Alan Carruth Article on Intonation
Posted: Wed Oct 31, 2012 1:58 pm
First: it's just about impossible to achieve 'perfect' intonation on an acoustic guitar. The fact that the top moves (which it has to or you would not hear the thing) means that at least one end of the strings is not 'fixed' as it has to be in order to work right. Temperament adds another level of complication: if you want to play in a number of keys, or use straight frets, there will always be compromises that render some intervals less 'pure' than you'd like. In short, there's not a lot you can do about some of the things that might sound 'off' to you.
The basic problem with setting up intonation is that the string tension rises when you fret them, throwing the pitch sharp. They go sharper at the first fret than you might think, because you displace them through a pretty sharp angle. As you go up the fretboard the pitch tends to get even sharper. How much it goes out depends on a lot of variables, with the nature of the particular string and the action height being big ones. Nylon strings, being more elastic than steel, tend to go less sharp, for example. A string that is fairly close to it's breaking point; a high E or wound G, will go less sharp than one that is relatively slacker. This draqs scale length into the problem, as well as tuning (play much in DADGAD?). It's possible to calculate this stuff if you have the math chops. For those of us who have not cultivated our inner Einstein, there is another way.
If you plot out the amount a string goes sharp in cents for each fret position, you get a line that starts out a bit high at the first fret, and rises as you go toward the saddle, as I said. Simplifying with desperate brevity; moving the nut toward the first fret shifts the whole line downward, while moving the saddle away from the 12th fret alters the slope. Moving the nut forward and re-tuning is the same as moving all of the frets back toward the nut, and shifts all the pitches downward by the same amount in cents. Moving the saddle away from the 12th fret adds proportionally more to the lengths of the higher notes, and thus makes them go flatter as you go up. Some combination of nut and saddle offset will get you pretty close to 'right' for any given string, but the offsets will be different for each string. The trick is to find those offsets.
As I say, it's possible to calculate this stuff, but for those of us who don't trust our math chops as much as we trust our tool chops, it's also possible to set up a rig to measure the offsets directly. The simplest setup is a beam with a flat top, that has the first, 11th and 12th frets set in at the right places. You have a movable nut and saddle, and some way of putting on a string and tuning it. It's easiest if the saddle has some sort of a pickup built in, so you can plug into a good tuner.
The way that I've found works pretty well is to put on a string, set up the action height, and start with the nut and saddle at their 'theoretical' positions, the same distance from the 12th fret. Tune the string as accurately as you can, and then fret it at the 12th fret, and see how much it's gone sharp. _Don't_ go by the 12th fret 'harmonic', which can actually be a bit sharp from the 'correct' pitch, due to string stiffness: always go by the fretted tone. Move the saddle away from the 12th fret and continue to check the pitches, re-tuning every time. When you get the octave as close as you think you can, go up and fret the string at the first fret. That note will be sharp too, so move the nut toward the fret until you get an exact semitone on the tuner. Now the 12th fret will be out, so you go back and fix it, which throws the first fret out, and so forth. Each time you go around the adjustment gets smaller, so at some point you just declare victory, note the offsets down, and go to the next string. I like to check each string three times, and average the results: somehow, no matter how careful I am, there's a certain amount of variation in the numbers.
I use these numbers to set up the nut, and establish the angle for the saddle slot. The lower strings often need to have the nut as much as 3mm closer to the first fret than it 'should' be, so I just cut off the fretboard there. I cut the nut, and use a Dremel to move the break point for the other strings back to the correct settings.
It seems to me that top movement is more likely to change the bridge offsets than the nut, so I don't file the saddle top before hand. Instead, I make it flat across the top, with the back edge a bit rounded, and put on the strings. Once I get the action right I use the old 'string under' trick to find the correct break points. Take a length of plain string, and put it sideways across the top of the saddle under one of the strings to lift it off the flat saddle top. Tune up the string, and move the lifter around until you get the octave pitch to be right at the 12th fret (not the 'harmonic!). Do each string, remove the saddle and file the peaks.
I did this on a 12-string I had at Montreal last summer. The octaves sounded like a Wes Montgomery solo, and when I checked it on a tuner no fretted note was more than 3 cents off. It was a certain amount of work, but I thought it was worth it. More to the point, the buyer is happy....
Last edited by Alan Carruth on Wed Oct 31, 2012 12:38 pm, edited 1 time in total.
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The basic problem with setting up intonation is that the string tension rises when you fret them, throwing the pitch sharp. They go sharper at the first fret than you might think, because you displace them through a pretty sharp angle. As you go up the fretboard the pitch tends to get even sharper. How much it goes out depends on a lot of variables, with the nature of the particular string and the action height being big ones. Nylon strings, being more elastic than steel, tend to go less sharp, for example. A string that is fairly close to it's breaking point; a high E or wound G, will go less sharp than one that is relatively slacker. This draqs scale length into the problem, as well as tuning (play much in DADGAD?). It's possible to calculate this stuff if you have the math chops. For those of us who have not cultivated our inner Einstein, there is another way.
If you plot out the amount a string goes sharp in cents for each fret position, you get a line that starts out a bit high at the first fret, and rises as you go toward the saddle, as I said. Simplifying with desperate brevity; moving the nut toward the first fret shifts the whole line downward, while moving the saddle away from the 12th fret alters the slope. Moving the nut forward and re-tuning is the same as moving all of the frets back toward the nut, and shifts all the pitches downward by the same amount in cents. Moving the saddle away from the 12th fret adds proportionally more to the lengths of the higher notes, and thus makes them go flatter as you go up. Some combination of nut and saddle offset will get you pretty close to 'right' for any given string, but the offsets will be different for each string. The trick is to find those offsets.
As I say, it's possible to calculate this stuff, but for those of us who don't trust our math chops as much as we trust our tool chops, it's also possible to set up a rig to measure the offsets directly. The simplest setup is a beam with a flat top, that has the first, 11th and 12th frets set in at the right places. You have a movable nut and saddle, and some way of putting on a string and tuning it. It's easiest if the saddle has some sort of a pickup built in, so you can plug into a good tuner.
The way that I've found works pretty well is to put on a string, set up the action height, and start with the nut and saddle at their 'theoretical' positions, the same distance from the 12th fret. Tune the string as accurately as you can, and then fret it at the 12th fret, and see how much it's gone sharp. _Don't_ go by the 12th fret 'harmonic', which can actually be a bit sharp from the 'correct' pitch, due to string stiffness: always go by the fretted tone. Move the saddle away from the 12th fret and continue to check the pitches, re-tuning every time. When you get the octave as close as you think you can, go up and fret the string at the first fret. That note will be sharp too, so move the nut toward the fret until you get an exact semitone on the tuner. Now the 12th fret will be out, so you go back and fix it, which throws the first fret out, and so forth. Each time you go around the adjustment gets smaller, so at some point you just declare victory, note the offsets down, and go to the next string. I like to check each string three times, and average the results: somehow, no matter how careful I am, there's a certain amount of variation in the numbers.
I use these numbers to set up the nut, and establish the angle for the saddle slot. The lower strings often need to have the nut as much as 3mm closer to the first fret than it 'should' be, so I just cut off the fretboard there. I cut the nut, and use a Dremel to move the break point for the other strings back to the correct settings.
It seems to me that top movement is more likely to change the bridge offsets than the nut, so I don't file the saddle top before hand. Instead, I make it flat across the top, with the back edge a bit rounded, and put on the strings. Once I get the action right I use the old 'string under' trick to find the correct break points. Take a length of plain string, and put it sideways across the top of the saddle under one of the strings to lift it off the flat saddle top. Tune up the string, and move the lifter around until you get the octave pitch to be right at the 12th fret (not the 'harmonic!). Do each string, remove the saddle and file the peaks.
I did this on a 12-string I had at Montreal last summer. The octaves sounded like a Wes Montgomery solo, and when I checked it on a tuner no fretted note was more than 3 cents off. It was a certain amount of work, but I thought it was worth it. More to the point, the buyer is happy....
Last edited by Alan Carruth on Wed Oct 31, 2012 12:38 pm, edited 1 time in total.
Report this post