Cluin,

You are right. I have actually confused the question haven't I? Tension caused by a tuner or tensioned caused by wieght is still tension. And tension on a wire equals a tone

There are no variables stated here other than the weight and the action of gravity or the tuner = mechanically created weight.

What follows I mistakenly assume would be understood.
Let us assume that we have two wire strings that are the same material, length, and diameter and attached to the same vibrating surface, soundboard.

If 20 lbs through application of a torque wrench is put on one string
and a 20lbs. weight is hung on the other will the strings have the same tones?

Don