Machine learning models of music typically break up the task of composition into a chronological process, composing a piece of music in a single pass from beginning to end. On the contrary, human composers write music in a nonlinear fashion, scribbling motifs here and there, often revisiting choices previously made. In order to better approximate this process, we train a convolutional neural network to complete partial musical scores, and explore the use of blocked Gibbs sampling as an analogue to rewriting. Neither the model nor the generative procedure are tied to a particular causal direction of composition. Our model is an instance of orderless NADE (, 2014), which allows more direct ancestral sampling. However, we find that Gibbs sampling greatly improves sample quality, which we demonstrate to be due to some conditional distributions being poorly modeled. Moreover, we show that even the cheap approximate blocked Gibbs procedure from (2014) yields better samples than ancestral sampling, based on both log-likelihood and human evaluation.
Computer music researchers have taken inspiration from this pedagogical scheme by first teaching computers to write species counterpoint as opposed to full-fledged counterpoint. Farbood @cite_30 uses Markov chains to capture transition probabilities of different melodic and harmonic transitions rules. Herremans @cite_3 @cite_8 takes an optimization approach by writing down an objective function that consists of existing rules of counterpoint and using a variable neighbourhood search (VNS) algorithm to optimize it.
@cite_30 @cite_3 @cite_8
147294073 2012433269 2123272248 2161850243
This paper presents a novel approach to computergenerated Palestrina-style counterpoint using probabilistic Markov Chains. It is shown how Markov Chains adequately capture the rules of species counterpoint and how they can be used to synthesize species counterpoint given a cantus firmus. It is also shown how such rules can be inferred from given counterpoint examples. Abstract We present a system for the automatic transcription of solo human singing into note sequences. Particular attention is devoted to the modelling of the transitions between consecutive notes of the sung passage. Hidden Markov models (HMMs) are used to represent both individual notes and the transitions between them, in order to capture the variability of the estimated pitch within a statistical framework. A database consisting of annotated passages sung by 26 soprano subjects is compiled and used for the development of the system. Explicit transition models are introduced in order to better identify note boundaries that are otherwise poorly modelled. Context-independent transition models are evaluated first, followed by context-dependent transition models which are shown to improve both the note recognition accuracy and the transition region time-alignment. The final system is found to be able to transcribe sung passages with an overall accuracy of 86.7 . We present a probabilistic generative model for timing deviations in expressive music performance. The structure of the proposed model is equivalent to a switching state space model. The switch variables correspond to discrete note locations as in a musical score. The continuous hidden variables denote the tempo. We formulate two well known music recognition problems, namely tempo tracking and automatic transcription (rhythm quantization) as filtering and maximum a posteriori (MAP) state estimation tasks. Exact computation of posterior features such as the MAP state is intractable in this model class, so we introduce Monte Carlo methods for integration and optimization. We compare Markov Chain Monte Carlo (MCMC) methods (such as Gibbs sampling, simulated annealing and iterative improvement) and sequential Monte Carlo methods (particle filters). Our simulation results suggest better results with sequential methods. The methods can be applied in both online and batch scenarios such as tempo tracking and transcription and are thus potentially useful in a number of music applications such as adaptive automatic accompaniment, score typesetting and music information retrieval. We describe how we used a data set of chorale harmonisations composed by Johann Sebastian Bach to train Hidden Markov Models. Using a probabilistic framework allows us to create a harmonisation system which learns from examples, and which can compose new harmonisations. We make a quantitative comparison of our system's harmonisation performance against simpler models, and provide example harmonisations.