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
Hope this helps..


Input stage: 2x 12AX7  Preamp tubes in this case, pre to the power amp section. Used to to amplify the signal from the driver tubes (my guess). In the actual preamp.

Rectifier: 1x 12AU7 Converts AC to DC, so the rest of the tubes can do their thing. Starts the whole thing off.

Drivers: 2x 6SN7 usually to drive a higher impedance load, normally into another valve, medium gain tube. Great preamp tube, so Dac, phono stage, guitar pick up, are amplified and handed to the next stage, each stage cleans and boost the signal (normally). In this case to the 12AX7s,
(again a guess) in the power amp section..

Power stage: 4x KT120 final stage, high gain valve. To the load, 

This guy explains a valve amp operation very simply, and thoroughly.
Just great..

How a tube amp works GREAT!!!

Regards
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.