Answer
An increase in tension causes the frequency increase.
Work Step by Step
The frequency of the wave on a string is equal to $$f_n=\frac{nv}{2L}=\frac{n}{2L}\sqrt{\frac{F_T}{\mu}}$$ The length of the string remains the same and the linear mass density remains constant. However, once the string is tightened and the tension is increased while tuning, the frequency becomes higher.
