‘Joy Spring’ certainly lives up to its name. A fairly straightforward harmonic language lets the melody shine. It’s a great tune to work on creating smooth horn-like phrases on the piano.
The following examples offer some analysis of the changes. Example 1 is firmly in the key of F Major. Example 2 moves between Gb Major and A Major. Example 3 moves from F to Eb to Gb and back to F.
These key centres are, for the most part, established enough to consider them modulations.