I know about complimentary colors and how to get them, since colors are basically frequency / wavelengths. Is it possible to find a signals complimentary, additive or subtractive frequencies in an audio file / from a signal. I know how to use FFT to get the phase, amplitude, and frequency of a signal. I'm just looking for a general idea of how I would go about creating similar color charts but for sound, we have a color charts of complimentary, additive or subtractive colors do we have one for the sound / audio range of humans?
Yes and no. Only monochromatic colors consist of a single wavelength, and those do not really "wrap around" in the form you describe. Color addition and subtraction have more to do with the three types of cone cells in our eyes than with wavelengths. Since there is no audio analogue to these cone cells, the concept of complimentary colors doesn't exist in the same way.
However, if you consider notes instead of frequencies, in the sense that two frequencies that are one or more octaves apart constitute the same note, then you can say that two notes are complimentary if they are a tritone apart.
No. There is no good definition of "complimentary" for sound.
It only works for colors because of the way the human eye is constructed and has nothing to do with the underlying physics (which perhaps could be applied to sound as well). Since the human ear works totally different the concept of complimentary doesn't translate.
My best interpretation of complimentary frequencies is this. We could assume that each frequency in an octave represents a colour. (All our visible colours are within one octave). If A is Green, A in any octave is green. So then lets compare the properties of complimentary colours and then use those as an assumption to calculate a complimentary frequency.
A property of complimentary colours is that there is only 1 complimentary colour for each colour.
If we assume that we find a complimentary frequency by taking it as a ratio of the original frequency. There is only 1 ratio that will give 1 complimentary frequency for each frequency. It would also have to have the property that multiplying the complimentary frequency by the same ratio gives you an octave of its original frequency. The only ratio that does this is The square root of 2 (2^0.5). multiplying or dividing by the square root of 2 finds only one other frequency per octave and will get you back to an octave of its original frequency.
This is equivalent of 6 semi-tones or 600 cents. Sebastian is correct !!