Calculating the tension required to tune a guitar G string to a desired frequency

  1. Does anyone know where I can find a full table that lists the frequency values for each fret on a standard tuned guitar G string? Or failing that can anyone suggest a method of calculating them accurately? I need to work out the change in tensions required to increase and decrease the frequency of the string. For example, if the tension in the 3rd string is 7.5kg, and it is tuned to 196 Hz (i.e. the same frequency as plucking an open G note on the 3rd string), then what does the tension need to be if I want to tune the 3rd string so that when I pluck it, it has the frequency of G sharp (207.6 Hz)? I'm working on designing a whammy system.

    What I had in mind was if I could get the frequency value for each fret along the g string and use the formula:

    where: f = frequency, L = scale length (working length) of the string, T = tension, m = mass of the scale length section of the string

    to work out the tension required to tune the string to the desired frequency. Am I using the right approach for this? The string in question is a Fender Original 150s regular g string for electric guitar, gauge 0.017", scale length 25.5". Its made of pure nickel. Using a density value for commercially pure nickel I worked out "m" for the above equation to be 8.445 x 10^-4 kg.

    Any help is greatly appreciated. Cheers.
  2. jcsd
  3. Here's a list of frequencies for (I suppose) standard tempered tuning:

    Your formula shows Frequency being proportional to the sqr-root of Tension.

    Is that what you were asking?
  4. Thanks so much, that link is exactly the kind of thing I had been trying (and failing) to find. I thought I may have had to work them all out by hand and I wasn't sure if I was using the right method.
  5. K^2

    K^2 2,470
    Science Advisor

    The formula for frequencies is very straight forward.

    [tex]f = f_0 * 2^(n/12)[tex]

    Where n is the number of semitones that f is above f0. (Or bellow - use negative values of n). By definition of the American Standard Pitch, A4 is at 440Hz. The G you are looking at is G3, which is 10 semi-tones above A2 : 110Hz. That gives you 110 * 2^(10/12) = 196 Hz for G3.

    This is for a well tempered tunning, which guitars are built around.
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