bebop

They might even specify "bebop." But those tags are only slightly meaningful, and as others have illustrated in the comments, it's still limited and misleading.

For the most part, the players have more freedom to stretch out on longer harmonic movement, rather than hopping around quickly like in bebop. If you look closely at transcriptions of the solos in kind of blue, some of the players do hint at chord progressions towards the beginning, middle, and end of their solos, which might be the dissonance you mentioned.

A purist, on the other hand, may be completely open to new ideas within the framework of bebop or within the framework of "real instruments"even if it ends up sounding bad. a purist with taste i think would be able to marry nostalgia with the new that is good, a purist without taste probably just wants to be safe, or can't be bothered to listen closely enough to the music to find out if it is any good.