Hi Jeremy,
Welcome to the not-so wonderful world of nylon string guitar “intonation” issues. There are a number of things for you to try regarding the issue with the B string you are having. Firstly, I might suggest that if you are off by, as you described it, almost a full ½ step at the 12<sup>th</sup> fret (compared to the open string), that is somewhat alarming as that would imply that the pitch at the median of your scale length would be sharp by nearly 100 cents. That’s pretty unusual, not to mention extreme and probably points to something other than the saddle.
The simple fact t the matte with classical guitar strings is that there is usually very minor differences in diameter between the E and B strings – hence there is usually little or no compensation. A normal tension set of strings that you described has an E string at diameter of 0.024” and a B string Diameter of .027”. That .003” difference is not enough to usually warrant a drastic difference in string length compensation – however there us a dramatic difference between the two strings in overall tension. The High E string of that same set (normal tension) has about 21 lbs of string pull while the B string has only about 15lbs of pull.
Your particular issue with that much of a discrepancy suggests that the problem is not at the saddle. However, it should be mentioned t is possible you have a couple of old or “false” strings on your hands. You did mention that you swapped out the B string without any improvement. Again, that suggests the problem is elsewhere. You might want to try a higher tension string for the b string to see it there is any change (as an experiment)
Before embarking on making any alterations to the guitar – Always look to the strings first. Nylon strings are a petroleum product and can decay over time – even “fresh Strings” sitting in a drawer (or a music store rack) for a long period of time can go false. You might try a different brand of string – D’Addario makes a great product, but they are mass manufactured and not infallible – it’s possible to have a bad batch or lot of strings.
The first place I would look as a possible issue is the nut – both the condition of the nut shelf and the height of the strings at the nut. I am not a big believer in compensation of the strings at the nut – long meandering conversations with classical guitar builder John Gilbert however compelling they were never convinced me that nut compensation was ever necessary.
With that said – you are also describing a circumstance where the B string is “Right from the get go the scale starts going sharp incrementally at every fret” Which implies to me that the string heigh at the nut is likely too tall and the string length compensation issues are emanating from the nut and not improving by lengthening the string at the saddle.
Secondly, I would make sure that the seat of the string in the nut slot is emanating from the front shelf of the front of the nut and not further back. If you string length is off from the fundamental, there’s no hope for any compensation at the saddle to make up the difference.
Thirdly, I wouldn’t necessarily put it past Yamaha to have located the nut correctly in relationship to the first fret. If it is too far from the first fret for the scale length – then you’ll always start off sharp at the first fret – that’s why John Gilbert developed his string length compensation method for classical guitars.
Very often – string length compensation issues can be bewildering – but there’s always a mathematical solution somewhere in the process.
If you get stumped after running through the possibilities I mentioned – feel free to reach out to me directly.
doug@guitarspecialist.com