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:G
['|{GA} GFGD B,DGe dBcA', 'cAca b^abg dBdg afge d2- d>^d ecAe']  
X:1
L:1/8
M:4/4
K:G
 D |{GA} GFGD B,DGe | dBcA BGAF |{GA} GFGD B,DGe | dBcA [B,G]2 [B,G] :| [df] |{a} gfgd BGBg | 
 a^gae cAca | b^abg dBdg | afge d2- d>^d | ecAe dBGd | cBAG FecA | GFGD B,DGe | 
 dBcA [B,G]2- [B,G] ||  