When the string on a guitar is tightened, its pitch_____. 

 The string of a guitar is like a stretched string fixed at both ends, and the frequency of a stretched string is directly proportional to the tension in the string,
          
$f \alpha \sqrt{T}$

When the string is tightened, tension T in the string increases, hence frequency f also increases.
As the pitch of a sound is directly proportional to its frequency, the pitch also increases.

Therefore, we can say that when the string on a guitar is tightened, its pitch increases.