Incorporating Structure and Chord Constraints in Symbolic Transformer-based Melodic Harmonization

Transformer architectures offer significant advantages regarding the generation of symbolic music; their capabilities for incorporating user preferences toward what they generate is being studied under many aspects. This paper studies the inclusion of predefined chord constraints in melodic harmonization, i.e., where a desired chord at a specific location is provided along with the melody as inputs and the autoregressive transformer model needs to incorporate the chord in the harmonization that it generates. The peculiarities of involving such constraints are discussed, and an algorithm is proposed for tackling this task. This algorithm is called B* and it combines aspects of beam search and A* along with backtracking to force pretrained transformers to satisfy the chord constraints, at the correct onset position within the correct bar. The algorithm is brute-force and has exponential complexity in the worst case; however, this paper is a first attempt to highlight the difficulties of the problem and proposes an algorithm that offers many possibilities for improvements since it accommodates the involvement of heuristics.