What the article means is: we dont have 12 notes (A B C D E F G H I J K L). Instead, for historical reasons (the choice of CMaj/Amin as a reference due to the notation evolution from heptatonic scales) we have A B C D E F G and we annotate with accidentals but, since those are not evenly spaced, there are some missing "black keys" there.
Also, what devnonymous says, which I agree with too (but that's another story...)
Hmm, I guess someone should tell those people, like Like
Tolgahan Çoğulu who are writing music in microtonal scales with 19, 24 or 31 notes in a scale, that their notes spacing is random.
Ah alright, I finally understand you. What you meant to say is the reason why Western classical music is built on the 12 note chromatic scale is because the musicians used the math! It has nothing to do with history. Sound about right?
Although I agree with you... didn't Pythagoras derive the pythagorean tuning of diatonic doing the math with the 3:2 ratio?
I know near zero music history, but I was under the impression that that's the evolution from diatonic scales and eventually into our western music system.
Not exactly, although I think I understand what you are getting at.
What I meant was that the interval between a major third and fourth in a 12-tone chromatic scale has to be a semitone due to math, not due to some historical accident or decision.
It might be an accident of history that we use a 12-step scale in the first place though, since you can have arbitrary many intervals in an octave - but you can't just divide the octave in arbitrarily places and get music out of it. The intervals still have to be ratios.
(Well I'm sure some avant-garde composer have tried making music with intervals that are not ratios just to be clever, but I hope you get my point!)
"For historical reasons the notes B/C and E/F are one semitone apart."