In some cases one can identify a substance by the color emitted as it burns in a flame. A green flame might indicate the presence of copper. So here is the question.
If we know wavelength and intensity of emission spectra for an element, isn't what we "see" as it burns simply a superposition of these? If I try to reconstruct the apparent color of copper from its spectrum as $\sum f_n \cdot i_n /\sum i_n$ in which $f_n$ and $i_n$ are the frequencies and relative intensities respectively, it seems to work. But trying this with, say, helium, using approximations because there are a lot of lines, I consistently get something in the green range.
This site gives a simplified spectrum for helium in a tube. Approximating the intensities I get something in the green range. I tried a more detailed calculation using selected NIST data and obtained a similar result. But helium is consistently shown as having a red appearance in a flame or in a tube (link).
One guess is that there are invisible emission lines, and helium has many. If these are included in the sum they might drag the apparent color toward the red.
Is my basic understanding incorrect? Any insights appreciated.