Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:4/4
K:Edor
['', 'gfed edBA G3 B EDBA GE E2', 'gB B2']  
X:1
L:1/8
M:4/4
K:Edor
 ef |: gfed edBA | G3 B EDBA | GE E2 G3 A | Beed Bdef | gfed edBA | G3 B EDBA | GE E2 G3 A | 
 Beed e2 ef :: gB B2 gabg | afde fgaf | gB B2 gabg | afdf e2 ef | gB B2 gbag | afde fga=c' | 
 bgaf gfed | Bgfg e2 ef :|  