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
['Beed e2 de']  
X:1
L:1/8
M:4/4
K:Edor
|:"Em" EB B2 dB B2 |"Em" EBBA"D" FDFA |"Em" BE E2 BABd |1"C" egfe"D" dBAF :|2"C" egfe"D" dBAe || 
"Em" Beed e2 de |"D" fede"Bm" fe e2 |"Em" febe febe |"D" fede"Bm" feed |"Em" Beed e2 de | 
"D" fede fa a2 |"G" b2 bf"D" a2 af |"C" egfe"Bm" dBAF ||  