In general, the higher partials on a piano tend to be more inharmonic than the lower partials, so I would expect that in the circumstance you indicated, the 4rd partial of A3 would be sharper than the 2nd partial of A4.

But, see page 9 of this paper: Inharmonicity of Piano Strings, Simon Hendry, October 2008.

Although the graph only spans one octave, we see that it is not as regular and smooth as the theoretical prediction, so presumably there could be a circumstance where the 4th partial of one note is flat compared to the 2nd partial of the note an octave above.

It's also worth noting that there is a big difference in inharmonicity between the wound strings of the lowest register and the plain strings of the middle and upper registers of a piano. A comparison of one note in the "wound" register to a note an octave above in a "plain" register will highlight this difference.

This is why octave stretching has to be a compromise, and is unique to each instrument.

In general, the higher partials on a piano tend to be more inharmonic than the lower partials, so I would expect that in the circumstance you indicated, the 4th partial of A3 would be sharper than the 2nd partial of A4.

But, see Figure 5, page 9 of this paper: Inharmonicity of Piano Strings, Simon Hendry, October 2008:

Although the graph only spans one octave, we see that it is not as regular and smooth as the theoretical prediction, so presumably there could be a circumstance where the 4th partial of one note is flat compared to the 2nd partial of the note an octave above.

It's also worth noting that there is a big difference in inharmonicity between the wound strings of the lowest register and the plain strings of the middle and upper registers of a piano (see Figure 12, p. 20 of that paper). A comparison of one note in the "wound" register to a note an octave above in a "plain" register will highlight this difference:

This is why octave stretching has to be a compromise, and is unique to each instrument.

In general, the higher partials on a piano tend to be more inharmonic than the lower partials, so I would expect that in the circumstance you indicated, the 4rd partial of A3 would be sharper than the 2nd partial of A4.

But, see page 9 of this paper: Inharmonicity of Piano Strings, Simon Hendry, October 2008.

Although the graph only spans one octave, we see that it is not as regular and smooth as the theoretical prediction, so presumably there could be a circumstance where the 4th partial of one note is flat compared to the 2nd partial of the note an octave above.

This is why octave stretching has to be a compromise, and is unique to each instrument.

In general, the higher partials on a piano tend to be more inharmonic than the lower partials, so I would expect that in the circumstance you indicated, the 4rd partial of A3 would be sharper than the 2nd partial of A4.

But, see page 9 of this paper: Inharmonicity of Piano Strings, Simon Hendry, October 2008.

Although the graph only spans one octave, we see that it is not as regular and smooth as the theoretical prediction, so presumably there could be a circumstance where the 4th partial of one note is flat compared to the 2nd partial of the note an octave above.

It's also worth noting that there is a big difference in inharmonicity between the wound strings of the lowest register and the plain strings of the middle and upper registers of a piano. A comparison of one note in the "wound" register to a note an octave above in a "plain" register will highlight this difference.

This is why octave stretching has to be a compromise, and is unique to each instrument.