* Inharmonicity *
In addition to the equal temperament described above, each piano has its own specific requirement for the piano technician to be familiarized with. Some would say, a piano has a ‘soul’…
A piano string, when struck by the hammer, will produce a specific series of [overtone] depending of its thickness, stiffness, length and whether it is a ‘wound string’ (with a core made of one metal and overwinding of another). Also, age and accumulation of rust deposit on a string may affect its resonance.
Such differences in strings, from piano to piano and even for different registers within the same instrument, will then exhibit [inharmonicity]. This very inharmonicity is responsible for the ‘warmth’ property common to real piano tones. Therefore, octaves might be ‘stretched’ in a piano to a certain amount depending on the exact [inharmonicity] of the strings involved.