Maths and Music

There is a correlation between maths and music. In my teens I bashed my way through Jongen's "Toccata" pretty well. It was one of my teacher's party pieces and I sought to emulate him. (Hear him playing it here)

There is one really awkward bit, if one thinks about it too hard. The hands have been doing septulets, then the left hand changes to sextuplets and finally to quintuplets: it is at this moment when I get stuck. I have analysed the maths for the purpose of slow practice. If each beat is divided into 20, then the music below can be represented by the chart below that. Sorted eh?

Jongen "Toccata" page 5 bar 4

The above bar (first 3 beats only)