Compose a piece of music by integrating the assigned letter representation and provided tune.
X:1
L:1/8
M:2/2
K:G
['B3 A', 'AGEG DGGF GABc', 'B3 A', 'DGBG DGBG AGEG DGGF G3 B dGBG', 'd2 (3Bcd']  
X:1
L:1/8
M:2/2
K:G
 B3 A BAGA | B2 GB AGEG |1 B3 A BAGB | cABG AGEG :|2 Bd d2 eBdB | AcBG AGEG || DG G2 DGBG | 
 DGBG AGEG | DGGF GABc | d2 BG ABGE | DG G2 AGBG | DGBG AGEG | DGGF GABc | dBAc BG G2 |: 
 d2 (3Bcd edge | dGBG AGEG | d2 (3Bcd eg g2 |1 agbg ageg :|2 a3 b aged |:"^Variations:" B3 A BAGA | 
 B2 GB AGED |1 B3 A BAGB | A2 BG AGED :|2 Bded BcdB | AcBG AGEG || DG G2 DGBG | DGBG AGEG | 
 DGGF G3 B | dGBG ABGE | DG G2 AGBG | dGBG AGBG | DGGF G3 B | dBAc BG G2 |: d2 (3Bcd egge | 
 dGBG AGEG | d2 (3Bcd eg g2 |1 agbg ageg :|2 a3 b aged ||  