This page offers some of my views on how to set up a guitar (primarily electric) for good playability and intonation. I'll also present some ideas on how to tune the instrument.
Before making any intonation adjustments or setting the action or neck relief, check the nut slot height. Ideally, the strings should sit at the same height as if the nut were just another fret. (Guitars with a zero fret achieve this by actually using a fret in place of the nut). If the slots are cut too deep, buzzing may be unavoidable. If too high, the action will be uncomfortably high near the nut, and intonation will be affected more, because fretting will increase the string tension more.
TODO: diagram
The slot heights can be checked with the guitar unstrung, using a short straight edge touching the first two frets and the front face of the nut. Where the edge meets the nut (or just above) is where the bottom of the string should be.
To check the heights with strings on and tuned up, press the string down to the frets between the second and third fret (as if you were fretting the string “backwards” at the second fret). There should be just the smallest amount of clearance between the string and the first fret (check for play using your other hand). If there is none at all, your nut slots may be cut too deep, or you may have a problem with fret wear. If there is more than about half a mm, consider deepening the nut slots (but be careful, or have a luthier do it for you).
TODO: diagram
Repeat for the other strings.
* bridge height? slant angle?Guitar necks are constructed to have a slight upward bow (“neck relief”), to minimise fret buzz across the fingerboard by accommodating the elliptical profile of the vibrating strings. However, if there is too much relief, the action will be too high and playability and intonation will suffer. If there is not enough, regions of the fingerboard will suffer fret buzz that may be difficult to correct by raising the action. Most guitars have an adjustable metal truss rod in the neck that pulls against the strings when tightened, straightening the neck. Loosening the truss rod allows the neck to bow upward more.
The neck relief will affect the action, and you don’t want to be using action adjustments when the root cause is too much or little neck relief, so set up the neck relief first. The amount of relief or bow in the neck can be measured with a feeler gauge. To make sure the measurement is independent of action, put a capo at the first fret, and hold the string down with your finger around the 15th fret(?). Measure the string height/clearance at/above the ?? fret using a set of feeler gauges. [TODO: table of measurements - varies with scale length?]
Correct the neck relief with strings at playing tension. action roughly set. You can expect some interaction between action, neck relief, saddle compensation and nut compensation, and of course changing string gauges will throw everything out of whack!
Intonation adjustments: Saddle compensation is for increased string tension due to fretting. This inrceases towards the bridge (but probably decreases again due to the flat area where the neck joins the body).
Mind you, does the effective fretting happen at the centre of the fret, or a little towards the bridge from there? And is the nut placed where the centre of the 0th fret would be, where the effective fretting point of the 0th fret would be?! Subtle, but could be around 1 mm difference...?
Changing the string height or “action” affects playability, fret buzz, and intonation. Unlike the neck relief, the action affects the entire fretboard more-or-less uniformly. A higher action is less prone to buzz but fretting requires more force, which also pulls the note sharper on the higher frets. A lower action is easier to play, but may be prone to buzzing, when the vibrating string strikes frets other than the one being played.
Because the action affects the intonation, the action should be set up first.
TODO: how to measure and table of common/typical values
The string length adjustments at the saddle are to compensate for the progressive sharpening of notes as you ascend the fretboard. Each time you stop/fret a note, you increase the string tension, thereby raising its pitch beyond what you would expect given the fret placement. Because of neck relief, neck angle, bridge height, and general action (string height), frets higher on the fingerboard have higher action and have to be stretched more to be fretted, so they experience greater sharpening in pitch. By lengthening the string at the saddle, you can compensate for this sharpening. Remember that a longer string has a lower pitch, all other things being equal, and lengthening the string at the saddle will lengthen the higher frets by a greater proportion than the lower frets. [Illustration?] If a high fret plays sharp compared to a low fret, lengthen the string at the saddle. If a high fret plays flat, shorten the string.
You may not be able to get all the frets exactly in tune with each other, but you should be able to get within a few cents if the frets are correctly positioned
Two important points: when setting the saddle compensation, do not use a harmonic or the open string as a reference pitch. Unless you have already set up string length compensation at the nut, the open strings will likely play flat compared to the rest of the fingerboard. Harmonics suffer from the same problem. Many guides I've seen suggest using the 12th-fret harmonic for intonation, comparing it with the fretted 12th fret. However, in general, a fretted note is expected to play sharp compared to an unfretted one (such as the open string or a harmonic). Trying to align the harmonic and the fretted note at the 12th fret will not necessarily give correct intonation. Harmonics in general are also problematic because you are trying to intonate and tune the guitar for equal temperament, and harmonics other than the octaves will not lie exactly on a chromatic note pitch. So, only compare apples with apples: a fretted note with another fretted note on the same string.
[use a high-precision tuner...stroboscopic tuners are particularly sensitive to small deviations. Link to my strobe tuner in Pd? Implement something for Android and/or iOS?]Nut compensation is to ensure that each open string plays in tune with fretted notes on the string. An open string is under less tension than a fretted one, so the open string will tend to be flat if the nut is where the 0th fret would be.
Most guitars do not have adjustable nuts. Ideally one could adjust the height and length of each string at the nut. Perhaps I should invent one.
TODO: mention Earvana, Buzz Feiten.
Now that the neck relief, action, and intonation have been set up, you can now attempt to tune the instrument precisely. Here I assume that tuning to equal temperament is the aim. In equal temperament, an octave is an exact doubling of frequency [mention stretched piano tunings?], and the octave is uniformly divided into 12 semitones or half-steps. That is, each semitone has a frequency of exactly [formula]. Because a certain amount of beating between harmonics is normal with equal temperament, I recommend not using your ear alone to tune. An electronic tuner (especially a stroboscopic tuner) offers an impartial, accurate and precise means of setting the tuning to the correct absolute pitch.
I have heard guitarists and bassists use harmonics on adjacent strings to tune, adjusting the string tension until the beating stops. This is misguided. The only harmonics that match pitches on the equally-tempered scale are the octaves. Furthermore, the error in tuning one string to the previous one will accumulate as you progress throuh the strings. [TODO: link to Flutini]Problem: fret buzz. If it's just in one small region of the fretboard, especially higher up, it's probably insufficient neck relief. Try loosening the truss rod to allow the strings to pull the neck forward further. If it covers a large area of the fingerboard, the action is probably too low. Remember that it could be a combination of the two.
Problem: fretted notes are sharp when tuned to the open strings. This is a problem with intonation in the general sense, but specifically a problem with the nut (not the bridge adjustments). Many guitars place the nut where the “zeroth” fret would be. This will generally result open strings being flat compared to the rest of the instrument, because the open strings are not subject to the extra tension due to fretting. A high nut slot height will exaggerate this problem, though it cannot be corrected by deepening the nut slots alone! Even guitars with a zero fret instead of a nut will have this problem.