Order statistics of periodic, Gaussian noise with 1/f^{\alpha} power spectrum
is investigated. Using simulations and phenomenological arguments, we find
three scaling regimes for the average gap d_k= between the k-th
and (k+1)-st largest values of the signal. The result d_k ~ 1/k known for
independent, identically distributed variables remains valid for 0<\alpha<1.
Nontrivial, \alpha-dependent scaling exponents d_k ~ k^{(\alpha -3)/2} emerge
for 1<\alpha<5 and, finally, \alpha-independent scaling, d_k ~ k is obtained
for \alpha>5. The spectra of average ordered values \epsilon_k= ~
k^{\beta} is also examined. The exponent {\beta} is derived from the gap
scaling as well as by relating \epsilon_k to the density of near extreme
states. Known results for the density of near extreme states combined with
scaling suggest that \beta(\alpha=2)=1/2, \beta(4)=3/2, and beta(infinity)=2
are exact values. We also show that parallels can be drawn between \epsilon_k
and the quantum mechanical spectra of a particle in power-law potentials.Comment: 8 pages, 5 figure
