The explanation of the origin of major scale in the article is pure voodoo. Minor third is not a simple fraction - is that the reason to exclude it from the scale? How do you explain minor scale then? Maybe it should be excluded, too?
Here're my thoughts on the subject.
For some reason no one can explain, Western music settled on a system of 12 tones with equal temperament, This system emerged as a result of long evolution of Western music, and experimentally proven to be very rich in possibilities.
Scales used in Western music (of which jazz is a part of) are built on two simple principles: 1) interval between adjacent notes of the scale is either tone or semitone 2) there's no two semitones in a row.
It's easy to check that all scales that satisfy these 2 rules are:
major scale and its modes (7-note scales; 7 modes)
melodic minor scale and its modes (7-note scales; 7 modes)
diminished scale and its modes (8-note scales; 2 modes)
whole-tone scale (6-note scale, single mode).
(Whole tone scale is not used very often, except by T.Monk)
But even after we "explain" scales, we need to figure out how to use them, what their role is, what the properties of each mode are. There's no hard science behind this, the properties just "emerge", and you have to experience them - theorizing is not of much help, math formulas don't explain anything, just lead to confusion.
In short: you have to play AND think; thinking alone won't help. It's an experimental subject.
Edit: forgot to say: scale is a very useful notion, but in some contexts, it's more convenient to think in terms of triads and interpolation. I know this all sounds hand-wavy, and it is! Unfortunately, without piano, it's impossible to to illustrate what it all means. The subject doesn't easily lend itself to verbalization.