I don't think the intervals of the octave are arbitrary, actually. If you take a fundamental and consider its harmonics (say a vibrating string with one, two, three, four etc standing waves), you start to get the other intervals that make up the musical scale. For example a C fundamental will have a 1st harmonic of C at the octave above, but the 3rd harmonic will be G at the octave plus a fifth above, the 4th will again be C but 2 octaves up, and the 5th harmonic will be E, a major third up from that (I think: it is hard to remember exactly how it works).
So it is not coincidence that the major triad in harmony has the tonic, fifth and major third in it. These pitches are all part of the same family of overtones, from an implied lower fundamental. From what I recall, most of the notes of the Pythagorean scale were derived in this sort of way.
The pentatonic scale, I think, still has the intervals of the third and the fifth in it, so is not inconsistent with the same physical principles - unsurprisingly.