Dissonant notes on certain strings - What could cause this?

That demo shows the problem very clearly. Great job on that! As others have mentioned, the first thing I'd look at is string height on that string. If you have any way of measuring it, check it. Visually, is it lower than the others. I don't suspect a neck/truss rod issue, since it isn't doing it on the other strings.

The first thing I'd try is raising that string just a little. If you don't have tools to measure, count your turns so you can return it to where it is if that's not the issue. If it's not, there are several other things to check, but check this first.
 
The first thing I'd try is raising that string just a little. If you don't have tools to measure, count your turns so you can return it to where it is if that's not the issue. If it's not, there are several other things to check, but check this first.

But if you do that make sure not to mess with the trem baseplate screws (phillips head) but with the three individual saddles themselves. Just give them about 1 turn clockwise on both (two on each saddle). This is also easy reversibel if that won’t solve the issue.
 
But if you do that make sure not to mess with the trem baseplate screws (phillips head) but with the three individual saddles themselves. Just give them about 1 turn clockwise on both (two on each saddle). This is also easy reversibel if that won’t solve the issue.
YES! Don't mess with the base plate screws, ONLY the saddle screws.
 
While terms when describing sound are often misused, I think it helps when describing them, if they are used correctly. In this case, I would not describe this as dissonant notes, but as fret buzz. Dissonant notes are "clashing" notes used to create tension... think Alice In Chains vocal harmonies. This is more of a noise, than a note.

That said, your video very clearly shows the problem, so that is good. But from your original explanation I was expecting weird harmonics or ghost notes or something. This is a noise that is probably caused by fret buzzing and may be a very simple fix of raising the saddle.
 
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That demo shows the problem very clearly. Great job on that! As others have mentioned, the first thing I'd look at is string height on that string. If you have any way of measuring it, check it. Visually, is it lower than the others. I don't suspect a neck/truss rod issue, since it isn't doing it on the other strings.

The first thing I'd try is raising that string just a little. If you don't have tools to measure, count your turns so you can return it to where it is if that's not the issue. If it's not, there are several other things to check, but check this first.

Ok I tried raising the G string a little bit, and then a lot... 5mm at the 12th fret! The issue is still present (though slightly less apparent simply because of the string's distance to the pickups making everything quieter in general.)

While terms when describing sound are often misused, I think it helps when describing them, if they are used correctly. In this case, I would not describe this as dissonant notes, but as fret buzz. Dissonant notes are "clashing" notes used to create tension... think Alice In Chains vocal harmonies. This is more of a noise, than a note.

That said, your video very clearly shows the problem, so that is good. But from your original explanation I was expecting weird harmonics or ghost notes or something. This is a noise that is probably caused by fret buzzing and may be a very simple fix of raising the saddle.

Fair point. I wasn't sure how to describe it or even exactly what it was I was hearing.
 
I ran into something similar when I bought my SE Custom 24. I tried lots of stuff, and nothing solved it until I heard a dude playing with a slide and thought, “that sounds a lot like my issue”. I checked the saddles, and noticed that they are rounded to facilitate the way the trem works. I had already blocked the trem, so I filed the front of the offending saddles to make the point of contact sharper. That fixed it for me.

That's interesting, though I hope it's not the case! I'm surprised it's not more of a well known issue if the design of the trem is the cause though.
 
Ok I tried raising the G string a little bit, and then a lot... 5mm at the 12th fret! The issue is still present (though slightly less apparent simply because of the string's distance to the pickups making everything quieter in general.)
Ok, this is interesting. At this point, I'd probably take it to dealer for a setup.
Fair point. I wasn't sure how to describe it or even exactly what it was I was hearing.
Yes, and I didn't mean that to sound critical. There are probably a bunch of guys here who could figure out the problem if we played the guitar, but when trying to offer help from the outskirts of the internet, the description is probably the only real chance we have to help. I grew up in the car business. The mechanics and service managers had running jokes about peoples descriptions of the noises their car was making when they had a problem. One of my favorites was "it has a rattle in the dash once I get it out on the highway." This rattle in the dash was a REAR tire that was out of balance. The driver, a non-smoker, had the ash tray full of change. The rattle in the dash, was the changed in the ashtray rattling due to the actual problem which was a rear tire out of balance. If you were ever around the car business, there are many more like that one.

But to your issue... I'm thinking it's a saddle issue. If you bought it new from a dealer, just take it back for a setup.
 
Ok, this is interesting. At this point, I'd probably take it to dealer for a setup.

Yes, and I didn't mean that to sound critical. There are probably a bunch of guys here who could figure out the problem if we played the guitar, but when trying to offer help from the outskirts of the internet, the description is probably the only real chance we have to help. I grew up in the car business. The mechanics and service managers had running jokes about peoples descriptions of the noises their car was making when they had a problem. One of my favorites was "it has a rattle in the dash once I get it out on the highway." This rattle in the dash was a REAR tire that was out of balance. The driver, a non-smoker, had the ash tray full of change. The rattle in the dash, was the changed in the ashtray rattling due to the actual problem which was a rear tire out of balance. If you were ever around the car business, there are many more like that one.

But to your issue... I'm thinking it's a saddle issue. If you bought it new from a dealer, just take it back for a setup.

Ha! I left a cricket ball in my car once and then wondered what the banging noise in the back was. Thankfully I realised before I took it to a mechanic.

Unfortunately I bought the guitar from eBay so I can’t take it back for a setup. I knew it was a risk but being left handed it’s very difficult to get hold of guitars in stores. I’ll find another tech to take it to.
 
Yes, that looks not right. But it’s any easy fix, just tighten the tremolo springs till the bridge is parallel to the body. See here:

 
Yes, that looks not right. But it’s any easy fix, just tighten the tremolo springs till the bridge is parallel to the body. See here:

Yes, do this! And, after you do it, re-check your string heights.

When doing this, tighten a couple twists with the screwdriver, then retune the strings to pitch. Repeat these two steps until you get a perfectly level vibrato, and strings tuned to pitch. THEN after getting it right, re-check those string heights. 4/64th inch at the 12th fret is about right.
 
Too bad for you to have this problem, your trem is too tilted forward, it's the first thing I would do, after I would change the strings, rare but not impossible to have failures, and check the intonation.
 
Would it be worth swapping the saddles around to see if the issue changes strings with it? I assume they're identical to each other and not intended for a specific string.
 
I think that would be poking around in the dark now. Is really hard to tell if we can't see the guitar and issue in person. One thing you could check, if you havent done already, would be the neck relief. Put a capo on the first fret, fret the string with (in your case) left hand and check the air between the string and the 8th fret. That is where the bow is the most proncounced in general. Should be around 0.2-0.3mm. If you don't have a feeler gauge at hand you can check by slightly tapping on the string to see if there is any air between at all. Maybe you can find some substitute with that thickness to check. I think thats the last thing you could do before you have to get the nut, the neck, the frets and the saddles checked.
 
@Jaymond
Check that every nut and screw is snug. I had a similar issue with a (not PRS) guitar.

TLDR
Remove the knobs and make sure that the nuts are snug. I'd also look at the tuners and tuner knobs.

Longer story
This was on a bucket-list guitar that had developed an annoying resonance - almost like a zinging sound, just on the upper three strings, just in the upper frets. This is very similar to what I hear in your video.

After checking all the regular points of contact (nut, bridge, frets) and then checking intonation and relief, adding fabric to mute the strings above the nut and below the bridge, I just gave up and went on to play other guitars. Occasionally, I'd pull it out because it is a very special guitar, and I couldn't imagine parting with it. Each time, I'd put it away because it was too annoying to play. After years of this (I've had the guitar for nearly three decades), a few months ago, I discovered that the nut securing the tone control pot was just a little loose. As soon as I tightened it, the annoying zinging sound went away.

Best of luck with your guitar.
 
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I think that would be poking around in the dark now. Is really hard to tell if we can't see the guitar and issue in person. One thing you could check, if you havent done already, would be the neck relief. Put a capo on the first fret, fret the string with (in your case) left hand and check the air between the string and the 8th fret. That is where the bow is the most proncounced in general. Should be around 0.2-0.3mm. If you don't have a feeler gauge at hand you can check by slightly tapping on the string to see if there is any air between at all. Maybe you can find some substitute with that thickness to check. I think thats the last thing you could do before you have to get the nut, the neck, the frets and the saddles checked.

The neck relief looks about right from what I can tell without a gauge. The issue is still there but I feel like I’m learning a lot about how to properly set up a guitar which is something I should have learned a long time ago.
 
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