A great variety of scales have been used in the past and in different cultures; no single interval is common to all of them. In the 6th cent. B.C., Pythagoras defined the mathematical relationship of the perfect intervals (the octave, fourth, and fifth) and of the intervals between them (an interval being the difference in pitch between two tones). The Greek system was taken up by the Christian church, which adapted its note series to a number of modes used in medieval music, especially in plainsong.
The church modes, under the impact of the composition of polyphonic vocal music, became reduced in due course to the two characteristic scales of later Western music, the major and the minor. The major scale, called diatonic, has five whole tones (t) and two semitones (s) arranged thus: ttsttts (as in the white notes on the piano keyboard taken from one C to the next C); this scale, with certain modifications, became the basis of Western musical tonality until the end of the 19th cent. The dissemination and influence of the diatonic scale was therefore very great. The minor scale is based on tsttstt. This arrangement produces the lower third, sixth, and seventh degrees that are characteristic of the minor mode; the higher seventh degree, a semitone rather than a whole tone below the main note, or "tonic," is often borrowed from the major mode for use at cadences.
Akin to the modes, the concept of key was developed, whereby a home tone, or tonic, is the principal focus of a composition, and the various other tones assume importance according to their relationship to the tonic. The increasing complexity of instruments demanded more refined tuning systems. By J. S. Bach's time equal temperament had become established. The resulting scale, called chromatic, consisted of 12 notes divided by semitone intervals (the white and black notes of the keyboard). Although the diatonic scale is basically heptatonic (seven-noted), music that is in a major or minor tonality usually employs the remaining five tones of the chromatic scale as auxiliary or ornamental tones. Music that employs them freely is said to be highly chromatic, while music that employs them sparingly is said to be diatonic.
The 12 scales, one for each note as the home tone, plus the 12 concomitant minor scales remained the basic organizing structure of Western music until the system was challenged by the dodecaphonic (twelve-tone scale) composers, in particular Arnold Schoenberg, who worked into the mid-20th cent. (see atonality; serial music). The whole-tone scale, which divides the octave into six equal whole tones (C, D, E, F sharp, G sharp, and A sharp, on the piano), gives a feeling of vagueness that made it adaptable to impressionism; its possibilities were thoroughly explored in the works of Debussy. The pentatonic scale (the black keys of the piano illustrate one form) has long been thought of as having an Asian character because of the prevalence of pentatonic scales in Chinese, Japanese, and Javanese music. The most complex scales known belong to Arabian music and Hindu music.
See N. Slonimsky, Thesaurus of Scales and Melodic Patterns (1947); C. Sachs, The Wellsprings of Music (1965).
See A. W. Green, How We Weigh and Measure (1961); B. Kisch, Scales and Weights (1965).