Construct a musical piece by amalgamating the designated alphabetical representation and the supplied musical theme.
X:1
L:1/8
M:2/2
K:Amix
['e2 g2', 'c4 BAGA BAGB A2 A2 c4 BA']  
X:1
L:1/8
M:2/2
K:Amix
|:"^A" e2 g2 e2 cd | e2 a2 abag | e2 g2 eged | BA ^G2 A4 ::"^B" A2 A2 c4 | BAGA BAGB | A2 A2 c4 | 
 BA ^G2 A4 :|  