# Guitar string tension and scale length

A simple question: you have an acoustic guitar with a 20 inch scale and tune it to say E. Now transfer the string to a 25 inch scale and retune it to E. By what percentage would the tension increase?

• You are assuming the same string gauges? A related question would be how to compensate (retain the same tension) by changing the string gauge. – Tim Oct 7 '18 at 8:22

The square of the frequency of a vibrating string is directly proportional to the tension, and inversely proportional to the square of the length of the string. So, for two strings of identical composition vibrating at the same frequency:

T2 = (L22 / L12) * T1.

For L1 = 20in and L2 = 25in, we have L2 = 1.25 * L1, or L22 = 1.5625 * L12. This means that:

T2 = 1.5625 * T1 = (1 + 0.5625) * T1.

The tension in the 25 inch string is 56.25% higher than the tension in the 20 inch string. Hmmm, in retrospect, you probably should have asked this over at the SE Physics site.

• does a 25 inch scale exist on acoustic? – Neil Meyer Oct 7 '18 at 2:40
• @NeilMeyer -- Stewie Mac shows some Nationals as 25" scale length, and some other acoustics as longer. I have a Taylor 12-string with a 25.5" scale length. – ex nihilo Oct 7 '18 at 2:54
• @NeilMeyer - My Fender, Epiphone and Yamaha acoustics are all pretty close to 25" scale. 25.5", 25.65" and exactly 25" respectively. Scale lengths are averaged across the strings, as the saddles are not parallel to the nut. Epi measured from the zero fret. – Tim Oct 7 '18 at 8:20
• In laymans' terms, I'd have said the sting is 25% longer, so it'd need 25% more tension. Guess it's not simply a straight line graph... +1 – Tim Oct 7 '18 at 8:28