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One more thing...that spreadsheet does not compensate for an overwound string. It could, but it has been setup for the simple case of a plain string.

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[QUOTE=Rick Turner] The basic reason for compensating is not string stretch when fretting, but rather string stiffness.
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String stretch does add to this issue, but it's not the underlying cause of the need for slanted compensation of the bridge saddle.[/QUOTE]

Awesome, I learned something today! I never considered the stiffness of the string moving the nodes. Thanks, Rick!

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Bob Garrish
Former Canonized Purveyor of Fine CNC Luthier Services

[quote=grumpy]

Whassa cure?

[/quote]

Its says you feel confined! Pull your head outta your ahhhhhhh just kidding there grumpy buddy!

Mitch

 

There was a fantastic article in Scientific American about 35 years ago on the node shifting of grand piano strings and how that leads to the need to stretch the tuning of those instruments.   The stretch moves higher notes' fundamental sharp so that they are more in tune with the overtones of the lower strings. When you understand this basic thing, then guitar compensation all makes sense.

The stretch moves higher notes' fundamental sharp so that they are more in tune with the overtones of the lower strings.

I understand that, but (ignoring intonation for a minute) does anyone tune a guitar that way, or cut frets that way - i.e. tune the higher strings or frets progressively sharper?

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David White, Toronto

"All my favourite singers can't sing."

Well, you can look at the Buzzy Feiten method as a kind of approach to this...among other issues.

It's more of a factor with pianos, though, because the treble strings are shorter compared to their diamter and they're strung to much higher tension.

String harmonic theory is based on an infinitely small diameter string of infinite flexibility. Real strings act more like stressed clamped bars than that, though, and the harmonic series for clamped bars is inherently enharmonic.

Rick:
I'm going to have to disagree with you on this one, at least partly. I'm not totally convinced that the stiffness of the string shifts the 'dead' point at the end in most cases, and I know that displacing the string alters the tension.

Let's look at a case where the 'dead' point at the end of the string is certainly moved away from the peak of the saddle: a large diameter wound string that makes a sharp break angle. This is really common on low E strings on Martins, because, for some reason, when they shifted the bass end of the saddle back they did not also shift the lower string pin holes, which remained on a line perpendicular to the center line of the top. Anyway, in a case like this the windings on the under side of the string jam together, and don't allow it to make a tight enough bend to cover the entire angle over the top of the saddle. The result is that the string actually rises a bit in front of the saddle, and can't vibrate in the 'vertical' direction over the lenght of that rise, since it's locked by the windings.

The question is, would a stiff _plain_ string also not be able to vibrate properly if it shows a similar rise? We know that a stiff string will not be able to make a short radius of bend in vibration, but that would apply to a straight string as well as to one that has a bend on the end. Does the bend itself change anything in that case? I don't know. I'd like to see some data.

Displacing a string does raise the tension. This is easy enough to calculate if you like doing math. I don't. I have measured the tension changes associated with vibration displacement of some different strings, though (it would have been quicker to do the math!). Static displacements (fretting) will also increase the tension, obviously.

For a given string at a given length the change in tension will depend on how much longer it gets when it is displaced. You might find that pushing a steel high E string 25.4" long aside by 1/8" increases the tension by, say, 1/2 pound. This increase will be the same no matter how tight the string was to begin with, within reason. If the string only has 5# of tension on it to begin with, the change will amount to a 10% increase, and the pitch will shift noticably. If the string is already carrying 15# of tension, the added 1/2# won't alter the pitch much. Thus the change in pitch will depend in part on how tight the string is to begin with.

This gets into what Mike said, about how close the string is to it's breaking point. A .009" string carrying 10# of tension might be ready to break, and won't shift upward in pitch much, but a .018", with four times the cross section area, can carry four times the tension, and will be relatively as slack as that .009" would be with only a couple of pounds on it. The thick string will also tighten up more for a given displacement, at any tension. Thus the amount of pitch shift for a given displacement will be related to how tight the string is relative to it's breaking strength. Since all strings of a given material and length will break at the same pitch (within limits) the pitch shift will depend more on the material and length than the diameter.

Nylon stretches more than steel, and that's one reason nylon strings don't require as much compensation as steel strings. For a given displacement a nylon string will change tension less. This, in itself, shows that the tension change with displacement accounts for at least some of the compensation.

Wound strings are, in effect, made of a different material than plain ones. It has only as much tensile strength as the core, but with the mass of the wrap added on. In theory, I think, if you made a set of strings that all had the same core size as the high E, and added the right amount of wrap so that they'd tune to the correct pitches at the same tension, you might not need any differential compensation. The core tension would change the same amount in each string for the same displacement.

In practice, I don't think that would be a very good set of strings for other reasons. However, it does suggest an experiment. Take any string and tune it up until the core stress (the pounds of tension per square inch of core cross section) is the same as a high E string. Then find out how much compensation it needs to play in tune. If it needs more than a plain E string, the difference could be due to the stiffness of the ends. This ought to work equally well for wound or plain strings.        &nbs p;        

   

Al, with all respect, the "Northern" shift of the actual nodal points is precisely why the saddle must move "South", away from the theoretical node of the end of the string, and yes, the steeper the break angle the worse this gets. I think we may actually agree on this, but we're looking at several aspects of it.

Note that floppier nylon core strings do not have this severe a need for compensation, though unwound nylon "G" strings can be problematic.

Do you remember a Boston area repairman named Jeff Tripp? He designed a bridge for electrics, the "Tripp Suspension Bridge" that held Fender Bullet strings in a kind of collet arrangement. This meant that the strings did not bend over the saddle, and so there was no bending preload of the string at the bridge.   Sustain was improved and intonation was better, though one still had to compensate the stiffer strings.   The thing was too out there for commercial acceptance, though I installed several on my Model 1 electrics, and I liked them.

Rick wrote:
"Al, with all respect, the "Northern" shift of the actual nodal points is precisely why the saddle must move "South", away from the theoretical node of the end of the string, and yes, the steeper the break angle the worse this gets. "

I've never seen that Tripp bridge, although I seem to remember hearing of him.

And I agree with you to some extent: at least on wound strings the jamming of the windings shifts the node point and requires the saddle being moved. I just don't think that the same argument holds for plain strings, since there is nothing except the intrinsic stiffness of the string that is causing the bend. That stiffness might cause the string to move a bit less near the saddle than it 'ought' to, but will it _stop_ it short of the real termination? Why?

It occurred to me after I posted yesterday that one could see a bend in the end of a plain string as evidence that it was at a relatively low tension. If it was tighter it would be pulled out straight. Since it is strings that are far from their breaking point that will require the most comensation, we'd expect the ones that are not pulled straight to need more compensation, regardless of whether they have a bend or not.

At any rate, I suspect we're discussing a pretty fine point here. It may well be that bending does shift the node point north a bit, but without some sort of experimental evidence one way or another we're not going to settle it.

I'll note that some people also argue that the anharmonicity of stiff strings requires its own compensation. If your hearing works by finding some sort of compromise pitch when presented with nearly harmonic intervals, a stiff string, with the upper partials shifted progressively sharp relative to the fundamental would tend to sound sharper than the pitch of the fundamental would imply. Lenghtening the string a bit would shift all the partials downward, and drop the percieved pitch. This argument has been advanced in particular for nylon string guitars.

It is also pointed out that the actual tension change when fretting tends to be greater for the lower frets, and the argument is made that compensation for the tension change should thus be made at the nut, with the bridge compensation taking care of the anharmonicity. This all gets quite complicated.    

It gets so complicated that only if you settle in on a particular string formula at a specific gauge and a set action height with a pre-determined amount of relief...only then could you work out a "stretch" for moving fret positions "north or south" of the 12th root of 2 rule to compensate for all those factors.   And then the player is the weak link.

I find this stuff very interesting to know...and then I just get the action as good as possible at the nut, maybe shaving a little off the nut to 1st fret distance, get the thing playing the way I like it, set the intonation decently at the bridge, and ship it.   I know I can make any guitar play out of tune...

Have you guys had a chance to check out the spreadsheet I posted?

According to this (which may or may not be correct), the saddle compensation is a minor factor in causing the string to go sharp in comparison to the effect that saddle compensation has in changing the first vibration mode.

Is this an reasonable statement to make, or is this wrong? Does saddle compensation have a drastic and noticeable effect on the "intonability" of the guitar?

I apologize for dragging this out...just trying to make sense of the physics behind this.

Thanks in advance for your comments.

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whoops, I mis-wrote.

It should read:

"..the saddle compensation is a minor factor in causing the string to go sharp in comparison to the effect that the height of the action has".

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That would not be my experience... Try setting up a guitar with the action exactly the same on every string. You'll find it still needs quite a bit of compensation.

Once again, some of this stuff is easier to understand if you have the chance to set up a couple of hundred Strats over a few years. Acoustic builders could really learn a lot from electric guitars...

keeping it basic I think of compensation as getting the saddle in a position that the width of that saddle provides enough material to properly intonate the instrument.

If you saddle is wide enough you could throw compensation position out the window. but then you have this big hunking piece femur protruding through the bridge

I use a compensation that leaves me with enough material to intonate. Outside of that the rest of this is just theoretical mechanics that is nice to know.

I agree that this is an area where theory is of limited use. I learned to intonate (is that even a word?) guitars before learning much theory. I then went back and learned gobs of theory and have not changed my methods at all.

It's not that hard to get an instrument to the point where even slightly inconsistent fretting technique is more of an issue than anything built in to the instrument. And a much bigger factor is the intonation problems inherent in the equally tempered scale.

What I'm more curious about is building the box in such a way that the high partials are less prominent, without loosing the high fundamentals. That would likely go a lot further toward making an instrument "sound" in tune than micro-tweaking the intonation, regardless of what the tuner says.

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http://www.chassonguitars.com

Yeah, at some point you just have to get out there and start cutting wood and bone. Then you learn. Still, the theory is nice, if only to keep you from doing something really supid.

I've got an acoustic in the works right now on which I have not compensated the saddle at all. The action is a little higher than it should be and that isn't helping things. Other than that, it sounds decent with the exception of the high E. The high E is obnoxiously sharp. I'll continue to tweak it and see how it comes out in the end...

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[QUOTE=Alan Carruth] Yeah, at some point you just have to get out there and start cutting wood and bone. Then you learn. Still, the theory is nice, if only to keep you from doing something really supid. [/QUOTE]
I find that knowing some theory doesn't slow me down a bit when it comes to doing something really stupid.

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