Incorporate the given motif and use the alphabetical representation of the specified musical sequence to compose a distinctive musical piece.
X:1
L:1/8
M:4/4
K:C
['FDF ABc ded def AGF', 'AGF G2 A BGE', 'f/g/ agf gfe ded def AGF BAG']  
X:1
L:1/8
M:4/4
K:C
[M:6/8][K:D] ae ae c a caed"^The Clare Jig""^Mug of Brown Ale" ad e ae[Q:1/8=160]G | FDF ABc | 
 ded def | AGF G2 A | BGE E2 G |"^5" FDF ABc | ded def | AGF BAG | FDD D2 :: g |"^9" fdf agf | 
 gfe dBG | AGF G2 A | BGE E2 [Gg] |1"^13" fdf agf | gfe dBG | AGA BAG | FDD D2 :|2"^13a" FDF ABc | 
 ded def | AGF BAG | FDD D2 |: g/f/ |"^17" eAA Agf | edc d2 B | AGF G2 A | BGE E2 f/g/ | 
"^21" agf gfe | ded def | AGF BAG | FDD D2 :|  