![]() ![]() Constraint Programming (CP) is a paradigm based on explicitly encoded compositional rules. This chapter introduces the use of Constraint Programming for modelling the algorithmic generation of harmonic progressions for composition. The presented model supports equal temperaments only we are currently working on an extension for arbitrary regular temperaments including just intonation. We modeled a diatonic cadence in 12-tone equal temperament (12-TET) a 7-limit harmony progression in 31-TET and adaptive just intonation a chord figuration of a chord from La Monte Young's The Well-Tuned Piano in 41-TET and finally first a melody and and then harmonic counterpoint with Paul Erlich's static symmetrical major scale in 22-TET. These case studies also showed how the model supports various equal temperaments. This paper demonstrates the proposed model in a number of case studies that implement microtonal theories of harmony, melody and counterpoint. The model has been implemented in Strasheela, so that this model can be used together with other Strasheela feature (e.g., temporal score object hierarchies). Constrainable representations for higher level pitch-related concepts such as chord and scale objects are defined. The fundamental layer of this model is its pitch representation, which introduces variables for pitches, pitch classes, and (chord or scale) degrees, as well as their their dependencies. This paper presents a computational model for microtonal music theories and composition based on the constraint programming paradigm. That draft makes the research reproducible by presenting the full source code for all its examples.
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