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).
Any member of several families of sap-sucking insects (order Homoptera) whose bodies are covered by a waxy shell (the scale). The eggs are protected by the female's body or scale or a waxy filamentous mass. Scale insects may attack any part of a plant, but each species is host-specific. Many species are serious plant pests; others have commercial value. The lac insect is used in a red dye and in shellac. Cochineal, a red dyestuff, consists of the dried, pulverized bodies of females of the species Dactylopius coccus. Seealso cottony-cushion scale, San Jose scale.
Learn more about scale insect with a free trial on Britannica.com.
Examples of the chromatic, major, and minor scales.
Learn more about scale with a free trial on Britannica.com.
Interval of time occupied by the Earth's geologic history, extending from circa 3.9 billion years ago (corresponding to the age of the oldest known rocks) to the present day. It is, in effect, the part of the Earth's history that is recorded in rock strata. The geologic time scale is classified in nested intervals distinguished by characteristic geologic and biologic features. From longest to shortest duration, the intervals are eon, era, period, and epoch.
Learn more about geologic time with a free trial on Britannica.com.
Cottony-cushion scales (Icerya purchasi, magnified)
Learn more about cottony-cushion scale with a free trial on Britannica.com.
Species (Aspidiotus perniciosus) of scale insect first discovered in North America at San Jose, Cal., in 1880 but probably a native of China. A waxy gray secretion (the scale) covers the yellow females, which are about 0.06 in. (1.5 mm) in diameter. The scale is elevated in the center and is surrounded by a yellow ring. The female produces several generations of living young each year. San Jose scales can completely cover tree branches and may eventually kill the tree.
Learn more about San Jose scale with a free trial on Britannica.com.
Widely used measure of the magnitude of an earthquake, introduced in 1935 by U.S. seismologists Beno Gutenberg (1889–1960) and Charles F. Richter (1900–1985). The scale is logarithmic, so that each increase of one unit represents a 10-fold increase in magnitude (amplitude of seismic waves). The magnitude is then translated into energy released. Earthquakes that are fainter than the ones originally chosen to define magnitude zero are accommodated by using negative numbers. Though the scale has no theoretical upper limit, the most severe earthquakes have not exceeded a scale value of 9. The moment magnitude scale, in use since 1993, is more accurate for large earthquakes; it takes into account the amount of fault slippage, the size of the area ruptured, and the nature of the materials that faulted.
Learn more about Richter scale with a free trial on Britannica.com.