What is stretch tuning?
The frequency ratio of octaves on a piano are found to be slightly greater than 2:1, especially for the very high and very low notes, and especially for small pianos. The reason for this is that the octaves are usually tuned to eliminate interference beats between the fundamental of the upper note and the second partial (or resonance frequency) of the lower note. The second resonance of a struck string usually has a frequency that is slightly higher than twice that of the first, because of the finite bending stiffness of the string. Playing an instrument that only sounds one note at a time, or singing, many musicians stretch octaves. However, playing chords with other instruments, they usually play 2:1 octaves.
