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. 
Thanks plga. I will take your advice.  Much appreciated.  
Also thanks imhififan.  Is there a decoder ring for rectifier?   I think i get the others, but still not sure what role each plays in sound production.  
imhififan979 posts03-25-2020 8:03pm
"Can someone help me understand what the specific function each type of tube performs in a power amp?"

This has yet to be answered...

Input stage: 2x 12AX7
Rectifier: 1x 12AU7
Drivers: 2x 6SN7
Power stage: 4x KT120

I read above the power tubes have some issues also. Nothing I've ever owned used KT120, or 150.  I have always been a 6L6 (lower wattage) 6550, KT88 and 90 user, when it comes to power tubes. I'll bet if they were bios different, the problem might go away. AUTO bios can be an issue..for some valves.

6SN7s have been around a long time, there has to be some great valves out there for that one too. Very good valve. Use to call um double trips,
actually two valves in one.. Can't tell me matching this valve isn't important.

The 12AX and AU7 will cost the least. TONs of options. MATCH the tubes. If there is no way to bios the signal tubes, matching makes a big difference. The quality of the valve, prone to vibration (BIG ISSUE).
(Valve tap with a thin wooden dowel), if you don't have a tester.  An old
school, valve amp guy, showed me that one, the tap test. (Lightly), not a snare drum. Hold the top, one finger, tap the side.
I've  also gotten serious changes with HOW the unit was and is bios,
there is a range say 200-300 (just a number). It can change how the amp sounds A LOT.. The 20-50.00 usd on signal tubes, bios options (if there is any), matching, unit vibrational control (good idea) TWEAKS in the valve world for sure, and dirt cheap..

These, along with, placement, treatment (heaver drapes), controlling the bass usually cleans up EVERYTHING.  just a bunch of stuff  you could do for just a few bucks, in the name of MIDS...You'll get it..

Respectfully The OldHvyMec..

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!!!

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.