Ralph Vaughan Williams (1872-1958) The Greek mathematician Pythagoras (c. 570-500 BC) carried out the earliest known acoustical experiments. Knowing that the shorter the length of a string the higher the pitch will be, Pythagoras demonstrated that pleasing intervals were sounded when a string is divided into certain ratios. When the length is halved, an octave is formed; when it is reduced to two-thirds the pitch is raised by a perfect fifth; when reduced to three-quarters it gives the perfect fourth. The same applies to the length of a column of air in a wind instrument. Over the years the remaining intervals of the scale were filled in with tones and semitones and thus began the gradual progress.
Notation The staff originated in medieval Europe as a means of recording plainsong. At first it was a single line around which the neumes, like small ticks, were placed to show the approximate melodic and rhythmic shape. Additional lines were added in the 11th century and the spaces, as well as the lines, were used to position the notes. By the 16th century, today's exactitude of recording pitch was arrived at when a pair of five-line staves became the norm, arranged as a "grand staff" with the top five lines.