In music a chromatic scale divides an octave into 12 equally

In music, a chromatic scale divides an octave into 12 equally-spaced pitches. An octave contains 1200 cents (a unit of measure for musical intervals), and each pitch in the chromatic scale is 100 cents apart. The relationship between cents and note frequency is given by the formula: C_2 - c_1 = 1200 (log_2 f_2/f_1) How many cents separate two notes, where one note is double the frequency of the other note? A. 2 B. 100 C. 200 D. 1200

Solution

c2 - c1 = 1200log(f2/f1)

Given f2 = 2f1

So, c2 - c1 = 1200log2(2f1/f1)

= 1200log2(2)

=1200(log2/log2)

= 1200