Scale Length Calculators

[spindlebox]

I am building a 34" scale bass and am going to be building a fret slotting template, and am in the design phase of the entire bass.

I went to two different websites:  The Tundra Man site and StewMac.  I got two different results from their calculators.  This is obviously concerning and I'm wondering why?  Is one just simply wrong?  Here are my results:

 

 

So which one is right?  Also, I used this template - scaled 1:1 and the frets on this template are NO WHERE NEAR where either one of these calculators estimate.

I will say that I have measured the scale length on my drawing umpteen times, and my drawing is DEFINITELY spot on.  (NOTE, I am building a 5 string bass so that's why that photo of the headstock is there LOL.  My drawing has taken into account a wider neck.)

I obviously want to get this right.  Any ideas?  Your insights will be very much appreciated!!!

Edited February 11, 2023 by spindlebox
Provided links to fret calculators

[curtisa]

It's because the Tundraman website uses a less-common divisor when calculating the fret spacing. The 'modern' way of doing it is to use the twelfth-root-of-two method which places the twelfth fret at exactly half the scale length (17" in your case). This gives an initial divisor for placing the first fret of 17.817, Ie, if you divide the scale length by this number, the result is how far away from the nut the first fret will be (34/17.817 = 1.908"). Working out the remaining frets is just a case of subtracting the sum of the previous frets you calculated from the scale length and repeatedly dividing by 17.817. The Stewmac calculator (and FretFind2D, LMII and many others) uses this method.

For some reason (which is a bit naughty of Tundrman for not disclosing) he's used 17.835 as the common divisor, and then erroneously explained away the discrepancy in the calculated results on his webpage as '...rounding errors...'. Using the above divisor will still work and give playable results, but it does look odd if you're trying to compare the results of the two tables,

Liutaio Mottola has a good explanation of the various methods of calculating fret placement on his website if you really want to get heavy with the math.

As an example, below are the differences when calculating the fret positions using the two divisor values of 17.817 and 17.835 on the first 12 frets at 34" scale length in a spreadsheet. The Stewmac results agree with column 'C'; Tundraman in column 'E':

[spindlebox]

Out of curiosity, Has anyone ever for instance done both To compare how it sounds? I am just wondering which is the most correct. Math is one thing but how does it sound?

I appreciate your hugely helpful and detailed reply!

[curtisa]

There's a related article on Mottola's website that compares fretboards slotted to the modern 17.817 factor against the traditional (pre-calculator) variant, where the constant used was simply 18. If you scoot down to the graphs and compare the green cross points (rule of 18 with intonation compensation applied) vs green diamonds (17.817 with compensation) for each string they're extremely similar. Probably within a couple of cents at their worst, and certainly questionable as to whether a regular hooman could detect the difference if played side-by-side.

Based on the info linked, the difference in fret placement using 18 vs 17.817 seems tiny. I've personally not built anything that might compare the two, but I would think that fret placement using 17.835 and 17.817 would result in even less intonation/pitch discrepancy still.

Bottom line: both the Stewmac and Tundraman fret calcs produce perfectly acceptable fret position results that work, even if the numbers don't quite line up. Entirely up to you as to which one you pick.

[spindlebox]

^{Thank you so much for your educated and thorough answers!  I hope this thread helps many people.  It certainly has helped me!!!}

^Cheers

[henrim]

23 hours ago, curtisa said:

he's used 17.835 as the common divisor, and then erroneously explained away the discrepancy in the calculated results on his webpage as '...rounding errors...'.

That's odd. 

Don't know how they came to that but if the twelfth root of two is truncated to four decimals you get 17,835:
r = 2^(1/12) = 1,059463094359295 = 1,0594
1/(1-(1/r)) = 17,835016835016835 = 17,835

With two more decimals you get:
r = 1,059463
1/(1-(1/r)) = 17,8171804315 = 17,817
 

[curtisa]

Correct - he's truncated the initial 12th root of two, not rounded it up. If he'd used r = 1.0595 the calculator would've provided more accurate results, and his disclaimer on his webpage that there's rounding error in the tables would be more relevant.

R = 1.0595 gives a constant of 17.808, which would yield a 12th fret position of 17.007" from the nut. We're splitting hairs, but it explains why the difference is there.