Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:2/2
K:Gdor
['DGGA BABG DF F2', 'B2 dB', 'gd d2 gbag', 'BABG DF F2', 'FBdB DFBd cAFA B2 FB fBdB cAFA', 'gbag fc c2 fgaf g2 dg gbag']  
X:1
L:1/8
M:2/2
K:Gdor
 DGGA BABG | DF F2 CFAF | DGGA BABd | (3cBA fc AGGF | DGGA BABG | DF F2 dFcF | DGGA BABd | 
 (3cBA fc AGGA || B2 dB FBdB | B2 dB cAFA | B2 dB fBdB | cAFA BGGA | (3Bcd Bd fBdc | 
 (3Bcd Bd cAFA | GB (3ABc Bbag | fdcA BG G2 || gd d2 gbag | fc c2 fgaf | gd d2 gbag | fdcA BGBd | 
 g2 fa g2 ag | f2 eg fdcA | GB (3ABc Bbag | fdcA BGGF ||"^variations" DGGA BABG | DF F2 CFAF | 
 DGGA BABd | cAfc AGGF | DGGA BABG | DF F2 FDCF | DGGA BABd | cAfc AGGA || B2 FB FBdB | DFBd cAFA | 
 B2 FB fBdB | cAFA BGGA | B3 d fB B2 | B2 dB cAFA | GBAc Bage | fdcA BG G2 || gd d2 gbag | 
 fc c2 fgaf | g2 dg gbag | fdcA BGBd | g3 d gbag | fgeg fdcA | GBAc Bage | fdcA BGGF ||  