Craft a piece of music that integrates both the suggested theme and letter-based structure.
X:1
L:1/8
Q:1/8=320
M:6/8
K:G
['e dBG ABA', 'dBG ABA']  
X:1
L:1/8
Q:1/8=320
M:6/8
K:G
"^Double Jig" DF/E/D GED | BGD ABc | B2 B dBG | AGF GFE | DF/E/D GED | ABc d2 e | dBG ABA |1 
 G3 GFE :|2 G3 GBd || c2 e dBG | ABA E2 F | GFG ABc | ded g2 f | ege dBG | ABA d2 e | dBG ABA |1 
 G3 GBd :|2 G3 GFE |]  