When I am checking intonation I let 1 to 1.5 cents go but I get a bit upset if its 4, 5, or 6! LOL
I'm a person who's never far away from a calculator and one of the most recent concepts I explored was - how many Hz or cents is there in a millimetre?
Most of my errors are in the upper region of the 22nd to 25th fret and up there 1mm is worth about 4 cents
You seem very confident about this, so its occured to me that you have done it. But nevertheless let me put forward my whole argument in one go (something which I have not yet done)
* Note: Before I begin I want to point out that everything I say is pure speculation yet based on the results of examining two guitars I used to own and untold calculations
Perhaps Gibson started off with a 24 ¾” scale back in 1920 (or whatever) then made it shorter over the years yet still called it 24 ¾ but it still doesn’t explain everything to me. But anyway I'll get started
The most common method of calculating fret distance these days (such as a fret calculator) is a perfect mathematical formula of dividing the scale by 2^1/12 or in decimals its 1.05946309436
Perfect mathematical formulas don’t take into account the actual physical elements which vary results to some degree. These involve string thickness, rigidity, tension and length. Then there’s playing action and player’s style and maybe other things I have missed
But what this means is the perfect mathematical formula naturally suits a light gauge string. I think the first reason we need compensation is because a thicker string will not vibrate all the way up to the break-off point (I think that’s what you call it) A very light gauge string like a .009 will vibrate all the way from the nut to the bridge and therefore very little or no compensation is needed on the first string
So a fret spacing that has been calculated on the 2^1/12 method will almost equal the scale on the first string length. And compensation angle is required up to the 6th string which ends up almost a quarter of an inch longer than the scale
I believe the Gibson 24 ¾ inch scale is worked out focusing on the sixth string and compensation is built into the fret spacing. I think they have played around with the compensation over the years to suit the most popular string gauges at the time, rather than the actual scale. And that’s why the distance from the nut to the 12th fret varies. The reason for my point of view:
First of all it measures 24 ¾ inches on the sixth string
It has good intonation all the way up the fret board on the sixth string
The intonation on the first string beyond the 12th fret becomes sharp
It doesn’t match any scale calculated by dividing by 1.05946309436
If it was worked out by the usual method it would have good intonation on the first string, not the 6th string
Always refer back to my note at the beggining *
To further explain - While examining the intonation on my Fender I found it to be good all the way on the first string but on the sixth string, beyond the 12th fret it became flat. If you were to correct this you would spread the frets out beyond the 12th fret, which is what I believe Gibson have done, which explains why it is sharp on the first string beyond the 12th fret (maybe it’s more suited for heavier gauge strings)
The 12th fret on my SG measured 12-9/32 inches. If you double that you get 24-9/16 If you put this into the fret calculator and compare the results with the SG. The 12th fret is the same (obviously) but the SG frets gradually move away so the first fret is closer to the nut and the 22nd is closer to the bridge. To me it looks like there is compensation involved
I have tried numerous ways to get the fret calculator to match the Gibson scale. Most recently, last night I explored the possibility that they moved the nut closer. Nine years ago I tried things like moving each fret back 1.43mm. (I didn’t have Excel or a Casio back in those days, I did it the hard way with a calculator that went 12 digits beyond the decimal point)
So anyway that’s about all I can say but I think I have a good point, based on the results from the guitars I tested. I am very eager to pay-off my new Les Paul and measure its fret spacing and test its intonation
By the way I forgot an important comment when you said "Thank god for adjustable bridges" Before deciding on the Les Paul recently, I went " " that close to buying a guitar that had a fixed tailpiece/bridge. Well you could move it back and forth but you couldn't intonate individual strings