TL;DR: Your discernment in a subject often improves as you dedicate time and attention to that subject. The space of possible subjects is huge, so on average your discernment is terrible, relative to what it could be. This is a serious problem if you create a machine that does everyone's job for them.

See also: Reality has a surprising amount of detail. (You lack awareness of how bad your staircase is and precisely how your staircase is bad.) You don't know what you don't know. You forget your own blind spots, shortly after you notice them.

An afternoon with a piano tuner

I recently played in an orchestra, as a violinist accompanying a piano soloist who was playing a concerto. My 'stand partner' (the person I was sitting next to) has a day job as a piano tuner.

I loved the rehearsal, and heard nothing at all wrong with the piano, but immediately afterwards, the conductor and piano soloist hurried over to the piano tuner and asked if he could tune the piano in the hours before the concert that evening. Annoyed at the presumptuous request, he quoted them his exorbitant Sunday rate, which they hastily agreed to pay.

I just stood there, confused.

(I'm really good at noticing when things are out of tune. Rather than beat my chest about it, I'll just hope you'll take my word for it that my pitch discrimination skills are definitely not the issue here. The point is, as developed as my skills are, there is a whole other level of discernment you can develop if you're a career piano soloist or 80-year-old conductor.)

I asked to sit with my new friend the piano tuner while he worked, to satisfy my curiosity. I expected to sit quietly, but to my surprise he seemed to want to show off to me, and talked me through what the problem was and how to fix it.

For the unfamiliar, most keys on the piano cause a hammer to strike three strings at once, all tuned to the same pitch. This provides a richer, louder sound. In a badly out-of-tune piano, pressing a single key will result in three very different pitches. In an in-tune piano, it just sounds like a single sound. Piano notes can be out of tune with each other, but they can also be out of tune with themselves.

Additionally, in order to solve 'God's prank on musicians' (where He cruelly rigged the structure of reality such that for any integers n, m but IT'S SO CLOSE CMON MAN ) some intervals must be tuned very slightly sharp on the piano, so that after 11 stacked 'equal-tempered' 5ths, each of them 1/50th of a semitone sharp, we arrive back at a perfect octave multiple of the original frequency.

I knew all this, but the keys really did sound in tune with themselves and with each other! It sounded really nicely in tune! (For a piano).

"Hear how it rolls over?"

The piano tuner raised an eyebrow and said "listen again" and pressed a single key, his other hand miming a soaring bird.

"Hear how it rolls over?"

He was right. Just at the beginning of the note, there was a slight 'flange' sound which quickly disappeared as the note was held. It wasn't really audible repeated 'beating' - the pitches were too close for that. It was the beginning of one very long slow beat, most obvious when the higher frequency overtones were at their greatest amplitudes, i.e. during the attack of the note.

So the piano's notes were in tune with each other, kinda, on average, and the notes were mostly in tune with themselves, but some had tiny deviations leading to the piano having a poor sound.

"Are any of these notes brighter than others?"

That wasn't all. He played a scale and said "how do the notes sound?" I had no idea. Like a normal, in-tune piano?

"Do you hear how this one is brighter?"

"Not really, honestly..."

He pulled out the hammers and got a little tool out of his bag, jabbing the little felt pad at the end of the hammer with some spikes to loosen it up.

"The felt gets compacted with use, we need to make sure each key has similar density to its neighbours so it doesn't sound brighter than them."

He replaced the hammers and played the scale again. I wish I could say it made a world of difference, but I could hardly tell anything had changed. He, on the other hand, looked satisfied.

"Yeah the beats get slower, but they don't get slower at an even rate..."

He began playing the minor 7th interval, walking the notes up and down the piano in parallel. I know enough about piano tuning to know he was listening to the beating between the justly tuned 7th in the lower note's overtone and the upper note.

"Hear that?" "The beating? Yeah I know about that." "No, listen, it doesn't change speed smoothly." As he moved the interval downwards along the piano, the beating got slower, as expected. But it felt like it got slower at a slightly uneven rate, which was obvious now he pointed it out, but I would never have known to listen for it. Many adjustments later, the beating now slowed down very smoothly as he played his descending intervals.

"This string probably has some rust on it somewhere."

Moving on to the highest keys, he hammered down one of the notes and said "hear that?". "YES!" I said, eager to show that I could hear the 'rolling over' sound now, clear as day. "So you'll tune the three strings to each other better?" "Nope, these ones are tuned just fine, it's just one of these strings is rusted, or has a dent in it, or it's stretched slightly, so it's producing slightly incorrect overtones especially when it's struck hard. These are called "false overtones." "What can you do about it?" "Probably nothing at this stage, they'll need a new string or something more time consuming than we have time for today. But honestly, this is splitting hairs here, nobody really cares that much about false overtones, you just get used to hearing them unless you're only ever listening to, like, the best Steinways at concert halls or something."

I asked him: "why don't you use a fancy electronic tuner for this, and just have a table to look up the frequencies for each string, and tune it that way?"

He scoffed "there are some people who do that, but that really only gets you close, and they'd have to finish by ear anyway, especially with the sort of pianos you typically have to work with, since you really need to finesse how the overtones interact with each other, and it's not guaranteed that the overtones are going to be exactly what they're supposed to be, given variations in string thickness, stretching, corrosion, dents, the harp flexing, you know... The whole thing is a negotiation with the piano, you can't just read it its orders and expect it to sound good."

Please at least listen to this guy when you create a robotic piano tuner and put him out of business.

If it weren't for the piano soloist (the conductor probably didn't notice, he just knew to defer to the piano soloist's concerns), we would have played the concert on a very slightly out-of-tune piano, and then...

What?

Nobody in the audience would probably notice. Certainly not in the specific. Nobody is standing up and saying, "there, see how G above middle C has one string that is 0.2hz out of tune with the others?!" Nobody is standing up and saying "that piano is out of tune, what a travesty." Perhaps some of the more sensitive listeners would have felt some vague sense that the piano could have sounded nicer, that maybe the hall needs a better piano, or something.

Did the piano sound better, after all that work? Yeah... it did, I think. Hard to say. I'd like to pretend it was some colossal difference, but that's really the point. My big stupid ears are not the best judge here. Just trust the people who have the best discernment.

Only a very few people possess the level of discernment needed to know how bad your local concert hall's piano is, and precisely how it is bad.

If their art dies out, maybe nobody will know how bad all the pianos are. And then we'll all have slightly worse pianos than we would otherwise have. And I mean if that's the way things are going to go, then let's just steer the Earth into the Sun, because what's the point of any of this.