This is just wrong. You are using western musical culture terms for what are actually physical phenomena.
I will quote to you from wikipedia:
> The harmonic series is an arithmetic progression (f, 2f, 3f, 4f, 5f, ...). In terms of frequency (measured in cycles per second, or hertz, where f is the fundamental frequency),
> The second harmonic, whose frequency is twice the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second harmonic. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third harmonic (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher).
> The frequencies of the harmonic series, being integer multiples of the fundamental frequency, are naturally related to each other by whole-numbered ratios and small whole-numbered ratios are likely the basis of the consonance of musical intervals
What you are describing is a musically significant set of intervals that are merely a subset of the harmonic series, created by what the wikipedia page describes as:
> If the harmonics are octave displaced and compressed into the span of one octave, some of them are approximated by the notes of what the West has adopted as the chromatic scale based on the fundamental tone
> some of the pitches in the harmonic series are approximated by the notes of the chromatic scale
is not the same thing as
> the chromatic scale is derived from the harmonic series
which is what the OP article claims.
You can find the chromatic scale in the harmonic series, yeah, if you ignore the majority of the notes in the harmonic series.
To find the chromatic scale in the harmonic series, you need to take the 2nd, 3rd, 4th, 5th, 9th, 15th, and 44th harmonics, and ignore of the rest. That's not a mathematically justified derivation, that's a post-hoc rationalization built on coincidence alone.
So, sure, fair question why these harmonics and not any of the others?
Well, powers of 2 are out because they are just higher octaves. Then we have a whole series of harmonics that are equivalent ratios to the fundamental when folded down into the octave range (3 (3:2),6 (6:4), 12 (12:8)), (5 (5:4), 10 (10:8)), (7,14,28), (13,26) and so on.
You'll notice the pattern: the harmonics the define the intervals in a 12T system are those that introduce new ratios into the list of intervals, so they lean toward being prime or only having factors not already introduced.
By the time you go through the list, it's easy to see that going up to the 31st harmonic really only leaves out a couple of possibilities from a 12T system: 25, 29, 31 and as far as I am aware this is because introducing them into the pitch class produces results extremely close to already existing members.
And sure, you could go higher, but the pattern will repeat: harmonics whose ratio folded into the octave range are identical, or which give rise to pitches extremely close to pitches defined already.
I will quote to you from wikipedia:
> The harmonic series is an arithmetic progression (f, 2f, 3f, 4f, 5f, ...). In terms of frequency (measured in cycles per second, or hertz, where f is the fundamental frequency),
> The second harmonic, whose frequency is twice the fundamental, sounds an octave higher; the third harmonic, three times the frequency of the fundamental, sounds a perfect fifth above the second harmonic. The fourth harmonic vibrates at four times the frequency of the fundamental and sounds a perfect fourth above the third harmonic (two octaves above the fundamental). Double the harmonic number means double the frequency (which sounds an octave higher).
> The frequencies of the harmonic series, being integer multiples of the fundamental frequency, are naturally related to each other by whole-numbered ratios and small whole-numbered ratios are likely the basis of the consonance of musical intervals
https://en.wikipedia.org/wiki/Harmonic_series_(music)
What you are describing is a musically significant set of intervals that are merely a subset of the harmonic series, created by what the wikipedia page describes as:
> If the harmonics are octave displaced and compressed into the span of one octave, some of them are approximated by the notes of what the West has adopted as the chromatic scale based on the fundamental tone