Master Guitar Luthier Talks Tech on Intonation
A simple change in a guitar’s geometry has been tested in over 200 instruments by some of the best musicians, engineers and record producers in the studio and onstage with full orchestra. One cut that will add 5 or 10 minutes during a nut replacement and zero time in a factory would make this world sound so much better. To test this yourself: tune your guitar so it plays a beautiful open G chord then play a D. Alternatively, if you have a digital tuner: tune an open string then play the same string on the first fret. If all is good then you are one of the lucky few. If the D chord sounds wonky or the tuner shows a problem, try this: put a toothpick or a stick under the strings right next to the nut. If the toothpick is just large enough so the strings are resting on it then it is just right. Now, repeat the tests. Do you notice any improvement? If yes then read more to find out why it is impossible for many guitars to play in tune.
Playing in tune may be the most important part of music. Proper intonation helps others understand what we are trying to communicate in our music and allows them to play along. If an instrument is not playing in tune, it takes extra effort to identify which note is being played. The confusion caused by a badly tuned instrument can ruin the concentration and performance of everyone involved. With the exception of folk music such as Blues or Jazz where off notes are expected, most music is intended to be played in tune and on key.
Usually, out of tune notes are sharp because a guitar can’t create a note lower than the fretted note by moving, pressing or stretching the string. As a guitar is being built or adjusted, changes are made to the length of strings where they attach to the guitar’s body. This is called adjusting the intonation. Without making the strings a little bit longer than their mathematical measurement, a player will find it impossible to play in tune on the 10th or 12th fret. If the fretted note is sharp on a guitar, no amount of pressing, bending or praying will get that note to be in tune.
Guitars have a number of qualities that reduce their ability to play in tune. Most instruments in the orchestra play only one note at a time. The key pads on wind instruments are carefully shaped to get each note perfect. Violins, cellos and trombones have a variable pitch so a player with a good ear will always be in tune. Guitars have some of each of these qualities. Like the wind instruments key pads, the frets on a guitar have to be carefully crafted to get the correct note intervals. Like the cello, the guitar can play notes beyond what is determined by the fret intervals. Unlike the cello, most guitars cannot play a lower note for a given fret unless they are fitted with a tremolo device such as played by Jimi Hendrix or Jeff Beck or Eddie Van Halen. Most importantly, guitars are required to play a group of notes like a piano but the notes must be squished into place by the guitar player’s fingers. An out of tune guitar is easily recognized when notes are played together in a chord. With this in mind, we can see how proper intonation is a crucial element in a guitar’s design.
The bad news is: the guitar’s intonation goes awry shortly after it leaves the drawing board. A guitar’s fretboard is laid out according to an equal temperament system developed in the 16th century by a Chinese prince name Zhu Zaiyu. At the time, if a stringed instrument had a neck on it, there were no frets or they could be moved. The “frets” would be a piece of gut tied around the neck which could be adjusted for a particular tuning or song. Had Zhu foreseen the guitar with its immoveable frets or been aware of the Railsback curve for strings under tension he may have warned us about a couple things. The Railsback curve illustrates the way a fraction of a string at the same tension will return a frequency higher than the same fraction of the fundamental frequency; e.g., by playing up the neck, the string’s relative mass changes to make the note sharper than intended. Additionally, pressing down on the string increases the tension, making the note sharper. These two forces are often cited by luthiers and musicians promoting proper guitar intonation at the bridge and saddle. Conversely, the other end of the string is ignored. The technician carefully adjusts the saddle height and compensation for best playability and intonation and the nut that equally defines the string length remains right where Zhu Zaiyu left it over 400 years ago: on the drawing board.
This is why your guitar won’t play in tune. Luthiers and technicians will dance around this and may recommend some better tuning machines, fret work, a saddle adjustment or a new nut. The biggest manufacturers believe that attention to detail at the saddle or the half-width of a fret slot (about 0.012”) when the fingerboard is cut to size at the end will be adequate compensation. Some of these improvements will increase clarity and playability or intonation on the higher frets but they cannot make a guitar play open chords in tune.
The Search for Perfect Intonation
Methods exist today for making a guitar play perfectly in tune. Well, with equal temperament nothing is perfect in the whole orchestra. Let’s just say that out of tune notes can be mitigated until they are no longer noticeable. Highly respected session and touring musician Buzz Feiten (he played Woodstock) was awarded a patent in 1998 for his method of using a special way to tune the guitar along with design modifications. In 1984, John and William Gilbert produced a method of repositioning all the frets which solves the problem but creates another: Moving the frets on an existing guitar would cost more than most guitars are worth. Feiten’s method is gaining popularity and the special tuning process is available on many digital tuners and phone tuner apps. Both seem to complicate a problem that is simpler than it appears.
We can assume the fretboard layout and the saddle compensation as fully developed. When a guitar is adjusted according to common knowledge the only intonation problem will be in the first position. Shortening the nut to saddle distance 2.4% by moving the nut will change the first fret frequency interval by 5-8%. This compensates for the string’s increased height at the nut which causes increased tension when the string is pressed down on a fret. We use a little more compensation than Feiten recommends because most guitars have the string height at the nut set higher to account for wear. Nylon string guitars may need more and super light steel strings may need less. Importantly, the change takes less effect as we play up the neck. At the third fret, the difference represents a 5% difference in the frequency of the note. Differences of less than 4% are unrecognized by normal humans. In other words, the nut compensation effects are encapsulated in the first position where most people play and unnoticed after the third or fourth fret.
So, in conclusion, it is fair to say that all guitars project a balance between precision and compromise. If we apply the proper math and observe then compensate for the results we will have a good outcome. Every guitar can play in tune. Checking the intonation at the nut is a good first or second step when tuning problems arise. Taking a slice off the end of the fingerboard and replacing the nut is an easy job for any good luthier. There are also special nut blanks that will allow the guitar to remain unchanged. A toothpick or a piece of copper wire will work in a pinch. If you are having problems with intonation and this article strikes a chord, please look into it. Your audience will thank you.
- Hermann von Helmholtz，Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik . p 258, 3rd edition, Longmans, Green and Co, London, 1895
- Fritz A. Kuttner. “Prince Chu Tsai-Yü’s Life and Work: A Re-Evaluation of His Contribution to Equal Temperament Theory”, p.163, Ethnomusicology, Vol. 19, No. 2 (May, 1975), pp. 163–206.
- Buzzy’s patent http://www.google.com/patents/US5814745
- Buzzy wikipedia https://en.wikipedia.org/wiki/Buzz_Feiten
- John and William Glbert method http://schrammguitars.com/intonation.html