Effects On Tuning
Inharmonicity "stretches" harmonics beyond their theoretical frequencies, and higher harmonics are stretched proportionally more than lower. Thus, in our example of an octave, exactly matching the lowest common harmonic causes a slight amount of stretch, matching the next higher common harmonic causes a greater amount of stretch, and so on. If the interval is a double octave, exactly matching the upper note to the fourth harmonic of the lower complicates the tuning of that upper note with the one an octave below it.
Solving such dilemmas is at the heart of precise tuning by ear, and all solutions involve some stretching of the higher notes upward and the lower notes downward from their theoretical frequencies. In shorter pianos the wire stiffness in the bass register is proportionately high and therefore causes greater stretch; on larger concert grand pianos this effect is reduced. Online sources suggest that the total amount of "stretch" over the full range of a concert grand piano may be on the order of ±35 cents.
Read more about this topic: Stretched Tuning
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