When we tune pianos, we are setting up the 12 notes in the scale in one particular way, out of a potentially infinite number that could exist. This is called setting the temperament. One main type, Equal Temperament, has been appearing on pianos since the 1910’s, although that system of tuning has existed since the fifth century BC.
In equal temperament, every interval except the octave is actually de-tuned. We perform this compromise to allow piano players to play in every key without sour-sounding chords. Now…. An important feature of this tuning work is as follows: every interval has a beat speed as determined by physics, and each interval of one type [ thirds, sixths, fourths, etc] has a speed that gradually increases as you go up the keyboard.
I have found that the average person can detect the speeds, and appreciate the gradual increase after being introduced to it for a time. It’s a sort of vibrato that listeners can begin to notice if they listen behind the music of the interval on a grand piano or larger upright piano. In modern piano tuning, a lot of the fine detail is held within the accuracy of these graduated beating intervals.