A lamp at 2700 kelvin and one at 3000 kelvin look almost identical on their own. Put them side by side on the same wall and the difference is obvious: one feels like evening, the other like a well-run office that has stayed open late.
Choosing the number
We choose colour temperature room by room. Living spaces and hotel rooms usually sit at 2700K, where timber and skin look their best. Galleries often sit at 3000K, warm enough to be welcoming but neutral enough not to tint a painting. Kitchens and workrooms may go to 3000K or 3500K, but rarely higher in a home.
Consistency is the harder part
The number on a datasheet is a promise, not a guarantee. Two batches of the same fitting can differ by a visible amount, and a wall washed by two slightly different whites looks patchy. We specify tight binning, check samples from the delivered stock, and keep a few spare fittings from the same batch for future maintenance.
Colour rendering matters as much as colour temperature. A high CRI source, and in particular a good R9 value for deep reds, keeps oak, leather and food looking as they should.
Precision, here, is in service of warmth.