Guitars are indeed supposed to be 'ideally' equal temperament. But they're not.

Even if you take out the dynamics of vibrating strings, the idea of 'frets' is to 'pre-divide' the string into its intervals for you. For example, the 12th fret is the halfway point on the string.

But look at the bridge of any guitar. Clearly, the saddles are not all an equal distance from the nut, so the 12th fret can't be actually halfway down all of them.

For this reason, a guitar is fretted in a way that is actually more of an approximation of equal temperament than actual equal temperament. It's rarely far enough out to be bothered about.

'True temperament' is a bit of a misnomer. There's no such thing as 'true' temperament. 'Temperament' by definition means a 'tempering' of the 'true' interval (the pure/just intonation).

SOME sort of temperament is required on a fretted instrument precisely because of the question that this article addresses: on a guitar, you can only pick one 'pitch' for a fret, even though the 'correct' frequency for a D# may well be different than the 'correct' frequency for an Eb depending on the key in which they appear.

So calling it 'true temperament' is a bit naughty. All it means is that it's trying to iron out some of the approximations which are inherent in the instrument design to get it closer to 12-TET.

True temperament appears to be a marketing term for a fret system providing equal temperament.

A "spherical cow" model of a guitar would be equal temperament, but that ignores the messy reality of how strings behave - chiefly they need to be some distance above the fretboard and pressing them naturally bends the string ever so slightly.

so slightly that it can be on the range of 0-5 cents, provided the instrument is sufficiently constructed and the player is sufficiently skilled.

this is why a guitar using equal temperment can play consistently in-tune with itself as well as with other instruments tuned in the same system. it’s not about perfection according to some abstract mathematical model.

Kinda is, considering that the frequencies for each note are a standard and used by all equal temperament instruments.

Guitars are almost never perfectly in tune according to that standard, but like I said - people generally don't mind.

yes, I am aware that conventional guitars have fundamental issues with intonation in equal temperament systems.

this has not prevented it from being a versatile instrument that is quite capable of being played “enough” in tune with ensembles of other instruments, such that the vast majority of people hear zero problems.

how is what we hear in music less relevant than whether or not a given instrument is not perfectly in tune, mathematically speaking, if that variation in tuning is imperceptible to human hearing?