#3
While that website contains much information that is useful it also contains some that is misleading, particularly the references to nut compensation which is based on a misunderstanding of guitar physics (although to his credit he doesn't claim to endorse some of these ideas).

Intonation is the process of compensating for the changes in pitch which result from stretching the string when it is pressed down to the fret.

We do this by lengthening the sounding length of the string fractionally by moving the saddle.

The received wisdom - which you see published on every website and book about guitar repair - is that you use the harmonics at the 12th fret to assess the pitch or the fretted note at the 12th and make adjustments accordingly.

If you intonate at the 12th however, your intonation will only be "accurate" up to the 12th fret.

The problem is that modern guitars use arc relief to obtain low actions. Arc relief is the barely perceptible curve in the fingerboard which allows room for the strings to vibrate. It is controlled by careful adjustment of the truss rod and enhanced by meticulous fret levelling so that low action can be achieved in the upper register without the buzzing in the lower register which would occur if the neck was dead straight

The amount by which the saddle is moved to compensate for the tension increment represents an increasing percentage of the string's sounding length. On a guitar with a dead straight neck the string's distance from each fret increases at a constant rate so there is approximate parity between the amount of compensation needed at each fret and the amount given.

The effect of arc relief is to cause a flattening of the angle presented to the string by the fret plane so that from about the 12th fret onwards the gap between the string and the fret changes very little; the string is, in fact, almost parallel to the fingerboard. so the amount of compensation needed changes little between the 12th and the 19th frets.

The saddle displacement however represents an increasing percentage of the string's sounding length with the effect that the notes above the 12th will sound increasingly flat if the intonation is fixed at the 12th fret.

Part of the skill of intonating a guitar is tempering the intonation to even out the errors between the 12th fret and the higher ones. To this end I use reference harmonics lower down the string to assess the pitch of notes above the 12th.

A further complication is the presence on stringed instruments of inharmonicity.

Inharmonicity is the acceleration of the higher harmonics as a result of the additional forces contained in the body of the string. Strings with a short length and a large cross-sectional area are most affected. High end harmonics on guitar strings are affected because the very short lengths of string over which they operate are behaving more like vibrating bars than strings.

The natural harmonic spectrum contains harmonics which exist on the string in the ratio of 1:2:3:4:5:6. Each subsequent step ratio (i.e. 1:2, 2:3 etc.) represents a unit of harmony or interval and our brains respond the these so that we seek them out as "true". Our sense-perception works on a system called pattern recognition. Unlike a meter our brains don't measure frequency, instead we assess pitch. When inharmonicity invades the harmonic range (as indicated above) we tend to assess the overall pitch of the note as flat, even if it measures exactly correct on a metre.

A good technician will have learnt to strike a compromise between all these requirements.
Last edited by octavedoctor at May 9, 2008,