Test data for intonation spreadsheet

[Munchkin]

Hi

What an inspirational book!

I've constructed a spreadsheet in Excel to calculate the compensation for nut & saddle and am using the premium solver (http://www.solver.com/exceluse.htm) to minimise the intonation error. However, I'm getting results that are not in the same ball park as the example.

Trevor, is it possible to get a bit more test data so that I can refine/test my model? Specifically, it would be useful to have the 'k' value and tension for each string for the Martin set that you used. I think I need to 'train' the solver.... (or maybe I have a coding error )

My first post on the forum from snowy London!

Martin

[Trevor Gore]

Hi Martin,

Those cold, dark nights are especially suited to messing with intonation problems! Please advise some more of your countrymen/women!

For a first shot at k for steel strings, use the formula on the bottom of page 4-109. The Young's modulus for steel is 210GPa, the string cross sectional area you can work out from the string's diameter. You only need the core diameter for the wound strings, and you can correct for the hex shape if you feel pedantic. That should get you in the ball park if everything else is coded correctly. Once you have the program running and giving sensible answers (the actual answers are VERY dependent on the neck geometry (i.e. relief) that you choose) you're best off feeding it with the string data you collect from your own test rig. This is quite quick for steel strings but takes an age (but is the only way to do it) for "nylon" strings.

For string tensions, the Martin 12s are essentially the same as D'Addario 12s (except for the slight difference in the 6th). You can get the D'Addario tensions from here:

http://www.daddario.com/DAstringtension ... iveID=2871

(Download the .pdf)

Keep us posted on how you go.

[Munchkin]

Thanks Trevor

I tackled the spreadsheet before building the test rig so I had already used the D'Addario tension chart and Young's Modulus.... so that means I have a coding error! My model keeps giving me very small nut compensation (if I let it!).

It seems to me the most significant deflection is the straight line component which is adjusted by Beta to give a 'conventional' set up. I've just multiplied the component by .91 which is the ratio of the action at frets 12 and 20. Is this correct? I'm getting a change in tension of between approx .21N and .24N on the 1st string Sounds about right....?

By the way, it seems to me that the cross sectional area of a hexagon and a circle are quite significantly different - I make it a factor of 1.209.

I'd better go wade through my formulae! If any of the above is wrong please let me know.

Martin

[Trevor Gore]

I'm getting a change in tension of between approx .21N and .24N on the 1st string Sounds about right....?

I'm looking at ~0.5N at fret 12 on the 1st string (action 2mm at 12th). This should be pretty straight forward to check. Doing a quick "reality check", frequency is proportional to sqrt(T), tension is ~100N, hence the computed tension change is ~0.5%, equivalent to 0.25% change in frequency, from say 329.6Hz to 330.45Hz = ~4.3 cents. Checking against Fig. 4.7-4, for the high E string error at fret 12, the graph reads ~4.1 cents. So that puts my 0.5N tension change figure in the ball park and you seem to be about half of that. Might have missed a SQRT? Have you got the finger wrap in?

By the way, it seems to me that the cross sectional area of a hexagon and a circle are quite significantly different - I make it a factor of 1.209.

Well, 21% error is in the ball park!

I'd better go wade through my formulae!

Unfortunately....

[Munchkin]

Well after many hours of de-bugging I seem to be getting rational answers from my intonation model - which is great. But I've just checked the pricing of the premium solver I mentioned - US$895

Back to the drawing board.... I may need to redesign the spreadsheet so that the bundled solver will function (this is a 'non-smooth' problem it seems...) I will report back on this...

Meantime, a question (or two) for Trevor.

On the string stretchable length mentioned on page 4-115 of design - If the string is not a straight pull between tuner and nut (my design is a slotted headstock) does the change in direction over the nut remove that portion of the string from the equation? I assume it does... but is this correct?

Also, I prefer a lower set up than the specs in Table 21-2 of Build (2.8mm to 2mm versus 1.7mm to 1.2mm). When I punch my set up into the model I find that the lower change in tension makes for a less accurate compensation across the frets of interest, which is less than +/- 0.5 cent for the higher action versus sharp 1.4 cents to flat 2 cents for the lower. The active string length is also less (which you would expect, but only 0.65mm versus 1.69mm?) Apart from the inputs the model is the same... Any insights/thoughts?

Martin

[Trevor Gore]

Well done on the de-bugging! Anything particular, or a variety of things?

On the string stretchable length mentioned on page 4-115 of design - If the string is not a straight pull between tuner and nut (my design is a slotted headstock) does the change in direction over the nut remove that portion of the string from the equation? I assume it does... but is this correct?

Well, that's the issue - it's hard to be sure either way. That's why my string pulls are straight, because I've found that with a straight string pull and the headstock angles I use, the stretchable length includes the nut-to-tuner string length.

Also, I prefer a lower set up than the specs in Table 21-2 of Build (2.8mm to 2mm versus 1.7mm to 1.2mm).

That sounds very low. How are you measuring this? Even measured with a capo at fret 1, (which I don't do, I use open strings) it is still low, even for an electric. However, that's by the by. As you've found, some set-ups give lower residual errors than others. If you shift the neck geometry around a bit by changing the shape of the relief, you will change the result and with some fiddling about you may well be able to improve it. You could stick it in the optimiser, if you want. I've found that 0.2mm to 0.3mm relief at fret 5 for a 12 fret neck usually gives the lowest residuals. But that might not give you a usable relief profile with the action you've chosen. And when you've found a good geometry, you then have to execute it! The relief profiles I suggest in the book are the "natural" profiles that my necks typically assume under load. You might be able to vary that profile with a different style of truss rod.

[Munchkin]

On the de-bugging - lots of subtle things; not really errors (although there were a few bloopers).

A few observations:

• It's important to keep in mind that the tension of the string is dynamic - that is when the model recalculates the string length including compensation then you need to recompute the tension to re-tune the string to concert pitch (obvious when you type it out but it took me a long while to work it out!).

• You need to allow for compensation when calculating the deflected string length but not the circular component.

• If you're going to use Excel keep all your table lookup functions out of the calculation model and use array formulae when you can.

• Replace the Beta action proportion with a straight line gradient calculated at the 12th fret (rather than last fret) - it's a straight line!

• You will need to force the model to solve for string lengths longer than scale and constrain the compensation within normal bounds.

That sounds very low. How are you measuring this? Even measured with a capo at fret 1, (which I don't do, I use open strings) it is still low, even for an electric.

I do a lot of set ups and I've found that I can achieve a buzz free action on most acoustic guitars with set ups approaching these. I use StewMac's excellent String action gauge http://www.stewmac.com/shop/Tools/Measu ... Gauge.html , a completely straight neck and a capo. Once I've roughed the saddle in close, I adjust the nut height and then refine the saddle height without the capo. Any buzz or choking can then be relieved with the truss rod. Electrics I can often take lower depending on fretboard radius (0.03" on 1st string for a flattish radius)

You might be able to vary that profile with a different style of truss rod.

I've built the guitar with a commercially available 2 way truss rod and I'll be aiming for a straight neck as above. Come to that, you've measured neck relief of 0.1mm - most folks would call that straight!

Again, thanks for all your help and encouragement, Trevor. We're all thinking about guitars in a different way now!

Has anybody else made an intonation calculator out there?

Martin

[Munchkin]

Trevor

Intrigued by your comments about finding a geometry that works and then building it, I found the following...

Scale: 647.7 (25.5")
Body Join: 14
Frets: 20
Measured relief (at 7th): 0.1mm
Finger pressure: 85%
Alpha: 0.7
6th String action at 12th: 2.2mm
Nut to tuner length: 0
String data: Mu = .009862 Kg/m
Core diameter= .018" Round (Newtone strings)

The model found a solution with a nut comp. of 2.64mm and a saddle comp. of 2.36mm -the string is shorter than nominal scale! But the intonation errors are less than +/- 0.5 cents.



Seems crazy but all the numbers seems to be consistent. And it sure is 'makeable'.

Intriguing....

Martin

[Trevor Gore]

Well done, Martin, on getting it all to work. It at least means that the stuff in the book is reasonably error free (I hope!). And thanks for posting those hints for other users. It's pretty easy to get into circular references when programming this stuff. So far, I think you're the first to have programmed an intonation calculator from the book and got it optimised, so well done again.

The graph you posted certainly has a familiar shape to it, so it looks like you have it all working. Let us all know how you go when you string up.

[Munchkin]

It's been a journey, Trevor!

I suppose we all expect the string to be longer than scale to compensate for the increase in tension from fretting and because all the commercially available intonation products (Buzz Feiten & Earvana) are made for the retro fit market. But for new builds we can shift the string compass towards the saddle and have a shorter string length with corresponding lower tension for concert pitch to compensate for fretting force, with the nut shifted to keep the open string in tune. Brilliant!

So forcing the model to have the string length greater than scale is actually unnecessary - but I've yet to determine this is correct in the real world!

My concern with the whole calculation centres on the string deflection g0 which you measure at 0.5mm. The string stretch is very dependant on this number - you mention in the book that you measured the fretting force from many players to come to this average. What variation did you observe from this average?

My model applies the fretting pressure factor to all the g's, including the first fret for a g1 of .425mm. Is this correct?

Martin

[Trevor Gore]

I suppose we all expect the string to be longer than scale to compensate for the increase in tension from fretting and because all the commercially available intonation products (Buzz Feiten & Earvana) are made for the retro fit market. But for new builds we can shift the string compass towards the saddle and have a shorter string length with corresponding lower tension for concert pitch to compensate for fretting force, with the nut shifted to keep the open string in tune. Brilliant!

So forcing the model to have the string length greater than scale is actually unnecessary - but I've yet to determine this is correct in the real world!

There's no reason at all to constrain the string length to greater than scale length. The optimiser will do what it will and if the string length comes out shorter than the design scale length, so be it! The answers are usually sensible. However, if you code up Section 4.7.2.3 and put some real data in you'll be surprised at where the optimiser will take you if you leave it unconstrained, e.g. 9mm nut compensation. The thing is right, but as this technique is usually used on existing guitars, you have to constrain it to something you can execute.

My concern with the whole calculation centres on the string deflection g0 which you measure at 0.5mm. The string stretch is very dependant on this number

Well, just squeeze a string hard when you're fretting and you'll see why! I can move a 6th string 30 cents and a 1st string 6 cents by changing finger pressure. However, good players tend to use the minimum they can get away with and seem to be very consistent. The really skilled ones will actually adjust intonation "on the fly" with finger pressure, pulling and pushing notes, usually to get closer to Just intonation.

you mention in the book that you measured the fretting force from many players to come to this average. What variation did you observe from this average?

Quote "We have measured the deflection of the string between the nut and first fret for a number of players and the typical fretting force exerted by the players deflects the string approximately 0.5mm..."
There were 5 or so of us messing with this with feeler gauges and that was the consensus we came to, so no mean and standard deviation, if that's what you were looking for. What's more significant than the particular player is the style being played. Flat pickers hit the strings harder and have to hold them down harder as a consequence. And that's why there is a finger pressure factor variable in there (Fp, Eqn 4.7-29). Ultimately, you have to calibrate it to suit.

My model applies the fretting pressure factor to all the g's, including the first fret for a g1 of .425mm. Is this correct?

Yes, as per Eqn. 4.7-29, which modifies the deflection for the fret spacing, too.

Don't forget that the body resonances can really screw things around as well, if you don't take care of them! However, even with all the potential limitations, the results, at least to my ears, are heaps better than what the conventional intonation methods give.

It's been a journey, Trevor!

Sounds like you had a fun trip!!

[Munchkin]

I''l be tackling the resonances when I enter the real world!

I'll update you all when I string the baby up.

By the way, the bundled solver in Excel will optimise this problem. I tried out the 'Premium' solver as I thought it might be where I was having trouble.... needless to say it was my design that was the challenge!

Martin

[Munchkin]

I promised an update on string up.

The intonation formulae seem to have worked perfectly! I am working on a few resonance 'challenges' (I'll post on that in a few minutes as I'd appreciate advice...) but the guitar appears to be in tune on every fret on every string - she sounds lovely!



The active string length came out shorter than scale length for the specified strings (Newtone Master Class 12-52 plus a 10 - round core strings).

Thanks again Trevor for your inspiration.

[woodrat]

Nice Work Martin....I have been following this thread with interest although I haven't yet got into nut and saddle compensation to the same degree. I am a bit lacking in the maths chops and the analytical understanding of it all but I continue to be fascinated with the problem! I used the quick and dirty method on my latest 2 builds...ie...I cut ~1.5 m from the end of the fretboard. It sweetened them up for sure. I will have a go to the higher level at some stage....

Well Done!

John

[inoz]

Nice Work Martin....I have been following this thread with interest although I haven't yet got into nut and saddle compensation to the same degree. I am a bit lacking in the maths chops and the analytical understanding of it all but I continue to be fascinated with the problem! I used the quick and dirty method on my latest 2 builds...ie...I cut ~1.5 m from the end of the fretboard. It sweetened them up for sure. I will have a go to the higher level at some stage....

Well Done!

John

I'm glad to hear you say this John, most of this is way over my head... the quick and dirty method will probably do me for life.

[Dominic]

OK, I am working through my spreadsheet for intonation so might ask a few questions along the way but one way or another I am going to work it out including testing my own strings.
So i hope anything I ask or write here is useful for others. Even if some is bleedingly obvious.

So just to clarify the neck geometry, it is modelled as a circle from the nut blending into an ecllipse before becoming straight. And the circle component (alpha) is 50% of the length, hence a=0.5. before I model everything to find out, what might a typical measure for the ellpitical component (beta) be? 0.25 at a guess.

Cheers
Dom

[Trevor Gore]

The neck is modelled as a superposition of a circle, an ellipse and a straight line rather than one type of curve running into another. So, for example, if the elliptical component is zero, all you have is a tilted section of a circle. Alpha=0.5 puts equal weighting on the circular and elliptical components. You can calculate beta by inverting Equ. 4.7-22. I think Munchkin might have found a more convenient method here.

[Dominic]

Thanks Trevor, does that mean that the C and E components run to the 12th fret so B is linear?

As for the geometry, so I can see it in my head, your hockey stick analogy implies that it is a circle, and ellipse and the line. I get that the proportions can change but I don't know what you mean by superposition. In physical terms, is it not important where C and E are in relation to frets n? We may be talking the same principle but different terminology. Hopefully.
Cheers
Dom

[Trevor Gore]

You can run the C and E components to any fret you like. If you do a more traditional neck joint with the fretboard extension glued down, probably best to stop at the neck joint fret, because, depending on when you do your fretting, you may not be able to control the build geometry well enough over the upper bout. With the BOBO neck, the fretboard plane is very stable, so you can run the C and E components up to the last full fret.

Superposition just means added together, or stacked on top of each other. So, suppose you have a semi-circle drawn on a chart so that it looks like a dish, with one end at x=0. The circle, up to the fret you have chosen (call it the 18th) has an x coordinate and a y coordinate. Likewise with a chart of a section of an ellipse. With alpha=0.5 you add 50% of the circle y coordinate to 50% of the ellipse y coordinate for each x coordinate, which is a superposition of the ellipse and circle. On to that lot you can add an inclined straight line, which basically just tilts the whole thing. Hope that helps.

There are any number of ways of describing the neck shape, not just this way. For example, you could actually measure the relief at every fret on a neck you've built, put a regression curve through the data points to smooth them and re-plot them. If you want to change action, superpose an inclined plane and if you want to change relief, apply an amplification factor to the fitted curve. Whatever you find it easiest to get your head around. The important thing is to be able to relate your calcs back to your building, so that your build parameters (e.g. action at fret 12) is what you input to your spreadsheet and any other manipulations are in the "black box".

[Dominic]

OK, so it is a mix of a circle and an ellipse on top of each other. That makes sense now.
I think the hockey stick analogy got me because in my mind, that shape is circular at the end, then blends into a straight handle. Or there is the Manns hockey stick with it exponential growth at the end. So that was always stuck in my head which made getting it hard. Now, back to the spreadsheet.
Thanks
Dom

[Dominic]

Hi Trevor, I am making good progress. I had all the equations done but not applied to all frets so its a matter of organising my data and tables without error.

On the circular component of the action, we are first measuring relief at fret 7 between fret 1 and fret 18. The circular component is the action between the nut and the string fretted at fret 18. Is that correct? It must be as we don't have enough information yet to go any further. And its what my equation calculates for the nut and the 18th fret.
So to paint a visual, measure relief between fret 1 and fret 18, then release string from fret 1 and recalculate relief/action which is just extending the radius to the nut and raising the string heights slightly.

Am I on the right track here?

This is equation 4.7.13 on page 4-111 for others reference.

Thanks Dom

[Trevor Gore]

Sounds about right, Dom.

[Dominic]

Cool, I'm just about finished. I need some string data first and I just got some parts for my string rig today So once that's done I can run the optimizer and hopefully get meaningful results.
Thanks for the tips Trevor
Cheers
Dom

[kiwigeo]

Cool, I'm just about finished. I need some string data first and I just got some parts for my string rig today So once that's done I can run the optimizer and hopefully get meaningful results.
Thanks for the tips Trevor
Cheers
Dom

Where did you source the pulley for the strings to run over? I guess a Meccano set would be a good source for such stuff?

[Trevor Gore]

Where did you source the pulley for the strings to run over? I guess a Meccano set would be a good source for such stuff?

Try a place that specialises in racing dinghy fittings. Whitworths is typically the go around here, https://www.whitworths.com.au. If you're building a rig like mine, you will need a small ball-bearing sheave box, ~25mm diameter, though all sorts of things can be pressed into action. Something like one of these would do.