Construct a musical piece that contains the provided motif and abides by the prescribed alphabetical scheme.
X:1
L:1/8
M:4/4
K:G
['BcBA G2 g2 BcBA', 'c2 c2']  
X:1
L:1/8
M:4/4
K:G
|:"^A" BcBA G2 g2 | BcBA G2 g2 | BcBA GABc | B2 G2 G4 ::"^B" c2 c2 c4 | B2 A2 A3 B | c2 c2 c2 dc | 
 B2 G2 G3 B :|  