OK. just wanted to check. In taht case, either the frets haven't been installed in the correct position or (more likely) the strings are very high.
Not recommended. A very 'tight' V shape can work (say less than 10°), but with a full equilateral triangle shape with a 60° angle, the sides of the slot don't keep the string in place very well, which can cause problems when playing.
Yes, or just slightly greater.
Lets take an extreme example to understand what's happening:
With the strings 20mm off the fretboard at each end, you have to increase the string length significantly to be able to press it down against the fret. To do that, you have to stretch the string by roughly 1.2mm if you fret at the 12th fret, and to do that, you have to put the string under a lot more tension. If you increase the tension of a string, its pitch goes up.
If you then fret that string at the first fret, then you have to increase the string length by 5.5mm, which means you put the string under a lot more tension to do so, so the string goes even sharper.
Now bring the string height down to a more sensible 2mm at both ends. At the 12th fret, you only have to stretch the string by 0.012mm, and at the 1st fret, by 0.059mm. That's not a huge amount, but it still means that at the 1st fret, the note is still going to sound sharper than at the 12th fret.
By intonating and moving the saddle back to increase the overall string length, the position of the 12th fret is effectively moved in relation to the string length, so that the distance from the 12th fret to the saddle is now just longer than half the scale length, which lowers the fretted note pitch, and which offsets the extra tension created by fretting it, so the open string and 12th fret note are both in tune.
But this isn't enough to get the first fret in tune, as it still requires more tension to fret than the 12th fret does. And which is why you are noticing the lower frets play sharp although you've intonated at the 12th.
The only way to help this is to lower the height of the strings at the 1st fret in relation to the height of the strings at the 12th fret. We do this by adjusting the nut slot depth to be as low as possible without the strings buzzing on the first fret.
Bring the height of the string at the first fret down to 0.3mm, and you actually then need to stretch the string less to fret it there than you do with 2.0mm at the 12th fret (0.0013mm vs 0.012mm).
Now a lot of this is compensated for by the position of the frets being adjusted for this effect, but any guitar tuning and fret position is always a compromise. It can never be in perfect tune, as such a thing doesn't exist. But you can certainly get it good enough for rock 'n' roll.
So you should now see the value of a good set-up, with a medium to low overall action and the nut set so that the strings are close to the first fret, and not a long way above it.








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