uery for Trevor re Compensation Calculations

[kiwigeo]

Martin, you're best off ignoring the tension/frequency data on the string packet. D'Addario, (for example) who are one of the few who publish this information, rarely have test results from the string you're using - they extrapolate them from the few tests they have done.

Trevor, your comments supported by results I'm getting for Daddario EJ17 string set I'm currently testing. For the 0.045" A5th string I've just tested I needed to apply 17.8Kg of mass (174.4N force) to bring the string up to correct pitch (110Hz). Scale length I used was 647.7mm (25.5mm). The required tension quoted from the packet is 14.86Kg. Quite a significant difference.

[Trevor Gore]

I needed ~165N to get that string to pitch.

Another thing that string manufacturers do is change the composition of strings but stick with the same labeling. The main culprits for this particular sin were Cleartone, who changed the core diameters of all their wound strings, which significantly affects the stiffness and hence the required compensation. The sound also went from brilliant to crap. Anyone want any excess Cleartone strings?

[kiwigeo]

18.2Kg to bring the D 4th up to target frequency versus 16.27Kg on the packet.

I've got a 10 pack of EJ17s and the oil patch isn't exactly busy at present so I might just run 5 sets on the rig and see how results vary.

[kiwigeo]

Currently 3/4 way through testing two sets of Daddario EJ17 strings.....results to be compiled over the weekend and will be available to those who are interested.

[Trevor Gore]

"Believe me, my young friend, there is nothing - absolutely nothing - half so challenging as simply messing about with strings".

(With apologies to Kenneth Gahame)

[kiwigeo]

“It's not courage so much as stubbornness," Alice said frankly. Her lips curled back from her teeth in a grim smile. "I don't like to lose.”
― Django Wexler, The Mad Apprentice

[kiwigeo]

Currently 3/4 way through testing two sets of Daddario EJ17 strings.....results to be compiled over the weekend and will be available to those who are interested.

Two sets done....have decided to do a third set.

[kiwigeo]

Still testing...interrupted today by a job interview. First time Ive had a formal interview for a job in 40 years

[Nick]

Still testing...interrupted today by a job interview. First time Ive had a formal interview for a job in 40 years

Ahhh, so you decided to apply for that pole dancing job after all then !

[kiwigeo]

Still testing...interrupted today by a job interview. First time Ive had a formal interview for a job in 40 years

Ahhh, so you decided to apply for that pole dancing job after all then !

Some of the questions were alot harder to deal with than a dancing pole. Am used to the traditional oilfield "interview" where you sit with the client and consume endless pints of beer and discuss everything except the job.

[kiwigeo]

Richard I rejigged my spreadsheet to present target and fretted string frequencies and it all seems to work.

I take that back.......saddle compensation values are reasonable but adding nut compensation doesnt result in much of a change in fretted frequencies. I think Ive screwed up adding nut compensation in the right place.

Heading off to the special Gore Army substandard recruit re-training facility

[kiwigeo]

The spreadsheet is driving me mad...time for a break and then a re-assessment.

Richard I PM and emailed you re your spreadsheet...did you receive the messages?

[Woodsy23]

Martin,

Oops. I didn't see that one. I thought I usually got an email notification of a pm.

Anyway, I'm happy to help if I can. I'll look into it tonight.

[kiwigeo]

Martin,

Oops. I didn't see that one. I thought I usually got an email notification of a pm.

Anyway, I'm happy to help if I can. I'll look into it tonight.

Thanks Richard.....as explained in PM/email the way nut compensation is handled in my spreadsheet seems to be not working properly...

[JurgenV]

Hi,

I´m building guitars as a hobby for some years. Actually these guitars have never been really bad but from 11 builds lets say 3 are really good sounding but I never really knew why. When I read about the "BOOK" I organized a copy in a library (actually I could find just one book in whole Germany) "I saw the LIGHT" and ordered it from Trevor. Now I´m in the same number frenzy as a lot of others in this forum.
I started with the nut / saddle compensation trying to do it with an excel spreadsheet. In order to have some reference numbers I used the data from "Woodsy23" for his neck model and the input data he posted in his pdf file. With two variables and some boundary conditions I could even use the "solver" from Excel to optimize the errors and recieved a very similar solution as he did with his manual approach. The differences due to me using the formula for theoretical fret positions instead, so basically just rounding errors. So far so good...
Now my questions:
how do I calculate "f" for the first fret? What ever I tried didn´t give me the value Woodsy23 used. Without any compensation the error on fret 1 with this data is -136 cent which i don´t believe (see second file)

Question 2 concerns the neck modelling: Ok, I can model the action at each fret according to equation 4.7-22. But how relieable are these models? Are you modelling the neck curve for every new guitar again? Or do you just change the values for relief, nut height and action at fret 12 (or fret 18) and it matches the action for each different model or even for every guitar you build independent of the model?

Hope you can help me out. Thanks in advance

btw if my english sounds sometimes a bit strange.... sorry

Juergen

[Woodsy23]

The value of f for all frets except fret 1 is calculated using pythagoras' rule using only the fret position values in column 2 and the action values in column 3 (as in equation 4.7-30 in the black book). For fret 1, there are two slight differences. There is no action value, as such, at the nut, so I use the value of 0.1, which you will see in column 3 on the Fret No 0 line. This is the distance from the plane of the fret tops to the bottom of the string slot. This is similar to the string action (dsn at other frets). For the distance between frets, I also subtract the trial nut compensation value (0.8mm) from the distance between fret 1 and the nut (36.125 - 0.00).

Regarding your second question, I didn't recalculate the string action for each guitar. For 12 fret guitars, I always aimed for the same action at the 12 fret so I adopted the same action at all other frets. I can't quite recall what I did for 14 fret guitars. I think I used similar values, that is, based on the target 12th fret actions.

[Trevor Gore]

Question 2 concerns the neck modelling: Ok, I can model the action at each fret according to equation 4.7-22. But how relieable are these models? Are you modelling the neck curve for every new guitar again? Or do you just change the values for relief, nut height and action at fret 12 (or fret 18) and it matches the action for each different model or even for every guitar you build independent of the model?

I'll take on this question as Richard took on Q1!

The neck is modeled as a continuous curve from fret 0 to the last fret (say fret 18). As neck shapes tend to be similar down the length, (and on my guitars similar from one instrument to the next) they all tend to have a very similar deflection profiles. So once the mix of curves has been "calibrated" for the style you are building in, the deflected shape can be represented sufficiently accurately by specifying just the action, nut height and relief. Nut height and relief are pretty much constants, anyway, on my set-ups. So no need to change the curve modeling for every different guitar you build, basically just the action.

[JurgenV]

Hi Trevor,
thanks for your input. Sounds promising. I´ll start with the new spreadsheet over christmas and use as reference for the neck my already existing guitars.

Btw. how would you determine the nut and saddle compensation on an already finished guitar? For input we have now the intonation errors which most probable don´t correspond to the theoretical errors. So how do you start... Add just the measured intonation errors to the theoretical values? Somehow I´m not sure that´s a sensible way. I´ll think about another approach, but your input would be appreciated..

[Trevor Gore]

Btw. how would you determine the nut and saddle compensation on an already finished guitar? For input we have now the intonation errors which most probable don´t correspond to the theoretical errors. So how do you start... Add just the measured intonation errors to the theoretical values? Somehow I´m not sure that´s a sensible way. I´ll think about another approach, but your input would be appreciated..

All explained in Section 4.7.2.3

[JurgenV]

Sorry, somehow I kind of forgot that I read this chapter I was so stuck with the rest of 4.7 ...

And already the obligatory spreadsheet done. Actually I was quite surprised that a variation of the scale length by 35mm didn´t change the solution for the compensation. I used the example data in table 4.7.1 and compared the solution with table 4.7.2 varying the scale length from 625mm up to 650.
@Richard: your way of dealing with the formulas bit by bit in excel in your example helped a lot

[GregHolmberg]

OK this thread's pretty old, but I thought I'd add my implementation to the pile. Here's a compensation spreadsheet using Google sheets. Yes, you can see the formulas. You can make a copy (File -> Make a copy).

I used the sample data for measured action from Woodsy23 (eight years ago!), and I got pretty much the same result. Like him, I don't have an optimizer that can handle two variables (nut and saddle), so I just try values until I get to minimum error. I think the LibreOffice spreadsheet software has a solver that can do that, so I should try it.

Woodsy23 found a nut compensation for the third string of 0.8 mm and a saddle compensation of 0.5 mm. I went out to hundredths of a mm, and got 0.76 and 0.49. Pretty close.

I summed the absolute values of all the errors, and got 0.6 cents. That's amazing. I did get different values for the errors (Hz and cents) than Woodsy23 did. Not sure why that is. I can't see his formulas though, so difficult to diagnose.

Woodsy23 did not implement the geometric modeling of the neck, he just used measured values. I took a stab at it. It was a real slog (circle + ellipse + line). I can't tell if it's correct, since I have nothing to compare it to. It seemed to produce reasonable values for the actions. I tried to fit the equations to the measured values, and ended up with α=50%, β=104% (to match the action at the 12th fret). I compared the values to the measured ones, and got a total difference of 0.872 mm over 18 frets. So that's pretty good.

I also tried two other methods to model the actions.

1. I simply inserted a chart of the measurements and asked Google sheets to fit a polynomial curve to it. It came up with:

Code: Select all

0.187 + 0.254x + -6.48E-03x^2

I compared these to the measured values, and got a total difference of 0.543 mm. Even closer than the circle+ellipse+line method.

2. I tried my own model. I remembered that a cantilevered beam (like a neck) with a moment at the end (like the strings) has a deflection of:

Code: Select all

δ = Mx^2 / 2EI

I used E for Hard Maple (12.62 GPa) and a neck thickness of 22 mm, and calculated the centroid, I (second moment of area), force of six strings, and M the moment around the centroid. With this I could calculate deflection at any fret position. The deflection is of the form x^2, so it's a parabola. A little different than the circle+ellipse method. Also much easier to implement.

The formula for y of the neck deflection I used was:

Code: Select all

y = M/2EI x(2*xlast - x)

I combined it with a line to get the target action at the 12th fret. In this case β=77%.

This produced a very good model of the measured actions, with a total error of 0.709 mm--better than the circle+ellipse method, not as good as the curve fit method.

You can see the four methods in the spreadsheet, color-coded. I can easily switch which method to use to calculate intonation errors, using column Q, "action selected".

I also compared the errors of the three models to the "correct" compensation of the measured method. I got total cents error of 0.598 for measured, 1.528 for curve fit, 1.898 for parabola, and 2.500 for circle+ellipse. All pretty small total errors--that's an average of 0.14 cents error per fret. Beyond human ability to distinguish.

I like the parabola method. Easy to calculate and quite accurate.

If anyone has any more measured actions, I'd love to try them out. Or if your spreadsheet got different results, let me know. We can compare.

I hope this helps someone.

Greg

[GregHolmberg]

OK, I made an improvement to the parabolic model. New formula is:

Code: Select all

y = M/2EI x(xlast - x)

This gives just the relief of the parabola compared to a straight line from the nut to the last fret. So, similar to the circular formula, it's 0 at the nut and at the 18th fret.

To get the right action at the 12th fret, I changed β (for the line) to 101.5%.

I also fit the β for the circle+ellipse method a little better, at 103.5%.

Now, the differences from the measured actions are even better. 0.543 for the curve fit (unchanged), 0.540 (was 0.709) for the parabolic method, and 0.863 (was 0.872) for the circle+ellipse method.

So the parabolic method actually beat the curve fit method!

The spreadsheet has been updated.

Greg