Colour temperature does not measure colour
Somewhat counterintuitively, colour temperature does not actually measure colour. Per Wikipedia, colour temperature “is the temperature of an ideal black-body radiator that radiates light of a colour comparable to that of the light source”.
In physics, a black-body radiator is actually exactly what it sounds like – a hypothetical black object that radiates heat and light solely due to the high temperature of the object (think something like a traditional incandescent light bulb). You’ll notice that the above description of a black-body radiator does not at all match the description of LEDs, which are neither black nor emit light as a result of high temperature. Herein lies the problem – LEDs are NOT black-body radiators.
“In practice, colour temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the colour temperature of, e.g., a green or a purple light.”
LEDs are NOT black-body radiators
The use of colour temperature to measure the ‘colour’ of LEDs is a flawed usage of this measurement. Because LEDs are not black-body radiators, and because LEDs emit light beyond the traditional red-orange-yellow-white-blue colour temperature spectrum, there is inherent variability in the actual colour of the light produced.
The diagram above shows the colour of an ideal black-body radiator (in the curving line from bottom left to top right) bisected by lines representing various colour temperatures. Where these lines intersect is the theoretical colour for each temperature for an ideal black-body radiator. You’ll notice, however, that the colour temperature lines extend far to either side of the ideal black-body curve. While the math on these lines is solid, it should be noted that the further away you get from the black-body curve, the less meaningful these values are. The International Commission on Illumination puts it as below:
Although the CCT can be calculated for any chromaticity coordinate, the result is meaningful only if the light sources are nearly white.
What this means is that any light source of a given colour temperature could fall anywhere along the line given in the above diagram – rather than on a single value. Incandescent light bulbs, which produce their light through thermal radiation (heat) correlate pretty closely with ideal black-body radiators. For these light sources, colour temperature values are generally pretty reliable. For LEDs (and indeed other light sources such as fluorescents and halogens), they are less reliable – and can fall within a range. This means that if you have an existing light source of a specific colour temperature, a new light source with the same colour temperature is not guaranteed to match the original appearance.