I Would like to understand the melody movement in Chopin's op.9 number 2 at minute 01:28 in this youtube video (you can find the score also). it's in the key of Bb But it seems he jumps to other keys like F major or D major?! but I am not sure. thanks a lot.
Chopin is playing around with the idea of enharmonic reinterpretation at 1:28.
He cadences in D♭ major at 1:26. This isn't anything too extraordinary, because it's just the relative major of B♭ minor.
Immediately after this chord, he takes that bass D♭ and enharmonically reinterprets it to become a C♯. Simultaneously, he uses that C♯ to create an A7/C♯ chord that then quickly leads to D major.
The cadence on F major is perhaps less interesting, because it's just the dominant of B♭ minor. Perhaps you could argue that F minor would be more normative, but at this point in the nineteenth century, F major was a viable option. (And certainly more viable than D major!)
Lastly, pay attention to the three harmonic areas we've pointed out: we start in B♭, and we also move to D♭, D, and F. We call this composing out, because at a larger scale the music is expressing the overall B♭ tonic triad .