Average of blackbodies of temperature T + ΔT and T − ΔT creates a new spectrum marked “Average(Y)” which is different from blackbody spectrum marked with temperature T. The average spectrum is just the usual y-type distortion with respect to a new blackbody at temperature T [1 + (ΔT/T)²] , with the two crossing at x = 3.83. At redshifts z ≳ 10⁵ the average spectrum will comptonize to Bose-Einstein spectrum marked μ above. All three spectra, T [1 + (ΔT/T)²] , Average (Y), and μ, have the same number density of photons. Average/y-type spectrum and Bose-Einstein/μ-type spectrum also have the same energy density which is greater than the energy density in the blackbody spectrum with temperature T [1 + (ΔT/T)²]  by 1/3 of the initial energy density excess over that of blackbody with temperature T. We have used linear order formulae to calculate the y and μ distortions in the figure but used a large value of ΔT/T to make differences between different curves visible.