Mathematics and music traditionally have been seen as very opposite areas of human development, one being rational and deterministic and the other more emotional and creative. A question that frequently arises is whether these two worlds can be joined in a certain manner, and that is what this work is about. Through the use of interpolation techniques we seek to generate functions for representing songs and thus determine new ways of musical improvisation which allow us to experience music not merely from the symmetry brought by the sounds themselves, but also from the rigour and accuracy of the mathematical and numerical methods.