Instruments in ancient greece were in pythagorean tuning. As explained above, the temperament is quite different, based on the natural overtone series. A pythagorean octave is actually quite sharp, and over multiple octaves the harmony can be rather shrill. But this was their chosen tuning system in ancient times. When the equal-tempered piano came on the scene (by Bach i think, but not quite sure?), I'm sure some thought it was alien, or at least very "modern" and "novel."
Far Eastern civilizations made music largely in the pentatonic scale, but there is also another vocabulary of sound utilized that, to be honest, I fail to understand. If you were to play an ancient chinese opera, I wouldn't be able to tell whether it is meant to convey joy, loss, or any other emotion. It would just sound out of tune and random. In other words: dissonant.
Middle Eastern cultures use a microtonal system for melodies. A scale can regularly dip into quarter and even eighth tones. Again, this level of complexity is not suited to the western ear, and there is more than just a simple language barrier seperating us from understanding of this type of music.
I think it's proven that dissonance is a subjective term; and beyond it's strict music theory meaning, there is an implication of inscrutability which can be found in more styles of music than just modern classical. It really does come down to the local culture.