Yes, it is possible for a dissonant chord to sound harmonious on a piano that is completely out of tune. When a piano is out of tune, it means that the relative pitches of its strings have shifted from their intended positions. This can result in the overall tonality of the instrument being altered.
In a dissonant chord, the combination of notes creates a sense of tension or clashing. However, when a piano is out of tune, the relationship between the notes in the chord may change, potentially creating new intervals and harmonic interactions that were not present in the properly tuned instrument.
These altered intervals can give rise to new harmonies and tonalities that may sound surprisingly pleasing or interesting, even if they are technically dissonant. This phenomenon can be attributed to the concept of "alternative tuning" or "microtonality," where musicians intentionally explore unconventional tuning systems to create unique and rich harmonies.
It's worth noting that the perception of harmony is subjective, and what one person finds harmonious, another may perceive as dissonant. Additionally, the specific degree and nature of the piano's detuning will greatly influence the resulting sound.