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If it sounds like I'm overthinking it that's just because I'm trying to work out if there is a solution that is not too much of a pain (like having to swap saddles when changing tuning long term)
also standard and drop-D
Take your guitar to a tech and have them cut a new custom intonated saddle (I've done it for 2 acoustics using the buzz feiten intonation offsets) and it will sound better for everything.
Then consider an earvana nut if your tuning problems are open chords in frets 1-3.
What is going on here (at least as I see it) is a combination of two things.
* The built-in errors of equal temperament, in particular major thirds (which are 13.7 cents sharp)
* Intonation errors on your guitar. (Or on almost any guitar, or any other fretted instrument for that matter.)
All normal guitars play a little sharp on the first few frets. This varies from string to string, and with string type. In theory, the 6th string is the worst, the 5th string next-worst, and so on, but in practice we tend not to notice it as much on the bass strings. For most players, the thickest plain string is the problem child (B string on normal acoustics), though others strings can be problematic too.
(I met a vivid example of this on my long-scale baritone, which was rather nasty on the 2nd string, a .18 plain. Swap that to a .22 wound (thank you John Pierce!) and magic! A vastly better sound.)
So why are intonation errors worse in different tunings? They aren't. Tuning of a given string (to a B or an A or whatever note) makes no difference worth mentioning. All it does is put the audible errors in different places.
A well-intonated standard guitar is likely to play about 5 cents sharp on the first fret, almost as much on the second fret, and gradually less, becoming perfect in tune on the 12th fret. 5 cents isn't really enough to bother anyone. The problems arise when that tiny 5 cent error is added to the 13.7 cent error of a major third, making the note almost 20 cents out, which is enough to hear. It's not only major thirds, major sixths are actually worse (15.6 cents plus intonation error) but it's the thirds you mostly notice.
Some guitarists try to deal with this by deliberately tuning slightly out. For example, in my normal standard tuning I habitually tune the B string very slightly flat and, on average, get a better sound that way. James Taylor has a useful video on You-tube talking about his method, which is considerably more advanced. Some players re-tune between songs depending on the key of the next tune, tweaking the tuning for one or two particular chord shapes. (That's only ever going to work if most of the song is repetitive: melodically varied tunes won't benefit.)
However, when you switch to an open tuning, you are putting the errors in different places. Your normal tricks won't work, and quite possibly make things worse. You could try some different tricks (different slight mis-tunings) but in the end they are never going to fix the basic problem, which is that normally setup guitars don't intonate correctly on the first few frets, and sometimes those very small errors interact with the built-in "errors" of the equal-tempered scale and produce a nasty sound.
Your answer, then, is to get the guitar set up, as far as possible, to play in tune all over the fretboard. (It doesn't matter which tuning you use, in tune will be in tune regardless.) And to achieve that, the first step is getting all the basics right. Many excellent guitars don't bother with compensated saddles and play well just the same, simply through getting the basics right. At home I have seven good quality guitars: two of them have compensated saddles, five do not. They all play acceptably well intonation-wise; the very best one in that regard (a Cole Clark) indeed has a compensated saddle - but so does the least-in-tune (a US-made Guild).
The second step is to compensate the saddle. That gets us closer.
The third - and I reckon this is where you need to be going - is to compensate at the nut as well. This seems counter-intuitive. When it was first mentioned to me I said "Nonsense, it's impossible - the moment you fret a note, the nut compensation becomes irrelevant". I was wrong, of course. Suppose a string plays sharp. It is tuned correctly for the open note, and the 12th fret note is also correct, but it plays sharp in the first few frets. Now move the nut (just for that string) a very small distance towards the first fret. Retune down a fraction to bring the open string back to the exact note. But the fret hasn't moved. So when you play a note on the first fret, it is slightly flat compared to the note it used to make, and that is exactly what we want - it now plays in closer to perfect tune.
For most of us, this probably isn't worth doing. We have learned how to get sounds we like from the instruments we have. Often much of that learning is unconscious. But in your case, with a finely attuned ear (we know you have this because otherwise you wouldn't be bothered by the problem) and many different tunings to negotiate, I reckon a compensated nut might be the way to go.
(As an aside, I'm wondering whether I should ask my luthier to do that on the new baritone he is going to start building fairly soon. Next time I see him I'll ask him what he thinks.)
You have to find a way that works for you
It’s most likely the nut grooves aren’t deep enough, so you’re pulling the strings sharp as you fret them - by different amounts depending on the tuning, since the pitch change varies with tension. (A lower tuning will have more pitch rise for a given distance to the fret.)
It’s not true that all guitars play sharp over the first few frets - before compensated nuts, many makers moved the whole nut very slightly forwards as well. If this is done and the nut isn’t too high then it will play perfectly in tune - or at least in equal temperament. To get it even ‘more in tune’ you need a fully compensated nut like the Earvana.
I would start by looking at the nut grooves - on almost all guitars that haven’t had a good set up, they won’t be deep enough. Fret each string at the third fret and look at the gap between the string and the first fret - it should be tiny, less than a quarter of the string diameter and preferably as little as a tenth of it on the thicker strings.
"Take these three items, some WD-40, a vise grip, and a roll of duct tape. Any man worth his salt can fix almost any problem with this stuff alone." - Walt Kowalski
"Just because I don't care, doesn't mean I don't understand." - Homer Simpson
https://www.amazon.co.uk/gp/product/B08M42WR5D/ref=ppx_yo_dt_b_asin_title_o01_s00?ie=UTF8&psc=1
https://www.musicnomadcare.com/Products/Nut-Height-Gauge
I know how to do it with feeler gauges or by touch, but because I don't do it very often, I need to look up the spec and youtube tutorials every time. this tool makes it a little easier to remember
I'd say any guitarist should consider getting one of these if they plan on owning more than 1 or 2 guitars, and/or buying and selling guitars over time
This also made for a more balanced feel across the neck
:-)
Music Nomad 6 pc. Acoustic Guitar Diamond Coated Nut File Set - Light/Medium Strings (MN670) : Amazon.co.uk: Musical Instruments & DJ
I lower nut slot depths by stages each time I change strings and, doing that, I often find that I reach optimal playability at string heights above those recommended by the gauge. I suppose that has to mean that I actually like a high action at the nut in comparison to the 'average'. Also, and call me Mr. Stupid, I find it quite difficult to use the tool and can't tell when I'm using the right blade. Overall, I think I prefer doing it by 'feel'. This would not be a practical approach for a luthier or a 'techie' lowering action for someone else. Also, my technique takes months! But I've not cocked it up ever. Yet. :-)
Exploring the world of modal tunings - The Guitar Social
I have adjusted them by feel as well, but it's nice to have the tool to increase confidence when doing that
The tuning used for "The Rain Song" is very nice too