Construct a musical piece that integrates the provided motif and corresponds to the indicated musical structure.
X:1
L:1/8
M:2/2
K:Dmix
['ecAG FD (3EFG AdcA G2 FG', 'a2 fa', 'AdcA G2 FG', 'b2 gb'  
X:1
L:1/8
M:2/2
K:Dmix
 f3 d ecAG | FD (3EFG AdcA | G2 FG Adde | fded ^cdeg | fd d2 ecAG | FD (3EFG AdcA | G2 FG Addc | 
 A2 GE FD D2 :: a2 fa dafa | a2 fa defa | b2 gb efgb | efgb efgb | a2 fa dafa | a2 fa defa | 
 aggf feed | ^cdAG FD D2 :|"^Variations:" f3 g ecAG | FD (3EFG AdcA | G2 FG Adde | fded ^cdeg | 
 fd d2 fdAG | FD D2 AdcA | G2 FG Addc | A2 GE FD D2 :: a3 f defg | a2 fa defa | b2 gb ebgb | 
 b2 gb efgb | a3 f defg | a3 f defa | bgaf gefd | ABAG FD D2 :|  