This article defends the view that theories of creativity should be computable and that only three sorts of algorithm can be creative. It proposes a central principle of algorithmic demands for jazz improvisation: a division of labor in terms of computational power occurs between the creation of chord sequences for improvisation and the creation of melodic improvisations in real time. An algorithm for producing chord sequences must be computationally powerful, that is, it calls for a working memory or a notation of intermediate results. Improvisation depends on the ability to extemporize new melodies that fit the chord sequence. The corresponding algorithm must operate rapidly in real time, and so it minimizes the computational load on working memory. The principle of algorithmic demands is supported by analysis and a computer model.

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