Let $d \in \mathbb{N}$, and let $C \in \mathbb{R}^{d \times d}$ be a symmetric positive semidefinite matrix. Then there exist a tracial noncommutative probability space $(\mathcal{A}, \varphi)$ and self-adjoint elements $s_1,\dots,s_d \in \mathcal{A}$ such that $(s_1,\dots,s_d)$ is a semicircular family and, for all $1 \leq i,j \leq d$,

\begin{align*} \varphi(s_i s_j)=C_{ij}. \end{align*}