Just interested to see why people's views are on the length of a tailpiece and its effect on the set up of a bass. I am thinking here that if the mensur is say a 103 short length 3/4 whether having a shorter tailpiece would improve the performance of a string given that the the tension of the string is related to the string length between the winder and the connection at the tail piece. i.e. in theory a shorter tailpiece should produce a higher tension as the string is longer.
The length of the Tailpiece does NOTHING to the string tension!
But the afterlengths might become longer and the mass of the vibrating system afterlength/tailpiece/tailgut-to-lower--saddle will be reduced. This can have an effect on wolf notes, good or bad.
There are a lot of discussions about lighter or heavier tailpieces on Talkbass you might want to read.
Thanks - I'll check them out.
Just thinking though that if a tailpiece were only 10 inches long ( say) as opposed to 12 inches then the string would be 2 inches longer between its anchor points ...that will have a huge affect upon the string's tension given the formula for string tension where 'L' is the string length and every variation of L becomes squared in the formula:-
T = 4 x L² x F² x r.
F equals frequency of a wave on the string
r equals mass per unit of volume or density of the string.
There's a worked example here -for anyone wanting to do the maths ! Source.
The strings tension is the same over the whole length of the string. The formula mean the vibrating part of the string (which is between nut and bridge). It is true, that the afterlength do vibrate too, but not as part of the main string part (between nut and bridge) but in a sympathetic manner. Reality is a bit more complicated (some small energy coupling between main part and afterlength by wiggling of the stiff string on the bridge and movement of the bridge), but of no interest for your calculation.
The formula means, that if you make the string length between nut and bridge shorter, the tension goes down if you keep the frequency. And not linearly but quadratic.
But this has nothing to do with the afterlengths. They have their own inharmonic pitch, because the tailpiece is part of this vibrational system and each string afterlength is coupled to the others via the vibrating tailpiece. This is the reason why the sound of the afterlengths is often inharmonic.
We had some discussions about that on talkbass in the last year, I think.
I need to look into that !! Many thanks - I think I follow the gist of what you are saying!
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