Scale Length & Intonation
So this month we are back to facts and science….I know I know, it’s so much more interesting to read about my opinions, but in fact my opinions are just that….opinions.
I have been emailing back and forth with one of our customers here at Solo Guitars, Dean….great guy who is currently assembling a few of our acoustic kits, and has had some issues with scale length and intonation. Hence, this months topic of… scale length and intonation. One could write a book on this subject (like so many subjects when it comes to guitars), so I am going to try and boil this down to some simple basics….not because you folks aren’t capable of comprehending the theory involved, but because I am not great at typing, and my fingers get tired…….
What is scale length….well a lot of people out there seem to think that scale length and string length are the same thing….they aren’t. Scale length is the mathematical factor that determines fret spacing. String length is, well, string length. If you measure the space between the first two frets on a Gibson, a Fender and a PRS guitar, you will get three different measurements because these guitars all have different scale lengths. 24 3/4″, 25 1/2″ and 25″ respectively. But wait you say…they all have adjustable bridge saddles, so where does this measurement come from? It could be an exact science but it’s not….the crowns on the frets are not always perfect, and they wear down, the breaking points over nuts and saddles vary due to age and string diameter, and different necks have different amounts of relief (bend) etc etc…..but remember, it’s not about string length. Here’s the formula for those brave enough to explore the math….
If the scale length is factor X, then the distance between the first and second fret is the 6th root of 2 times X, minus the 12th root of 2 times X. If Y is the distance between frets 1 and 2, then the scale length is Y divided by (the 6th root of 2, minus the 12th root of two).
So once you decide on a scale length, the space between your frets is pre-determined. Which leads us to measuring scale length….scale length is the distance between the nut and the peak of the 12fth fret….x 2. So on our acoustic kits here at Solo Guitars, as my pal Dean has found out, the distance between the nut and the 12fth fret is 12 3/4″ giving us a scale length of 25 1/2″. This measurement is taken down the middle of the fretboard to the middle of the bridge saddle. But wait!!! The bridge saddle is on an angle… it’s compensated…not in one but in two ways! (Are you still with me?) The bridge saddle is on an angle and the measurement between the nut and the bridge is not 25 1/2″. Compensation is defined as lengthening or shortening a string length which will either flatten or sharpen a note. Because guitars aren’t perfect, necks are not actually flat (they have relief so the strings can vibrate freely without buzzing on the frets), the pressure of fretting sharpens the notes and of course different string diameters essentially will require different lengths to achieve the same notes (think of a piano) and that’s yet another formula. Therefore, even though the scale length is 25 1/2″, the actual measurement between the nut (down the centre of the fretboard) and the saddle will be slightly more. Here’s another formula to check where the saddle should be placed…..
Find the point on the bridge that is double the length of the nut to the 12th fret and add 1/16″ where the 1st string will cross the saddle and add 5/32″ where the 6th string will cross. Mark a pinpoint on those two points then draw a line between the points. This will be the forward edge (not the center) of a ramped 3/32″ saddle slot.
You can use this formula to place a bridge (the measurements in this case are to the edge of the slot closest to the nut) or even to more or less check if your bridge has been properly placed. I’m sending this to my pal Dean as well to check his bridge placement.
So where does all this leave us? Well, you now know some (and I stress that) of the science behind bridge placement and scale length. It is not a perfect science….Gibson has changed their measurements of scale length several times in the last 50 years and still consider it 24 3/4″, and you can literally spend hours stressing over this, but really it comes down to intonation…..which we will be defining and hopefully pulling the fog off of next time. I’ll try to let you know how Dean makes out on his Solo Guitar Acoustic builds as well….