. Moreover, models for rendering different expressive intentions were developed for both analysis and deeper multimedia products fruition.
@cite_16: Trained musicians intuitively produce expressive variations that add to their audience's enjoyment. However, there is little quantitative information about the kinds of strategies used in different musical contexts. Since the literal synthesis of notes from a score is bland and unappealing, there is an opportunity for learning systems that can automatically produce compelling expressive variations. The ESP (Expressive Synthetic Performance) system generates expressive renditions using hierarchical hidden Markov models trained on the stylistic variations employed by human performers. Furthermore, the generative models learned by the ESP system provide insight into a number of musicological issues related to expressive performance.
@cite_6: This article presents a new rule discovery algorithm named PLCG that can find simple, robust partial rule models (sets of classification rules) in complex data where it is difficult or impossible to find models that completely account for all the phenomena of interest. Technically speaking, PLCG is an ensemble learning method that learns multiple models via some standard rule learning algorithm, and then combines these into one final rule set via clustering, generalization, and heuristic rule selection. The algorithm was developed in the context of an interdisciplinary research project that aims at discovering fundamental principles of expressive music performance from large amounts of complex real-world data (specifically, measurements of actual performances by concert pianists). It will be shown that PLCG succeeds in finding some surprisingly simple and robust performance principles, some of which represent truly novel and musically meaningful discoveries. A set of more systematic experiments shows that PLCG usually discovers significantly simpler theories than more direct approaches to rule learning (including the state-of-the-art learning algorithm RIPPER), while striking a compromise between coverage and precision. The experiments also show how easy it is to use PLCG as a meta-learning strategy to explore different parts of the space of rule models.
@cite_15: This contribution gives an overview of the state of the art in the field of computational modeling of expressive music performance. The notion of predictive computational model is briefly discussed, and a number of quantitative models of various aspects of expressive performance are briefly reviewed. Four selected computational models are reviewed in some detail. Their basic principles and assumptions are explained and, wherever possible, empirical evaluations of the models on real performance data are reported. In addition to these models, which focus on general, common principles of performance, currently ongoing research on the formal characterisation of differences in individual performance style are briefly presented.
@cite_34: So far, many of the computational models for rendering music performance have been proposed, but they often consist of many heuristic rules and tend to be complex. It makes difficult to generate and select the useful rules, or perform the optimization of parameters in the rules. In this study, we present a new approach that automatically learns a computational model for rendering music performance with score information as an input and the corresponding real performance data as an output. We use a Gaussian Process (GP) incorporated with a Bayesian Committee Machine to reduce naive GP's heavy computation cost, to learn those input-output relationships. We compared three normalized errors: dynamics, attack time and release time between the real and predicted performance by the trained GP to evaluate our proposed scheme. We evaluated the learning ability and the generalization ability. The results show that the trained GP has an acceptable learning ability for 'known' pieces, but show insufficient generalization ability for 'unknown' pieces, suggesting that the GP can learn the expressive music performance without setting many parameters manually, but the size of the current training dataset is not sufficiently large so as to generalize the training pieces to 'unknown' test pieces.
@cite_20: The paper presents a new approach to discovering general rules of expressive music performance from real performance data via inductive machine learning. A new learning algorithm is briefly presented, and then an experiment with a very large data set (performances of 13 Mozart piano sonatas) is described. The new learning algorithm succeeds in discovering some extremely simple and general principles of musical performance (at the level of individual notes), in the form of categorical prediction rules. These rules turn out to be very robust and general: when tested on performances by a different pianist and even on music of a different style (Chopin), they exhibit a surprisingly high degree of predictive accuracy.
Computational models of expressive music performance seek to clarify the relationships between certain properties of the musical score and performance context with the actual performance of the score @cite_15 . These models can serve mainly analytical purposes @cite_20 @cite_28 , by showing the relation between structural properties of the music and its effect in the performance of such music, mainly predictive purposes @cite_34 , i.e. the models are used to render expressive performances, or both @cite_16 , @cite_32 @cite_29 . Computational models of music performance tend to follow two basic paradigms: approaches, where the models are defined through music-theoretically informed rules that intend to map structural aspects of a music score to quantitative parameters that describe the performance of a musical piece, and (or ) approaches, where the models try to infer the rules of performance from analyzing patterns obtained from (large) datasets of observed (expert) performances @cite_6 .