Calculating string tension on long scale fan fret guitar

[Quickstep192]

I have a long scale fan fret guitar that I want to try Newtone DADGAD strings on.

Newtone lists the tension for their strings for 25.5” scale but not for other scale lengths.

D’Addario string tension pro lets you calculate tension for various tunings and string lengths, but of course only for D’Addario strings.

If I have a string length of let’s say 27”, is it reasonable to multiply the published string tension by a factor of the longer string length divided by 25.5?

[nikpearson]

...then you could then adjust the scale length in the tension calculator.

I’m guessing that with the huge range of strings D’Addario offer there’ll be something very close to the tension of the Newtones.

[charles Tauber]

Mersenne's law provides the following equation relating frequency of vibration(f), string length (L), "bulk modulus" (mass/unit length) (u) and string tension, (F)



In the situation you have, the frequency of vibration and the bulk modulus are constant. For the frequency to stay constant (i.e. tuned to the same pitch), the ratio of (F)*1/2 to L must be a constant.

Rearranging the equation, T2/T1= (L2/L1)*2, or T2=T1(L2/L1)*2,
where
L2 is the longer string (scale) length (e.g. 27"),
L1 is the published scale length (e.g. 25.5"),
T1 is the published tension for scale length L1 and
T2 is the tension of the same string at scale length L2

If the published value for T1 was 10 lb, the longer string would be 11.2 lb (1.12 times T1).

[Quickstep192]

Originally Posted by charles Tauber

Mersenne's law provides the following equation relating frequency of vibration(f), string length (L), "bulk modulus" (mass/unit length) (u) and string tension, (F)



In the situation you have, the frequency of vibration and the bulk modulus are constant. For the frequency to stay constant (i.e. tuned to the same pitch), the ratio of (F)*1/2 to L must be a constant.

Rearranging the equation, T2/T1= (L2/L1)*2, or T2=T1(L2/L1)*2,
where
L2 is the longer string (scale) length (e.g. 27"),
L1 is the published scale length (e.g. 25.5"),
T1 is the published tension for scale length L1 and
T2 is the tension of the same string at scale length L2

If the published value for T1 was 10 lb, the longer string would be 11.2 lb (1.12 times T1).

Thanks for this; it's just what I needed. Question though - In the formula T2=T1(L2/L1)*2 I interpret the "*" as multiplication, but it's really squaring the quantity L1/L2, correct?

[charles Tauber]

Originally Posted by Quickstep192

Thanks for this; it's just what I needed. Question though - In the formula T2=T1(L2/L1)*2 I interpret the "*" as multiplication, but it's really squaring the quantity L1/L2, correct?

Squared, (L2/L1) yes.

[nikpearson]

I’ll be keeping this equation for future reference. Thanks.