The idea is to compare, in terms of mathematical and musical interest, different ways in which the division algorithm produces melodies, starting from the Fibonacci series. This will require the student to understand some mathematical properties of this particular recursive number series; understand some connections between cyclic groups and representations of musical theory. the output will be a number of different melodies, along with their rhythmic patterns (also extracted from the Fibonacci series), and if there is enough time, along with harmonic progressions obtained from such series.
Schedule: To be determined with the student(s).
Supervisors: Eduardo Ibarguengoytia
Difficulty level: Introductory/intermediate (some basic knowledge of probability theory is needed)
Tools: Programming can be done in C/C++, Python, R, Matlab/Octave, Wolfram Mathematica, Maple etc., depending on the knowledge of the student.
Results: To be completed at the end of the project.