Guitar chords don't follow this rule, so ignore it if you like. Anyway, it's probably not a coincidence that consonant triads are found in the overtone series. Some people think otherwise, and it's best not arguing with them. The 7th overtone leads to 7-limit hamony and the 8th overtone is an octave above the 4th. Partials that are out of tune with the idealized overtone series described so far are called inharmonic .
Bells have a lot of inharmonic partials.
A piano has a slightly stretched overtone series and so octaves are usually tuned sharp to compensate for this. There's lots about Just Intonation on the Web. Try The Just Intonation Network for starters. This means integer frequency ratios. Recall that overtone 3 is a fifth above overtone 2.