We study the probability that a real stationary Gaussian process has at least $ηT$ zeros in $[0,T]$ (overcrowding), or at most this number (undercrowding). We show that if the spectral measure of the process is supported on $\pm[B,A]$, overcrowding probability transitions from exponential decay to Gaussian decay at $η=\tfrac{A}π$, while undercrowding probability undergoes the reverse transition at $η=\tfrac{B}π$.