 # Fret Position Calculator

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I know there's a ton of fret position calculators out there, but on a whim about building a guitar with an odd string scale length, I wrote up a quick Excel spread sheet to write out all the meaurements.

I wrote it in about 5 minutes and it'll dump out inches and mm and measurements from the nut to the fret, from the bridge to the fret, and from fret to fret.

Like I said, it was just for fun, but I thought others around here could find use for it.

Let me know if you spot any errors in it. Thanks and enjoy!

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Just wanted to add that the scale length I've been thinking of is 25 1/8. That's right in between the 25.5 Fender scale and the Gibson 24 3/4. Strangly enough, it seems that there's only one company that uses this scale, see here... McIntruff Guitars. It seems so plainly obvious to use this scale for getting the best of both worlds. Why don't people use this more often?

Anyone have any thoughts on the 25 1/8 string scale? Have you used it or played a guitar with it?

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• 3 weeks later...

Jehle - Very well done. Makes it quite simple to make small adjustments to a scale for artistic reasons.

For those of you who want the formula in a mathematical way, here it is if I am not wrong!

f(x) = distance from nut to X is

f(x) = ( [Z]-[x-1] ) / A + [x-1]

Where:

X - distance from nut to chosen fret

Z - scale length in inches

A - "cosmological constant" for guitar - 17.81700000

There ya go - fun stuff!

PS: So if you ever want to make a guitar that goes by quarter steps as well, just fit it into the formula!

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Mastermind, I am not sure how to work with your formula (I am probably not understanding it). Could you give an example of ditance from nut to 12 fret based on 24" scale. ( I know 12th fret will be 1/2 the scale length, but I am trying to figure out how to use your formula).

My understanding of the formula (mind you I never do this manually, I use fret calcs).

SL= total scale length

a=distance from nut to 1st fret

b=distance from 1st to 2nd fret

c=distance from 2nd to 3rd fret.......and so on.

a=SL/17.817

b=(SL-a)/17.817

c=(SL-a- b )/17.817

example(24" scale)

dist to n to 1=24/17.817

dist to n to 1=1.347

dist to 1 to 2=(24-1.347)/17.817

dist to 1 to 2=1.2714

dist to 2 to 3=(24-1.347-1.2714)/17.817

dist to 2 to 3=1.200

Looks like you have a shorter way to calc this, I just am not following.

Peace, Rich

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f(x) = string length from nut to the x nut = [ [ [Z] - [x-1] ] / [A] + [x-1] ]

Distance of nut to nut is = 0

plug in "24" and x = 1 for first fret

[ [  - [1-1] ] / [17.817] + [1-1]]

reduce

24 / 17.817 = 1.347 -- as you stated.

Now do second nut, x = 2

[ [  - [2-1] ] / [17.817] + [ 2-1 ] ]

reduce

[ [24 - 1] / [17.817] ] + 1

[23/17.817] + 1

distance from nut to fret 2 is 2.2909

Be sure you use the right order of operations, i was a bit vague above - here is the proper syntax

distance from nut to x = f(x) = [ [ [Z] - [x-1] ] / [A] + [x-1] ]

let me know how it goes and I can share results to make sure you got it for 24 scale length, thanks!

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Ok,

So 24" scale nut to 12th. fret.

distance from nut to x = f(x) = [ [ [Z] - [x-1] ] / [A] + [x-1] ]

[[-[12-1]]/[17.817]+[12-1]]

[24-11]/[17.817+11]

13/28.817

.4511????

distance from nut to fret 2 is 2.2909

Are you sure this is correct? I think 2.6185 is the correct distance.

Peace, Rich

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[[-[12-1]]/[17.817]+[12-1]]

The way I'm reading it, the ones that are bold aren't correct. It's a little bit confusing but I can't get your formula to work accurately MM. If you give us a proof, or even just an example it would probably help. I've tried working this formula several different ways and I just can't get it to work. I'm usually pretty decent with this kind of thing. The way Rich wrote it out is the way I do it. I could just be missing something from your formula, but I doubt it. Also, the way I understand MMs formula to work, it (supposing I can get it to work) it would be the extremely long way around. Like I said, it just isn't making much sense to me, and some kind of a proof would be nice here.

Devon

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Okay, here's how to do it.

The distance from the first fret to the hypothetical (uncompensated) bridge is:

(scale length) X .94387

The distance from the nut is (scale length)(1-.94387).

The distance from the second fret to the bridge is the same proportion from the first fret to the bridge as the first fret was to the scale length. So, the distance of the second fret to the bridge is:

((scale length) X .94387) X .94387 = (scale length) X (.94387)²

The distance from the nut to the second fret is (scale length)(1 -(.94387)²)

See the pattern yet? The third fret distance from the bridge:

(scale length) X (.94387)³

The distance from the nut is (scale length)(1 - (.94387)³)

So, the formula for the distance from the nut to fret number, n, is:

(scale length)(1 -.94387^n)

I checked it against the online fret calculator at Stewmac and it matches.

So, where does .94387 come from?

The 12th fret is at half the scale length, so, if factor^12 = 0.5

factor = 0.5^(1/12) = .94387431268169...

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tirapop - that formula is not helpful, because it's not a function. One must use a function to describe this situation, and you've not posted it in that form.

I will explain with another example.

DISTANCE FROM NUT TO FRET X = [ A - B / C ] + B

A - scale length in inches

B - distance from fret x-1 to nut

C - 17.81700000

It's really simple. First we will calculate first fret, on a 25.5 scale - since any decent person here knows that this value is 1.431217

A = 25.5

B = distance from fret x-1 (which is 1-1) is 0, distance from 0 to 0 = 0

C = 17.817

[25.5 - 0 / 17.817] + 0 = 1.431217

simple.

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tirapop - that formula is not helpful, because it's not a function. One must use a function to describe this situation, and you've not posted it in that form.

Speak for yourself.

Why does x = 1? I'm using you formula and getting kind of close results, but something isn't coming out right. I understand why it works on fret 1, but if you could use it to find say, fret 13 with accurate results that would help. I don't quite understand what x is supposed to be. You say distance from nut, but that can't be it, because that's what the formula is attempting to find. The way Rich explained it is still the simplest way in my opinion. Other than just using online fret calculators or course ##### Share on other sites

MasterMinds,

I'll admit that I've never been to physicsforums.com. But, the formula I gave should be easy enough for most people, physicist included, to figure out. I'm not a rocket scientist, but, I do work with them.

I'll try to phrase it as a function for you.

X = f(n) = A(1 - D^n)

n = number of fret, an integer

D = .94387 = 1 - 1/17.817

If you're not familiar with the notation D^n means "D" raised to the power of "n".

example

fret 1: A(1-D^n) = 25.5(1 - (.94387)^1) = 25.5(1 - .94387) = 1.431"

fret 2: 25.5(1 - (.94387)²) = 25.5(1 - .89089) = 2.782"

fret 12: 25.5(1 - (.94387)^12) = 25.5(1 - .5) = 12.75"

Easy?

With your method, you have to calculate the fret locations in sequence. To calculate the distance to fret # 10, you need to already have calculated the distance to fret #9 ("B" in your formula), which in turn required the calculated distance to fret #8 and so on.

In the example you gave earlier, Fryovanni was right. For a 24" scale, the distance to fret #2 is 2.6185". Check with the Stewmac online fret calculator. When you calculated "[x - 1]" you put in the fret number "2" in for x instead of the distance of fret number 1 to the nut, 1.347", for the whole term "[x - 1]".

As an example, YOU calculate the distance from the nut to fret 12. If you come up with anything other than half the scale length, stick with an online calculator or Jehle's spreadsheet.

For you kids, trying this at home, if you don't have a scientific calculator or a spreadsheet , use the calculator built into Windows. If you can't find it in the Programs-Accessories menu, under the "Start" button, search the hard drive for "calc.exe". You can toggle to a scientific calculator from the "View" menu on the calculator. The "x^y" button raises "x" to the power of "y". Punch in value "x", press the "x^y" button, punch in value "y", then press the "=" button or hit 'enter'.

Edited by tirapop
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Guys. Snap out of it. This is why I wrote the spreadsheet. All you really need to know to get from one fret to the next is the twelth root of 2 (that's the fretting cosomological constant).

`string-length-at-fret-N / (2^(1/12)) = string-length-at-fret-N+1`
Do that 12 times at you get one octave up, etc... <edit> Come to think of it, if you wanted to find the 13th fret (as mentioned above) the formula would be:
```
string-scale / {[2 ^(1/12)] ^ N} = string-length-at-fret-N```

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Hey Bill, you started it!

Your formula works from the bridge, mine works from the nut... I'm kind of a glass is half empty type of guy.

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