we (a group of university students), are currently asking ourselves the same questions. we have to design a innovative way of selling musical instruments for a course and are currently planning to do some kind of quantified learning, visualized progress (like a mobile game level system or something) plattform integration.
One way we thought of, was to display learned chords and which songs you could play with it in comparison to all available songs. the best woud be to visualize this as a time trend.
The bpm idea and the overall precision would be interesting too.
Furthermore, at least concerning instruments that cant play harmonies like guitars, pianos etc. some kind of tune recognition should be possible. we arent exactly sure about it, but fortunately we dont have to lay out our ideas down to the technical level.
any more ideas on your side?