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
["A>df>a b>gd>d' a>fd>a g>eB>g f>dA>f", 'A>af>d B>bg>d B>bg>d']  
X:1
L:1/8
M:4/4
K:D
 (A>.G) | (F>.A)D>F A>df>a | b>gd>d' a>fd>a | g>eB>g f>dA>f | e>dc>B (3Age (3cAG | F>AD>F A>df>a | 
 b>gd>d' a>fd>a | g>eB>g f>dA>f | e>ac>e d2 :: (A>.G) | (F>.a)f>d A>af>d | B>bg>d B>bg>d | 
 A>af>d A>af>d | A>ge>c A>GF>G | A>af>d A>af>d | B>bg>d B>bg>d | a>ag>e c>AB>c | d2 f2 d2 :|  