Understanding Guitar Intonation
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These pages will enable you to understand how guitar setup and guitar intonation work. The principles of compensated nut and compensated saddle will flow easily from that understanding, enabling you to do a better guitar setup, or to better work with your luthier.
A few summers ago, I was admiring a friend’s beautiful J-45 sunburst. He said: “it’s amazing that people who make such fine and expensive guitars, don’t make them so that the open strings are in tune with the fretted notes”. I had been thinking the same thing myself for years! Most acoustic guitars are sharp about 5 - 10 cents on the lower frets on the sixth string. Unwound 3rd strings on electric and classical guitars also typically play quite sharp. All of the other strings are off too, but not as much.
That's why people are discouraged when they tune with an electronic tuner, and then have to re-tune, until their favorite chords sound OK. (It might help to tune the strings that are sharp on the lower frets a bit flat.)
Acoustic guitar builders and manufactures routinely provide just OK compensation by bridge placement, slanting the saddle for more length on the lower strings, and sometimes shaping the saddle to improve intonation for some of the individual strings.
Subsequent improvements and adjustments can be made in the areas of neck relief, string height, and saddle compensation by luthiers and players, in order to increase playability, and adjust to individual player’s preferences. But still ignoring nut compensation.
These efforts make most guitars sound fairly adequate, but, in my opinion, prevalent intonation methods are often rather crude, especially considering the high quality of modern instruments in most other respects. Good intonation requires compensation at both ends of the strings!
The big advantage of the traditional mode of intonation is that it is quick and relatively inexpensive. Though some players are satisfied with this, many are not. The traditional method completely ignores the need for compensation at the nut, and then uses the open strings (which have not been intonated to the fretboard) as the references for adjustment of the saddle. The result is that only the open strings and the notes at the 12th fret are in good tune. (But, after tweaking, even these will be compromised.)
The main reason that the open strings are not in tune with the fretboard is that the string tension is less for the open strings than when you pull the string to any fret. The added tension causes the fretted notes to play sharp compared to open. However, for intonation purposes, it is more logical to say that the opens are in error and are flat compared to the fretted notes.
The fretboard layout on a modern instrument is usually quite mathematically accurate. When the saddle is properly adjusted, it will produce a wide range of notes in excellent tune. The saddle is adjusted to a point where any two fretted notes (somewhat distant from each other) are in tune with each other. (That is what fretboards are designed to do.) This will provide the best possible intonation of the fretboard. You can however, choose which reference frets to use, so as to enhance accuracy in the area that you choose, ie for playing mostly open chords, closed chords, or high leads.
After he saddle is adjusted (compensated) on each string (or, on an acoustic, is declared to be satisfactory) then we can adjust (compensate) the leading edge of the nut to a point where the open string is in tune with the lower frets.
So to summarize, there are just three important elements for accurate guitar intonation that have been largely overlooked and resisted – and they are:
1. We must let go of using open string pitch as a reference for adjusting the saddle. The saddle is for adjusting pitch distribution of fretted notes.
2. Adjust the saddle for intonation, comparing two notes on the fretboard, and not to the open strings.
3. Adjust (compensate) the nut so that the open strings are then in tune with the lower frets.
Traditional compensation at the bridge intonates notes at the 12th fret to play in tune with the open strings, however, after doing this, lacking nut compensation, notes played on the lower frets will play sharp, and notes above the 12
Intonation error should be corrected at the nut, as well as the saddle. It’s a blind spot in the industry – a deficiency, but it presents an opportunity - an opportunity for you to make you or your customer’s guitars sound a lot better!
Why has compensation at the nut been neglected? Besides the powerful anchor of tradition and the added cost, I would say that it's mainly due to insufficient understanding - particularly in the inability to understand the separate effects of saddle compensation versus that of nut compensation.
Nut compensation is generally more difficult than saddle compensation; more expensive in both time and $. Some solutions are costly, but there are other, fairly simple methods that can produce improvements, without much effort or on-going expense. Once a manufacturer, builder or luthier is properly set up, then nut compensation could become more routine, and far less costly.
This is indeed a turning point, because awareness and desire is growing. Luthiers, builders, and manufacturers would benefit by becoming knowledgeable sooner, rather than later, and be able to provide better intonation to those willing to pay for it. This site is not only to inform luthiers, but also do-it-your-selfers, and players who rely upon luthiers - anyone who desires better intonation.
The goal should be to better understand the causes of intonation problems, and to actually understand the solutions that are available. With that understanding, one can creatively evaluate the most practical course of action for a guitar or for a building process.
In my own quest for knowledge (from the web and books) I found that there was great lack of knowledge of nut compensation – much confusion, and, unfortunately, even a lot of misinformation. Web postings often fail to consider guitar intonation holistically. There are a few sites with good information, though, and, combining that with some reasoning of my own (some understanding of geometry and physics helps) I came up with good answers, that I would like to share with you. I was able to greatly improve the sound of several guitars of varying type and quality.
Although I only mention guitars, these principles are relevant, to varying extent, to all fretted musical instruments, and especially to fretted bases.
Note that the following intonation directives assume that neck relief and action height has already been properly adjusted on the guitar in processed.
Open strings are out of tune with fretted notes because all fretted notes are sharped by the increased tension caused by the fretting action, while the open strings are not.
1. If you believe that nut compensation is worthwhile, you must stop using the uncompensated open string pitch as a reference for intonation.
2. A guitar player, by nature, thinks of achieving pitch by the distance from the nut. Instead, think of how a guitar actually works: the pitch of a note is determined by the distance from the fretted note to the saddle, not to the nut!
3. The main playing surface of the guitar is the fretboard. We are not going to alter the fretboard nor fret positions. The fretboard intonation will be just fine if you make the correct adjustments to the saddle.
There is only one way you can compensate the saddle, and that is by locating the saddle adjustment place where 2 frets, a distance apart, are in tune with each other. That aligns the whole fretboard (with imperfections). That is simply how it works! However, you can choose which 2 frets to align, in order to favor which playing area is most important to you.
4. With the saddle compensated, and strings in tune at fret 2 or 3, open string tension is established, and nothing that you do to compensate the nut (unless you change the action height) will affect the pitch accuracy of the fretboard.
Prove this to yourself by gently (to not increase string tension) placing a small piece of wood or wire under a string anywhere between the nut and first fret – then re-check the pitch at fret 2 or 3 - they will not have changed!.
5. With the saddle compensated, and strings in tune at fret 2 or 3, you will find some open strings to be flat, especially low E, then A on acoustics, and unwound G on electrics. Recall that pitch is determined by distance to the saddle. So, to raise the open string pitch, positive nut compensation is done by moving the nut release point toward the saddle. Moving the nut release point will shorten the vibrating string length, raising pitch, but it will not increase the string tension, nor affect the pitch of fretted notes.
Some may have a hard time understanding these principles; you can successfully do intonation work without full understanding, but if you would like to fully understand stringed instrument intonation, I challenge you to study the above, and re-read several times, if necessary until it makes sense! This is the 'secret sauce' that has eluded most! It's not that it's particularly difficult, it's just that it's contrary to popular opinions.
The above diagram shows the poor intonation pattern of a guitar set up in the traditional manor, and open strings tuned. See this and additional diagrams on a subsequent page.
P.S: My friend with the J-45 improved his guitar's intonation by placing a piece of a wooden matchstick against the nut under the 6th string. Although I chuckled, I could not criticize this method, because it does effect an improvement for the worst intonation problem on most acoustic guitars!