  We study typical ranks with respect to a real variety $X$. Examples of such
are tensor rank ($X$ is the Segre variety) and symmetric tensor rank ($X$ is
the Veronese variety). We show that any rank between the minimal typical rank
and the maximal typical rank is also typical. We investigate typical ranks of
$n$-variate symmetric tensors of order $d$, or equivalently homogeneous
polynomials of degree $d$ in $n$ variables, for small values of $n$ and $d$. We
show that $4$ is the unique typical rank of real ternary cubics, and quaternary
cubics have typical ranks $5$ and $6$ only. For ternary quartics we show that
$6$ and $7$ are typical ranks and that all typical ranks are between $6$ and
$8$. For ternary quintics we show that the typical ranks are between $7$ and
$13$.
