 To study tuning systems and other aspects of music theory that require finer distinctions between tones , it is helpful to have a measure of the size of an interval that is finer than an octave and is additive ( as logarithms are ) rather than multiplicative ( as frequency ratios are ) . That is , if tones x , y , and z form a rising sequence of tones , then the measure of the interval from x to y plus the measure of the interval from y to z should equal the measure of the interval from x to z . Such a measure is given by the cent , which divides the octave into 1200 equal intervals ( 12 semitones of 100 cents each ) . Mathematically , given tones with frequencies f1 and f2 , the number of cents in the interval from f1 to f2 is 
