Knoxville being a midsize market, we don't seem to be missing a lot of formats.
Country---we've got redundant Country stations, 2 current (WIVK, WCYQ) and two classic classic 80s-90s (WDKW, Duke 95.7; Merle 96.7 FM). Several more in the outlying areas, like almost every caucasian-dominant southern market.
Classic Rock---The perennial powerhouse WIMZ, and Classic Hits 93.1 WNOX, with their revised playlist under Summit being more light Classic Rock than Classic Hits (no black artists other than Prince).
Jack----Got one of those in WNFZ
Adult Contemporary---WJXB/B97.3
Contemporary Christian--Knoxville must really need savin', we've got K-Love and Air 1, Victory 92.7/1240/94.7tr, WFGW (co-owned with WMIT, Asheville NC.
Not so contemporary Christian---Got a Bible Broadcasting Network station, maybe the only Southern Gospel station on FM with a decent signal in a big market. Several preacher stations on the left side of the dial, and an AM with fire and brimstone preaching, and a larger Christian talk/teaching station
Top 40, we have WWST but it leans hot A/C. Hip hop now has a 3 way race in a non-ethnic market. The new Jump, WJBE (more classic hip-hop), and Summit's Hot 104.5
Americana--It doesn't get better than WDVX
Adult Album Alternative---Still in the market on 105.3.
News-Talk: WOKI, 98.7, with 3 locals shows and Rush during the day, Hannity, Levin and Red-Eye by night). Also, WETR, 760 and 92.3tr, has the second tier talk show host. To their credit, they tried to do a "Knoxville Morning News" but it flopped.
Sprots talk: Anybody can broker out time to talk sports, but the perrenial Sports Talk leader is WNML. There are several other sports stations with brokered hosts. We have left-wing talk in the 2 LPFMs that share a frequency but function as one radio station, WOZO/WOZW.
Oldies--yep, although I find Mid-Century Radio a lot to be desired, with it's obscure playlist, and even more obscure old country. The high school station plays a little better mix of 60s-80s but it's still hodge podge.
Classical---takes up the bulk of NPR affiliate and the University of Tennessee's WUOT, with pauses. for Morning and Edition and All Things Considered.
Then we have college radio----in WUTK, "The Rock".
Rock---The new WVLZ.
I declare the missing formats to be:
Fulltime NPR talk/features, like Chattanooga's WUTC.
A straight-ahead CHR Top 40
A decent oldies station
Soft A/C-but you'd really need a building-penetrating signal, and this may not be the best time to launch an "at-work" format.
Classic Hits that's not Classic Rock
Smooth Jazz but very few do that.