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Ok I understand there is no real solution for this problem yet.
As far as I can see you know a lot about it. Did you ever think how could you build a guitar to work out all the tuning problems?
Thank you very much. I appreciate your answers.
Actually there is no solution... ever.
I'll try and explain more clearly.
Yes, there are a number of things you can do to make a guitar (or any instrument for that matter) better, but there is a fundamental problem with the way music works...
Pleasing intervals between notes correspond to simple rations of frequencies e.g.
Octave 2:1 (i.e. a note an octave above has twice the frequency of the original)
Fifth 3:2
Fourth 4:3
Maj 3rd 5:4
Min 3rd 6:5
etc.
Now it turns out that three Maj 3rds equals an octave (Augmented chord) i.e. C E G# back to C.
if you apply the ratios:
5:4 x 5:4 x 5:4 gives 125:64 which is not quite 2! (should be 128:64)
(or 1.25 x 1.25 x 1.25 = 1.953125)
If you use the normal technique, you make a semitone ratio the 12th root of 2.
This means a Maj 3rd is 4 semitones i.e. cube root of 2 (trust me on this if you're not sure!) or 1.25992.
That means 3 Maj 3rds is exactly 2 or a perfect octave.
(1.25992 x 1.25992 x 1.25992 = 2)
In the first case your 3rds are correct, but your octave is flat in the second the thirds are sharp but the octave is great!
This is a problem for all music, any solution will be a compromise and won't work for everything, but, you can come up with a solution that works for some scales or chords better than others, this is what the guys at true temperament have done, but they still need different versions for different temperament solutions.
Jim