Utilizing the provided musical theme and letter-based structure, compose a piece of music.
X:1
L:1/8
Q:1/4=120
M:6/8
K:F
['f cAF', 'D2 f cAF GAc dcB AGF BAG', 'D2 e f>gf fed g>ag gfe f>ed', 'd2 e f>gf fed gag gfe f>ed']  
X:1
L:1/8
Q:1/4=120
M:6/8
K:F
"^Gaily" f | cAF GAc | d2 G G2 f | cAF GA^c | d2 D D2 || f | cAF GAc | dcB AGF | BAG A=B^c | 
 d2 D D2 |] | e | f>gf fed | g>ag gfe | f>ed g>fe | a2 d d2 || e | f>gf fed | gag gfe | 
 f>ed A=B^c | d2 D D2 |]  