Some interesting charts on how a piano is tuned. The low bass is much lower than theoretical and the high treble much higher. This is done because of inharmonicity. Inharmonicity is when the tight, short, fat string does not vibrate well and harmonics sound louder than the fundamental. Because of this, the tuning must be stretched to make it sound pleasant. Bigger pianos with longer strings sound better because they have lower inharmonicity than a small piano. Harpsichords, violins, guitars, etc. have low inharmonicity because the string tension is much lower than that of a piano.