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Double Bass string length and string tension

AFAIK, the distance between the tailpiece and bridge won't affect the tension or feel.
The original question was about the fact that a shorter vibrating lenght will diminish the tension for a given string.
This is easy to prove:
If you stop the string at half position and want to produce the same pitch as the open string, you need to detune the string flat an half step. You just lowered the string tension by doing so.