For large amplitude, a linear model is not sufficient for describing the motion of the string. The non-linear model used in the simulations accounts for the variation of tension due to large amplitude, and for the resulting coupling between transverse and longitudinal waves in the strings. Example 4 shows the differences between the two models.

Modifying the tension of the string not only changes the coupling conditions with the soundboard, but also the temporal and spectral properties of the tone. This results in audible differences. Example 5 shows an example of tension modification on a modern piano (Steinway D). Similar effects can be heard on historic pianos.

Example 6 shows to what extent the timbre of piano tones depend on the position of the attachment point of the strings at the bridge. The reference position corresponds to the usual point for the note C4 of a J.B. Streicher piano (1873). For comparison, piano tones are simulated where the C4-strings are attached in the bass region (position of note C2) and in the treble region (note C6).

Example 7 shows that the design of a soundboard critically influences the temporal evolution and the tone quality of piano tones. Simulations are made for the note C#5 of a modern piano (Steinway D), comparing the tones obtained with a normal soundboard, a thin soundboard, and a more rigid soundboard with the same thickness as the reference one, respectively. Similar effects are obtained on historic pianos.

The sounds of pianos perceived by the listeners not only depend on the vibrating elements (mainly the soundboard) but also on the reflection of waves on rigid surfaces situated near the piano. Closing the lid and adding a back plate below the soundboard as a reflector, for example, contributes to create a cavity inside the piano which modifies the spectral balance of the instrument. This property is illustrated in Example 8.