Colinsmum, I disagree that incentives are always childish. Personally, I wouldn't do the unpleasant parts of my job if I weren't getting paid. Students work harder in college to keep their grades up. It's part of how the world works.
It's lovely when they are intrinsically motivated to do good things, and we give high praise when our kids show that kind of motivation. But when they're not, I don't think there's anything wrong with an appropriate incentive (deployed in advance, not as a midstream negotiation).
Ren, I know my kids would never be able to do a task like learning to read music right after swimming; they are always brain dead for a while after the pool. And I don't think I'd be inclined to force the issue with something "optional" like reading music, not with a child that young. She might just hate it later because she was pushed, which would be a shame. But your mileage may vary.
Just my two cents,
DeeDee