Just Intonation

But it's not always the difference between "Just" tuning and even temperament. Guitar is an even-temperament instrument by design but it requires a bit of attention to first achieve that fully.

Also I was wondering how your B-string is 11 cents flat after you have tuned it by comparison to a reference instrument. So I'll assume a "special case" that in practice amounts to more of a general case than people think. In your particular case I would then think you are fretting the B-string when you tune, therefore finding it flat when played open. Or maybe the "intonation" on that string is not correct resulting in the string length being too long so that the fretted notes get relatively flatter than they should be as you go up the fretboard?

Probably the biggest percentage of players tune open strings by comparison to references, then find notes fretted on the B-string to be slightly sharp, especially in the lower positions.

When playing along with a piano sometimes one of the tricks was to slightly detune the B, ending up, it seems like you've got now. Where the fretted C agrees with the piano well, but the open B is a little rough together.

On a conventional fretted fingerboard each string ideally plays in equal temperament when fretted, and this is supposed to be in equal temperament relative to that string played open. But things are not always like they are supposed to be.

Usually there is no "zero fret" and the slots in the nut are not as deep as as they could be, mainly in order to avoid buzzing when played open. Careful adjustment always needs to be made here. String deformation or stretch can also be more signficant in the lower positions, depending on manual playing technique. Beyond that Buzz Feiten addressed this his own way.

You've got to first determine your perfect gauge and composition for each string optimized for that instrument at a certain tuning reference such as A=440 (after that you need to stick to the exact replacement strings), and then each corresponding string height and intonation are meticulously adjusted at the bridge saddle at that particular tension. What you then have is every string starting at the same point from the nut but all ending up at slightly different lengths over the same simple fixed geometric layout of mathematically even-tempered frets. This compensates as much as possible for the fretting process at that particular gauge & tension, but still doesn't quite get you to the complete even-temperament that the geometric layout is supposed to deliver. And if you're going to play along with some just-tuning instruments you could use some further tweaking, but might as well make the guitar sound as good on its own as a foundation.

You want to do all that when the strings are well broken in but not worn significantly. (Or with strings of comparable age and use compared to performance or recording sessions if very new strings are utilized on those occasions, however unstable that can be.)

Beyond that then you might think about things like a "compensated" nut ala Feiten[0] or Music Man[1]. Within the narrow range available this has offsets at the opposite end of the neck from the saddle. So then not every string starts at the same point at the nut either, and not only do they all have slightly different string lengths, but they are all more-completely offset above the common fixed fret pattern.

Then even more drastically there's the staggered frets as seen on the True Temperament[2] guitar necks. I can only imagine that's the kind of thing posted on kagi.

Or you could "just" move up to heavier strings where the deviations in cents decline mathematically overall due to materials behavior, physics, and trigonometry. Tuning discrepancy is usually the most prominent using very light gauge strings like Wimpy or Extra-Wimpy. Plus actual instrument tone increases with tension within reason in a mathematically rewarding way. It really has a hard-to-pinpoint effect for listeners that gives a more professional impact when you have high quality, thicker strings at higher tension for better tone, along with better intonation and better tuning than average.

Or maybe just a heavier B-string, the lowest-effort step that could be taken.

Or play a regular spanish guitar with nylon-style strings which are basically OK without any nut or bridge compensation at all.

Most times the best way to get the most resonance out of the instrument is if all the open strings sound good when played together. So regardless of whether you use tuning fork(s), electronic tuners, piano or whatever, you still might need to tweak the guitar accordingly since you want it to at least sound the best it can on its own. You're going to be playing an even-tempered instrument in a more-just world than you can do perfectly no matter what, it's always going to be up to you to make some kind of minor compensations. The fretless string players can instinctively compensate by feel as they go along without the restriction of the fixed fretboard, if the only adjustment you can realistically make is by turning a mere 6 knobs in advance, as always depending on the situation that's going to need to be finalized very carefully by ear as might be needed for solo or ensemble playing.

It's kind of like trying to exactly represent integer multiples using only floating point values, but worse. You've got a continuous analog range using the tuning knob, but you can not go exactly to any one desired setting nor even return precisely to a previous setting. From that point you've got a fixed series of floating-point intervals as notes are fretted up the fingerboard.

Another hint is to manually deaden the unplucked strings when tuning so they are not allowed to vibrate in sympathy with the one you are trying to tune. Otherwise this can throw off electronic tuners more so than it confuses the human ear. Or sometimes even worse there is stray noise or other people trying to tune at the same time.

[0] buzzfeiten.com

[1] https://www.ultimate-guitar.com/articles/features/guitar_tec...

[2] truetemperament.com