Craft a composition that integrates the assigned alphabet-related musical pattern and the provided melodic theme.
X:1
L:1/4
M:4/4
K:C
['a g']  
X:1
L:1/4
M:4/4
K:C
 G | c c2 d | e g2 g | a a2 b | c' c'2 a | g g2 e | f f2 g | e e2 c | d3 G | c c2 d | e g2 g | 
 a a2 b | c' c'2 g | c' b a g | c' b a g | c'2 d'2 | c'4- | c'2 z ||  