> Music doesn't live in an abstract realm of perfections

I agree with this in spirit, but there are practical ramifications of getting the frequency domain wrong. The human brain is very particular in this space. Even for completely untrained listeners. It's nothing like the human visual system. You're working on timescales measured in microseconds with auditory signals. Even where the instruments are physically positioned on stage is significant. Getting their pitch slightly wrong can be catastrophic.

Many musicians can readily confirm that the difference between temperaments can be felt and heard by trained ears. A guitar tuned to equal temperament has major thirds that warble audibly. It feels different when you use just intonation, which isn’t generally possible on a guitar.

This article is just an introduction to the math behind 12-TET, why it exists, the tradeoffs, etc.

The only thing that is absurd here is your bizarre strawman that discussing equal temperament is somehow non-musical and that engineers can’t understand what music is because they want to measure things.

Have you heard of even tempering, on piano?

Engineers hate it and so they invented the true temperament guitar. It’s like a regular guitar except the frets are a bit funky.

Any musician with enough training will tell you which notes are out of tune on their well-tuned instrument, and how they correct for it as they play.

Just because we live with the trade-off doesn’t make it correct in any other sense.

I am a jazz guitarist and am sympathetic to this comment: the way I tune my guitar these days is hitting an E tuning fork, playing a particular E7 chord, and deciding if it sounds good:

  e —0–
  B —0–
  G —7–
  D —6–
  A —7–
  E —0–

Learned it from Jimmy Bruno. I despise digital tuners. However it is worth noting: a properly-tuned guitar will never be able to play a “barbershop seventh,” which hits the natural harmonic dominant 7th and is so flat compared to TET that it’s really almost a 6th. The chord itself sounds more bittersweet and less “funky” than a TET dominant 7th. OTOH the TET chord is an essential part of modern blues-influenced music: being “out of tune” makes the chord sharp and strong, almost like a blue cheese being “moldy.” So I’m not beaten up about the limitations, it’s just worth keeping in mind: no instrument can beat a group of human voices.

In general your ears do not hear these little arithmetical games around mismatched harmonies. They hear things like “this chord sounds warm and a little sad, this one is bright and fun.”

Even your fancy guitar is not exempt from harmonics math. TFA has nothing to do with the quality of a guitar and everything to do with 12-Tone Equal Temperament.

Weird to describe 99%+ of all guitars, including some of the best made guitars in the world, as "poorly made."

This article is relevant to a theoretic perfectly designed and built guitar.

You’re assuming that the goal for a guitar player is to have perfectly optimal instrument when in reality many players want an instrument that feels and sounds like the artists that inspire them. Aesthetics is part of that but if they enjoy the sound of the instrument then who’s to say that another one is “better”?