Harmony, I'd wager, comes from the relationship between consonances and dissonances; consonance and dissonance come from the relative tunings of the harmonics of the harmonic series, and how they're reinforced/countered.
As to defining music itself, I'd say that music is any sound which is intended to be percieved as music. The audience's reaction to music really has no say is whether it's music or not; only whether its GOOD music
Your art metaphor kind of breaks down just a little bit.
The kinds of people who really hate modern art are very likely to have a preference for folk or contemporary music. They appreciate "art" when it's the kind of visual cues which depict something; they likely appreciate "music" when it's the kind of auditory cues which depict something... here, LYRICS.
