I don’t think it’s unreasonable to say 2/1, 3/2, 4/3, 5/4, and 6/5 are intervals which sound pleasant to the human ear. [1]
Once that is established, as per the linked article, 12-tone equal temperament makes a lot of sense (but isn’t universal, obviously) because it’s resulting tuning gives us a really close 3/2 and 4/3, and having a simple 12-tone scale reasonably in tune everyone can agree on makes sense.
We can then explain that 5/4 and 6/5 are a bit off in 12-tone, but are “good enough” that we tolerate them being slightly out of tune when using equal temperament. Once we accept that 12-tone has imperfect thirds, we can then look at the I IV V chord progression (I IV V comes from 3/2, 5/4, and 4/3 sounding pleasant to the human ear), and explain why that chord progression is so common in western popular music.
These aren’t universal truths—12-tone equal temperament is a compromise, but, as per the linked article, a reasonable one. Just intonation is, of course, another possible compromise.
[1] 2/1: Octave; 3/2: Perfect fifth; 4/3: Perfect fourth; 5/4: Major third; 6/5: Minor third
Once that is established, as per the linked article, 12-tone equal temperament makes a lot of sense (but isn’t universal, obviously) because it’s resulting tuning gives us a really close 3/2 and 4/3, and having a simple 12-tone scale reasonably in tune everyone can agree on makes sense.
We can then explain that 5/4 and 6/5 are a bit off in 12-tone, but are “good enough” that we tolerate them being slightly out of tune when using equal temperament. Once we accept that 12-tone has imperfect thirds, we can then look at the I IV V chord progression (I IV V comes from 3/2, 5/4, and 4/3 sounding pleasant to the human ear), and explain why that chord progression is so common in western popular music.
These aren’t universal truths—12-tone equal temperament is a compromise, but, as per the linked article, a reasonable one. Just intonation is, of course, another possible compromise.
[1] 2/1: Octave; 3/2: Perfect fifth; 4/3: Perfect fourth; 5/4: Major third; 6/5: Minor third