Re: The law of fives, it is significant that the first attempt at harmony is organum built on intervals of fifths and then gynmel, on fourths.

The fifth has a resonance in music that seems international. It is an essential part of the overtone series beyond the first octave.

It's significant that as a harmonic device it doesn't sound discordant to most ears.

I'm not sure the Law of Fives has anything practical to do with music but it engenders speculation.