In this question the OP is looking for a way to see light that is outside of the visible spectrum without using electronic sensors. This got me wondering about the visible spectrum itself. Typically when the visible spectrum is defined it is defined casually both in terms of frequency and wavelength (e.g. here). Obviously this cannot both be true, because the wavelength of light changes depending on the medium according to the refractive index.
The story on this page and in the question here explains that color is related to frequency, not wavelength. My question is fairly straightforward: does this mean that the visible spectrum should be defined in terms of frequencies?
If this is not the case then that would mean that we can see a different range of colors when, e.g. under water then we can in air, which sounds strange to me.