Relevant MinutePhysics video which dives deep: https://www.youtube.com/watch?v=tCsl6ZcY9ag

Even if you tuned two string to ensure that two specific notes on them vibrated at a perfect interval, there are non-multiplicative overtones modulated by resonance with the rest of the instrument. Those intervals are ideals for minimizing dissonance. Practically, the dissonance of 12TET intervals falls below the noise floor of all the other acoustic distortions that give instruments character.

I thought this was going to be about stiffness of the strings and how the modes even on a single string are not in tune compared to the mathematical model, which assumes infinitely flexible strings.

> Not everyone in history thought that 12-TET was an acceptable compromise. Johann Sebastian Bach thought we should use other tuning systems

This is presented as fact, but as I understand it there is no conclusive evidence for what Bach intended wrt temperament. There is a theory that the title page of the Well-Tempered Clavier encodes Bach’s preference in the calligraphic squiggles, but this is a recent theory and speculative. I don’t believe there are any direct statements by Bach as to his intention.

I wondered why this article was so high on the front page but now I realize it’s simply because everyone else wanted to “um actually” it. I guess that makes sense.

fun fact: some bands, like red hot chilli peppers, will tune the G string slightly flat such that major thirds become just, for some of their riffs. Listen to "scar tissue" for example

Close enough for rock'n roll, as it is called.

I read the title and felt personally attacked :(