Compose melodious music utilizing the prescribed letter representation and integrating the given thematic element.
X:1
L:1/8
M:4/4
K:G
['dge^c dBA=c BGAF', 'G2 Bc dg g2 (3bag fg dgBd']  
X:1
L:1/8
M:4/4
K:G
 Bc | dge^c dBA=c | BGAF GDB,D | G,B,DG Bdgd | (3cBA ag fdcA | dge^c dBA=c | BGAF GDB,G, | 
 dB (3BBB gd (3ddd | cAFA G2 :| Bc | dg g2 (3bag fg | dgBd cAFA | (3DDD FA adfd | 
 ed (3ddd fd (3ddd | dge^c dBA=c | BGAF GDB,G, | dB (3BBB gd (3ddd | cAFA G2 :|  