Earlier quoted context omitted.
For people with the mind of a programmer, explaining the mathematical basis of equal temperament and then the major scale (the article doesn’t explain the major scale well, but simply says “it sounds better than a chromatic scale”) allows a programmer to understand not just the how but the why for the basics of western music. For people that just want the how, one would start with “here is a pentatonic scale” followe…
It's also a really strong example of "missing the forest for the trees". Deriving Western music traditions from first principles does not help you to understand why, what, and how any of it actually works.
However, first principles explain “why” a major chord sounds the way it does, and “why” a minor chord has more tension.
Let’s look at the five-limit just intervals: 2/1, 3/2, 4/3, 5/4, and 6/5. 2/1 is a perfect interval; two notes an octave apart sound nearly the same. 3/2 and 4/3 are also perfect intervals, but there’s a little more tension and beating than with 2/1. 5/4 has a little more tension than 4/3, and 6/5 has even more tension. I just explained, using first principles, the octave, perfect fifth, perfect fourth, major third, and minor third. That’s most of the scale right there.
Now, let’s make a chord. Experience has shown that three notes is more interesting to the human ear than just two notes. That in mind, we want three distinct notes where the intervals between notes have a minimum of tension. Take the root, take 5/4 of that, then take 3/2 of the root. That’s a major chord. The reason we use 5/4 instead of 4/3 is because the interval between 5/4 and 3/2 is 6/5; the interval between 4/3 and 3/2 is 9/8. Since 9/8 has more tension than 6/5, that gives us a suspended chord, and it’s better to use a major chord with less tension to make a simple chord progression.
Now that we have our first chord, we can hear that having a 1-chord song becomes repetitive very quickly to the human ear. We can make the song more dynamic and interesting by giving it three chords: I, IV, and V. Take that chord: 1, 5/4, and 3/2 (a major chord). Move all three notes up 4/3, because 4/3 is a perfect interval with a minimum of tension. That’s our IV chord (F chord in the key of C major) Next, from the root position, instead of moving up the chord 4/3, we instead move it up 3/2. That’s a V (or dominant) chord—a G chord when played in the key of C major.
Now, from first principles, namely that the intervals 3/2, 4/3, and 5/4 sound pleasant to the human ear, that 6/5 has more tension, and 9/8 has even more tension (so we avoid suspended chords for now), we have a I IV V chord progression, which is the basis for countless rock and popular songs.
If we take all of the individual notes from the I IV V chord progression, that gives us the seven notes of the major scale, after explaining that, once we cross the octave threshold, we can transpose an octave down without affecting the musicality of the notes. We might even explain chord inversions here.
So instead of just parroting “I IV V makes a nice simple chord progression”, we now know the underlying physics which make I IV V sound so nice to the human ear, and how to get the major scale from those chords. I prefer understanding both the why and the how.
(I would have used two slightly detuned sawtooth waves instead of a sine wave for most of the examples if I were to write an article like the one this discussion links to, explaining this has a more pleasant, piano or violin like sound to it. Maybe even a low pass filter to tame the harmonics. Another option is to run a single sawtooth wave through a Solina style chorus, but explaining two detuned sawtooth waves is easier than trying to explain the Solina chorus effect)