That leads me to thinking about when do the tails matter? Sure, for perhaps a small number of people in the world the better tuned piano makes the world a better place for them. For most the improvement is beyond their comprehension so the world has really not improved.
I think the tails basically always matter, and even though you can’t consciously register the differences between a well-tuned and an adequately-tuned piano, you still do subconsciously register the difference.
In particular, I’d expect that a concert with the same players, same instruments, same venue, same songs, etc but with only adequately-tuned instruments will (in expectation) be rated slightly worse than one with well-tuned instruments, even by those with untrained ears. I don’t think it will be rated as badly as those with trained ears would rate, but I do still expect the imperfections to add up to measureables.
I bet that the size of the difference from actually tuning the piano perfectly is smaller than the difference from merely telling the audience that the piano has been perfectly tuned.
I’m not quite sure what to make of “adequately tuned” here. If that means tuned well enough that 99% of the audiance cannot tell the difference between that and a better tuned piano then I’m not sure how they then rate the performance lower than the alternative performance with a better tuned piano.
I do agree that there is likely to be a range in which those like me might actually hear the difference but not be able to articulate, even to ourselves, the source of the sense something is not quite right. Perhaps that’s the area you’re thinking of. If so then I think that’s something this post helps with. Knowing more about the mechancis of the tool we might have more ability to understand where our sense of “offness” is coming from.
So was going out to that 1% tail level the right level? I don’t know and am pretty sure I only have something of an arbitrary and ad hoc way of trying to say what I might think is the right level for most situations I might think about. I don’t know if that is just a feature of the world or a problem in getting less wrong.
I think the tails basically always matter, and even though you can’t consciously register the differences between a well-tuned and an adequately-tuned piano, you still do subconsciously register the difference.
In particular, I’d expect that a concert with the same players, same instruments, same venue, same songs, etc but with only adequately-tuned instruments will (in expectation) be rated slightly worse than one with well-tuned instruments, even by those with untrained ears. I don’t think it will be rated as badly as those with trained ears would rate, but I do still expect the imperfections to add up to measureables.
I bet that the size of the difference from actually tuning the piano perfectly is smaller than the difference from merely telling the audience that the piano has been perfectly tuned.
I’m not quite sure what to make of “adequately tuned” here. If that means tuned well enough that 99% of the audiance cannot tell the difference between that and a better tuned piano then I’m not sure how they then rate the performance lower than the alternative performance with a better tuned piano.
I do agree that there is likely to be a range in which those like me might actually hear the difference but not be able to articulate, even to ourselves, the source of the sense something is not quite right. Perhaps that’s the area you’re thinking of. If so then I think that’s something this post helps with. Knowing more about the mechancis of the tool we might have more ability to understand where our sense of “offness” is coming from.
So was going out to that 1% tail level the right level? I don’t know and am pretty sure I only have something of an arbitrary and ad hoc way of trying to say what I might think is the right level for most situations I might think about. I don’t know if that is just a feature of the world or a problem in getting less wrong.