Fretboard Calculator

Replies to This Discussion

Permalink Reply by Joseph Oster on March 7, 2017 at 9:12am

I had no luck with your "fret rule 2^(1/12)" so searched for a source and found a different algorithm:

Calculating Fret Positions

http://www.liutaiomottola.com/formulae/fret.htm

Calculating the positions of the frets requires the simplest bit of math. The (really) historical technique is called the rule of 18, and it involves successively dividing the scale length minus the offset to the previous fret by 18. [...] The invention of the pocket calculator made it possible to make use of a more accurate constant, and so these days we conventionally calculate fret positions for equal temperament by successively dividing the scale length minus the offset to the previous fret by 17.817.

And from here: http://www.stewmac.com/How-To/Online_Resources/Learn_About_Guitar_a...

The "factor" for fret spacing is 17.817154.

So using Anemone to loop, I got this:

I must admit that it doesn't look quite right, and I'm not sure why...?

Attachments:

• fretruler_2017Mar7a.gh, 16 KB

Permalink Reply by Justin Michael Bush on March 7, 2017 at 11:17am

Hi Joseph, thanks for that. The proportions look right, but it's not quite there. The 12th fret should be half the length scale length from the starting point, (12.75 from the "nut" or starting point if scale length is 25.5)

I knew there was a factor. Back in the day they used 18/17. However, this is kind of like using 3.14 rather than pi. Though it would probably be close enough for practical application, since I have the ability, I'd rather use the actual math. I'm not very good at math, but my understanding is that the "twelfth root of two" (2^(1/12)) is derived because an octave of a note is double (or half) the frequency of another. There are 12 notes, 13 being the octave, so 12 steps between the octaves. So you need a number that multiplied by itself 12 times results in it's doubling, hence 2^1/12. Like I said, I'm not great at math, so I'm not sure if I explained or even understand that correctly!

Thanks for your help, I'm going to look into using anemone!

Permalink Reply by Joseph Oster on March 7, 2017 at 11:47am

If you look at the values from the 'D1' output (flattened for readability), you can see that line 12 is exactly half of line 0:

So maybe it's an "off-by-one" issue?  I'm not happy with this output...  I would expect the frets to be distributed over a distance equal to "Scale Length", for one thing.  But it's just far enough out of my realm that I'm not sure how to fix it?

Ricardo's solution looks promising, though, as a way to use your fret rule.  Here is his function plugged into my Anemone loop:

Doesn't meet your criteria, though.

Just a little too today distracted to figure this out as well as I would like.  Anemone is a GREAT tool, though maybe not necessary in this case?

Attachments:

• fretruler_2017Mar7b.gh, 15 KB

Permalink Reply by Justin Michael Bush on March 7, 2017 at 12:03pm

Ahh ok, yes, now that I see those values and referencing them to the fret ruler they ARE the correct values from fret to fret. So, that data should be usable. The frets shouldn't span the entire scale length, but definitely more than they were.

Thanks again, I will play around with both solutions. Great way to learn and get more ideas.

Permalink Reply by Riccardo Majewski on March 7, 2017 at 10:26am

Hi guys.

Have a look at this, maybe it is ok.

Double check, i don't understand the math behind it....

Cya.

Attachments:

• fretruler_V2.gh, 12 KB

Permalink Reply by Justin Michael Bush on March 7, 2017 at 11:24am

Hey Riccardo, thanks for the help!

The lengths of the frets aren't quite right, but the math for their spacing is spot on. You even included the bridge (end of the scale)!

I should be able to tinker to get the fret lengths right. I want to be able to pick a point on the datum of the nut location and then use the nut width and width at 12th fret to draw straight lines between (and beyond the 12th) and then have the parallel frets meet at those unparalleled lines.

Getting the creation and spacing of the lines for the frets was the biggest thing though, and you've done that, so thanks. I just hope I am able to deconstruct and understand what you did.

Permalink Reply by Justin Michael Bush on March 7, 2017 at 11:35am

Re: the math,

Here's my understanding, c/p from my response to Joseph above:

"I knew there was a factor. Back in the day they used 18/17. However, this is kind of like using 3.14 rather than pi. Though it would probably be close enough for practical application, since I have the ability, I'd rather use the actual math. I'm not very good at math, but my understanding is that the "twelfth root of two" (2^(1/12)) is derived because an octave of a note is double (or half) the frequency of another. There are 12 notes, 13 being the octave, so 12 steps between the octaves. So you need a number that multiplied by itself 12 times results in it's doubling, hence 2^1/12. Like I said, I'm not great at math, so I'm not sure if I explained or even understand that correctly!"

Permalink Reply by Joseph Oster on June 28, 2017 at 6:39pm

This thread was referenced on a later one:

Guitar Nut conundrum: equal spaces and equal centers question
http://www.grasshopper3d.com/forum/topics/guitar-nut-conundrum-equa...

so I want to update the relevant part of that thread here, the 'Frets' component:

It defers on the option of setting the 'Start (S)' of the internal 'Series' component to one instead of zero, creating a "fret zero" that is co-linear with the Nut.

Attachments:

• Frets_2017Jun28a.gh, 21 KB