Self-similar melodies and Tom Johnson's relationship with maths

The “selfRep melodies” as defined and explored by Tom Johnson in his compositions and books are a stunning example of the sheer mathematical power of Tom's questioning. Most of the results that he established empirically could be proved (using affine maps and their actions on cyclic groups modelling the indexes of periodic melodies), and a wealth of original results followed from his ideas. It shows the strength and depth of the link between mathematical and musical thinking, and very specially how Tom Johnson influenced and worked with the mathematical community in a way no one else could.