Craft a piece of music that integrates both the suggested theme and letter-based structure.
X:1
L:1/8
M:2/2
K:G
['BG G2', 'bg g2', 'G2 BGBd', 'agea gfge dega']  
X:1
L:1/8
M:2/2
K:G
 A3 c BG G2 | BG (3Bcd g2 fg | eA A2 BG (3Bcd | (3ege dc BG G2 | A3 c BG G2 | BG (3Bcd g3 a | 
 agag (3efg fa | gedc BG G2 :: bg g2 agef | g3 e dega | bg g2 aged | eaag a2 ga | bg g2 agef | 
 g3 e dega | agag (3efg fa | gedc BG G2 ::"^Variations:" AFAc BG G2 | BGBd gedB | AFAc BGBd | 
 (3efg dc BGdB | AFAc BG G2 | BGBd g3 a | bgag egfa | gedc BG G2 :: bggb agea | gfge dega | 
 bggb aged | eaag ea a2 | bggb agea | gfge dega | (3bag ag egfa | gedc BG G2 :|  