This is another piece based on harmonic minor harmony. The analysis of ‘Nica’s Dream’ goes into some detail about this harmony and can be used as a primer (Link). Jordan sets up the minor harmony in bar 2 with a II – V – I sequence to the tonic C minor. The listener doesn’t know it’s in a minor key (or probably cares!) but the listener does recognize a II – V -I. Example 1 shows the difference between an “expected” II – V – I sequence and a minor one. Instead of D minor 7 – G7 – C7 we have D major 7 – G7 – C minor 6.
Getting ready for improvisation you probably want to start by working on II-V-I changes in C harmonic minor (Example 2). Notice how the flat 7 (Cm7) is going to clash with the natural 7 of the scale – play around with that b6 instead. Notice how the Cm b6 is the same as an Ab7 (a good chance to play with some expectations!)