Frequency and Pitch

Author: N.H. Crowhurst

Frequency is measured in cycles per second

The frequency of a sound is a measure of how many vibrations occur in a given time; it is usually measured in vibrations per second. When the sound vibrations are converted into electrical waves for amplification, the frequency is referred to as cycles per second, often called cycles for short.

In music, difference of frequency is recognized as a change in pitch. In a piano, for example, the long, heavy strings vibrate slowly (you can actually see the individual vibrations), whereas the short light ones vibrate very rapidly. The slow (low-frequency) vibrations are recognized musically as low in pitch; the rapid (high-frequency) vibrations are recognized musically as high pitched.

The frequency range of a piano

Every time frequency is doubled, pitch changes one octave. A two-octave rise in pitch quadruples the frequency; a three-octave rise in pitch multiplies it eight times. Any two adjacent notes on a piano keyboard have a constant ratio between their frequencies; since there are twelve notes per octave, this ratio is a number that, multiplied by itself twelve times, equals 2. The difference in frequency between two successive notes on the keyboard is not constant, but the ratio between their frequencies is constant; the frequency of the upper note is 1.059 times that of the lower one.

In ordinary arithmetic, the difference between successive numbers is always the same - one. A system of numbers or quantities where successive items are separated by a constant fraction, rather than by the same amount, is called a logarithmic system. The relationship between frequency and pitch is logarithmic, as may be seen from the fact that to raise the pitch each octave, the frequency has to be multiplied by a power of two, and to raise the pitch by any desired musical interval, the frequency has to be multiplied by a figure corresponding to that pitch interval.

This can be shown visually by using "logarithmic" paper, where the pattern of lines is repeated for every numerical increase of ten times, and the distance covered by each change of ten times is the same. Similarly, each ratio of two is the same distance on the scale, as is any other ratio.

Plotting frequencies on a logarithmic scale

Different kinds of sound, both musical and otherwise, are characterized by different ranges of frequencies:

Distribution of different sounds over audible frequency range