  We introduce a new class of numerical semigroups, which we call the class of
{\it acute} semigroups and we prove that they generalize symmetric and
pseudo-symmetric numerical semigroups, Arf numerical semigroups and the
semigroups generated by an interval. For a numerical semigroup
$\Lambda=\{\lambda_0<\lambda_1<\dots\}$ denote
$\nu_i=\#\{j\mid\lambda_i-\lambda_j\in\Lambda\}$. Given an acute numerical
semigroup $\Lambda$ we find the smallest non-negative integer $m$ for which the
order bound on the minimum distance of one-point Goppa codes with associated
semigroup $\Lambda$ satisfies $d_{ORD}(C_i)(:=\min\{\nu_j\mid j>i\})=\nu_{i+1}$
for all $i\geq m$. We prove that the only numerical semigroups for which the
sequence $(\nu_i)$ is always non-decreasing are ordinary numerical semigroups.
Furthermore we show that a semigroup can be uniquely determined by its sequence
$(\nu_i)$.
