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I have been playing a classical guitar for some years now and I recently purchased a steel-string acoustic guitar.

I am puzzled by the placement of the bridge saddle on my steel-string.

On my classical guitar the bridge saddle is placed exactly parallel to the nut. On my new steel-string, the bridge saddle is placed at a slight, but noticeable angle to the nut. This appears to be a common feature of steel-string guitars.

Physical law says that the pitch of a vibrating string is raised an octave when its length is divided exactly in two.

So why would a guitar maker choose to violate this law?

I don't believe that thicker gauge strings obey different laws.

  • 1
    You may find it interesting to look at electric guitars, a lot of which have individual saddles. This is so that each string can be intonated separately. When strings of a different gauge are put onto a guitar, often the intonation (along with other settings) will need checking and changing. Very difficult to do on an acoustic, even with a compensated bridge, which at best is a compromise. – Tim Jul 6 '15 at 5:13
  • Yes, every time I'm trying to play Greek music :) – Ben Kushigian Aug 1 '18 at 13:21
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The difference is that the nylon strings on the classical are all close to the same diameter, whereas on the steel string the diameter of the smallest string might be about 20% of the size of the diameter of the largest.

This matters because the physics you have learned is simplified. Only string that have no thickness and no stiffness exactly fit the model, and of course such strings don't exist.

Since real strings deviate from the ideal model more or less depending on their thickness, the sounding lengths need to be adjusted slightly to try to keep the intonation even across the frets. This compensates for the reality of the string geometry and so the angled saddle (technically the bridge is the bigger piece of wood glued to the top, the angled thin piece of bone is the saddle) is called a compensated saddle.

Compensated saddles cannot make intonation perfect, in fact all intonation on fretted instruments is a compromise. But at least a compensated saddle is a straightforward way to make the intonation a lot closer to perfect for varying string thicknesses.

  • I like your point that real strings deviate from the ideal model, but I'm not so keen on the role of thickness. My naive understanding of the physics is that a vibrating strings pitch is a function of the frequency of vibration and that doubling the frequency by dividing it in two will cause the pitch to raise an octave. There's no dependence on thickness. Something so fundamental would be a feature of the ideal model, wouldn't it? I'm still inclined to accept this answer, but I'll wait and see if anyone else cares to contribute. – UserZero Jul 6 '15 at 3:27
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    When you fret a string it bends around the fret, the guage of the string affects how it bends and creates slight differences in the sounding length. Also the stiffness of the string affects the behavior of ripples that flow along the string which can shift upper harmonics and change the apparent pitch, which is not always the same as frequency. The ideal model is based on length, inertia (mass) and restitution force (tension) and intentionally leaves much out because the math is too complicated. – Todd Wilcox Jul 6 '15 at 10:45
  • Thank-you for answering my question. This is the correct answer. It took me a while to digest it because I've never really considered these issues in any depth. If I'm reading your answer correctly, I would say that the need to keep intonation even across the frets resulting from different string thickness is the most important contributor (amongst others) to the angled design feature. – UserZero Jul 7 '15 at 0:17
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    Intonation is the only reason that I know of for the angled saddle. There's a lot to be said for Wheat Williams' answer, especially the pictures. – Todd Wilcox Jul 7 '15 at 1:23
  • I was thinking that perhaps the way different gauge string interact with the nut would also create intonation issues. It is still an intonation issue, but it relates to the nut rather than the frets. Maybe I'm wrong here. And yes, @Wheat's answer is excellent and informative. – UserZero Jul 7 '15 at 2:33
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You are incorrect in your assertion that there is a physical law being broken here. A guitar has six strings of different diameters, different materials (some strings are a plain length of steel wire, whereas others have other wires wrapped around the steel wire core) and tensile strengths, tuned to different pitches. As a result, there must be a compromise in the setup and intonation of each individual string to account for several factors to make the guitar play more-or-less in tune. And tuning and intonation are always a compromise -- they can never be exact.

If your guitar had, say, 6 plain "e" strings of the exact same diameter and composition all tuned to the same pitch, then it would be appropriate to have a bridge saddle that is perfectly straight and perfectly perpendicular to the direction of the strings.

But your guitar has six strings, each of a different composition and thickness, each tuned to a different pitch, so it is necessary to compensate for these factors, which is why the bridge saddle is slanted.

Furthermore some luthiers go farther than this and construct a bridge saddle that has a different string length under each string. Note the example below, where the saddle position for the high "b" string is notably moved back and longer than that of the "e" or "g" strings. This is to achieve better intonation.

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  • This is more or less the way I have been thinking about it. So why does my low E string sound slightly flat at the 12th fret while my high E string sounds slightly sharp. The physics of frequency, pitch, and string length does not mention string thickness or initial length, etc... – UserZero Jul 6 '15 at 3:34
  • Each string has to be fretted at each different pitch. Depressing a string down to the fret on the fingerboard distorts the string and its tension and can throw the intonation off just a bit compared to other strings or other notes at other positions. When the guitar is "set up" or calibrated, the technician adjusts the depth of each string slot in the nut, and the height of each string over the bridge saddle, and the slight amount of bow or "relief" in the neck (it's not perfectly flat; it's not supposed to be) and other factors to try to take all of this into account and produce... – user1044 Jul 6 '15 at 3:37
  • an instrument with the closest to optimal intonation that is feasible. And this holds until the guitar itself is exposed to significant changes in temperature or humidity which causes the wood to shift. So if you want the best intonation, pay a professional repair person for a "set up" every year or so and he will attempt to calibrate everything to make the intonation as optimal as possible for your particular instrument. – user1044 Jul 6 '15 at 3:38
  • I like the point you make about the issue of intonation and the need to maintain optimal intonation via regular maintenance. If only my playing warranted the effort and expense - just kidding. I'm not sure the issue of distortion resulting from fretting is relevant since it is a given on all guitars. But yes, intonation will definitely affect string length in a subtle way, so maybe I should accept this answer? – UserZero Jul 6 '15 at 3:47
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    Many factors interact. Nut-slot height, fret height, neck relief (bow), saddle height, saddle position, compensating for differing string thicknesses and gauges, and probably other things I can't think of. Some people prefer extra-heavy-gauge steel strings and high action. Some people prefer extra-light-gauge strings and low action. This is why spending money on a professional setup is worthwhile -- to calibrate your particular guitar according to the way you like to play it, to achieve the easiest playability with the best intonation. – user1044 Jul 6 '15 at 4:30
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Everything I have read is correct but one major point is where the fulcrum is, at both the nut and the saddle effects intonation the most with a properly made steel string acoustic guitar. It is very hard to see and make the actual fulcrum point correct.

The nut is usually filed by hand using eyesight but if you look at each string slot they are always off, one way or the other. It may appear to be a very small difference but that is the trick to intonation. That is why your E string sounds out of tune at the 12th fret. That little difference amplifies itself as you go down the frets. At the 12th fret your string should be cut in half but you have something off. Most makers try to compensate at the saddle.

Buzz Feiten created a nut compensation setup. It is unusual and if you read about it you will scratch your head and say when will it end.

Very simply getting the actual high point on the nut (the fulcrum) and the same on the saddle, you will be close but is the actual high point on each fret correct and was it placed at the exact position? This is where the math comes in. On my personal guitars I set them up a little at a time because so many things can alter the overall dimensions.

High or low humidity can move your neck, the bridge and top of the guitar will drop down or go up depending on humidity and temperature. Your guitar is always moving. I don't try to fix everything at once but over time I listen to differences. One thing I do is listen to each string plucked open than I fret it and listen for clarity. If it sounds better fretted the nut is pinching the sides of the string or the fulcrum is wrong. I take my saddle and polish it with 600 emery cloth then 0000 steel wool. I use a gem eye scope and look at each point on the saddle and make sure it is right. I do the same on the nut.

So many things affect the intonation all you can do is get everything correct according to all the information luthiers have passed on and if you have anything to add to it than do so. People are very creative and someone will come up with a way to get it perfect. Machines have been made to do all of this but it still comes down to all the little things that can be off by microscopic differences. I get it right over time and always keep my guitars comfortable with the right temperature and humidity.

One last thing, strings are all a little different. Playing around with different string brands and type may also help . You have to have a very good ear and some very good tuners that can be placed at different points on the guitar giving me slightly different readings. Think about a violin, your finger placed at exactly the right place creates the intonation. Guitars have frets, nuts and saddles to do this so listen to anyone that has an idea and you will learn.

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I don't believe that thicker gauge strings obey different laws.

Well, they don't, but thinner gauge strings better approximate the oversimplified laws you state before that:

Physical law says that the pitch of a vibrating string is raised an octave when its length is divided exactly in two.

There is no such "physical law". An octave interval is distinguished by a doubling of frequency. That is a mathematical law.

A string that is infinitely thin and has no resistance against bending while having a certain tension and mass density will in first order approximation have an oscillation frequency for small amplitudes that is proportional to the string length.

Physical strings are not infinitely thin, have thickness- and material-dependent resistance against bending and will change length and tension (depending on the clearance of its setup) when pressed against the fretboard rather than being divided with something like a bottleneck.

If you want to look at the differences needed to accommodate differing strings properly, you will not be able to apply "physical laws" that magically disappear while you thicken a string until it becomes a rod.

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