Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:D
['fe e2']  
X:1
L:1/8
M:2/2
K:D
"D" AddA"G" BAFA |"D" dAFA"A" GFED |"D" FAAB AFEF |1"G" ABde"A" fe e2 :|2"A" ABde"D" fd d2 |] 
"D" a2{b} af"G" g2{a} ge |"D" f2 fd"A" ec A2 |"D" a2{b} ag fedB |"G" ABde"A" fe e2 | 
"D" a2 fa"G" g2 eg |"D" f2 df"A" ecAF |"G" G2 BG"D" F2 AF |"A" ABde"D" fd d2 |]  