Let $(\mathcal A,\psi)$ be a noncommutative probability space, and let $\kappa_m:\mathcal A^m\to\mathbb C$, for $m\geq 1$, be the free cumulants associated to $\psi$. Let $s_1,\dots,s_d\in\mathcal A$, and let $C=(c_{ij})_{1\leq i,j\leq d}$ be a complex $d\times d$ matrix. Assume that $(s_1,\dots,s_d)$ is a semicircular system with covariance matrix $C$, meaning that for every $m\geq 1$ and every $i_1,\dots,i_m\in\{1,\dots,d\}$ one has $\kappa_2(s_{i_1},s_{i_2})=c_{i_1i_2}$ when $m=2$, and $\kappa_m(s_{i_1},\dots,s_{i_m})=0$ when $m\neq 2$. Then for every integer $m\geq 1$ and every $i_1,\dots,i_m\in\{1,\dots,d\}$, \begin{align*} \psi(s_{i_1}\cdots s_{i_m})=\sum_{\pi\in NC_2(m)}\prod_{\{p,q\}\in\pi}c_{i_pi_q}, \end{align*} where $NC_2(m)$ is the set of noncrossing pair partitions of $\{1,\dots,m\}$. If $m$ is odd, this sum is empty and the moment is $0$.