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
['E2 (BG) E2', 'E(BTBA) Bdef']  
X:1
L:1/8
M:4/4
K:D
 F | E2 (BG) E2 (B,E) | D2 (FG) AFDF | E2 (BG) E2 B,^c | dBAF dEE :| F | E(BTBA) Bdef | dBAd FDAF | 
 E(BTBA) Bdef | dBAF BEEF | E(BTBA) Bdef | dBAd FDAF | GBEF GABg | f[^da][gg][ff] [eg][Ee][Ee] |]  