Why no general agreement on what the optimum saddle compensation is ?

[Long Jon]

My guitars of different makes have different amounts of compensation on the saddles.

Surely the requirements to get intonation as good as pos are all the same over any given scale length ?

In fact it doesn’t even seem to be governed by scale length ,
I have some different sized guitars from the same makers and the short or long scale ones all have identical saddles.

So, how come there isn’t a definite “winning” standard shape , agreed by all ?

[printer2]

Depends on what strings you have on it.

[Long Jon]

WOW ! I see my question has really set the internet alight !

24 hours and one gnomic response (thankyou Fred, certainly food for thought there....)

I knew I shoulda worked harder on the title, maybe put the word “NUDE” in there or something ....

[devellis]

Originally Posted by Long Jon

WOW ! I see my question has really set the internet alight !

24 hours and one gnomic response (thankyou Fred, certainly food for thought there....)

I knew I shoulda worked harder on the title, maybe put the word “NUDE” in there or something ....

LJ:

You got a pretty definitive answer. String gauge will have everything in the world to do with how intonation is set. Different manufacturers will use different brands and gauges and those will dictate different compensation at the saddle. Some saddles might also be raked more steeply, which will influence how the saddle needs to be cut to achieve adequate compensation.

Other factors are cost and time needed for more precise compensation. Some brands will go the extra distance while others won't.

Not much more to it than that.

[Alan Carruth]

The problem is that you asked a much bigger question than you thought. The only answers are either gnomic, or too comprehensive to be subsumed in a post limited to ASCII text. Trevor Gore devotes a long chapter full of complicated equations to the subject in his book, and there are other, similar, treatments that disagree to some extent.

If you assume that the only thing that matters is the change in tension as you fret the string (and no everybody agrees with that), then there's a simple equation that tells you what that change is:

T = Tzero+ ((E*A)/Lzero)*deltaL) where
T = displaced tension,
Tzero = the initial tension,
E = Young's modulus of the string material,
A = the cross section area of the string,
Lzero = the initial length of the string, and,
deltaL = the change in length

Given the new tension and the string length you can calculate the pitch. This assumes further that both ends of the string are 'fixed'; if, say, one end is tied to a top that vibrates that can alter the pitch.

String construction is one of the big variables in this. Let's say you're confining yourself to steel strings wound with p-bronze. All of the tension is carried by the steel core, so you plug those values in as the cross section area and Young's modulus. There are any number of ways to make a .035" string: you could use a .015" core and .010" wrap, or a .019" core and .008" wrap, for example. The compensation needed for the two strings will be much different, even though they will both be the same diameter, and within an ace of the same tension. A plain .021" G string requires much more compensation than a wound .021" string tuned to the same pitch, due the bigger core. And so on.

In the end, even if you assume that there's one 'perfect' way to set up the compensation for a given guitar/string set/action height/relief, it's likely to be slightly different for another guitar, even with similar specs. And it turns out in reality that there can be a range of compensation values of nut and saddle compensation that will be 'acceptably close' for any given setup. Your ear is only so good at hearing deviations from 'perfect'.

Finally, keep in mind that compensation is a way of matching the pitches you get with some standard. For most guitars the standard is '12 tone Equal Temperament', which has the advantages of allowing you to use straight frets, and to modulate freely into any key. The straight frets come from the fact that in ET al the semitones are the same size musically. Freedom of modulation comes from the fact that all the major keys are out of tune in the same way. But that's the kicker: they're all out of tune. It's simply mathematically impossible to construct a scale with only 'perfect' octaves and fifths: you're going to have to put up with some out of tune intervals someplace. Hence 'temperament'. There are lots of different compromises there, some of which work better than others for select cases, but you can't get away from the need. At some point, no matter how well your guitar is compensated, there will be some problem intervals. You can mitigate them in the usual guitar keys by 'sweetened' tunings, or maybe 'fudged' compensation, but there's no escape from those zombies.

[JeffreyAK]

I think different people have different tolerances on what constitutes "good enough", is part of it. You can compensate at the saddle (or the nut, or both) to get "perfect" intonation at the 12th fret, and how much compensation you need depends on string gauge and action, so thinner strings and lower action make compensation less important. But now you've changed the scale lengths on each string, and therefore all the other fret positions ideally should change too, and you get into wavy frets like the true temperament necks if you truly want "perfect" - but don't ever change string gauges or action, or bend strings while playing. So you decide when to stop the madness and just play, and different players (and builders) have different thresholds.

[Pitar]

Profundity about intonation isn't in the stars, I'm afraid. Saddle compensation is a per-unit adjustment, meaning, change the strings and expect a change in intonation if only by the slightest measure. Sonic perfection is not the stuff of a stringed instrument so setting intonation is a temporary thing. The guitar itself contracts and expands proportionately to the slightest changes in atmospheric changes. Strings are slaved to those changes. Also, as much as we want to think the gauges we buy are qualitatively repetitive, they aren't. In a sampling of same-make, same-set strings over a 6 month period I found the actual sizes wandered by as much as 0.001", meaning the intonation wandered accordingly. The measuring device was accurate to 4 digits and was calibrated to NIST standards.

[Athens]

Originally Posted by Alan Carruth

The problem is that you asked a much bigger question than you thought. The only answers are either gnomic, or too comprehensive to be subsumed in a post limited to ASCII text. Trevor Gore devotes a long chapter full of complicated equations to the subject in his book, and there are other, similar, treatments that disagree to some extent.

If you assume that the only thing that matters is the change in tension as you fret the string (and no everybody agrees with that), then there's a simple equation that tells you what that change is:

T = Tzero+ ((E*A)/Lzero)*deltaL) where
T = displaced tension,
Tzero = the initial tension,
E = Young's modulus of the string material,
A = the cross section area of the string,
Lzero = the initial length of the string, and,
deltaL = the change in length

Given the new tension and the string length you can calculate the pitch. This assumes further that both ends of the string are 'fixed'; if, say, one end is tied to a top that vibrates that can alter the pitch.

String construction is one of the big variables in this. Let's say you're confining yourself to steel strings wound with p-bronze. All of the tension is carried by the steel core, so you plug those values in as the cross section area and Young's modulus. There are any number of ways to make a .035" string: you could use a .015" core and .010" wrap, or a .019" core and .008" wrap, for example. The compensation needed for the two strings will be much different, even though they will both be the same diameter, and within an ace of the same tension. A plain .021" G string requires much more compensation than a wound .021" string tuned to the same pitch, due the bigger core. And so on.

In the end, even if you assume that there's one 'perfect' way to set up the compensation for a given guitar/string set/action height/relief, it's likely to be slightly different for another guitar, even with similar specs. And it turns out in reality that there can be a range of compensation values of nut and saddle compensation that will be 'acceptably close' for any given setup. Your ear is only so good at hearing deviations from 'perfect'.

Finally, keep in mind that compensation is a way of matching the pitches you get with some standard. For most guitars the standard is '12 tone Equal Temperament', which has the advantages of allowing you to use straight frets, and to modulate freely into any key. The straight frets come from the fact that in ET al the semitones are the same size musically. Freedom of modulation comes from the fact that all the major keys are out of tune in the same way. But that's the kicker: they're all out of tune. It's simply mathematically impossible to construct a scale with only 'perfect' octaves and fifths: you're going to have to put up with some out of tune intervals someplace. Hence 'temperament'. There are lots of different compromises there, some of which work better than others for select cases, but you can't get away from the need. At some point, no matter how well your guitar is compensated, there will be some problem intervals. You can mitigate them in the usual guitar keys by 'sweetened' tunings, or maybe 'fudged' compensation, but there's no escape from those zombies.

Woah! Way too much thinking for a Sunday morning. I'm gonna just go play guitar.

[fazool]

Originally Posted by Alan Carruth

The problem is that you asked a much bigger question than you thought. The only answers are either gnomic, or too comprehensive to be subsumed in a post limited to ASCII text.....

Take a look at this (not mine)

[Long Jon]

Haha ! OK, I did have to go n ask !

Thank you all (esp Alan) ,

apologies to Fred for underestimating his original answer.

[sabatini]

I am going to add this to my list of important issues that I am glad someone else is tackling.

The guitars I buy all sound good with whatever compensation has been applied to the saddles and I am good with that.

[stringjunky]

Originally Posted by sabatini

I am going to add this to my list of important issues that I am glad someone else is tackling.

The guitars I buy all sound good with whatever compensation has been applied to the saddles and I am good with that.

But this is AGF...we like minutiae. Understanding them helps to understand the bigger issues. And I think it's awesome that people like Alan can dissect things to such a degree of finesse.

[StevenL]

I generally agree with everything that's been said here.