rick-slo wrotes:
"Saddle recession helps to compensate for string stiffness..."
This is a matter of some discussion. Gore's intonation model was based on the differences in the way the tension changes as the string is depressed. If you can accept his math he showed that the stiffness model is not a very good fit to what happens with strings. As always, there is no 'perfect' model, and I don't think anybody will argue that stiffness can't have an effect, it just doesn't seem to be the major one.
One fly in the ointment is that the guitar itself can affect the amount of compensation needed. Vibration of the top can 'feed back' into the string and alter it's pitch. This is usually only noticeable on very responsive instruments, and normally only in the lower range, but it can make a difference if you're looking for the best possible intonation.
It's also necessary to keep 'intonation' and 'temperament' straight. It's mathematically impossible to construct a scale that will sound good for all keys, so musicians have to compromise ('temper' the scale) shifting the pitches of notes depending on the circumstances. Guitars default to 12-tone Equal Temperament, in which all of the semitones are musically the same size (so the frets are straight), and every major key is equally 'out' in the same way (so you can modulate freely). Intonation is set up to produce the 'correct' pitches for that temperament, but once you start to hear the problems (major thirds are 'off' by a lot!) they never go away.
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