Surprised to see no mention of fundamental frequencies or harmonics
This is pretty well studied, but kudos to the author for trying to explain it again, it's an odd topic. But I suggest looking up "timbre" at least and perhaps updating the article with the terms used by actual musicians to mean exactly this.
Timbre - "the quality of tone distinctive of a particular singing voice or musical instrument"
(Yeah, OK, that was terribly said, sorry 'bout that.)
For timbre, see https://en.wikipedia.org/wiki/Timbre e.g.
FFTs, etc., give us visualization tools, but they miss the point. Different materials resonate differently across the auditory spectrum, emphasizing or diminishing various harmonics, resulting in complex sound profiles that make each instrument distinctive.
Or, to put it most simply: Different materials react to sound differently, and each instrument's materials and construction are what give it its distinctive timbre.
On an unrelated note, Daniel Levitin, former music producer and director of the Grammys, and current neuroscientist at McGill, was once asked what makes each musical era distinctive: timbre was, in his opinion, the single most important factor (source: one of his books, probably still in a moving box in my basement, otherwise I'd look it up).
That's a fascinating idea; I googled and found what might be the story you're looking for:
[quote]
In the best seller “This is your brain on music” by Daniel Levitin, he talks about John R. Pierce (inventor of the travelling wave vacuum tube and the first telecommunications satellite) who, interested to discover rock music, asked him to summarize the genre in a concise list of six songs. Levitin ended up with a list of songs from Little Richards, the Beatles, Jimi Hendrix, Eric Clapton, Prince and the Sex Pistols.
Interestingly, while listening, Pierce was not really interested by the songs themselves, their melodies, their harmonic structures or their rhythm characteristics, but he said he found the “timbres” to be remarkable and described them as being new, unfamiliar, and exciting.
Levitin concludes his story by saying: “The way in which instruments were combined to create a unified whole - bass, drums, electric and acoustic guitars, and voice – that was something he (Pierce) had never heard before. Timbre was what defined rock for Pierce. And it was a revelation for both of us.”
Quoted from "An Overview of the Concept of Timbre and its Use in Contemporary Music and Record Production" by Mathieu Bedwani
Anyone interested in this might enjoy the paper about the "Scanning the Dial" experiment. (It's about contemporary music rather than historical eras, but the idea is related)
https://www.researchgate.net/publication/248906443_Scanning_...
The punchline is that listeners can typically assign a genre to a recording after hearing a single quarter-of-a-second clip, but the paper is worth reading for its notes on genre and timbre in general.
Andrew Huang's video on the harmonic series does a really cool dive into this
This was my attempt to show you how you can derive the answer from first principles, just by analyzing the sound, and forming your own hypothesis/getting to these conclusions yourself.
The links at the end do have resources for the physics and theory behind it.
It's like that popular Monad tutorial that has you implementing Functors and Monads in order to solve a problem without ever telling you until the end that what you just created were Functors and Monads.
Starting off with the well-known terminology kind of colors the discussion from the beginning--even folks who don't really know what harmonics or timbre or monads or applicatives are probably have some general impression, and that impression could be wrong in a way that prevents them from learning.
No reason that learning a fairly interesting word's definition can't be part of the lesson...