overtones and the major scale and a question

In his Theory Of Harmony Arnold Schoenberg gives a rationale for the major scale based upon the overtone series. It goes something like this. The easiest to discern different overtones (or harmonics) are the octave, the perfect fifth and the major 3rd. If you consider a C major scale, the C will produce a G and an E. The G, if considered as a fundamental tone, will produce a D and a B. He then backs up and considers that C is an overtone of F: F produces C and A. A bit more graphically this looks so:

G (D, B)
C (G, E)
F (C, A)

Then, omitting repetitions and reordering one has all the tones of the C major scale: c, d, e, f, g, a, b.

You hear this often: that the overtone series is responsible for the tones of the major scale (or at least implies a major scale collection of tones). But it's really, really, really hard for me to imagine what the process was that brought the major scale into being from the overtones. It's easy to imagine people 10,000 years ago singing and playing instruments. It's difficult to imagine that they had an idea of the overtone series, and that it was somehow responsible for the music that they were making. (It's actually much easier to imagine a scale being built out of successive perfect 5ths: f, c, g, d, a, e, b. In fact the first five tones of this series can account for the major pentatonic scale: f, g, a, c, d.)

But then here is the question: how did the tones of scales develop? Was the first vocal music only made out of perfect fifths and octaves? Without ever hearing the music of our earliest ancestors we won't ever be able to analyze or theorize too much (except upon shaky ground). But it is worth pondering...