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:Dmix
['^cF F2 Bcdc BGBd e2 ed cdeg', 'g3 a fggf gfe^c dfed ^cded ^cF']  
X:1
L:1/8
M:4/4
K:Dmix
 ed | ^cF F2 Bcdc | BGBd e2 ed | cdeg d2 Ad | dfed ^cded | ^cF F2 Bcdc | BGBd e2 ed | cdeg fde^c | 
 dfe^c d2 :| ag | fdfg a2 gf | ecef g3 a | fggf gfe^c | dfed ^cded | ^cF F2 Bcdc | BGBd e2 ed | 
 cdeg fde^c | dfe^c d2 ag | =fdfg a2 gf | ece=f g3 a | fggf gfe^c | dfed ^cded | ^cF F2 Bcdc | 
 BGBd e2 ed | cdeg fde^c | dfe^c d2 |]  