[dhosek]

For that matter, the first 5 stacked fifths gives you the standard pentatonic scale. Extending by a fifth on either end and you get the most common accidentals in Western music (if your first seven give C major you’ll get F# and B♭). I think (but I’m not sure) that some of the non-Western microtonal scales extend the tonality by not ignoring the Pythagorean comma when you’ve done the 12th fifth, but by continuing to stack fifths for more harmonies.

[brudgers]

From C the first six stacked fifths give C Lydian, not C major. (You get an F#, the 5th of B as the seventh pitch, not F the 5th of Bb).

You don’t get the perfect fourth until you go all the way around the circle of fifths.

You cannot stack perfect fifths and get a major scale.

[dhosek]

I was being sloppy and should have said diatonic scale.

[brudgers]

Sloppiness is why music theory is not scientific.

You can’t get to a scientific rationalization of the primacy of the major scale without it.