Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
Q:3/8=100
M:6/8
K:G
['', 'B2 e dBG', 'g2 g']  
X:1
L:1/8
Q:3/8=100
M:6/8
K:G
 G |: B2 e dBG | ABA A2 G | B2 g dBG | BcB B2 A | B2 e dBG | A>BA gab | geg dBG | BcB B2 A :: 
 g2 g g>ab | d>ed dBG | g2 g gab | geg e2 d | def gfe | dBd gab | geg dBG | BcB B2 A :|  