Let $I$ be an index set, let $(\mathcal{A}, \varphi)$ be a noncommutative probability space, and let $\kappa_r: \mathcal{A}^r \to \mathbb{C}$ denote the $r$-th joint free cumulant map determined by the free moment-cumulant formula for $(\mathcal{A}, \varphi)$. Let $(s_i)_{i \in I}$ be a semicircular family in $\mathcal{A}$, meaning that for every $r \in \mathbb{N}$ with $r \neq 2$ and every $i_1, \dots, i_r \in I$, one has $\kappa_r(s_{i_1}, \dots, s_{i_r}) = 0$. Define $C: I \times I \to \mathbb{C}$ by $C(i,j) = C_{ij} := \kappa_2(s_i, s_j)$. For every $m \in \mathbb{N}$, let $NC(m)$ denote the set of noncrossing partitions of $\{1,\dots,m\}$, and for every $n \in \mathbb{N}$ let $NC_2(2n)$ denote the set of noncrossing pair partitions of $\{1,\dots,2n\}$. Then $\kappa_1(s_i) = 0$ for every $i \in I$, and $C_{ij} = \varphi(s_i s_j)$ for all $i,j \in I$. Moreover, for every $m \in \mathbb{N}$ and every $i_1, \dots, i_m \in I$, if $m$ is odd then $\varphi(s_{i_1} \cdots s_{i_m}) = 0$. If $m = 2n$ for some $n \in \mathbb{N}$, then $\varphi(s_{i_1} \cdots s_{i_{2n}}) = \sum_{\pi \in NC_2(2n)} \prod_{\{p,q\} \in \pi} C_{i_p i_q}$.