Different Tubes and general purpose?


I’m trying to get a better midrange push or clarity out of my Line Magnetic 501ia tube amp.   Can someone help me understand what the specific function each type of tube performs in a power amp?  

I would like to upgrade several or all of my “stock” tubes but would like to understand where to start to beat enhance each aspect of the sound spectrum.   On my 501ia i have 4x KT120 and i believe those are power tubes, but please help clarify if wrong.  There are 2x 6SN7EH 1x 12AU7 and 2x 12AX7 (but the AU7 and AX7 look interchangeable to me).   As i look to upgrade where to i look to start, and why?  
Thanks in advance for help. 
gunners01
Just read the Uncle Doug's explanation, thanks. 
Gunners, while this forum will give many points of view and numerous prescriptions for getting that midrange that you are looking for it will come down to trial and error. Getting the balance of frequencies in a tube amp to your satisfaction can involve anything in the system. Fuses, power cords, tubes and much more. 
I can speak 6SN7s. I have Chrome domes, Bad boys, GE, Psvane CV181-T11, Shuguang , RCA, Ken Rads. My fav is the Psvane, with the Ken Rad close behind. The Shuguang WE6SN7 had the cleanest midrange presentation but with loss of bass present in the Ken Rads and Psvane. 
It's like cooking to taste. No shortcuts.
Fuses don't make any difference in the sound of any component unless they blow or rot somehow. It's because they're fuses. 
Agree. It definitely does make a difference in the sound of any component when a fuse blows. There ain't any. 
+1 and +100 on more time on Amp. At an average of 2&1/2 hours a month that could take you another two years just to make it to 100 hours.

Did you move your speakers around (what kind)? Please do that first! What's the room like? Power like? Connects like? Sources like? Tube rolling may/may not be the answer.
Wsrrsw 
I’ve perhaps underestimated my hours, but not by much.  On average i may get 6-8 hours a month, but with the current quarantine its maybe 4-5 hours a week.  
Room is large with 14ft ceiling.  Speakers are Harbeth HL5 plus.  Power seems fine and I do use a conditioner, contacts all fine to the. Eat of my knowledge.  All equipment is 3-4 years old.