The Low E string on your guitar is under $87\mathrm{.}0$ N of tension. When this string is plucked along with a $82\mathrm{.}8$ Hz tuning fork you hear beats with a frequency of $12\mathrm{.}4$ Hz $.$

What higher tension might tune your guitar string to $82\mathrm{.}8$ Hz $?$

What lower tension might tune your guitar string to $82\mathrm{.}8$ Hz $?$