Construct a musical piece that follows the designated lettered structure and integrates the provided motif throughout.
X:1
L:1/8
M:6/8
K:D
['A2 A', 'A2 A']  
X:1
L:1/8
M:6/8
K:D
 (3(A/B/c/) | d2 d A2 G | FEF DFA | B2 A G2 F | F3 E2 A | A^GA BAB | cdc A2 A | dcd ede | 
 faf d2 A | Bcd efg | Bed cBA | d2 F A2 A | F D2 z z |: D/F/ | A2 A ABA | A3 A z (3(A/B/c/) | 
 d2 d dfe | d3- d z A | Bcd efg | Bed cBA | d2 F A2 A | F D2 z z :|  