Develop a musical composition based on the provided pattern of letters and incorporating the given motif within it.
X:1
L:1/8
M:6/8
K:G
['DG^F GAF DGB dgd BG^F GAF']  
X:1
L:1/8
M:6/8
K:G
 DG^F GAF | DGB dgd | BG^F GAF | DAB A A2 | DG^F GAF | DGB dgd | BG^F GAF | DGA G G2 | DG^F GAF | 
 DGB dgd | BG^F GAF | DAB A A2 | DG^F GAF | DGB dgd | BG^F GAF | DGA G G2 | dga gge | ded e g2 | 
 dBA GAG | EAB AAd | gag ged | ede g2 d | BAG AGD | GAG G2 d | gag ged | ede g2 d | BAG AGE | 
 ABA A2 D | G^FG AFD | GBd gdB | G^FG AFD | GAG G3- ||  