Musical Scales

A sound of constant frequency is called a tone or musical note. Music is a combination of such sounds. As music developed it came to be recognised that notes with a certain relationship between their frequencies gave a pleasing result when played together while other gave a harsh effect. This led to the evolution of musical scales consisting of a series of notes whose frequency relationships enabled the maximum number of pleasing relationships to be obtained.

Music evolved differently in different parts of the world, and scales were adopted which differed both in the number and the frequencies of the notes they contained. From the middle of the sixteenth to the middle of the nineteenth centuries, European music came to be based on the diatonic scale – eight notes which may be represented in various forms.

The diatonic scale has been standardized at a series of notes ranging from c' (middle C, 256 Hz) to upper C (512 Hz). The frequency of the notes has never been regarded as important as the ratio of the frequencies of the notes in the scale. The same notes on many instruments did not for many years have the same frequencies, but the ratios on different instruments were observed. In the twentieth century attempts were made to standardise the frequencies of musical notes. In 1939, it was agreed internationally that standard musical pitch would be based on a frequency of 440 Hz for a' (middle A).

Other intervals exist. In the above table the ratio 9/8 is called a major tone, 10/9 is a minor tone, 16/15 is called a semitone, but also a ratio 2/1 is called an octave and 3/2 is called a fifth.