Correct me if I'm wrong but, if the formula doesn't change, and is all based on the scale length of the guitar, couldn't he just adjust the intonation while in Eb?
If he's tuned to Eb, and he's adjusts for an Eb at the 12th fret, then wouldn't that result in proper intonation anyways?

Eb is the tuning I want this guitar in. Last time I took it to the tech he asked specifically for the tuning I wanted to keep it in and set it up for.[/quote]

Eb is the tuning you return to after setting up the intonation. your intonation is set up according to the scale of your guitar and the distance is from nut to saddles.
For proper intonation, at the 12th fret your tuner must read the same frequency.
You would have to redesign the guitar if you wanted to tune to different tunings
If you tune to drop D or to Open G or to DADGAD, the formula does not change. you tune to whatever tuning you wish after the intonation is set correctly.
Your tech is mistaken... if your intonation is off from the scale it was designed for , you will never be able to have your guitar in tempered tuning...period..[/quote]

Correct me if I'm wrong but, if the formula doesn't change, and is all based on the scale length of the guitar, couldn't he just adjust the intonation while in Eb?
If he's tuned to Eb, and he's adjusts for an Eb at the 12th fret, then wouldn't that result in proper intonation anyways?[/quote]

No because the 12th fret is the mid point or the octave point. So if you move the saddles either way you still have the problem of from nut to the 12fret that is a set lenght which is not adjustable. Your open string plucked will not coincide with the string pressed at the 12th fret and plucked.

Look at it this way, when you tune to Eb or E or D or even E# you are loosening or increasing the tension of the string. You are not lenghtening or shortening the string between the contact points of saddle and nut.
If you read into a guitar building book, you will find certain formula's and certain scale lenghts for a guitars nut to saddle distance. I don't have all the technical reasons but suffice to say that it is a mathematical equation, if you change the data in an equation, you will arrive at a different summation.
Music is math, ( as it is written and arranged ) it follows mathematical progressions.
It is all based on frequencies which all have numerical values. change the numbers and the results change or in this case will be incorrect.
As I mentioned earlier the fretboard corresponds to a tempered system, not exact but a compromise where certain notes are not going to be exact as they should be in a perfect world.

If you wish to get an idea on this kind of theoretical reasoning, I would suggest this book.

" Godel, Escher, Bach : An eternal golden braid, A metaphorical fugue on minds and machines in the spirit of Lewis Carroll.
By Douglas R. Hofstadter.

Godel was a highly revered mathematician, Bach needs no introduction and Escher was the graphic artist who experimented with 3 dimensional space continuum in architectural renderings in pointillism...

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