Craft a piece of music that integrates both the suggested theme and letter-based structure.
X:1
L:1/8
M:2/2
K:Ador
['cded cAGE G3 E GAcd', 'cdef g2', '', 'cAGE G3 E GAcd (3edc gc acgc', '(3Bcd ef']  
X:1
L:1/8
M:2/2
K:Ador
|: cded cAGE | G3 E GAcd | ecgc acgc | eaag edcA | cded cAGE | G3 E GAcd | eaag (3efg ed | 
 cABG A3 B :: cdef g2 ef | gfgd BG G2 | cdef g2 fg | eaag aged | cdef g3 e | a3 f g3 e | 
 f3 d efed | cABG A3 B :|"^variations" |: cded cAGE | G3 E GAcd | (3edc gc acgc | eaag eged | 
 cded cAGE | G2 GE GAcd | eaag e3 d | cABG A2 AB :: cdef g2 ef | gfgd BG G2 | (3Bcd ef gedg | 
 eaag aged | (3Bcd ef g3 e | a3 f g3 e | =f3 d efed | cABG A3 B :|  