Like binaural beats for the eyes?

This is 100% incorrect. Not in terms of science, but in terms of a qualifier of what a colour is. Just because a colour doesn't exist on the rainbow spectrum, doesn't mean it's not an "actual colour".

What you're referring to is the definition of colour specifically by physics. There are other professional fields and areas of science that use different qualifiers for colour. I work with color everyday and I can with certainty say that purple, pink, rust, teal, and sky blue are all colours.

Kind of like how different fields have different definitions of entropy or different cultures have different names for snow. It's all dependent on the framework you use and ignoring every other framework is wrong.

Would this not disqualify any mixed color? We only have receptors for three colors, and if we're arguing that purple isn't a color because it's actually two mixed together, that should also mean colors like orange, yellow, cyan, magenta, atc are also not colors by that definition right?

ah a similar explanation to why yellow is not an actual colour either

the silly explanation that has no effect on how we perceive, use, or think about colour. sigh why are the people responsible for those studies calling those colours not real? Why not just colours resulting from mixing other colours like the artists have done since the invention of paint?

Your definition of color is based only on human perception? Is purple a color for a mantis shrimp?

Edit: I guess not in a pure sense because it's still two wavelengths of light. Perhaps a mantis shrimp can detect a totally different wavelength and sees it as "purple" or something.

Now I'm thinking about how we don't know how other humans interpret colors. Like what I see as red, you may see as blue. Ugh.

What is violet at the end of the visible spectrum, then? We call the higher wavelength stuff ultraviolet, and violet looks purple to me, so I'm having trouble reconciling this stuff with what you're saying.