Craft a piece of music that integrates both the suggested theme and letter-based structure.
X:1
L:1/8
Q:1/2=100
M:2/2
K:G
['G3 d BdGB A2', 'B3 c dBGg e2 ce', 'GDGd B/c/d/B/ GB A2', 'BGcA dBGg']  
X:1
L:1/8
Q:1/2=100
M:2/2
K:G
 G3 d BdGB | A2 D2 G/A/B/A/ GD | G3 d BdGB | A2 D2 G4 :| B3 c dBGg | e2 ce dBAG | B3 c dBGg | 
 e2 ce d2 D2 | G3 d BdGB | A2 D2 G/A/B/c/ GD | G3 d BdGB | A2 D2 G4 :| 
"^Variations" GDGd B/c/d/B/ GB | A2 D2 G/A/B/A/ GD | GDGd B/c/d/B/ GB | A2 D2 G4 :| BGcA dBGg | 
 ecBc dBAG | BGcA dBGg | e2 ce dDEF | GDGd Bd G/A/B/G/ | A2 D2 G/A/B/A/ GD | GDGd B/c/d/B/ GB | 
 A2 D2 G4 :|  