In very broad terms, the pitch a vibrating string makes when it is held motionless on both ends depends on :-
a) the length of the vibrating part of the string – the longer the length the lower the pitch
b) the tension on the string – the more tension, the higher the pitch
c) the construction of the string – ie the type of material and how it is made. Generally speaking the “heavier” the string, the lower the pitch.
The frets on a guitar are used to help guide the player to make the correct pitch changes from note to note. For most music, the players want the pitch to go from ‘note to note’ accurately rather than say, something in between a C and C sharp etc. So the frets allow this to happen more easily, as compared to a fretless guitar or violin where the position of the finger must be very accurate in order to get the notes accurate.
Of course, some people bend notes and want other sound effects but that is another story altogether.
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