Intonation and string gauge

jaymenon

I’m curious, when we adjust saddle intonation screws and move saddles to make the intonation more accurate, the 1st E string usually has the shortest scale length; the B saddle is pulled back a bit, and the G saddle pulled back even more, giving those two strings slightly longer scale lengths (on a common set of 10-46 strings)

So does the scale length depend upon the gauge of the string, or the note that it is tuned to? (i.e. when you change for example the first string from .009 to .010 but tune it to the same note E do you need to increase the scale length by pulling the saddle back?)

I know that for example with a wound G string the saddle needs to be moved forwards (closer to the nut) reducing significantly the scale length compared to an unwound G string.  But that may not be related purely to string gauge since the very structure of the wound string is different...

ICBM

It’s related to the thickness of the string. A thicker string is more pitch-sensitive to tension than a thinner one, so it goes sharper as you pull it down to the fingerboard. To fix that you lengthen the scale slightly which lowers the pitch again - hence, thicker strings need a longer scale than thin ones to intonate correctly.

With a wound string, the tension is carried by the core not the wrap (which just adds mass), so it intonates like a plain string of the same core diameter - ie shorter than a plain string of the same overall gauge.