Unraveling the Mystery of Music Intervals

[Pythagorean]

Thanks Pythagorean for your answer.
But, the more I think of it, the more I disagree with my previous statement. It's not that 12 can be divided by 2,3,4 or six.
It's that, as DrGreg before pointed out,Minor third: 2^{(1/12) x 3} ≈ 6:5
Major third: 2^{(1/12) x 4} ≈ 5:4
Perfect fourth: 2^{(1/12) x 5} ≈ 4:3
Perfect fifth: 2^{(1/12) x 7} ≈ 3:2
Octave: 2^{(1/12) x 12} is of course 2:1
Don't you think so Pythagorean?

I guess this is the answer of my curiosity for years. So simple
Okay..., one more question for anybody.
π, e, golden ratio, they are all, I think, universally accepted. I mean really universally. Any civilization even outside the Earth will use those constants. What about [itex]\sqrt[12]{2}[/itex], is it universally used?

Any idea?

My point was that these are two distinct issues. One is the issue of how many notes you subdivide the octave by, the other is how you distribute that subdivision. There's not one way to do it, the only reason that Dr Greg can talk about approximating these ratios in the first place is because these are the ratios that are already desired, and these ratios come from higher order subdivisions (dividing the string in half, thirds, and fourths).