Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:D
['dfd AGF DED AFA', 'd3 dfe f2 d cdf edc deg', 'AGF A2 D AGF', 'GFE DED']  
X:1
L:1/8
M:6/8
K:D
 dfd AGF | DED AFA | BGB AFA | BEF GFE | dfd AGF | DED AFA | Add ede | fdd d3 || dfe f2 d | 
 cdf edc | deg f2 g | ece gfe | agf bge | afd cBA | BGB AGF | BEF GFE || AGF A2 D | AGF A2 D | 
 AGF AGF | BEF GFE | AGF A2 D | AGF ABd | fdB AGF | BEF GFE || DED dAF | DED AFD | DED dAF | 
 BEF GFE | DED dcd | BAB ABd | fdB AGF | BEF GFE ||  