Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/16
M:2/4
K:G
['GBAF GDB,D', 'd2dB g2gd e2ec a2ag']  
X:1
L:1/16
M:2/4
K:G
 uD2 | GBAF GDB,D | GB"^4"ec d2"^0"vef | gfed cBAG | FGAB ADEF | GBAF GDB,D | GB"^$"ec d2"^0"vef | 
 gfgd ecAF | G2G2G2 :: (uBc) | d2dB g2gd |"^4" e2ec a2ag | f2f"^0"e dcBA | Bed^c ud2B=c | 
 d2dB g2gd |"^4" e2ec a2ag | fgfe dcBA | G2G2G2 :|  