[LegionMammal978]

The thing is, unless you're playing with other instruments, no one is forcing you to tune to equal temperament. E.g., it's very common to tune a violin's A string to an A440 reference, then tune the other strings to 3:2 perfect fifths by ear. It just gets more complicated for fretted instruments like the guitar.

[coliveira]

If you tune the strings in a guitar to a perfect 4th, which is the case except the 3rd between strings b-e, the lower e will significantly differ from the high e open string. There's no way to get around it.

[dahart]

Wanting to play in any key and not be locked into a key automatically pushes musicians toward equal temperament, even when playing solo, and even on a violin. Saying no one’s forcing you is technically true but sounds pretty naive, and (forgive the pun) tone deaf to me; there’s no realistic alternative for modern music. Some people do choose to play with other tuning systems on occasion, but there’s a reason why 12 TET is so popular and widespread.

[kazinator]

Wanting to change keys freely only pushes fixed-pitch musical instruments toward equal temperament. Since many important instruments are like that, and virtually all instruments that are capable of accurate intonation not relying on ear are like that.

If an ensemble includes instruments that are equal temperament, then the non-fixed-pitched instrumentalists adjust their pitch to sound good with those.

An ensemble consisting only of instruments that can play any interval can change keys by pure intervals.

E.g. switching from the original major key to the relative dominant key can mean changing the root by a pure fifth. In equal temperament, this modulation is done by altering only a single note: sharpening the subdominant. All other notes are from the original scale. If we change key by a pure fifth, that is obviously not so; all notes are detuned off the original scale.

If we change through all the keys along the circle of fifths, perfectly purely, we arrive at the Pythagorean comma: the gap between the destination root and the original.

Another possibility is to progress the roots through the diatonic fifths of the original scale, rather than pure fifths. Like, we start with a pure, just intonated C major, and then change keys through G,D,A,E,B,F#,C#,Ab,Eb,Bb,F back to C using the notes of that pure C major scale, or sharps/flats relative to those. Then we don't run into the Pythagorean comma; but of course all the pure scales we end up using are detuned from C major, and in a different way from following pure fifths.