Most people do not realize that a beautiful tuning does not come from having a perfect equal temperament in the central octave e.g. A3-A4 or the correct stretch for the inharmonicity of you individual instruments.
Aural tuners are trained in a specific way to count beats for intervals in the central octave in order to make them as even as possible. Most teachers have their own version of which intervals to start with, but in the end it boils down to having the same quality of beats when you play a chromatic scale of thirds in that area.
ETDs these days are doing doing a perfect job to achieve this - and they are agnostic to imperfections of the human ear when it comes to represent the perfect equal temperament of the section that initially has the red felt strip that mutes the outer strings.
This is not where the beauty of a really good tuning comes from, it's tuning the unisons that makes all the difference.
I wrote a little piece in /r/piano that might be helpful to give you an idea of why I wrote this bold statement:
Most people are stuck in tuning unisons to sound beatless on their fundamental. This won't get you anywhere in terms of tuning beautiful unisons.
Before you start tuning unisons you should put away the tuning hammer, put wedges between the strings so only one string can be heard. And then you sit down and listen to that one string. If you don't know what to listen for, you will be stuck with the fundamental, but that's not where the music plays.
Take F3 as your starting point and listen to the cacophony of other notes contained in this one string. You need to understand that every single string by nature contains overtones/harmonics and you need to learn to listen to these and train your ears to filter them out. Hitting F3 will give you F4, C4, F5 as a first starting point of what to listen for. Hit the note, then hit the first overtone (mute it, so only one string is heard), go back to F3 and now try to hear the octave to F4 contained therein.
Take this step by step, don't rush, just make sure that your brain learns to identify various overtones correctly every time you hit your blueprint note.
There will be a point where you will identify A5 or even A6 as harmonics contained in your beloved F3 - and this is where fun starts. Soon you will be able to identify this major third consistently as part of your F3. And this is the time where you pull out the wedge and move it so that now there are two strings of the unison that can be tuned. Leave the first string alone and focus on the second one in trying to tune it. I believe by now you know where this is going.
You are now supposed not to tune F3 but A5 or A6. Use the filter you trained your ears to listen to and focus on the beats of A5 or A6. Your goal must be to tune these overtones beatless.
The physics behind it is simple. If your fundamental is almost beatless i.e. like half a beat per second, your ear will be happy and tell you that it's tuned OK. Well, it is not. F4 is already off by one beat per second, F5 is off by two beats per second and F5 is off by four beats per second. This exponential drift is what makes seemingly well tuned fundamentals sound off anyway.
Beautiful unisons come from tuning high overtones, usually fifths and major thirds.
That's the gist of it.
Now there's a thread title I couldn't avoid opening! Congrats on finding the right person at last!
Now we think I like Perfect 12ths but with more stretch than what the device calculated for my piano because it has less inharmonicity than a Steinway. It is so much more complicated than I ever imagined. I did really like the Perfect 12ths tuning a different tech did using his app but I like my current tech more as the long term caretaker for my piano. He thinks he's figured out what app the other guy used and is going to try to replicate that setting.