Fender DUO SONIC - neck length question
I own a short scale fender duo sonic, and i spoke to a guitar builder/tech about fitting it with a longer neck. He explained that the bridge would have to be moved back a bit in order to compensate the longer neck, otherwise I would have tuning/intonation problems. (this would mean needing to cut me a custom scratch plate, chisel a new hole for the pick up - quite a big ball ache and also messing up a 1950s guitar) If you have read this far and understand the reasoning behind this, maybe you can help me....
I just bought ANOTHER duo sonic which has a longer neck (duo sonic II) but the body and bridge placement of the two guitars are identical - this i don't understand. It should mean that i could take the longer neck and fit it to the other guitar (which i prefer and sounds better) but I'm a bit confused as to the advice I have been given about having to move the bridge. This advice was confirmed by another luthier.
any suggestions, or explanations?
Ok, without examining the guitar and neck I'll just give you the explanation, and hopefully you can figure the specifics from there....
When you mount a finished neck on a guitar that already has a fixed bridge, you're giving it a string length - the distance from the nut to the bridge. Each fret has to be exactly placed along that length for the notes to be in tune.
The formula is a little complicated, but it's also not really needed for what you want to do. I'll just give it for information, and then explain the easy way for you to figure things out.
When you cut the length of a string in half, but keep the tension and string mass the same, the string will vibrate at exactly twice the frequency - you get an octave; that's where the 12th fret goes. Going up another octave, to the 24th fret, means you cut the remaining distance in half - you're now exactly 3/4 of the way from the nut to the bridge. We use a 12TET (12 tone equal temperament) scale, so each fret has to be placed to give us exactly 1/12th of the frequency - not the distance - of a full octave (which is half the remaining string length). Each pair of frets will be progressively closer together and can be calculated by this formula:
d(x) = s - (s x (2^(x/12)))
In English, the distance from the nut to any given fret is the original scale length minus the scale length multiplied by 2 to the power of x/12, where x is the number of the fret.
Ok.... here's why you don't have to understand the math involved: somebody else placed the frets! That means all you need to worry about is getting the 12th fret placed exactly halfway between the nut and the bridge. If you do that, all the frets will be where they should be.
So measure the distance from the nut to the 12th fret of the replacement neck. Then figure out where the 12th fret will fall if you bolt the neck into the existing neck pocket, and calculate the distance between that spot and the bridge. If the two match, the neck will work without any modifications. If they don't match, all your notes will be off (except for the open strings) - you'll be sharp across the board if the 12th fret is too close to the bridge, and flat across the board if the 12th fret is closer to the nut.
The stock answer for a luthier is to say the bridge will need to be moved, because that's usually true. But it's entirely possible to design a replacement neck that will work - at any desired scale length. All the neck manufacturer would need to know is the exact distance from the neck pocket to the bridge. So it sounds to me like the duo sonic might have been produced in two different stock scale lengths, and no modification is needed. A simple measurement will tell you if that's the case. (But by "simple" I actually mean a pretty precise measurement - plus or minus a millimeter or so and you'll start to hear a difference)
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noteboat- I could not have asked for a more concise and educative answer, that really does make so much sense and is quite simple now that you've put it like that.
I really appreciate your time in answering me.