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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 2:50 pm
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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 3:47 pm
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OK. I've been thinking about this and also doing some reading to refresh my memory on a few things.
There is something that does not seem right about your assertions, Arth1, regarding longer scales needing more compensation. Actually, it's more than something, it's a number of things. It’s not my intention to start a fight, just debate. With that in mind, here is what I know.

Longer strings see a smaller relative increase in tension when they are subjected to the sideways deflection and the accompanying stretching induced by the action of fretting. This is because the angles of deflection are more obtuse with longer strings, resulting in a smaller percentage of overall elongation. All of this is assuming same gauge strings are used.

Stiffer strings require more compensation because they increase more in tension when fretted. The same angle and tension issues come into play here.

Short strings are stiffer than long strings when tuned to the same pitch. Again, assuming same gauge.

The differential between the fundamental of a string and its partials or harmonics increases progressively. This odd and misunderstood natural phenomenon with the progressively increasing differential between the theoretical and the actual is the reason why standard guitars can never truly be properly intoned. It’s why Sheldon Dingwall took the approach he did. The point here is that it is a progressively increasing differential. That means as the length decreases the partials become increasingly further away from formula. It's also the reason I shudder whenever I hear people advocating tuning by harmonics. The fact is, the theoreticals and the actuals don't align. It's one of those mysteries of nature. It should work out but it doesn't. That, and the fact that finger crud in the windings increases the harmonic confusion even further but that's another topic altogether.

It seems to me that since we both agree a longer string will require a longer movement of the saddle to achieve a given change in pitch, a longer string should make it easier to find that “good enough” approximation of intonation we all deal with every time we pick up a guitar. It should be easier because if a longer travel is required then a given amount of travel will yield a finer adjustment.

It also seems to me that at the time of guitar assembly the precise placement of the frets on a longer scale guitar should be more accurate as well and for the same reason. When calculating the algorithmic “12th root of 2” pattern and all that geek-speak, there will be a greater degree of accuracy with a longer scale when confirming the fret locations than there would be using a shorter scale. This would seem to me to indicate a longer scale length should yield a more accurate overall intonation, assuming the measuring and machining tools used in the making of both guitars are graduated to the same degree of accuracy. When combined with the progressively increasing differential this seems to pretty much kill your theory completely.

I am trying to understand your argument but it seems to defy everything I know to be true.
You must be referring to something outside of what I am taking into consideration.
Either that or I am considering factors you have not encountered before.

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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 3:52 pm
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Solid Body Love Songs wrote:
I'm entering this conversation even though I don't know much about it.
My .02 cents is that watching Jimi Hendrix play and then try to tune his guitar during the set must have been frustrating, but he managed to do it and it made me wonder, how did he do that?
He knew where on the fret board to press harder or softer perhaps. You have to spend an enormous amount of time playing to learn that control, to learn finger position and muting technique to the point of changing your tuning, developing chords to fit your songs/playing.
With all of the tuner options today, the best guitarists still have problems with it.
Remember when Jimi asked Eric to come onstage to help him tune his guitar? He was smiling because he knew God (for awhile in the past people said Eric was God, lol) wouldn't be able to.


Now Hendrix is a prime example. I mean, what a bloke, what an utter bloke. I saw a vid of him tune midsong, I think it was the Lulu show.
I saw a vid of him play Killing Floor at like double tempo. He looked at the board once for reference in the intro and that was it.
The bloke was an utter genius.
However I also saw videos of him stoned, out of time, out of tune and pretty not into it and poor.
I dunno perhaps he was just too stoned to tune right and it did his head in. Maybe. Cos he was pretty blasted at woodstock and did fine there.

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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 4:01 pm
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I spoke to the guy at Zachary guitars about low fret intonation and my compensated nut, years ago. He wasn't interested. He started talking about his string sets. Now however much of a controversial character that fella is. His guitars are something else.
He hinted that the mass of the core of wound strings had a lot to do with intonation.
For the life of me, I haven't been able to see what he was getting at.
There are many many problems with intonation, from many different sources.
I resolved myself to, rock and roll, good enough, have fun mentality.

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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 4:12 pm
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nikininja wrote:
Solid Body Love Songs wrote:
I'm entering this conversation even though I don't know much about it.
My .02 cents is that watching Jimi Hendrix play and then try to tune his guitar during the set must have been frustrating, but he managed to do it and it made me wonder, how did he do that?
He knew where on the fret board to press harder or softer perhaps. You have to spend an enormous amount of time playing to learn that control, to learn finger position and muting technique to the point of changing your tuning, developing chords to fit your songs/playing.
With all of the tuner options today, the best guitarists still have problems with it.
Remember when Jimi asked Eric to come onstage to help him tune his guitar? He was smiling because he knew God (for awhile in the past people said Eric was God, lol) wouldn't be able to.


Now Hendrix is a prime example. I mean, what a bloke, what an utter bloke. I saw a vid of him tune midsong, I think it was the Lulu show.
I saw a vid of him play Killing Floor at like double tempo. He looked at the board once for reference in the intro and that was it.
The bloke was an utter genius.
However I also saw videos of him stoned, out of time, out of tune and pretty not into it and poor.
I dunno perhaps he was just too stoned to tune right and it did his head in. Maybe. Cos he was pretty blasted at woodstock and did fine there.


Yes Niki, too much downer and you have to chew on your tongue or punch your self in the face to keep from passing out. Been there done that, not ever again please and thank you. The Isle of White video scared me. The people that turned him on to barb's and smack should have been horse-whipped.

(I searched for the Isle of White Machine Gun video and it has been taken down. There are a few other videos from that concert and his eyes are droopy, half of the time his mouth hanging open. He doesn't look happy and it isn't the Jimi that I met. Bad drugs will kill.)

and now back to the scheduled programming "Tuners and Intonation"

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Last edited by Solid Body Love Songs on Thu Apr 28, 2016 10:27 am, edited 1 time in total.

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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 7:26 pm
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BMW-KTM wrote:
When calculating the algorithmic “12th root of 2” pattern and all that geek-speak, there will be a greater degree of accuracy with a longer scale when confirming the fret locations than there would be using a shorter scale.

That would be true for strings with no internal friction (100% elasticity). For that kind of strings, there would be no difference in intonation between the six strings. The bridge would be perpendicular to the strings, at exactly twice the length from the nut to the twelfth fret. The pitch would always be dependent on the string length, density and tension.
However, strings aren't 100% elastic, but have internal friction based on the stiffness of the material and the thickness of the string, which makes them ring higher than a perfect string would.

The stiffness and gauge are unknowns to the luthier who makes the instrument, although reasonable range guesses can be made. So the frets aren't placed at 12th root of 2 intervals, but rather, at compromise position that reduce the offset (as in pitch offset) as much as possible for all strings. If one string is going to be 10 cents sharp and another 10 cents flat, that is preferable to one being perfect and the other 20 cents off either way.

You're right in that the accuracy with which you can place the frets is higher for a longer scale, but that doesn't help much, because the frets are going to be off no matter how accurately placed they are, unless curved like the True Temperament ones.

Then enter another factor: Delta tension. Because action is never zero, a string is depressed a certain distance, which increases the tension. The shorter the scale length, for the same action, you depress the string relatively more compared to the string length, and increase the tension relatively more. The tension increase directly counteracts the density (mass per length) of the string (one part of the formula for the pitch contains tension/density), making the density of the string less significant. When the densities of the strings become less significant, the strings behave more similar. So even if intonation from the 12th-root-of-2 position for a fret is more off, the fret isn't placed exactly there anyhow, but at the position that gives the least offset considering all the strings, given a good guess at how the strings will intonate. With less variation between the strings, that position has less maximum error.

With my 25.5" Tele and 24.75" Revstar, both intonation adjusted for 12th fret, and the same strings, the pitch for the treble G and E strings on the 22nd fret is slightly off from "perfect" for both, as can be expected, but ever so slightly worse for the Tele. The B string is pretty near perfect on both. But the difference is minimal. If I were a shredder that spent all my time in the upper register, I probably would have adjusted both for better intonation at the 22nd fret at the expense of it being worse at lower frets.

Now for my Flamenco guitar, it's a different issue. The 26.6" scale length and low action makes it difficult to intone precisely, even though the strings being more elastic should help. It still is off noticeably both ways on the top frets, even if pretty good at the middle of the fretboard.
But, even so, I've accepted that "that's them breaks". I don't think it's noticeable when I play it.

Same for the (shorter scale) 12-string, which doesn't even have individual adjustment for the strings in a pair. The intonation definitely is off, especially for the G string pair. But for a 12-string, that inaccuracy generally drowns in the overall sound.

Again, nothing to fret about - adjust as well as can be done, and accept that a fretted instrument is never going to be in tune on all frets. With vibrato, tremolo, attack, and other people playing it's not going to be noticed.


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Post subject: Re: Tuners and Intonation
Posted: Wed Apr 27, 2016 8:38 pm
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I assume by "Delta tension" you mean "P-Delta".
I'm pretty sure Delta tension refers to surface tensions in a liquid.
P-Delta forces I am familiar with in my line of work and they do relate to structural stiffness within a material.

I'll have to ponder that a while because I'm unsure how P-Delta forces play in this scenario because I've never thought of a (W) wide-flange or (C) channel or (L) angle or even crane hoist line as being in the same dynamic as a guitar string.
My head has just never gone there before, likely because except for the hoist line those shapes are usually under compression rather than tension .... and vibration is considered a bad thing. LOL

I'm not convinced a change in string density due to tension occurs.
The string will elongate and become thinner but the mass will not change and the density should also be unaffected.
Lower mass per unit length, perhaps but not by volume.
Even if a density change does occur, I'm not sure how that will affect ... I need to think about this more.

I am going to double check the 12th fret intonation on both my Tele and my Les Paul and then I'm going to compare and see if I can discover what you're talking about because it still sounds wrong to me.

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Post subject: Re: Tuners and Intonation
Posted: Thu Apr 28, 2016 6:21 am
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BMW-KTM wrote:
I'm not convinced a change in string density due to tension occurs.
The string will elongate and become thinner but the mass will not change and the density should also be unaffected. Lower mass per unit length, perhaps but not by volume.


For strings, density is defined as mass per length :) (Yup, I blundered on that one too.)

But anyhow, the effect of density going down because the length increases is likely going to be tiny; unless you have a Uli Jon Roth guitar with frets almost all the way to the bridge, or an action higher than a steel string guitar, I can't imagine that being significant. :)

The relative increase in tension, however, should be more significant than the density going down or the length going up.
frequency = sqrt(tension/density)/(2*length)

That's the theoretical formulat for 100% elasticity, but strings are stiff with internal stresses, so they vibrate less than the theoretical string, especially near the ends. The result is that they act like they're shorter than they are, giving a brighter sound.

BMW-KTM wrote:
I am going to double check the 12th fret intonation on both my Tele and my Les Paul and then I'm going to compare and see if I can discover what you're talking about because it still sounds wrong to me.

I'm always open for the possibility that I'm wrong. I may well have missed part of the equation here, and jumped to conclusions based on observations or bias.
It could be that the frets are more optimally placed for high fret playing on the Yamaha, or part of the effect is due to maple stretching/contracting more than mahogany, or the string stretch length (not just the vibrating span) affecting intonation in ways I haven't thought of, or I might have made an error or seven.

I probably should go measure a few other guitars too. More experimental data should help validate and refine our thinking.


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