From the statistical principles to a new method for identifying the main structures of musical melodies. An international research team, of which Vittorio Loreto and Francesca Tria of Sapienza University of Rome are part, developed a new method to identify the fundamental association structures in musical sequences.

The model can also be used to artificially create musical pieces of the same style of a given corpus, while avoiding plagiarism.
Music can be viewed as a complex network of interacting components, notes, comparable to neurons in the nervous system;  a statistical approach is able to detect the existing relationships between the notes and to guide the algorithmic composition of new melodies.

The challenge of the research group was to find a model based on Maximum Entropy for determining probability distributions from "partial" information, capable of generating new melodies with the same stylistic elements as the reference tracks.

Given a sequence of elements, in this case the notes, one can determine for each pair of notes "x" and "y", the probability that "x" is followed by "y"; from this set of probabilities, an artificially generated sequence that holds the same probabilities can be obtained by digital processing: from a given corpus of tracks, the method is able to generate, using a specific algorithm, musical tracks with the same style as the reference corpus.

"To avoid plagiarism", explains Vittorio Loreto, professor of Physics at Sapienza, "we use a special algorithm to limit the length of copied sequences in artificially generated songs. By using compression algorithms we can then verify both the proximity of the new composition to the reference corpus and the degree of plagiarism. In this way one can control the balance between innovation and similarity".

"Its generality", adds Loreto, "gives our model a wide freedom in creating new melodies echoing the style of a given piece of music and opens up a series of applications both in music (to address issues related to rhythm, polyphony and expressiveness) and in other areas (such as language or art) where stylistic and creative elements are crucial elements, contributing to the great debate on artificial creativity and creative interactions between humans and machines".