Not another stupid question - Part 2; string tension and intonation

[michelew]

You're our pot of gold Demont.

You're funny enough to be a leprechaun.

[wrench]

This question is not stupid at all. It is one of the best questions I ever heard about stringed instruments. And the short answer is - YES.

The thorough and quantified explanation is complicated though because it calls on some difficult concepts of string theory and lots of advanced math.

Intonation is essentially the fine tuning of compensation, and the compensation equations use string mass, string length, string stiffness, and string tension as its variables. When we explore the math, we find that the stiffness at the ends of the string is affected dramatically by the string tension, and both of those will change a compensation/intonation value. So when you change the tuning of a string, thereby changing its tension, you are changing the values of two of the variables that determine the ideal compensation/intonation.

The reason you never see this math is because the calculations are beyond the daily math skills of most people, it yields numbers small enough to fit on the width of a saddle, and trial-and-error methods serve luthiers adequately.

The best luthiers I know of, many of them engineers, hate to talk about the science of intonation, and often angrily conclude such a discussion with "guidelines", "trial-and-error", or "empirical" solutions.

[michelew]

Wrench,

Thanks so much for responding with such detail. That's very enlightening.

Is there anything I can do to improve the intonation of my ukulele at the lower tuning without making any physical changes (which can't be removed when I want to return to std tuning)?

Crazy idea - would tuning it down another half step and then placing a capo at the first fret help to compensate at all? Obviously you'd need to retune to the desired pitch at the first fret.

I'm open to suggestions. Otherwise I'm assuming I just have to find a tuning of the open strings that gives the least increase in pitch from the desired note at each subsequent fret. That sounds like a trial and error exercise to be sure. Are there any good rules of thumb for dealing with these sort of intonation issues when trying to achieve a good average tuning for a string. For example, should I be aiming to have the tuning exactly at the correct pitch at say the fourth or sixth fret?

Thanks again.

M.

[RicksPick]

Very intresting question Michelle ( as always)

Im totally in tune with Wrench lol
After spending several hours trying to set up my father in laws electric
Each string can be set up for intonation and it takes some time
Unless you have those kinda bridges its impossible to adjust on a acoustic
Once made, it is set, so its all down to the luthier
As to your Q bout going another step down and capo dont think it will work,
string tension wont change just the length of the neck

As I see it, the further away from standard the worst it will get
Trying to find a ballance will work a little but not much, but if playing up the neck more than open position deffo go for it

Rick

[thereshopeyet]

Michelle Wrote:

You're our pot of gold Demot.
You're funny enough to be a leprechaun.

I'll give you some gold later Michelle !!

[wrench]

michelew wrote:

Wrench,

Thanks so much for responding with such detail. That's very enlightening.

Is there anything I can do to improve the intonation of my ukulele at the lower tuning without making any physical changes (which can't be removed when I want to return to std tuning)?

Crazy idea - would tuning it down another half step and then placing a capo at the first fret help to compensate at all? Obviously you'd need to retune to the desired pitch at the first fret.

I'm open to suggestions. Otherwise I'm assuming I just have to find a tuning of the open strings that gives the least increase in pitch from the desired note at each subsequent fret. That sounds like a trial and error exercise to be sure. Are there any good rules of thumb for dealing with these sort of intonation issues when trying to achieve a good average tuning for a string. For example, should I be aiming to have the tuning exactly at the correct pitch at say the fourth or sixth fret?

Thanks again.

M.

I think tuning down further will make the problem worse because it lowers the tension, which is changing your compensation values away from your current saddle geometry. The capo certainly gets you back to the desired key, but doesn't change the intonation because it doesn't change the tension. If you plan to play frequently in an altered tuning, I would consider a different saddle to use for that tuning. Another approach is a compromise saddle, meaning take intonation measurements in standard tuning and altered tuning, then intonate the saddle in between. Neither tuning will be in perfect tune, but neither will be in worst-case tune either.

Just to clarify a question you asked in your original post about intonation and fret location - no, frets have no effect on intonation. Intonation is strictly a function of string physics and saddle (and nut) geometry.

It sounds to me like your ears of such quality that you can hear these differences. A curse or a blessing, depending on how you look at it. I work on intonation issues for folks, and I readily admit I cannot always hear what they do. In fact sometimes they hear what my electronic tuners can't. On the plus side, straight uncompensated saddles are working just great in my guitars. :laugh:

A tip I will offer if you are messing with saddles and intonation issues is to make sure you have a fast and steep clearance angle on the back side of the saddle. Start this clearance angle just .3 or .4 mm behind the contact point on the saddle. I have seen several saddles where the contact point was mistaken by interference on the back side radius of the saddle. In fact I don't use a radius on the back side - I cut a flat plane for clearance. In fact, as I think about it, try this first, as it may resolve your original problem.

[thereshopeyet]

Generally speaking, if when tuning down / up to alternate tunings, could the the stings have been damaged?
Could overstretching damage a string resulting in an out of tune string mistakenly identifying the issue as intonation
when changing a damaged string(s) might reslove the issue?


Wrench Wrote:

It sounds to me like your ears of such quality that you can hear these differences. A curse or a blessing,

Assuming that in Michelle's situation, intonation saddle compensation has been optimised but she still hears
that the pitch is still off does that then mean she should tune the string slightly till what she hears sounds correct to her?

Wrench Wrote:

Start this clearance angle just .3 or .4 mm behind the contact point on the saddle.

Wrench, is there anyway you could post an image identifying the angle clearance you refer to?

[wrench]

thereshopeyet wrote:

Generally speaking, if when tuning down / up to alternate tunings, could the the stings have been damaged?
Could overstretching damage a string resulting in an out of tune string mistakenly identifying the issue as intonation
when changing a damaged string(s) might reslove the issue?

Theoretically, no, because by ASTM 228 (music wire) definitions and standards, as soon as a string is stretched beyond its modulus of elasticity, it breaks. Empirically, however, I believe the elastic range is a little wider than than the ASTM spec says. I was curious about what moves when you tune a new string up to concert pitch, so I measured a guitar's vibrating string length and the amount a string stretched under tension. I found the guitar didn't move at all, while the string stretched nearly .200". ASTM's formula said the string would break at .007" of stretch. After initial tensioning, the string moved only .010" from dead slack to concert pitch. I believe coiled storage may have something to do with a string's initial behavior. The Mapes Wire Co., who makes most of the music wire in the world, advises piano technicians to hang piano strings straight for 30 days before installation. I suspect something similar of guitar strings. You know that period when new strings go flat for a while before staying in tune? I have found that doesn't happen when I over-tune each new string a half step, then lower it and re-tune. Now, all this leads to your point about a string being damaged by alternate tuning. In terms of breakage, I don't think so because I play mostly one guitar, I change tunings a lot, and I haven't broken a string in about 3-1/2 years now. But as a string fatigues, its elasticity declines, and yes that could affect intonation because elasticity is a property which affects how a string vibrates (although I failed to mention it in my earlier post ). So, after all that, can alternate tuning damage a string? I say no because I interpret damage to mean something that results in breakage, but I agree that fatigue from frequent alternate tuning will reduce the elasticity thereby changing the mechanical properties of a string such that it could affect intonation.

Assuming that in Michelle's situation, intonation saddle compensation has been optimised but she still hears
that the pitch is still off does that then mean she should tune the string slightly till what she hears sounds correct to her?

That's a subjective question, but my opinion is, I think it depends on who is listening. If playing privately, absolutely tune for the player. But if playing publicly, tune for the audience.

Wrench, is there anyway you could post an image identifying the angle clearance you refer to?

Yes, I'm going to do string change shortly, I will take some photos and post them here.

[thereshopeyet]

Wrench thanks for taking the time to explain your findings.

Wrench Wrote:

I interpret damage to mean something that results in breakage.

When explaining myself I wasn't sure how to describe a strings condition.
Damage - Does sound rather permanent - snapped.

Wrench Wrote:

I agree that fatigue from frequent alternate tuning will reduce the elasticity thereby changing the mechanical properties of a string such that it could affect intonation.

Fatigue - Is more what meant (result of regular alternate tuning changes)... thanks for that explanation.

Wrench Wrote:

That's a subjective question, but my opinion is, I think it depends on who is listening. If playing privately, absolutely tune for the player. But if playing publicly, tune for the audience.

So how does she tune for an audience if it sounds incorrect to her?
An Electronic Tuner?
Thought
I suppose she has yet to determine if there is an actual instrument fault,
before concluding that it's a tuning issue.

Wrench Wrote:

Yes, I'm going to do string change shortly, I will take some photos and post them here.

That would be great
Thanks.

[justinjustin]

Put it this way stringed instruments work on sound waves. Sound waves get produced with the vibrations after the strings have been plucked or strummed.
The vibrations are changing for one tuning to another I take it. The problem sometimes is sometimes structual i.e. the wooden structure not being straight and true or a bridge that has lifted or is lifting. Occasionally its just a loose machine head the causes the strings not vibrate at an even cycle. (By that i mean when all strings are in tune they usually resonate at the same frequency usually 440Hz for standard E guitar tuning)