Piano Spiral

When Katherine was four or so, I made her a little toy for transposing music on piano. Since then, I've been showing it to musicians and mathematicians alike. Mathematicians who know any music get it immediately, and so do musicians who know enough math to recognize "modulo 12 cycles." For most people, it's incomprehensible without seeing a few examples.

Lavon Page interviewing Katherine about the device:

Spiral Music Transposer from Lavon Page on Vimeo.

Printable piano spiral:
A photo of the assembled device, with the rotating transparency and a simple four-note composition being transposed on it:

An essay by Don Cohen "The Mathman" on the topic. Teaser picture: