Lutherie Myth/Science: The Distance Between Nut and 12th Fret is Half the Scale Length
A widely held belief is that the scale length of an instrument can be forensically determined by measuring the distance from the nut to the crown of the 12th fret and multiplying by 2. It turns out this is only true under certain conditions, and those conditions are not met frequently enough to make this a useful forensic technique. Fortunately there is a forensic tool which can yield more accurate results than this rule of thumb.
Initially appeared: December 8, 2022
December 08, 2022
The measured distance between the nut and the crown of the 12th fret is equal to half the scale length only under all of the following conditions:
- the nut is accurately positioned relative to the rest of the frets;
- the 12th fret is accurately positioned relative to the rest of the frets;
- the frets were laid out based on the 12th root of 2.
Note that it is no simple matter to determine that any of these conditions are met for an instrument where the construction details are not also known. It is probably not apparent just how often all of these conditions are not met. Some research I did on the subject revealed that these conditions are not met often enough to preclude a simple determination of scale length based on the nut to 12th fret measurement.1
The reasons why these conditions are so often not met is different for each condition:
- The nut is often inaccurately (for forensic purposes) positioned relative to the rest of the frets (that is, it is not positioned at the 0th fret position) due to intentional or unintentional changes in its relative position during construction. When the nut end of the fretboard is cut off using the same saw used to cut fret slots, care must be taken to offset the saw away from the first fret kerf by half the thickness of the saw blade. This is necessary because fret crowns will end up on the centerlines of fret slots, but the fretboard side of the nut will be the termination point at the nut. Sometimes the nut end of the fretboard is cut too short by accident. Sometimes the luthier knows that some compensation for the width of the fretting saw must be made, but gets the direction or the math wrong. Sometimes luthiers will purposely add nut end compensation, purposely shortening the distance between nut and first fret. Although these differences rarely cause any audible intonation issues (and some may actually improve intonation), for forensic purposes they render measurements from the nut inaccurate for determining scale length. When doing my research I was amazed at how often this happens, even in many modern factory-built guitars.
- The 12th fret is inaccurately positioned relative to the rest of the frets only in older instruments that were poorly slotted by hand. This is rarely an issue with modern factory-built instruments.
- The distance between nut and crown of the 12th fret will only equal half the scale length if the frets were laid out based on the 12th root of 2. When frets are laid out using the Rule of 18, the distance between nut and crown of the 12th fret will always be less than half the scale length. This can be verified using this calculator or by doing the fret location math yourself. Here again, Rule of 18 is usually only used in older instruments, but because the change to use of the modern 12th root of 2 method happened over such a long period of time, it is often difficult to determine if the Rule of 18 was used for an instrument by date of construction alone, unless the instrument is known to be from the 19th century or earlier.
More information on this topic and a calculator which is very useful for forensic scale length analysis can be found on this page of this website.
1. Mottola, R.M. "Measuring Scale Length of Fretted Instruments"
American Lutherie #136, 2019, p. 48.