Computational Complexity of Arranging Music

TL;DR

This paper demonstrates that arranging music with constraints such as dissonance avoidance and transition limits is NP-hard, highlighting the computational difficulty of related musical tasks like choreography and rhythm game design.

Contribution

It establishes the NP-hardness of musical arrangement problems under multiple constraints, a novel theoretical result in computational musicology.

Findings

Musical arrangement with constraints is NP-hard.

Related problems like choreography and rhythm games are computationally complex.

Provides a foundation for understanding the difficulty of automated music arrangement.

Abstract

This paper proves that arrangement of music is NP-hard when subject to various constraints: avoiding musical dissonance, limiting how many notes can be played simultaneously, and limiting transition speed between chords. These results imply the computational complexity of related musical problems, including musical choreography and rhythm games.