Long scale strings on medium scale bass, tension calculations

[thermodog]

I have a medium scale bass (Fender Urge) that will accommodate long scale strings, but I wanted to know what the string tension would be with any given long set on my medium bass, and I found a way. GHS has a Bass String Tension Guide on their website:

http://www.ghsrep.net/uploads/2/2/2/5/22258814/2020-ghs-bass-guitar-tension.pdf

If you use their formula and do the math (I have), it turns out that there is a simple ratio that applies. The tension of a long scale string on a medium bass will be about 88.6% of what the same string's tension is on a long scale bass (both tuned to the same note of course). I've uploaded a PDF file that shows my calculations.

 

[HaphAsSard]

I have a medium scale bass (Fender Urge) that will accommodate long scale strings, but I wanted to know what the string tension would be with any given long set on my medium bass, and I found a way. GHS has a Bass String Tension Guide on their website:

http://www.ghsrep.net/uploads/2/2/2/5/22258814/2020-ghs-bass-guitar-tension.pdf

If you use their formula and do the math (I have), it turns out that there is a simple ratio that applies. The tension of a long scale string on a medium bass will be about 88.6% of what the same string's tension is on a long scale bass (both tuned to the same note of course). I've uploaded a PDF file that shows my calculations.

The more general rule is "multiply by the ratio of scale lengths (with the target one as the numerator), squared".
(32/34)^2=0.8858 etc., indeed.

On a chromatic tension chart, the near equivalent is looking at the tension figure a half step down (playing an E natural on the first fret of a low E tuned Eb, you're now almost exactly at 32" from the bridge).
On a non-chromatic chart, to pull off the same trick without having tensions at Eb etc. handy, one needs simply to look at tensions of notes a tritone away, and then halve or double them, depending on whether said note in the chart (in our example - looking for tension at Eb - we need tension at A) is higher or lower than the sharp/flat we need.
Why? Because tension doubles or halves for every half-octave increase/decrease.