Though the middle A may be at 440 Hz, a grand piano will be increasingly flat in the lower octaves and increasingly sharp in the higher octaves.
All the strings have overtones sharp to their fundamentals. A piano tuner takes this into account when tuning.
A piano tuner told me this is referred to as temper.
Though well tempered scales are another matter.
Is the word temper correctly used here?
Why would the strings have overtones sharp to their fundamentals?
I have actually seen this effect displayed on a strobe tuner as outer rings of overtones rotating clockwise to the stationary fundamental.
Photo - Bruce T