I'd like to challenge your idea that the fact that a mix of red and blue gives something resembling violet implies that violet must be between red and blue.

In practice, what you get from such mixture is a shade of purple. See the figure below. Here the black dashed line from blue to red covers the colors you can get by changing the amount of red and blue in the mixture. The purest violet is on the bottom-most part of the border of the colored shape (the visible gamut).

On the other hand, if you mix violet and sky blue, you can get the set of colors covered by the green dotted line in the diagram. See that blue is among the colors you can get from this mixture.

Do these two facts conflict? No. Most colors are not spectral: they are desaturated. Together they fill a two-dimensional shape, on which the internal points can be found as mixtures of pairs of spectral colors. And this pair is not unique: you can get white e.g. by mixing orange and sky-blue, or by mixing yellow and royal-blue, etc.. So what you call violet is not a point in this gamut—rather it is an area, where you can pick any point and still call it violet.

I'd like to challenge your idea that the fact that a mix of red and blue gives something resembling violet implies that violet must be between red and blue.

In practice, what you get from such mixture is a shade of purple. See the figure below. Here the black dashed line from blue to red covers the colors you can get by changing the amount of red and blue in the mixture. The purest violet is on the bottom-most part of the border of the colored shape (the visible gamut).

On the other hand, if you mix violet and sky blue, you can get the set of colors covered by the green dotted line in the diagram. See that blue is among the colors you can get from this mixture.

Do these two facts conflict? No. Most colors are not spectral: they are desaturated. Together they fill a two-dimensional shape, on which the internal points can be found as mixtures of pairs of spectral colors. And the pairs are not unique: e.g. you can get white by mixing orange and sky-blue, or by mixing yellow and royal-blue, etc.. So what you call violet is not a point in this gamut—rather it is an area, where you can pick any point and still call it violet.