The fact that the distortion goes away when you turn down the volume tells me that it's got nothing to do with the ROMs or the piano electronics, and it's got to be physical moving parts buzzing, or amp clipping. Everything is at the amplification stage or later.

Which notes are they? Low ones or high ones?

If low notes:
- Bad woofer, or stuff leaning on the speaker cone.
- Loose panels or objects inside the casing rattling with certain low frequencies.
- Bad amplifier for the speakers that is clipping at some threshold on certain frequencies.

If high notes:
- Blown tweeter.