How Does Cosmology Constrain the Number of Neutrino Species? I've asked this question already on the Physics SE, but I felt it would be worth posting here as well.

I know that based upon theories of structure formation cosmologists can constrain the sum of the masses of neutrinos - if neutrinos were too light or too heavy it would simply change the power spectrum of the universe. 

My question is how exactly is the number of neutrino species constrained by cosmological measurements (i.e. - $N_{eff}$ as measured by WMAP or Planck)? The recent results from the Planck Satellite give us $3.3\pm0.3$, which is consistent with three neutrino species. How is this measured?
The original research paper, p.43, section 6.3.2.

I leave it to someone else to find comprehensible words to describe the connection between CMB, redshift and effective neutrino number.