That makes some sense, but if you look at a spectrum analysis of any signal that isn't a sine wave (and specially for highly clipped signals like you mention here), they consist of many tens or hundreds of even and odd harmonics, which is what you're referring to here when you say a root/fifth chord under distortion produces a major third phantom note. In truth, it creates many, many phantom notes, and pretty much any instrument, even a flute, does as well. Yes, that's the timbre - the relationship of the harmonics that result from a waveform. That's the very idea behind additive synthesis, where the harmonic nodes are individually created from a series of sine waves. So I guess it could be said that a single non-sine note would produce a harmony (multiple notes with a harmonic relationship), but this is not the same thing as a harmonic progression, where that relationship would change.