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Dominic R -> RE: nut compensation (Apr. 12 2012 16:13:02)
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Thanks guys that's not how it works but it is a common mistake. Firstly, nut compensation effects intonation at all frets, not just the open string. So using a cappo does not eliminate the effect of nut compensation just as playing a bar cord does not.
This is because you tune the open string using the new nut position and each fret is in a different position relative to the uncompensated nut. Imagine that the fretboard is cut longwise into 6 segments, nut compensation on the G string of 2mm is like you have moved the G string segment and all its frets towards the nut by 2mm. Instead the nut is moved but it the same effect. And using this method accurately both nut and saddle compensation must be calculated together because changing one means the other one is wrong. The mathematical optimisation model does this for us and cycles through all the possible combinations of nut and saddle comp and finds the one that minimises the sum of the absolute values of the cents error at each fret and does it for each string.
So lets look at the facts.
A normally compensated steel string guitar that's been properly set up, good action including at the nut, bit of relief etc etc, will have perfect in tune open strings and be in perfect tune at the 12 fret. However, all the notes between the nut and the 12th fret are sharp to some degree with the greatest degree of inaccuracy around fret positions 1 2 and 3. The E string at the first fret has an error of over 6 cents, the A about 6 and the other strings about 4 cents. This is enough to be heard, particularly when playing some intervals that include an open string as the intonation error combines with the error built in to the equal temperament scale. Once we are past the 12th fret all notes become increasingly flat and again the E string become flat by around 7 cents at the 18th fret.
Subtracting 1.5mm from the nut end of the fretboard can reduce the errors around the first few frets by almost 2/3rds. That in itself is a vast improvement.
However, fully modelling the variables for the guitar and the player including strings, action, relief and playing pressure, the intonation errors can be virtually eliminated. The error at the first fret is reduced to around 0.5 cent and at every other fret, the error is less than 0.1 cent. This is a significant improvement over standard saddle compensation and will be a delight to those with sensitive ears.
Cheers
Dom
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