Compose a piece of music that follows both the given musical theme and the letter-based structure provided.
X:1
L:1/8
M:2/2
K:G
['', 'g2 f2']  
X:1
L:1/8
M:2/2
K:G
"^A" |: Bc |"G" d4 d2 Bc | d2 B2 AGAB |"C" c4 c2 AB | c2 B2 AGEG |"G" DEGA Bdef | g2 f2 edBA | 
 G2 BG"D" AG F2 |"G" G6 :|"^B" |: Bc |"G" d4 g4 | g2 f2 e2 d2 |"D" fa- a2 a2 fg | a2 f2 edef | 
"G" gfef gfef |"C" g2 f2 edBA |"G" G2 BG"D" AG F2 |"G" G6 :|  