This idea is often presented as soon as anyone mentions "harmonic series" and "Western music theory" in the same breath, and in the same hand-wavey terms. Do you have any material to support these claims?
I don't see how this is so questionable. Frequency is continuous, so the way we subdivide into discrete notes is quite arbitrary. You don't even have to go outside of western music to find examples. Modernist classical composers of the 20th century experimented with microphones. Just look up "microtonal music" and you'll find many examples.
No disrespect, and I could be misreading your point, but I think it only seems hand-wavey to you because you're not familiar with the definitions of the terms being used. It's just statement of facts that is in basically no dispute by the musical community. A few definitions:
> Harmony
The frequency ratio of two or more pitches
> Scale and mode
The set of frequency ratios out of which a given piece of music can be constructed
> The 12-note Western chromatic scale
The modern western chromatic scale is formed out frequency ratios which are powers of the twelfth root of 2, or ~1.059. This is called the "12 note" scale, because 1.059^12 == 2, and our brains are predisposed to find pitches who are multiples of two apart similar. This is because pitch classification in humans (along with many other human senses) measures inbound signal in exponential, rather than linear, terms, and 2:1 is also the simplest ratio by which two pitches can have constructive interference.
As far as why the 12-note scale is the Western scale, there's a fair amount of debate, but most are in agreement that it likely comes from the fact that 12 is a low number with a fair number of integer factors (1, 2, 3, 4, 6). Integer factors translates very directly into constructive wave interference (3:2 has less destructive interference than 101:100). So, one can easily construct many constructive interference ratios out of the (2^^(1/12)) atomic element (e.g. the "major chord", the most common set of three pitches in western music, is (1.059^7):(1.059^4):1 ~= 6:5:4). Each exponent of the twelfth root of two is very close to, respectively: 16/15, 9/8, 6/5, 5/4, 4/3, 7/5, 3/2, 8/5, 5/3, 16/9, 15/8
So! Now the only remaining question is just a question of the antropological evidence: do all other cultures also use the twelfth root of two as their simplest harmonic difference? And the answer is very clearly no:
* Arabic music uses the twentyfourth root of two ( https://en.wikipedia.org/wiki/Arabic_maqam#Notation although to be fair, this is just the square root of the western twelfth root of two, but this conceit is largely used for notation, while actual performance uses adjustments smaller than the twenty-fourth root of two)
Does this constitute "A large portion of the world (possibly a majority)"? I'd probably say not a majority, but certainly more than 15%, likely at least 25%.