Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/8
Q:1/8=232
M:4/4
K:G
['g2 dc Bc dB', 'ce dc BG']  
X:1
L:1/8
Q:1/8=232
M:4/4
K:G
|: g2 dc Bc dB | A2 ag fd ef | g2 dc Bc dB | cA dc BG G2 | g2 dc Bc dB | ce ag fd ef | 
 gb fa eg dB | ce Ad BG G2 :: Bc dB cd ec | Bd gg ba a2 | ba gf gd BG | ce dc BG G2 | 
 Bd ^cd =ce ^de | Bd ^cd cA A2 | bg af gd eB | ce dc BG G2 :|  