The term classical is meaningless and tautological.
Given enough time even Bryan Adams could be one day considered "classical" compared to the "contemporary".
Classical is nothing but a chronological term and that's what make it so useless.
In my opinion the only meaningful terms to describe a style of music are those terms that are/can be used by the authors when the music is contemporary.
So for example rock'n'roll was rock'n'roll for the rock'n'rollers.
Nothing written by the "classical" authors was "classical" for them.
Classical can be compared to "pop" in that they both are not terms descriptive of the style but of extra-musical and extra-stylistical concepts like chronological time and level of popularity.
Just like given enough time whatever kind of music can become "classical" (in fact many are already using the term "classical" form 80's electro-pop music) given enough chance-popularity whatever niche style can get within the definition "pop"
Within the "pop" category have been songs that actually belong to specific styles like: experimental electronic, ambient, ethnic, new-age, lounge, soundtrack, celtic, ballad, country, chanson, metal, gothic, happy hardcore, dream, progressive, jungle, chillout, downbeat, punk, house, new beat, coldwave, rap, R&B ....
I would get rid of the terms classical, contemporary and pop once and for all.
Anyway the search for alternative terms should not make us fall prey of the same mistake of using extra-musical and extra-stylistical (enterily subjective and biased) terms. If using chronology or popularity as criteria as criteria even more is using biased concept like "value" or "quality" or "seriousness" or "importance"
To philosophically look for an objective degree of such criteria is unteanable and self-contradictory as shown by the failure of such attempt.