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I had something odd happen today and was wondering if anyone else had noticed something like this or if anyone could offer an explanation. I may be crazy so feel free to say so.

Anyway, while measuring for proper intonation of some bass strings on a 34" scale(see other post regarding that) I noticed that the G string had a constant diameter and played in tune at 34". The E string had a long section of thinner diameter at the tuner end. Because of my holding jig while measuring, the thin section made contact with the nut and the thick section made contact with the saddle. The string played in tune at the 12th fret when the vibrating string length was adjusted to 33 1/2". The other two middle strings behaved similarly.

When I re-worked the jig so the string diameter was constant at both the nut and saddle, the E string played in tune with a VSL of 34 1/8". I'm assuming the cause of the discrepancy in the first measurements was because of the inconsistent string diameter.

Has anyone ever noticed anything like this? Can anyone offer an explanation as to why the VSL would need to be shortened on the E string? I would have still expected to need to lengthen the VSL since even the thin portion is thicker than the G string.

The starting point for fret placement assumes that the string is perfectly uniform over the entire vibrating length. By having a lower mass at the nut end, intonation at the 12th fret will tend to be flat. That is because when the string is open, the tension is a bit less, because the mass of the string is less than it would be if it was the full diameter over the entire length. Once fretted at the 12th fret, the vibrating part of the string is full diameter, meaning it is more than half the mass of the entire string. More mass and less tension means flat intonation. That is why the string length had to be shortened to play in tune at the 12th.
I first noticed this phenomenon when I was a teen. I tended to rust the plain strings due to my body chemistry. I didn't have a lot of extra money to spend on new strings, so I would use fine sandpaper and steel wool to renew the strings instead of changing them....but there was a problem. Once the string rusted, (which occurred mostly from the nut to the 7th fret), I found that intonation became flat. This was because of the corrosion of the string, whch reduced its mass more near the nut.

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John

Thanks John. That's a good explanation and well stated. Much appreciated!