Everything you wanted to know about Intonation

(but were afraid to ask!)

What is Intonation?

Roughly speaking “does it play in tune?”

Obviously the open strings will be in tune: because you tuned them. Intonation describes how well all the other notes on the fretboard are in tune compared to the open strings.

How Do I Measure Intonation?

Lets start with the traditional method: sound a note at the 12 th fret, then play the 12th fret harmonic, these should each sound the same note.

Unfortunately while this method may be convenient if you don't happen to have an electronic tuner around, it has a number of defects:

  • Most people (does not apply to you obviously!) are actually rather poor are determining whether two notes are exactly the same.

  • Depending how I play it, I can play harmonics that are up to 5 cents out, or to put it another way “ harmonics are not guaranteed to be exactly double the base frequency” .

  • In practice, tunes do not consist of a series of harmonics, we're much more interested in the fretted notes.

  • Intonation is so much more than whether the instrument plays in tune at the 12 th fret, you need to check it everywhere.

Now look look at the correct (or at least “less wrong”) way to check intonation:

  • You need an accurate measuring device – there are free strobe tuners online that give you an accurate measure of pitch, and some clip-on chromatic tuners are also accurate enough for the job. Note though that some clip on tuners, are completely unsuited to this task: these are the tuners that give a coarse reading and just tell you “in tune” or “not in tune”.

  • With the open string in tune, fret at each position in turn (or at least a good selection) and measure how in or out of tune the fretted note is. Even on a good instrument, it's unlikely that the intonation will be absolutely perfect at every fret: what you're looking for is a good general overview.

  • Use the flat of you finger to pluck the string – try to avoid picks or fingernails as you get a less reliable reading.

  • Use spare fingers to mute the strings you're not measuring, otherwise sympathetic vibrations can push the readings out. This is particularly important on double strung instruments where the second string in a pair needs to be muted when measuring intonation.

  • Keep the instrument upright and in normal playing position when doing this. While it generally doesn't make too much difference, there can sometimes be a difference in measured intonation between an instrument on the workbench and flat on it's back, and one on it's side in playing position.

  • As well as each fret position, you're going to have to check each string, including both strings in a pair separately.

  • After each reading, mute all the strings, and let the reading on the “measuring device” subside back to zero before taking the next measurement: otherwise the current reading can be be confused by the previous one.

  • And finally.... how hard do you push the strings down on the frets? I guess like you would when playing” is the obvious answer, but that's actually rather hard to do in an artificial situation like this. On the basis that slightly-sharp sounds marginally less awful than slightly-flat I tend to go for “ just hard enough to get a clean note” and set-up the instrument accordingly. This does mean that pressing harder in the heat of the moment may bend strings sharp, and likewise if the instrument goes to someone with a Gorilla like grip!

Causes of poor intonation (and what to do about it)

First the science bit, the principles behind this are easy to understand, and once you remember them, almost any problem should be easy to diagnose:

  1. If the note sound sharp, then either it's vibrating length is too short , or it's being stretched to a higher tension.

  2. If the note sounds flat, then it's vibrating length is too long.

Now that we've got that out of the way, lets look at the most common specific issues, their causes, and solutions:

1) Notes get increasingly sharp as you move up the fretboard.

Cause 1: The bridge (or bridge saddle) is too close to the nut. Fix by moving the bridge away from the nut, or by cutting compensation in the bridge saddle.

Cause 2: The action is much too high, so that notes are bent sharp. Fix by lowering the action.

2) Notes get increasingly flat as you move up the fretboard.

Cause: the bridge (or bridge saddle) is too far from the nut. For floating bridges, move the bridge closer to the nut, for fixed bridges check that the string is making contact with the very front edge of the saddle, if it's not then re-shape the saddle top so that it does. Otherwise a new saddle, perhaps with a small “extension” on the front edge may be required.

3) Notes are sharp close to the nut.

Cause 1: The action at the nut is too high. This tends to be a bigger issue for the thicker strings which are often very susceptible to even slight set-up issues.

Cause 2: The strings aren't making contact with the front edge of the nut. Either the nut has lost a chip off the front edge (can happen any time), or the nut slot is incorrectly cut. Either way the fix typically involves filling the slot and starting over.

Cause 3: The first fret is too long, in effect pushing all the frets too close to the bridge. This is uncommon, but does occur. Check by printing out a fretboard template, line up the nut and 12th fret and compare everything else. Here's a mandolin template online . The fix is to remove the nut, then remove some material from the end of the fretboard and then fit a new wider nut.

4) Notes are flat close to the nut.

Cause: The nut is too close to the first fret. This is rather uncommon, and can be fixed either by cutting a little compensation into the nut (ie removing material from it's front edge), or by placing a shim between the front of the nut and the end of the fretboard.

5) Notes are all over the place – some sharp some flat.

If this is a new situation then suspect either a manufacturing defect in a new string, or wear to an old one. It only takes a little variation in string density along it's length and nothing will be in tune anymore. An alternative is fret-placement: this can be an issue especially on older instruments and can be easily checked by placing a fret spacing template next to the fretboard. Here's an example of an old Ceccherini mandolin, with the template lined up at fret 12 and the nut, the issues on the remaining frets are obvious:

In this situation, assuming you don't want to replace the whole fretboard, then you're left with trying to adjust nut and bridge to achieve the best compromise. With bar frets as shown above, you can also re-shape the fret crown to push the location that the string makes contact over to one side of the fret.

6) Notes are OK when I test the instrument, but sound wrong when played.

Cause: user error. Lot's of things can go wrong here, squeezing the strings too hard (if you do this consistently, then set-up adjustments can be made, but squeezing extra hard at certain moments can't be dealt with by a set-up), or accidentally bending the strings sharp by not pushing straight down, but across the fretboard as well. You will know if you have an issue with the latter problem if the 2 strings in a pair sometimes get squashed together when fretting a note – don't ask me how I know!

7) Notes are OK up to fret X, but after that are all over the place.

A certain dose of realism may be in order here. Consider that we can usually hear notes greater than 3cents off as “out of tune”, which means the distance from fret X to fret X+1 must be accurate to within 3%. Let's look at what that means for a typical guitar with a 25.5” scale first:

Fret number.

Accuracy required to be within 3 cents of the true note.

1

1.1mm

5

0.87mm

12

0.58mm

24

0.29mm

Clearly a 0.5mm accuracy at fret 12 is achievable, even the 0.3mm accuracy at fret 24 should be achievable for a careful luthier. However, now let's take make the same calculations for a classical mandolin with a 13” scale:

Fret number

Accuracy required to be within 3 cents of the true note.

1

0.56mm

5

0.44mm

12

0.29mm

24

0.15mm

In this case accurate placement of the 12th fret looks doable (even by hand), but the 24th fret accuracy is surely out of reach. Even if you use a machine to cut fret slots to some crazy level of accuracy, remember that the frets are still fitted, levelled, and dressed by hand, and that's before you even start to consider the factors that come into play once you start playing (variations in finger pressure etc).

What is Compensation and why do we need it?

Compensation is the practice of adjusting the bridge and occasionally the nut to improve intonation. In an ideal world, and with perfectly flexible strings, the distance from nut to bridge, would always be exactly double the distance from nut to 12th fret. There are two main reasons why this is not the case:

  1. When you fret a string, you inevitably bend it sharp. That's because a fretted string has to cover a very slightly longer distance than one going direct from nut to bridge. And of course the harder you press and the closer to the fret your finger is, the more sharp you bend the note. What's more a bit of elementary geometry will soon convince you that for any given action, the effect gets worse the shorter the scale length of the instrument.

  2. While certainly important, the first effect isn't necessarily the largest. A larger effect comes from the imperfect nature of “real” strings as opposed to “theoretical” ones. In the real world strings are not perfectly flexible, so you get an edge-effect at either end of the vibrating string length where the string doesn't really move or flex as much as it should. As a result the effective vibrating length of the string is always less than the distance from nut to bridge. Further, the effect gets worse as the string become thicker and less flexible: in this case it's the string's core diameter that really matters, in comparison the windings on the string have only a small effect on it's flexibility. When you think about it, this is exactly why we use wound strings rather than thicker and thicker plain strings (which would basically become metal rods at the diameter of most wound strings). By way of example, take a look at this 0.056” bottom string as it passes over the zero fret and notice how it doesn't immediately change direction, but keeps on going up for a short while. Not only does this part of the string not take part in the vibration as much as it should, but it also makes the effective height of the zero fret (or nut) higher:

How Much Compensation Do I Need?

The usual answer to this question is either “it depends”, or else “use trial and error”. Unfortunately neither of those answers are all that useful! What we really need is some guidance that will at least give us an idea of where to start, and this online calculator does exactly that .

It's instructive to use the calculator to look at some sample compensation requirements, starting with a mandolin (Gibson style, J74 strings):

StringActionCompensation
E1mm (.040")1.8mm (0.073")
A1mm (.040")3.9mm (0.153")
D1mm (.040")2.2mm (0.087")
G1mm (.040")2.9mm (0.114")
E1.5mm (.060")2.3mm (0.091")
A1.5mm (.060")4.8mm (0.192")
D1.5mm (.060")2.7mm (0.108")
G1.5mm (.060")3.5mm (0.139")
E2mm (.080")2.9mm (0.115")
A2mm (.080")6.2mm (0.245")
D2mm (.080")3.5mm (0.136")
G2mm (.080")4.4mm (0.175")

And similarly for steel string acoustic guitar:

StringActionCompensation
E1.5mm (.060")2.3mm (0.091")
B1.5mm (.060")4.1mm (0.16")
G1.5mm (.060")2.3mm (0.091")
D1.5mm (.060")3.0mm (0.121")
A1.5mm (.060")3.5mm (0.139")
E1.5mm (.060")4.3mm (0.171")
E2.0mm (.080")2.7mm (0.106")
B2.0mm (.080")4.8mm (0.190")
G2.0mm (.080")2.7mm (0.105")
D2.0mm (.080")3.5mm (0.139")
A2.0mm (.080")4.1mm (0.161")
E2.0mm (.080")5.0mm (0.199")
E3.0mm (.120")3.8mm (0.151")
B3.0mm (.120")6.8mm (0.268")
G3.0mm (.120")3.7mm (0.145")
D3.0mm (.120")4.9mm (0.192")
A3.0mm (.120")5.6mm (0.222")
E3.0mm (.120")7.6mm (0.278")

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