Music Generator Applying Markov Chain and Lagrange Interpolation

Abstract

Algorithmic composition is the process that composes music based on algorithms by formulating specific rules that incorporate relevant music arranging theory and assigning these rules to a suitable computer algorithm. One common approach is to use Markov models to generate note sequences. However, the generated notes do not consider the overall chord progression and the rhythmic pattern of the section, which is not effective when dealing with long multi-track music, especially for more structured works, e.g., classical and pop music. Therefore, this paper introduces an improved approach that uses Markov chains for chord generation, and then uses Lagrange Interpolation to generate melodies and accompaniments for multitrack customized instruments using chord progression notes as anchor points. In this study, only 30 common chord progressions and 30 rhythmic progressions were used as the input data to generate a sample music with cat sounds as the main melody, violins as the sub-melody, and pianos as the accompaniment. It eliminates the mentioned problems associated with the adoption of Markov chains for melodic composition. In this case, it allows for the creation of tonal music with an overall structural, multi-track approach, by using chord progressions as a guide to the melody and even the accompaniment, and by controlling the structural characteristics of the music through rhythmic patterns.