Craft a piece of music that integrates both the suggested theme and letter-based structure.
X:1
L:1/8
M:2/4
K:F
['AG A2 GAGA']  
X:1
L:1/8
M:2/4
K:F
 AG A2 | GAGA | c>df>g | d c3- | c3 d | c>df>g | G A3- | A4 | AG A2 | GAGA | c>dfg/a/ | dccd | 
 F2 G>F | D3 ^C | FGBG | F4 |]  