Develop a musical piece using the given theme and incorporating the letter-based structure provided.
X:1
L:1/8
M:6/8
K:Dmix
['', 'd^cd AFD A,DF (A2 d) cBc', 'd^cd A2', 'd^cd .A2 (A A4) z B cBc']  
X:1
L:1/8
M:6/8
K:Dmix
 A |: d^cd AFD | A,DF (A2 d) | cBc GEC | G,CE (G2 c) | d^cd AFD | A,DF (A2 d) | cBc AGE | 
 ADD (D2 A) :| d^cd A2 A | d^cd A z2 | cBc E2 E | GAB BAG | d^cd A2 A | d^cd A2 B | cBc AGE | 
 ADD (D2 A) || d^cd .A2 (A | A4) z B | cBc .E2 (E | E4) z ^c | d^cd .A2 (A | A4) z B | cBc AGE | 
 ADD D3 ||  