Your eyes will simulate detection of both a frequency, and peak width. I'm saying this in response to your statement that the eyes detect "one frequency". This is true, they will identify one frequency as the center of a (roughly) bell-curve shaped spectrum of frequencies. If the spectrum is sharply peaked at one frequency, it will look like a very "pure" color. If it's a broad spectrum (wider bell curve, including additional nearby frequencies), the color will look de-saturated. Broadening or sharpening the peak width is what you are doing when you play with the saturation slider on an HSB widget (Hue, Saturation, Brightness). Fully desaturated means the peak is wide enough to equally include the whole spectrum, and it looks white or grey.

(And yeah, things are a little funny when you mix red and blue light, omitting green, to get purple. Technically it's a double-peaked spectrum, but your eyes/brain treat the spectrum as if it wraps around at the edges, thus locating a pseudo single peak on a ring-shaped continuum.)