They also acknowledge the great moments of the big bands and the master in chief Duke Ellington in the album dedicated to him.
Unfortunately, some descriptions like the above are just press release from people who never really heard their work.
MJQ is part of a ramification of the bebop era, once some brilliant musicians started to assemble smaller combos, and this was one of the most technical, artistic and innovative sets. The term "Modern" is exactly that tentative to produce new frontiers for jazz. The Atlantic/Rhino Atlantic years produce some of the most innovative and avant garde jazz heard until then, albums like "Piramid", "The Comedy", "Three Windows" are truly remarkable.
They never forgot the DNA of Jazz and blues, and the live recordings at the Carneige Hall (The Last Concert, Blues at Carnegie Hall) are masterpieces. The blues verve is noticeable in so many ways, but one of the most interesting is the "tempo" they worked, with inspiring improvisations at heart touching use of silence.
Well, it is creepy what they have done in the tags and albums. This is nothing of smooth or cool jazz. Cool Jazz is honestly just the way some romantic but ungroovy guy got their way to play in the East Coast, with all respect and love I have for Chet Baker and Gerry Mulligan.