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Intonating

I just got my 4 string EBMM Sterling put back together and I’ve got an intonation issue. The open E is dead on, the 12th harmonic is dead on, but the 12 fretted is very flat, even when bottoming the string to the neck just behind the fret.

How do I resolve it so that all three are in tune?

Thanks for any advice.
 
The octave harmonic at the 12th fret is ALWAYS an exact octave of the open string and has nothing to do with the bridge adjustments. You have to compare the open string (and/or its 12th fret harmonic) as a reference to the fretted note.

If the fretted note is sharp of the open string, that means the string between. The saddle and 12th fret is too short so you need to make it longer by moving the saddle farther from the nut. If the fretted note is flat or means the string is too long between the saddle and 12th fret, so shorten the string by moving the saddle towards the nut.
 
Okay, thanks. I would have thought that since getting a higher frequency, easier tuner-reading note that puts your hand in the right position to play the fretted note would be the way to go since it's identical in fundamental pitch as the open string.

Are there reasons why it's better to use the open string?
 
Okay, thanks. I would have thought that since getting a higher frequency, easier tuner-reading note that puts your hand in the right position to play the fretted note would be the way to go since it's identical in fundamental pitch as the open string.

Are there reasons why it's better to use the open string?
Better - not really. But the harmonic is not identical in fundamental pitch as the open string. It's an octave above the fundamental of the open string. And strictly speaking it's not necessarily an exact octave - in theory it is, in the real world it's sometimes off a bit.
 
I think I was fast and loose with terminology saying the harmonic is the same fundamental pitch - thanks for clarifying.

The strictly speaking part of your comment is what seems to contrast with JTE's first reply. It's sounding to me like intonating at the 12th fret with a compromise between the open string and the harmonic is the reality. Please correct me if I'm wrong. If that's right as it seems to be for my case, how do you strike a balance?
 
In most cases it make no difference whether you intonate to the harmonic or the open string. Either will be a compromise even if you could get the octave dead on. Get the 12th fret spot on, check the 5th and 17th frets - probably one of them is off a bit. Correct them and the 3rd fret will be off along with the 8th and 14th, etc. It's all a compromise since none of the notes we play have a specific in-tune pitch. For instance, did you know that to sound in tune the note E in the key of C is actually different than E in the key of A?
 
It comes down to having a fretted instrument. It uses even temperament. The notes in a scale are based off a physical phenomenon called the overtone series. In perfect temperament there are 21 notes in an octave. Each note A, B, C, etc has a sharp, a flat, and a natural. Most instruments, with the exception of non fretted sting instruments, could only play in a few keys. As composers started writing with more key changes and fretted instruments and keyboards became more common, a compromise system of tuning was devised. For instance, the pitch difference between a G# and and Ab is very small. These differences were ignored giving what is called even temperament AKA well tempered instruments. So a fretted instrument will never have perfectly intonation at every fret.
 
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