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:D
['a2 a2']  
X:1
L:1/8
M:4/4
K:D
 dB |"D" ABde f2 ed |"Em" efed"A7" B2 dB |"D" ABde fdaf |"Em" e4"A7" e2 fg |"D" a2 a2 f2 ed | 
"G" BcdB"A7" A2 de |"D" f2 af"A7" edef |"D" d4 d2 :| fg |"D" a2 a2 fade |"A7" fe e2"D" f2 df | 
"D" a2 a2 fdaf |"Em" e4"A7" e2 fg |"D" a2 a2 f2 ed |"G" BcdB"A7" A2 de |"D" f2 af"A7" edef | 
"D" d4 d2 |] fg |"D" a2 a2 fade |"A7" fe e2"D" f2 df |"D" a2 a2"Bm" fdaf |"Em" e4"A7" egfe | 
"D" defe d3 A |"G" BABd"A7" A2 de |"D" f2 af"A7" edef |"D" d4 d2 |]  