# fret calculator version 3.0

Discussion in 'Luthier's Corner' started by tpsbassist, Aug 13, 2002.

1. ### tpsbassist

May 20, 2002
Butler, Pennsylvania
here is my third version of the fret calculator program, it now calculates fret distances for both inches and millimeters. It calculates distances both from the previous fret as well as from the nut. hope this can help somebody. it is a simple program and requires no spreadsheet programs, it also prints the output to a notepad file for easy printing. any suggestions for future versions of the program welcome.

2. ### pilotjonesSupporting Member

Nov 8, 2001
US-NY-NYC
tps
Thanks for the new revision. More useful all the time!
After looking over the results of your (previous rev 2.0) program, and those from JP Basses' spreadsheet, I noticed that they were very close, but not identical. So I researched to find out the cause of the discrepancy. I turns out that not only does fret placement by successive division (which I assume you are using) by 17.817 introduce rounding errors, but that there are even other numbers being used! It turns out that the successive division method is "easier method" that approximates the actual exponential formula. (It is easier because it does not use exponents, just division, and so is easier to figure.) The actual formula, which produces the exact position (accurate within the digit limits of your spreadsheet, calculator or program) from the bridge to any fret, is:

dist(x) = s / (2 ^ (x/d) )

where

x = number of the fret being evaluated
dist(x) = distance from bridge to fret x
s = scale length (distance nut or zero fret to bridge)
d = number of divisions per octave ( = 12 in western music)

This produces the positions for the standard equal-tempered scale. The nut-to-fret positions and fret-to-fret positions are then produced by simple subtractions.

(There are no adjustments for string stretch, à la Buzz Feiten. These are the standard positions.)

I have taken the liberty of modifying the spreadsheet that JP Basses posted in the previous thread. (JP- hope that's OK with you, otherwise I'll gladly delete this.)

3. ### tpsbassist

May 20, 2002
Butler, Pennsylvania
I took my equations from a guitar/bass construction book and turned it into that program. in the book it suggested rounding off but in my program i used full length decimals and leave the rounding off to the user.

nut Distance starts out at 0.
rule = 17.817

{
distance = scale length / rule;
nut Distance = nut Distance + distance;
and then for the next fret
scaleLength = scaleLength - distance;
and start the equation over again.
}

the output matches the chart in the book only with a few more decimal places because my program does not round off like the book.

4. ### JP Basses

Mar 22, 2002
Paris FRANCE
No problem Pilotjones! You're welcome.

I've just opened your excel file. Nice Job.
Anyway, I think that most guitar and bass builder use the simpler "rule of 18" (17.817) which provides a "good enough" fret positioning. Cutting fret slots by hand can't lead to 2 or 3 igits precision so...

I'm curious about which formula CNC equiped factory use!

JP

5. ### pilotjonesSupporting Member

Nov 8, 2001
US-NY-NYC
tps

A more exact number for the division method would be
rule = 17.8171537451057.

If you use this value you should find the numbers very close to perfect, e.g. 12th fret on 860mm scale = 430.000000x mm

(Maybe I'm getting a little too picky here! )

JP

I imagine, if you were using CNC, why not be as exact as possible!

6. ### Suburban

Jan 15, 2001
lower mid Sweden
There was a thread about fretless playing recently, where Steve Lawson asked: "How close to in tune is 'close enough'".

I believe this discrepancy is why I prefer playing fretless...unlined.

7. ### action510

Dec 9, 2002
WIlmington, NC
if you put in frets using that program what if your not exactly on target with the distance? will just a little mistake mess everything up?

8. ### l0calh05t

Oct 14, 2001
Cottbus, Germany
action510 hat depends on what you think is a "little mistake". The error introduced by the division method is insignificant especially because the effect of the neck relief might even be bigger.

(BTW: That big number in my signature is the 12th root of 2)

9. ### Hambone

Mar 18, 2000
Atlanta/Loganville
Probably not. That's the difference between accuracy and precision! Besides, a fret saw is only .020" thick and with that thickness you can make a small error just in blade placement before you make the first draw with the saw. Add to that the possibility of crowning the fret a little off center and you begin to see how small errors are nearly impossible to avoid but would have little affect as long as they are centered on the proper location measurement.

10. ### ax_mann

Aug 21, 2006
hi guys im new to this forum so not too sure how it works but im about to start making a bass and that spreadsheet would be really handy, how do i go about downloading it as its not showing up on the page

thanks a bundle and if anyone has it that they could email me it'd be much appreciated - email is labrat_66@hotmail.com

thankyou!
scott

11. ### Phil Mailloux

Mar 25, 2005
Brisbane, Australia
Builder: Mailloux Basses