Aplicação de cadeias de Markov em música

Abstract

Music is one of the forms of artistic expression that has been present in our society for a long time, there is evidence that it is not only known but also practiced since prehistory. This art form is the result of the combination of sounds and silences over a period of time. Although we live in a world immersed in music, the musical composition process is not always something so simple, involving, in addition to the artistic part, logical and mathematical reasoning. Different works have been studying different tools for the elaboration of algorithmic musical composition, that is, the elaboration of music with the support of computational algorithms, in which there is an input (provided by human beings), followed by the application of some set of rules (algorithm) and returns a new melody. This work aims to present definitions and properties of Markov chains, in addition to exposing a musical composition model using this probabilistic model from existing music and applications. For this purpose, the R language was used to implement the algorithm and obtain the new melody. It was found that the new generated melodies followed a certain logic in the combination of notes and did not present much resemblance to the initial melody. However, it was noticed that, in some cases, when the melody ends, it may feel like it was interrupted before completion. From this result it can be concluded that this model is in fact able to help in the composition of new musical excerpts, obeying the basic principle of music theory, that is, with the notes within the tonality of the music, however it may not be enough to completely replace the human artistic touch.