None of this is objective. The construction of our scale is subjective, other countries use different scales. Even with this same scale, there are multiple different tuning systems. There is micro-tonal music. Musical keys are arbitrary too. We teach the way we do because it is a culmination of musical history, our particular western musical history, and it's own arbitrary decisions that western musicians have made over the past hundreds, even thousands of years. If you like, there is also solfege, which replaces letter names with just sounds, "do re mi" etc, Also what makes you think colours are objective? Different languages have words for a single colour that map onto multiple other words in other countries, does not seem very objective to me, unless you are talking about notating colours as hex or RGB number values, or wavelengths (which we don't do in natural language)