# Calculating Frequency Values for a G String on a Standard Tuned Guitar

In summary: If you want to tune a guitar for a European Standard, which has a higher pitch, then you would need to lower the tension by .5kg or 1/10 of a pound.
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:

f=(1/2L)[(TL/m)^1/2]
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.

Here's a list of frequencies for (I suppose) standard tempered tuning:
http://www.phy.mtu.edu/~suits/notefreqs.html

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

Is that what you were asking?

schip666! said:
Here's a list of frequencies for (I suppose) standard tempered tuning:
http://www.phy.mtu.edu/~suits/notefreqs.html

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

Is that what you were asking?

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.

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.

I would suggest using a frequency chart specifically designed for guitar strings. These charts are readily available online and can provide accurate frequency values for each fret on a standard tuned guitar G string. This will save you time and ensure accuracy in your calculations.

Additionally, your approach using the formula for frequency is correct, but it may be helpful to double check your calculations and make sure all the values are accurate. It may also be beneficial to take into account any other factors that could affect the tension and frequency of the string, such as the material and thickness of the string.

Overall, it is important to have accurate frequency values in order to properly design a whammy system for your guitar. I would recommend using a combination of a frequency chart and your formula to ensure the most accurate results.

## 1. How do I calculate the frequency of a G string on a standard tuned guitar?

To calculate the frequency of a G string on a standard tuned guitar, you can use the following formula: f = (2^(n/12)) * 440, where n represents the number of frets on the G string. For example, if the G string is fretted at the 5th fret, n would be equal to 5. Plugging in this value to the formula, we get f = (2^(5/12)) * 440 = 392 Hz. This is the frequency of a G string on a standard tuned guitar.

## 2. What is the standard tuning for a guitar?

The standard tuning for a guitar is E-A-D-G-B-E, from the thickest string to the thinnest. This means that the sixth string (the thickest one) is tuned to E, the fifth string to A, the fourth string to D, the third string to G, the second string to B, and the first string (the thinnest one) to E.

## 3. Can I use a tuner to calculate the frequency of a G string on a standard tuned guitar?

Yes, you can use a tuner to calculate the frequency of a G string on a standard tuned guitar. Most electronic tuners will display the frequency of the string being played, so you can simply play the G string and read the frequency value from the tuner's display. Make sure the tuner is set to chromatic mode so it can accurately detect the frequency of the G string.

## 4. How does the length of the string affect the frequency of a G string on a standard tuned guitar?

The length of the string does not affect the frequency of a G string on a standard tuned guitar. The formula for calculating frequency takes into account the number of frets, not the length of the string. However, the length of the string can affect the tension and therefore the pitch of the string. Longer strings will have a lower tension and a lower pitch, while shorter strings will have a higher tension and a higher pitch.

## 5. Are there any other factors that can affect the frequency of a G string on a standard tuned guitar?

Yes, there are a few other factors that can affect the frequency of a G string on a standard tuned guitar. These include the gauge (thickness) of the string, the type of material the string is made of, and the temperature and humidity of the environment. These factors can all have a slight impact on the tension and therefore the pitch of the string, but the difference is usually minimal and may not be noticeable to the human ear.

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