Coleman Acoustic Guitars lutherie tips

Intonation of Acoustic Guitars

~ without splitting hairs ~

Copyright 1999 Howard Coleman


I feel that there is a lack of impartial advice on what guitarists and luthiers really need to do to achieve good intonation. My aim in this article is to fill the gaps using my own experience and judgement. I hope this provokes a bit of discussion. I am happy to amend any of it if proved wrong. Unbiased opinions.

Background

Several factors affect intonation - string gauge, composition and age, fret positioning, action (at nut, saddle and along the fingerboard) and compensation at the saddle or fingerboard/nut. Some appreciate that for string to string intonation (all chords sounding equally good - or should that be "equally OK"?) the tuning itself has an effect. Tuning open strings to concert pitch might not be good enough. Some claim that an in-tune guitar cannot sound good with a piano as, apparently, the tuning of pianos is often altered very slightly away from equal temperament (sharp above middle C and flat below in order to make a more pleasing sound). We seem to have a system of standard concert pitches (equal temperament) and instrument technicians who feel they can improve on it. I am going to stick my neck out and call this this a piano tuner's problem not ours. I believe that thoughtfully designed, well made and set up guitars sound great, play in tune and always have. I do not believe in making adjustments that only oscilloscopes can appreciate. This article will discuss and recommend reasonable measures to take to provide good intonation.


String Gauge and Composition

When the guitar has been set up the intonation may be affected if a different set of strings is used. Different brands often use different gauges for their sets so it is better to choose according to the gauges not whether they are called "Light" or "Extra Light". The composition of a string affects its density and stiffness, which in turn affect pitch and tension, and hence intonation. To find out more on the effects of string gauge and composition Arto's String Calculator is the place to go.


Fingerboard/Nut Compensation

Some guitars do not play completely in tune. Some appear to play in tune but sound bad next to keyboards. According to Feiten and Back (see below) the problem lies with the way guitars are set up and the way pianos are tuned. They quote that "...your first three frets will always be a little sharp. The middle register - the 4th through the 10th frets tends to be a little flat." One of the ways in which they compensate for this is by lopping a fraction from the end of the fingerboard. The actual amount they lop off is 1.4% of the distance from the nut to the first fret for acoustic steel string guitars. (To the the nearest measurable degree of accuracy this translates as 0.5mm or 0.020" for long or short scale guitars.) Elsewhere, I demonstrate the difference this makes to the vibrating string length. It is zero at the nut because I adjusted the scale length to allow for the shortening; 0.4mm for the first 3 frets; 0.3mm for the next 6 frets; 0.2mm for the next 9 frets. I would therefore say that the only significant change occurs between open strings and fretted strings.

The even more pernickety give different compensation for all six strings, not by slanting the nut, a compromise which is much too easy, but by carving the notches in the nut by different amounts. To be fair, I have only come across this in one make of banjo and one make of classical guitar.

I am interested to find out who invented fingerboard shortening. It must have been around for a long time because I have a Frets magazine from 1981 where a Stelling banjo is advertised as having a compensated nut. Stelling currently say that "By selectively notching the nut slots to different lengths, relative string distance from the nut to each fret is adjusted." To do this they shorten the fingerboard first. Frank Ford says, "...a lot of makers cut about .020" from the nut end to improve the intonation in lower ranges. This really does work, and it's been done for as long as I can remember by various technicians as a repair technique."

My personal conclusion is that, for my guitars, fingerboard shortening and nut compensation are unnecessary because intonation is taken care of by good design and setting up. (See Charles Tauber's article on setting up.) However, I think that it may be beneficial in adjusting guitars with intentional high action.

Here is some food for thought. There is a change in intonation when a flat area has developed on a fret. This fret wear could easily move the last point of contact with the fret 1mm, ie several times the offset that fingerboard/nut compensation methods use. It is therefore worth considering a refret before anything more drastic.


An Alternative Non-patented Solution

I have found the nut to be one of the most underestimated parts of an acoustic guitar. In my experience, if it is accurately cut in the first place, then the instrument's intonation will be acceptable to the keenest ear. It is simply to do with the height of the strings as they leave the nut. If there are intonation problems the nut may just need its grooves deepening a little - or maybe someone has fitted a shim to raise the whole nut to stop buzzing after a refret? Putting a capo at the first fret is a good way to diagnose a nut that is too high. If intonation is improved by the capo then its your nut at fault. The way I approach setting string height at the nut is to deepen the grooves gradually, checking visually, and aiming to get the height of the string over the first fret very slightly greater than it is over the second fret when fretted at the first. I then proceed to deepen them very gingerly. I recommend Frank Ford's excellent articles on the subject. If not enough care is taken there could well be intonation problems.


Saddle Compensation

Did you notice in the 80's that the bridge saddles of some acoustic guitars were in two or three separate sections ? Funny how they reverted to single saddles when under-saddle transducers became the latest fashion! Don't you think that says it all - that the separate saddles were more important for marketing than for intonation. I also have serious reservations about adding metalwork to the bridge of any purely acoustic instrument to make intonation adjustable. I find that a single non-adjustable bridge saddle that is slanted and has its top carefully bevelled to give different take-off points for all the strings can work perfectly.


Tuning Methods

I'm afraid it's not straightforward. However, I feel that there are some rules worth following while others are "splitting hairs". Well, what else can I say when all my guitar heroes just tuned up using simple means yet sounded fantastic?

Tuning open strings with an electronic tuner gives good results for me. I am aware of the pitch dropping about 5 cents (hundredths of a semitone) a fraction of a second after twanging but try to do the same for all strings - either going by the initial pitch or the sustained pitch. I suppose the extra pernickety could choose which to follow according to the type of music they are going to play. If it's fast and loud it could be argued that the initial pitch is more relevant and vice versa. Once the guitar is tuned try to resist the temptation to improve the tuning. You might make one chord better but only at the expense of several others. That is the compromise of equal temperament. Once you have trained your ears to accept it, it will sound fine.

If you tune using a tuning fork to give you the pitch of one string perhaps the best way of tuning the others from this is by the 5th fret/ 4th fret method.

E|--------------------------------0-----
B|--------------------------0-----5-----
G|--------------------0-----4-----------
D|--------------0-----5-----------------
A|--------0-----5-----------------------
E|--0-----5-----------------------------

You should definitely not use the 7th fret harmonic when tuning one string from another because the note it gives is not part of the equal temperament scale but the Pythagorean scale which is slightly different. The advantage claimed for this method is that the strings are not being fretted and therefore not being stretched unduly. In practice though what happens is that the discrepancy becomes magnified as the player tunes across successive strings.

E|-------------------------------------7<>-----
B|-------------------------------0-----5<>-----
G|-----------------------7<>-------------------
D|---------------7<>-----5<>-------------------
A|--------7<>----5<>---------------------------
E|--0-----5<>-------------------7<>------------

However, if the 7th fret harmonics of the 3rd, 4th, 5th and 6th strings are each tuned separately with a meter then you get what are claimed to be desirable tuning offsets as in the Feiten Temper Tuning Table (US Patent 5814745). In my opinion an offset of only one or two cents would not make an appreciable difference as this is only just at the limit of perception of the best trained musical ear. I doubt if I can tune up to within 1 cent anyway because the pitch of a guitar string changes as I have said. I could do it by plucking the strings only lightly but this would be unrealistic because that's not how I play.

This method comes from the Guild of American Luthiers (Data Sheet #45) and is very sound. Apart from being hard to remember I can't fault it.

E|--0-----0---------------------------------3--------------
B|------------------------3--------------------------------
G|----------------------------------7------12<>------2-----
D|----------------2------12<>-----12<>---------------------
A|--------------------------------------------------12<>---
E|-------5<>-----12<>--------------------------------------

This challenging method came from Simon Husbands via Fretbox. The only unison is the 1st string tuned from the 6th. The others have to be slightly sharp or flat according to the # and b signs. You have to judge how sharp or flat by listening to the beat note. When it beats about once every 2 seconds you are there. If you then check the G to B interval on open strings, this should beat at about 8 beats per second.

This method is therefore a variation of the 7th fret harmonic method but with offsets designed to remove the inaccuracies. The object is to stretch the fourths and shorten the fifths of the scale. On a practical note, to tune up this way you need complete silence and total concentration to focus on the beat notes. It is easier on a responsive guitar as you can then also feel the beat notes in the neck and body. I recommend picking hard quite close to the bridge.

E|---------------------------------------0-------7<>-----
B|-----------------------------------------------5<>b----
G|-----------------------------7<>#----------------------
D|-------------------7<>#------5<>-----------------------
A|---------7<>#------5<>---------------------------------
E|--0------5<>--------------------------5<>---------------

So, there you are - what seems like perfection to one player is less than perfection to another. As I have mentioned, the pitch of a string changes after being plucked so it is virtually impossible to tune it to perfection. That is the nature of the beast - a guitar cannot be played absolutely perfectly in tune. It isn't a synthesiser after all but something organic, almost living, and I wouldn't want it any other way.


Patents

Feiten and Back's patents, US Patent 5404783, 1995; US Patent 5600079, 1997; US Patent 5728956, 1998 and US Patent 5814745, 1998 can be read for free at US Patent and Trademark Office or US Patent Search - (Download patents from the United States Patent Office for free.) While you are there have a look at Salazar's patent for fret positioning (US Patent 5063818, 1991).


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Last revised: July 06, 2006.