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This article describes experiments conducted with the system and 3- to 5-year-old children. We highlight several dimensions of the study pertaining to music education, including attention span, spontaneous development of playing modes, and capacity to listen analytically. We describe very encouraging preliminary results and stress the importance of using reflective interactive systems for triggering musical interest in children and creating stimulating, nonsupervised music learning environments. We conclude by setting up our research in the context of the theory of flow as an optimal experience.

Markov chains are a well known tool to model temporal properties of many phenomena, from text structure to fluctuations in economics. Because they are easy to generate, Markovian sequences, i.e. temporal sequences having the Markov property, are also used for content generation applications such as text or music generation that imitate a given style. However, Markov sequences are traditionally generated using greedy, left-to-right algorithms. While this approach is computationally cheap, it is fundamentally unsuited for interactive control. This paper addresses the issue of generating steerable Markovian sequences. We target interactive applications such as games, in which users want to control, through simple input devices, the way the system generates a Markovian sequence, such as a text, a musical sequence or a drawing. To this aim, we propose to revisit Markov sequence generation as a branch and bound constraint satisfaction problem (CSP). We propose a CSP formulation of the basic Markovian hypothesis as elementary Markov Constraints (EMC). We propose algorithms that achieve domain-consistency for the propagators of EMCs, in an event-based implementation of CSP. We show how EMCs can be combined to estimate the global Markovian probability of a whole sequence, and accommodate for different species of Markov generation such as fixed order, variable-order, or smoothing. Such a formulation, although more costly than traditional greedy generation algorithms, yields the immense advantage of being naturally steerable, since control specifications can be represented by arbitrary additional constraints, without any modification of the generation algorithm. We illustrate our approach on simple yet combinatorial chord sequence and melody generation problems and give some performance results.

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This paper addresses the issue of designing interactive systems that create flow experiences in users. I first describe an interactive musical system called the Continuator, which is able to learn the musical style of users in an agnostic, continuous fashion. I then describe experiments conducted with professional musicians and with 3 to 5-year old children and the Continuator. I show that these interactions are -- almost - typical of the Flow phenomenon, as introduced by Csikszentmihalyi. I then focus on the abstraction of the design principles behind the Continuator and propose the notion of Reflective Interactive System as a class of applications which trigger Flow experiences. Based on the analysis of the various psychological experiments conducted so far, I identify the issue of flexibility in interaction protocols as a crucial step to enhance the efficiency of Reflective Systems as we envisage them today.

Many systems use Markov models to generate finite-length sequences that imitate a given style. These systems often need to enforce specific control constraints on the sequences to generate. Unfortunately, control constraints are not compatible with Markov models, as they induce long-range dependencies that violate the Markov hypothesis of limited memory. Attempts to solve this issue using heuristic search do not give any guarantee on the nature and probability of the sequences generated. We propose a novel and efficient approach to controlled Markov generation for a specific class of control constraints that 1) guarantees that generated sequences satisfy control constraints and 2) follow the statistical distribution of the initial Markov model. Revisiting Markov generation in the framework of constraint satisfaction, we show how constraints can be compiled into a non-homogeneous Markov model, using arc-consistency techniques and renormalization. We illustrate the approach on a melody generation problem and sketch some realtime applications in which control constraints are given by gesture controllers. 1