  Using a result of Gessel and Reutenauer, we find a simple formula for the
number of cyclic permutations with a given descent set, by expressing it in
terms of ordinary descent numbers (i.e., those counting all permutations with a
given descent set). We then use this formula to show that, for almost all sets
$I \subseteq [n-1]$, the fraction of size-$n$ permutations with descent set $I$
which are $n$-cycles is asymptotically $1/n$. As a special case, we recover a
result of Stanley for alternating cycles. We also use our formula to count the
cycles that do not have two consecutive descents.
