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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. –  DRL Jan 15 '11 at 22:12

2 Answers 2

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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Excellent answer, well put. –  Ali Maxwell Jan 15 '11 at 22:16
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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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If I could vote up again, I would. The elaboration makes this answer outstanding. –  Anonymous Jan 16 '11 at 1:38
    
Thanks for the extra info! Top. –  Anonymous Jan 17 '11 at 14:13
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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

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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