Math question: scale length

Tele295

OK, there was no math prereq to get into law school, so don't burn me in effigy!

I'm trying to compare the scale length of my Gitane DG300 to some of the fine European and vintage models.

Gitane website lists the DG300 scale length at 26-5/8". With my poor math skills, I figure this to be around 676.275mm. According to information found elsewhere on this board, vintage Busatos and Duponts have scale lengths of 675mm, and vintage Selmers around 670mm.

Am I figuring/comparing this correctly? Without access to such fine instruments, I can't make an in-hand comparison of the scale lengths.

Bob Holo

Yes, the standard Selmer length is 670 -but all scale lengths are somewhat longer than stated due to compensation and action. In other words, on a fretboard with no relief (a perfect plane) the length from the center of the base of the zero fret to the center of the base of the 12th fret should be exactly 335mm, but the effective scale is longer since you're actually measuring the string which is the hypotenuse of the triangle described by the zero fret, the contact point of the string to the bridge, and the point at the base of the bridge directly under the string contact point which defines a 90 degree angle between the point at the base of the bridge running out to those two other points... and compensation adds a little - which is actually a good thing because to make a long story short, notes don't always sound best together when they're mathematically perfect. (read up on tuning temperaments or find a piano tuner and buy him a few beers and you'll know more than you ever wanted to know about scale lengths, intonation, temperaments, harmonics etc.

But in General, yes... Selmers 670, Macs 640. There are a bunch of other scale lengths, 655, 665, 672, 675 - and three or four others that are really obscure. Various makers at various times in their careers have worked with a lot of these.

bill raymond

Your math skills are fine. I get the same answer! To clarify, there is the "scale length" which determines the fret spacing, and the "string length" which is somewhat longer because of the need to add some distance between the 12th fret and bridge. This compensation helps to make the harmonic at the 12th fret match the pitch of the fretted note at that fret. Occasionally, you can run across a situation where the 1st fret space has been shortened by a very small amount to also help the guitar play in tune--nut compensation.

Maccaferris are usually stated to be 640mm scale length, but some authoritative sources say 638mm. Which is correct? Beats the hell out of me, but I'm guessing that perhaps 638mm with 2mm compensation to give a string length of 640mm. Selmers post Maccaferri are stated to be 670mm.

Bob, I'm not sure where you're going with this "hypotenuse" thing, because we generally measure the scale length along the fretboard and the string length along the--string, I guess. The additional distance attributable to the height of the strings above the plane of the fretboard is, I would estimate, negligible compared to the compensation.

Which is all to say that this is rather esoteric stuff that usually is worked out and agonized over by luthiers and theorists, but needn't worry the average (or even the above-average) player too much, except to know that string length is longer by somewhere in the neighborhood of 2-3mm than scale length. If you really need to know the scale length, measure from the 2nd fret to the 13th fret and consult a good fret distance calculator and "reverse engineer" the scale length from that, then you will be eliminating both bridge compensation and nut compensation (if it is being used) from the equation.

Bob Holo

I think you interpreted it correctly... the string is the hypotenuse, not the scale length...

Assuming the nut end is not compensated, the scale length is 2x the distance from the center of the zero fret to the center of the 12th fret assuming the fretboard is reasonably flat.

These things are perhaps esoteric but they can turn out to be important. Good intonation does a lot for a guitar.

bill raymond

You're absolutely right, Bob. And I meant no criticism. The original questioner seemed to be a player who didn't need to be confused with all our agonizing over the exact scale length--only needed to be sure his guitar would play in tune as best it could--perhaps I was mistaken. Esoteric only in the sense that he needn't be worried if he couldn't follow all the twists and turns, because we hope that we as luthiers do our job of making sure that all this stuff is worked out and put into place correctly.