>> Some of those frequencies we detect with our eyes, and the frequency determines its color

>This is common misconception. It's not singular frequency of light that determines color, but the entire distribution of intensity over visible light spectrum.

Why can't it be both?

The CIE spectrum locus, which is a saturation plot for the visible spectrum, labels perimeter by monochromatic wavelength, yet the CIE color model is tri-stimulus (three primaries) with the plot providing helpful symmetry for calculating chromatic mixes.

Note that there's no contradiction in the language which regards a "spectrum" in the sense of physics with a model of mixed "primaries" in the sense the physiology of human vision.

As to the surrounding points in this thread regarding what does or does not constitute a logical color wheel, the arguments are too invested in labels for effects of a given medium, and lacking sufficient discrimination of context of media, application, psychology, history and science. Color is a subject wherein many seemingly divergent views can all be correct when regarded in specific narrow contexts.

I think there's an obvious bifurcation of understanding, between art and science.

Ultimately, the topic of color forces the thinker to confront the question that all understanding is purely psychological. The first step on a slippery slope towards this question is the observation that color is both as real as anything we experience, and that objectively color is a pure qualia. That people reliably atomize a perceptually smooth chromatic gradient into ROYGBIV is a true conundrum-- that we should so readily and implicitly partition a continuum seems characteristically linguistic, in the sense of counting, which is at once a form of pure vocabulary (naming) but also a system of reasoning (mathematics).

This conundrum prohibits coherent dialog about color topics because common thinking, such as immediate topic of the color wheel based on mixing primaries, ignores that the term "primary" has different connotations for additive versus subtractive media, so it can't distinguish that RGB (CIE) and RYB (classical artistic theory) are distinguishable taxonomically by observing the effect of silent (in context) "secondary" colloquially known as "cyan".

To be clear, by secondary I mean the negation of additive (projected incident light) primaries, colloquially known as RGB, which negation gives rise to secondaries CMY of the form –R, –G, –B. In painting the medium is inherently subtractive, incident light reflected by a medium. This gets confusing because "primary" in the taxonomy of color substantially predates the projector technology and the CIE model we now take for granted. Today "primary" should first mean the CIE vernacular because its model can explain painting and many other media, whereas the older vernacular of painting can't even explain itself, because it's not a science, it's merely a structuralist cataloging of particulars.

Understanding the physical properties of a medium is insufficient to generation of clarity. Arguments about the correctness of color wheels that don't scrupulously examine assumptions about the vernacular of qualia are ideological even when attended by a coherent physics of stimulus. We can't rectify contentions of color ideology with appeals to a narrow physics of any artistic medium. The science of the CIE avoids color names except as a sort of adjunct mapping just to be helpful for correlating conventions of vernacular with the spectrum locus. To the CIE, the primaries are idealizations of long, medium, short wavelengths that excite a normalized model for human retinal cone photoreceptors. It's the Munsell color system that truly bridges the gap from the CIE's science to aesthetics via a rigorous system of correlation of effects.

The takesway here is that arguments over the objective correctness of any color wheel are pointless.

But such arguments do strongly indicate (or illuminate, so to speak) that we regard color as profoundly real. This realization is interesting as it deeply troubles epistemology: any example of a profound reality of qualia disrupts the prospect that we can truly understand anything but ourselves. We are trapped in Plato's cave with no way out but a sort of divine resurrection (in the Christian sense) of thought. A large rock must be moved from the cave entrance by God to free the soul to fully manifest itself.