  We prove that the parameter $x$ of a tight set $\mathcal{T}$ of a hyperbolic
quadric $\mathsf{Q}^+(2n+1,q)$ of an odd rank $n+1$ satisfies ${x\choose
2}+w(w-x)\equiv 0\mod q+1$, where $w$ is the number of points of $\mathcal{T}$
in any generator of $\mathsf{Q}^+(2n+1,q)$. As this modular equation should
have an integer solution in $w$ if such a $\mathcal{T}$ exists, this condition
rules out roughly at least one half of all possible parameters $x$. It
generalizes a previous result by the author and K. Metsch shown for tight sets
of a hyperbolic quadric $\mathsf{Q}^+(5,q)$ (also known as Cameron-Liebler line
classes in $\mathrm{PG}(3,q)$).
