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Most acoustic guitars I've seen, including my own, have an angled saddle (the white strip holding up the strings):

alt text

This makes the bass strings longer than the treble strings. Why is this?

Additionally, why is the second-to-highest string (B in standard tuning) offset slightly from the slant, so as to be longer than it 'should' be? I suspect this might be to do with the fact that it is four semitones above the string below it, rather than five as all the others are, but why should this make a difference?

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    +1 I know that thickness of string is a factor and that to give the guitar correct intonation, the saddle has to be adjusted to to compensate for this. I don't know if this is fully related though. – Bella Jan 15 '11 at 22:12
  • its called a compensated saddle – bigbadmouse Jun 12 '19 at 12:50
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The angle is there to improve the intonation. If you've ever set the intonation on an electric guitar with individually-adjustable saddles, you'd see that the bass strings are slightly longer than the treble strings. This is due to the gauge of the strings: heavier strings need to be slightly longer than lighter-gauge strings. The B-string anomaly that you point out has to do with the fact that it and the high-E string are plain steel instead of wound, and so their intonation adjustment is different than for the wound strings. Still, though, because the B-string is heavier than the E-string, it needs to be slightly longer.

What Does String Gauge Have To Do With Length?

When you set the intonation of a string, you want the 12th fret harmonic to match the pitch of the string when fretted at the 12th fret. But when you fret a string, you increase both its length and its tension slightly. Given two strings of equal length, their fretted lengths will also be equal, so since the tension of a string is proportional to the product of its mass and its length, the heavier string's tension will increase more than the lighter string when fretted. Therefore the heavier string's pitch will increase (slightly) more than the lighter string's pitch when fretted. To compensate for this greater increase, the heavier string needs to be slightly longer than the lighter string.

Update: I'll just point out that if you look closely at the photo, you'll see that the saddle itself is carved in such a way that the point of contact for the low-E string is towards the back of the saddle while the point of contact for the G string is in the front. So not only is the saddle angled, but the strings contact the saddle itself at different points, increasing the differences between their lengths.

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    +1 Thanks, this is a good answer. But can you explain in any more detail why a heavier string needs to be longer for the intonation? (I shall not be scared by intense amounts of technical info/equations). – Anonymous Jan 15 '11 at 23:19
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    @Bill Cheatham: One reason the heavier strings have to be longer is the physical properties of strings in general. A perfect string has no "thickness" and will vibrate freely between two fixed points. A string in the real world has thickness, and the point at which vibration can start is offset a tiny bit from its fixed point. This is due to the material properties of the string so thickness and material composition matter. The thicker the string or stiffer the material the farther this offset is from the end point. – Anonymous Jan 26 '11 at 15:49
  • I'm pretty sure the explanation of why thicker strings need to be longer here is just flat out wrong. The explanation I always saw was that the stiffness of thick strings causes the effective witness point of the string to be in front of the actual witness point where it touches the saddle. This discrepancy is greater for thicker/stiffer strings, and thus the saddles need to be farther back. This also explains the B string anomaly, since unwound strings are stiffer. – Edward Mar 13 at 23:37
  • The tension after stretching a string a certain length (e.g. fretting a string) depends on how "stretchy" a string is, for lack of a better word, and not how heavy it is. If you wound your B string to make it as thick as your low E string you'd end up with a string that's basically the same "stretchiness", even though it has much more mass. This winding doesn't automatically make the string's tension go up. – Edward Mar 13 at 23:46
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Another reason is the action of the string (the distance between string and fretboard). The lower strings need more space to vibrate than the higher strings and therefore they need a higher action. When you fret a string with a higher action the string tension increases more compared to a string with lower action. As far as I know this is the main reason for the different compensation lengths of the strings.

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  • On a classical guitar, the saddle is thicker towards the thicker strings. On an acoustic guitar, the saddle has even thickness, but has the slanting. Both ways increase the length of the thick strings. Is there any reason why it's done one way or the other? – JoJo Aug 7 '14 at 15:05
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Engineer and musician's answer:

Another way you can think about it is that when you fret up the neck, you are essentially creating "fatter" strings. Imagine fretting almost all the way up to the bridge; the segment of string would start looking like a barrel. The engineering answer is that the barrel has a different area to length ratio (actually area-moment-of-inertia to length ratio).

If you can, imagine rotating a barrel end-over-end. How fast will it go? Now imagine taking all the same mass and stretching it out into a long bar. Hopefully you can see that the bar would rotate more slowly. Same mass, but different mass moments of inertia.

An idealized string is long and slender. When it starts getting short, the "barrel" nature of the string becomes more and more apparent. Vibrations of the string are a combination of 1) each string segment moving up and down, and 2) rotating back and forth. The barrel-like string (or shorter string) will rotate faster, which means a faster vibration and higher pitch.

When you fret up the neck you want a little bit of extra length to lower the pitch back down. That is what the slanted bridge does.

The b-string part on many guitar bridges is dipped down because the high e-string and the b-string are usually solid strings while the lower strings are wound. You're actually looking at two different slants because the strings are different types.

The wound strings have a lower area moment of inertia for a given diameter— there is some empty space between the different wires. This means the barrel nature of the short string takes longer to come into play as you fret up the neck. The bridge for the wound strings has a shallower slant and the bridge for the solid strings has a steeper slant.

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I have another reason to consider that can be combined with the above answers.

Strings have two lengths.

  1. Physical length,
  2. Speaking length.

The physical length is related to the 12th root of 2. Look this up on the internet and see that it is the note spacing of Western music. The number is slightly less than 6%. Since there are 12 intervals in a scale, the frequency at the 12th fret is twice the open string frequency. Each fret is about 6% higher than the previous note and it also physically represents what a 6% compound interest means for your money by the closer fret spacing going up the neck as it relates to the time to double your money. If the 6% was not compounded all the frets would be the same space as the length of the nut to the first fret.

Speaking length has more to do about where does the vibrating string actually start vibrating. Thicker wound strings start vibrating slightly forward of their resting place at the nut, bridge and played fret. When you combine this with the above answer you will have a more comprehensive answer to the question.

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