I would imagine that one of the three strings is detuned somewhere
around 10 cents sharp or 10 cents flat.  You only have to have one
string detuned and the other two to be 'on pitch'.  Having two strings
out of tune would not sound nice, as you have to have some reference
point.

On an accordion, when the 'Musette' sound is played (two reeds), one
is off pitch to get the musette sound.  I will check on my accordion
by how much the 'other' reed is out of tune.  This may be altogether
different pitch-wise than the out of tune piano method.

A nickelodeon does not seem to matter too much if the piano is off
tune a little, playing ragtime and bar room tunes only.

Stephen Bentley
Vancouver, British Columbia