Strings Intonation

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Strings Intonation

Post by apaclin »

Hey guys, just wanted to ask, a certain sting intonation (position of a saddle that provides a certain scale length) entirely depends on the strings height, right? Cos if you put the strings higher, you increase the string tension on the 12th fret by pushing it down, which raises the pitch.
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Re: Strings Intonation

Post by Sam Spoons »

Various things will affect the amount of compensation you need for good intonation, string height (as set at the bridge and at the nut) is one of them, neck relief, tuning and string gauge will all have an effect too.
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Re: Strings Intonation

Post by Wonks »

Not just that, but also the string stiffness (related to string thickness, but a wound string isn't as stiff as a solid string of the same diameter). There is a very small length of string by the nut and bridge that isn't vibrating freely. The string has to transition from not moving to moving, and it takes a small distance to do that.

The stiffer the string, the greater the distance is before the string is vibrating fully, so the intonated length is always a bit greater than the scale length (twice the nut to 12th fret distance). The thinner and more flexible the string, the closer it behaves to an 'ideal' string that vibrates exactly from each end.

The top E saddle is almost always the furthest forward saddle, the B is back a bit from that and a plain G a bit further back from that.

As string stiffness is mainly driven by the core wire diameter, a wound D string is slightly more flexible than a plain G string as the core wire is thinner than the G string, so the D saddle normally sits a bit further forward than the G. The A sits a bit further back from the D, and the bottom E furthest back of all.

With a thicker string set with a wound third, the G saddle will normally sit a bit further forward than the B saddle, again due to the G string core wire being thinner than the solid B string.

On top of this basic intonation requirement, the string action will also play a part. The higher the action, the greater the tension added when fretting it. Extra tension makes the string sharp, so the saddle has to go back a bit.

For completeness, this tension increase is very slightly offset by the very slightly longer string length created when pressing down a string sitting high above a fret when compared to a string that's sitting just above the fret. It's almost a negligible increase, but it is there. E.g. at a fret 323mm from the bridge (roughly 12th fret on a 25.5" scale guitar), the string will be 0.001mm longer if pressed down by 1mm, but will be 0.006mm longer if pressed down by 2mm (I did say it was almost negligible).

It's effectively this small increase in string length that increases the string tension; though as the string is lengthened both on the nut and bridge side of the fret, the overall increase in string length to be considered is longer than just the vibrating string length. The minimum increase in overall string length is at the 12th fret.

Pressing harder with your fingers to fret a note than the minimum necessary force can add extra tension and stretch the string further, making it sharper. the taller the fret, the more scope there is for this to happen.

As you move further up or down the neck, the string length increase gets larger, with the largest increase normally happening at the 1st fret. Which is why you don't want your nut slots cut too high and why the first few frets can sound very sharp if the slots are too tall.

Nylon strings are a lot more flexible than steel strings, and the wound strings over silk or nylon filament are flexible as well, so on a classical guitar, the non-fully vibrating portion of the string as very short and very similar for all the strings, which is why they can get away with having a straight saddle. I'm not saying it couldn't be improved slightly by some compensation, but the distances involved would be very small indeed.
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