This is because the pieces of the sharp singularize Theta. Let s_n be the sequence of the first n cardinals above continuum and let a_n be the nth cardinal above continuum. Then the theory of reals with a parameter s_n in L_{a_n+1}(R) is a set of reals A_n. They are Wadge cofinal in Theta, another words the sequence <A_n: n is not in L(R) but each A_n is and that is why you get a singularization.

This is because the pieces of the sharp singularize $\Theta$. Let $s_n$ be the sequence of the first $n$ cardinals above continuum and let $a_n$ be the $n$th cardinal above continuum. Then the theory of reals with a parameter $s_n$ in $L_{a_n+1}(\mathbb R)$ is a set of reals $A_n$. They are Wadge cofinal in $\Theta$, another words the sequence $\langle A_n: n<\omega\rangle$ is not in $L(\mathbb R)$ but each $A_n$ is and that is why you get a singularization.