Trained ears.

gawdbless

Good advice as above. A piano is both melodic and percussive in nature.
Test these characteristics with familar music, passages, for accurate texture and timbre when evaluating electronics. Ask yourself, "does this music reflect the live event"?  Possessing the ability to tune a piano requires an awesome ear. You already have an awesome ear. And yes, you can't tuna fish.  Enjoy the music and have fun.

Happy Listening!

If you can tune a piano, then you know what the notes should sound like.

Just listen to as many systems as you can, and form your own opinion.
B

gawdbless,

You hear pitch with exquisite precision because you understand the concept of pitch extremely well. Okay. So what's your understanding of grain? Attack? Decay? Ambience? Sibilance? Harmonics? Timbre? Timing? Presence? Palpability? 

I'm no piano tuner, but pretty sure you could write volumes on pitch, tension, humidity, fundamental, harmonics, etc. Some of what you're familiar with you will be familiar with here. A lot of it will be new. Doubt you've spent much time listening for grain. No piano ever made was grainy. Grain is an artifact of the recording-playback chain. Just one random example.

I was once like you, in that having played musical instruments I was pretty good at pitch and tone. Yet I couldn't tell one CD player or amp from another to save my life. Now, no problem. Takes a while, but you can learn.

If you really do want to learn here's the best help I know of:
https://www.amazon.com/Complete-Guide-High-End-Audio/dp/0978649311

Robert Harley clearly covers not only all the equipment, but how it works and how to evaluate it including how to listen. Whole chapter devoted to how to listen and why and what to listen for. All the terms. Been out forever but updated and so well done that even my 30 year old copy is still worth reading.

There is the classic book by Alton Everest called Listening Skills for Audio Professionals.

More recently, Jason Corey has written an excellent book which is complemented with online training by the author.

And before you ask, Yes I am trained. And Yes, training makes a night and day difference. Critical Listening requires training. Those who listen to music daily are like frequent flyers. They have been to many places. Can they land a commercial jet at SF airport - Absolutely Not - they are just armchair amateurs.