Characterisation of the degree of musical non-Markovianity

As an aid for musical analysis, in computational musicology mathematical and informatics tools have been developed to characterise quantitatively some aspects of musical compositions. A musical composition can be attributed by ear a certain amount of memory. These results are associated with repetitions and similarities of the patterns in musical scores. To higher variations, a lower amount of memory is perceived. However, the musical memory of a score has never been quantitatively defined. Here we aim to give such a measure following an approach similar to that used in physics to quantify the memory (non-Markovianity) of open quantum systems. We apply this measure to some existing musical compositions, showingthat the results obtained via this quantifier agree with what one expects by ear.The musical non-Markovianity quantifier can thus be used as a new tool that can aid quantitative musical analysis. It can also lead to future quantum computing controllers to manipulate structures in the framework of generative music.