At one point I had been trying to construct an equation which would calculate the tension on a tuned string with a change in temperature (and therefore the fundamental frequency), but found my calculations were wrong. By extension, the purpose of the project was to be able to calculate what frequency the string should be tuned to beforehand so that with a change in temperature the change in tension will retune the string to the desired final frequency. For the sake of clarity and realism let's say that the string instrument is an electric guitar equipped with a double-locking tremolo where the tremolo is also 'blocked', which means that the tremolo does not move with a change in tension, and the effective length of string is merely the scale length of the instrument (i.e. the length of string from the locking but to the locking bridge). Let's also say that the body, neck, and headstock of the instrument remain immobilized even when all strings at their maximum tensile strength.