XYZ

Yes, there is a space called the XYZ space that includes every color that we can see. Let us first explain the X, Y and Z channels.

The X channel models what a cone retina cell sensitive to red receives. The value ranges from 0 to 1. A red cone has a response curve centered at red, but it is like a bell curve. In other words, a red cone is also slightly sensitive to frequencies other than red. The Y channel models what a green cone receives, and the Z channel models what a blue cone receives. The response curve of each channel is modeled after the actual color cone cells in a human retina.

That's why the XYZ space includes all the visible colors, and then some!

The magnitude of X, Y and Z determines the brightness of a color, but the color is determined by the relative ratio among X, Y and Z. As a result, if we are only interested in the color, but not the brightness, it is sufficient to use a normalized representation, x, y, and z. We make $x + y + z = 1$. The conversion from XYZ to xyz is simple, $x = \frac{X}{X + Y + Z}$, $y = \frac{Y}{X+Y+Z}$ and $z=\frac{Z}{X+Y+Z}$.

Because $x + y + z = 1$, we can get away with only two of the three values (the third one can be computed from two given ones). This is the xy space in which luminance (brightness) is not represented. http://www.efg2.com/Lab/Graphics/Colors/Chromaticity.htm is a link to a figure of the xy space. This diagram is also called the chromaticity diagram. The horseshoe represents colors that are visible to the human eye. You can see that certain areas in the xy space are not visible.

It'd be nice if we can invent an image sensor that senses directly in the XYZ space. This way, the sensor can truely see what we can see.