Apparent color of flame as superposition of spectral lines?

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.

• Identifying materials by flame is best done w/ a spectrometer, since your eye does 'merge' various wavelengths. But as to summing, see DumpsterDoofus' answer. Feb 27, 2014 at 15:43
• The eyes' perception of color has more complexity than the equation you propose. For instance, if you add together red, green, and blue, the resultant "color" isn't a weighted average of the frequencies but white. Feb 27, 2014 at 15:48
• @Joshua: For sure the question is an oversimplification in several respects and I think you hit on one of the important ones. Feb 27, 2014 at 15:55
• Helium does not have many visible spectral lines, as I show in my annotated helium discharge tube spectrum here: physics.stackexchange.com/a/770049/313612. The most intense visible line is yellow, around 587.6 nm, and the discharge looks rather yellow to me, same as in the HyperPhysics link you provided.
– Ed V
Jul 2 at 23:24

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.