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:Dmix
['FDFG A3 B cAdB cAGB Add^c', 'Adde f2 eg fde^c AGAB c3 d']  
X:1
L:1/8
M:4/4
K:Dmix
|: FDFG A3 B | cAdB cAGB | Add^c d2 de | fde^c dcAG | FDFG A3 B | cAdB cAGB | Add^c ABAG |1 
 EFGE FDDE :|2 EFGE FD D2 |: f2 eg fde^c | Add^c Adde | f2 eg fde^c | AGAB c3 d | eaag efge | 
 dfed cAGB | Add^c ABAG |1 EFGE FD D2 :|2 EFGE FDDE ||  