In algorithmic music composition, a simple technique involves selecting notes sequentially according to a transition table that specifies the probability of the next note as a function of the previous context. An extension of this transition-table approach is described, using a recurrent autopredictive connectionist network called CONCERT. CONCERT is trained on a set of pieces with the aim of extracting stylistic regularities. CONCERT can then be used to compose new pieces. A central ingredient of CONCERT is the incorporation of psychologically grounded representations of pitch, duration and harmonic structure. CONCERT was tested on sets of examples artificially generated according to simple rules and was shown to learn the underlying structure, even where other approaches failed. In larger experiments, CONCERT was trained on sets of J. S. Bach pieces and traditional European folk melodies and was then allowed to compose novel melodies. Although the compositions are occasionally pleasant, and are preferred over compositions generated by a third-order transition table, the compositions suffer from a lack of global coherence. To overcome this limitation, several methods are explored to permit CONCERT to induce structure at both fine and coarse scales. In experiments with a training set of waltzes, these methods yielded limited success, but the overall results cast doubt on the promise of note-by-note prediction for composition.