I'm no expert, but I understand that pianos are tuned slightly sharper than normal pitch at the higher octaves (with each note interval per octave representing the 12th root of two - the semitone interval), and this is deliberate, because the human ear hears 'flatter' at higher frequencies.

Certainly my Yamaha Concert Grand is tuned this way. In this case, it relates to the human ear perception of 'what is in tune',

I think I read somewhere that the 88th note on a piano is approximately a semitone sharper.

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