Let $C$ be a smooth curve of genus $g$. For each positive integer $r$, the $r$-gonality $d_r(C)$ of $C$ is the minimal integer $t$ such that there is $L \in \mathrm{Pic}^t(C)$ with $h^0(C,L)=r+1$. In this paper, for all $g \ge 40805$ we construct several examples of smooth curves $C$ of genus $g$ with $d_3(C)/3 < d_4(C)/4$, i.e., for which a slope inequality fails.