Construct a melodic piece using the designated alphabetic pattern and the provided musical theme.
X:1
L:1/8
M:4/4
K:Amix
['BG G2']  
X:1
L:1/8
M:4/4
K:Amix
 BAEA BAEA | BAed BG G2 | Be e2 d2 ed | BG G2 BcdA :|  