Nuts About Intonation
Why compensate at the nut?
Fretted notes sound sharp compared to the open string because the string is bent to press it against the fret. If the error in pitch is known, an equivalent amount of flattening can be used to cancel out the error by moving the nut position towards the first fret.
The traditional method of saddle compensation is used as well, setting the 12th fret harmonic and fretted 12th fret notes to be the same pitch.
If no nut compensation is used, then the open string and 12th fret notes will be in tune, but the lower frets will sound sharp, gradually becoming more in tune up the fretboard as the 12th fret is approached. This has the most audible effect on open chords, as fretted notes on the first few frets (sharp) are played at the same time as open strings (in tune).
Each string is sharpened by a different amount when fretting. To demonstrate this, bend the top E string by a tone (two frets, two semitones). Look at the distance the string has been bent across the fret. Repeat this with each string, and note the different distances the string must be bent to achieve the same bend in pitch. For example, the top E must be bent about twice as far as the G to achieve the same pitch bend.
The conventional position of the nut (or zero fret) is calculated mathematically (as are the positions of each fret).
My research has shown that some makes are more likely to have the nut incorrectly positioned (due to manufacturing errors). In general, “Fender” style nuts (i.e. where the nut is in a slot) are likely to be correctly placed. “Gibson” style nuts (i.e. where the nut is attached to the end of the fretboard) can be quite a bit out. Floyd Rose type locking nuts are also frequently incorrectly positioned.
If the error is away from the first fret, then the sharpening effect will be increased. If the error is towards the first fret, then the sharpening effect will be reduced.
If the error is towards the 1st fret, but by a large amount, then the first few frets will play flat.
Nut slot height and shape
If the nut slots are not cut deep enough, then the first few frets will sound sharper than if the nut slots are cut to the correct depth. In addition, if the shape of the slot is such that the vibrating part of the string starts “inside” the slot, the effective position of the nut will be incorrect for that string.
It is unusual to find a modern mass produced guitar with incorrectly placed frets, but hand made instruments can have some randomness in the placement, due to cutting the fret slots by hand.
This will not make much difference to players with excellent technique, but for those who play with too much finger pressure, the sharpening due to fretting will be greater with taller frets.
Lower frets prevent the string being bent more than a certain amount, as the finger is pressing against the fingerboard itself, without increasing the string bending.
Player’s fretting technique
When a note is fretted, the player presses the string down until it contacts the fret. In addition, an extra pressure is applied to prevent the string moving around on the fret as it vibrates. Most players will then press even more (perhaps due to the excitement of playing in front of an audience, or just heavy handedness).
Even with a very careful fretting technique, some sharpening will occur on all fretted notes (though not on the open notes).
For new (or freshly dressed) frets, the width makes little difference, but the width is important for worn frets, as the contact point can be moved more.
Fret condition (wear)
As frets wear, the top part of the fret is deformed in such a way as to make the contact point move towards the bridge. This causes the notes to be sharp. Those notes played most often will show the greatest wear, and will therefore be most out of tune.
If the frets have been poorly dressed, they can become slightly asymmetrical in shape. This will cause a random pitch error.
The effect of neck relief is subtle. The action at each fret is varied somewhat by the neck relief. A perfectly straight neck would have a slightly larger action for each fret, from nut to bridge. A neck with some relief might have a lower action at the top fret than at the 12th fret (for example).
Neck Shape (e.g. S-bend, twists etc.)
Any odd shape to the neck can alter the respective action distance at each fret in a non-standard way.
Pickup heights and magnetic effects
If the pickups are adjusted too close to the strings (especially the neck pickup) the string’s vibration can be altered by the magnetic pull of the pickups. The upper frets in particular will sound sharp.
Many single coil pickups have magnetic poles, which can pull the string out of tune from quite a distance. Humbuckers tend to have a bar magnet under the coils, so the magnetic pull is less severe. Some pickups (e.g. Kinman, EMG) have a very low magnetic pull, so they can be adjusted closer without tuning issues.
Action height at the saddle
This affects the degree to which the action increases from nut to the top fret. A higher action will increase the sharpening effect due to fretting.
Altering the saddle position is the most common method used to improve the intonation on guitars and basses. A small extra length is added to the “scale length”.
In the case of very heavy gauge strings, the sharpening effect due to fretting pressure is reduced. Very light strings are more prone to the sharpening effect.
The “dead zone” at the end of the vibrating length is increased the heavier the gauge. It is this “dead zone” that can be compensated for at the saddle.
String condition (age)
As strings age, they become less uniform along their length, which causes them to vibrate in an odd manner. In addition, the part of the string just in front of the saddle is altered in nature by repeated vibration and string bending. It is important to play the strings in a little before making final intonation adjustments at the saddle.
Tuning techniques and accuracy
If the guitar is incorrectly tuned, then it will be out of tune!
There are many methods used by players to tune;
- Electronic tuner
- Tuning fork
- Comparison with keyboard notes
- Unisons on adjacent strings
- Unisons on non-adjacent strings
- 12th fret harmonic with adjacent string fretted at the unison
- 12th fret harmonic with non-adjacent string fretted at the unison
- 5th fret harmonic on low E with open top E
- All the above are good ways to tune, especially in various combinations.
Note that the commonly used 5th fret harmonic, fret on low E, 7th fret harmonic on A (etc) method is flawed, as the 7th fret harmonic is “out of tune” (according to equal temperament).
Also, it is not advisable to tune to a chord, as most players will tune so that the chord sounds “sweet”, by making major thirds flat. Playing another chord with a major third on a different string will produce extreme dissonance.
In equal Temperament, all the semitones are the same “size” (the same ratio of frequencies). This allows fretted and keyboard instruments to be played in any key. In fact, some musical intervals (especially Major Thirds) have a quite pronounced dissonance in Equal Temperament. If the Major Third is flattened by about 13 cents, the dissonance is removed. In some chord fingerings, it is possible to sweeten (flatten) the Major third by bending along the string (not sideways across the string as usual) in the direction of the bridge. This is a tricky technique to master, and works best on wound strings and with lighter gauge strings.
The Harmonic Series
Most guitarists are familiar with harmonics. These are played at the 12th, 7th, 5th and 4th frets. In fact the series goes on, with each subsequent harmonic dividing the string length into more, shorter, parts. When a string is plucked normally, it vibrates at all the harmonic notes simultaneously. As the string ages, its ability to produce the upper harmonics is reduced, and the tome becomes less bright. In the case of very stiff (heavy gauge) strings, the frequencies of the harmonic series are altered, with the upper harmonics becoming progressively sharper.
The 4th fret harmonic is the Major Third (up two octaves). This is the true sounding Major Third, rather than the dissonant True Temperament Major Third.
Stretch Tuning on the guitar
Stretch tuning is used by piano tuners to compensate for the harmonic series frequency distortion caused by thick strings used for the lower notes. The lower notes are flattened slightly, and the upper notes sharpened slightly. This allows the upper harmonics of the lower notes to be more in tune with the upper notes.
In the case of guitars with heavy, stiff bass strings, it can be beneficial to apply a small amount of stretch tuning. This would take the form of slightly flattening the lowest one or two strings, and perhaps altering the intonation setting at the bridge saddle (used by BFTS)
The difference between intonation and tuning stability
Tuning stability measures the ability of a guitar to remain tuned correctly during normal playing. Factors affecting tuning stability include stringing method, tuners (machine heads), nut material and slots, bridge type and materials.
Intonation is a measure of a guitar’s ability, once correctly tuned, to play equally well in tune on any fret and on any string.
Currently available solutions using compensated nuts
The “Buzz Feiten Tuning System” consists of three parts. Firstly, the nut is moved closer to the first fret (reducing the sharpening effect due to fretting). Secondly, the intonation is set unconventionally, with some specially designed offsets from normal. Thirdly, the open strings are tuned unconventionally, with some slightly flat or sharp from the normal equal temperament notes.
Unfortunately, the equal distance compensation used on each string produces a different amount of pitch compensation on each string. For guitars with a plain G, the G and low E will be close to perfectly compensated. But all the other strings will be overcompensated by differing pitch amounts.
The top E shows the greatest error, and the D and A strings are nearly as bad. On these strings, the lower frets will sound flat, becoming more in tune up the fretboard as the 12th fret is approached.
The unconventional intonation settings at 12th fret, and the unusual tuning of the open strings, allow for a degree of stretch tuning.
Unlike the BFTS, the Earvana system is a shaped (and in some cases adjustable) nut, which allows a different amount of compensation for each string. IMO, the offsets are incorrect, being considerably exaggerated. My experiments with the Earvana nut have shown that it is impossible to intonate the guitar correctly, unless the offsets are reduced by altering the shape of the nut.
The non-adjustable versions rely on the original nut position being correct. This is not always the case!
Recently, the American made MusicMan guitars have been fitted with compensated nuts, with individual compensation for each string. The compensation is similar to the Funky Nut, but the material used is very prone to wear and has a relatively high degree of friction. The choice of material is due perhaps to the ease with which it can be molded…
Bent frets (“True Temperament”)
Instead of straight frets, this method uses shaped frets, so that the fret position is moved for each string from its conventional position. This looks amazing (if a little odd), but perhaps the simpler approach is the better one? Also, dressing the frets when they have become worn could not be performed to the same degree of accuracy as with straight frets. (A concave fret file could not be used.)
The Funky Nut
The Funky Nut has a different amount of compensation for each string. This is required because each string sharpens by a different amount when fretted.
This is my own invention. It is a carefully handmade nut, made to fit the individual guitar. It is cut from a low friction, hard wearing, cream (or black) coloured material. The amount of compensation on each string is measured from the position of the first fret, once the accuracy of fret placement has been verified. No unusual tuning or intonation offsets are required. The intonation is set as usual, at the 12th fret.
I first became aware of these in about 1980. They were made in the 1960’s (I think). They featured a complicated (and quite ugly) fully adjustable nut, which tended to fall apart without warning! Very clever though and WAY ahead of their time. The guitars were quite challenging from an aesthetic point of view, and the tremolo system is best left unmentioned!
If your guitar has a conventional (straight) nut at the mathematically calculated “zero fret” position, then notes on the lower frets will sound sharp (especially on the plain G string). (So that’s about 99% of guitars out there!)
If your guitar has its nut incorrectly positioned away from the first fret, then the sharpening will be even worse.
So if you care about being in tune get Funky!