In music, a scale is a set of musical notes in order by pitch, either ascending or descending.

A scale is contrasted with a musical mode in one of two ways:

• as a pattern of notes or pitches regardless of tonic or other notes' importance, as opposed to a scale with a tonic and possible frame
• as an ordered collection of notes or pitches, as opposed to a series of intervals, which is a musical mode.

Each note in a scale is referred to as a scale degree. Though the scales from musical traditions around the world are often quite different, the pitches of the notes in any given scale are usually related by mathematical rules.

Scales may be described according to the intervals they contain, for example

• tonal, modal, diatonic, derived , chromatic, synthetic

or by the number of different pitch classes they contain:

• most common: pentatonic, hexatonic, heptatonic or five, six, and seven tone scales, respectively.
• used in prehistoric music: ditonic or two, tritonic or three, tetratonic or four
• in modern classical music: octatonic or eight.

Scales are often abstracted from performance or composition, though they are often used Precompositionally to guide or limit a composition. One or more scales may be used in a composition, such as in Claude Debussy's L'Isle Joyeuse.

Scales in Western music

Scales in traditional Western music standardly consist of seven notes, made up of a root note and six other scale degrees whose pitches lie between the root and the root's first octave. Notes in the commonly used scales (see just below) are separated by whole and half step intervals of tones and semitones (the harmonic minor scale including a three-semitone interval; the pentatonic including two of these).

There are a number of different types of scales used commonly in Western music, including:

• The major scale (seven notes)
• The minor scale (seven notes)
• The chromatic scale (twelve notes)
• The modal scales (seven notes)
• The whole tone scale (six notes)
• The pentatonic scale (five notes)

Synthetic scales:

• The diminished scales (also known as octatonic)
• The altered scale
• The Spanish and Jewish scale
• The Arabic scale
• The psychoacoustical scales

Scale degrees

A scale degree is a numeric position of a note within a scale ordered by increasing pitch. The simplest system is to name each degree after its numerical position in the scale, for example: the first, the fourth. Because intervals are inclusive, a fifth describes a note which is four notes after the tonic.

Major scales have seven notes which are named, in order: tonic, supertonic, mediant, subdominant, dominant, submediant, leading-tone (or leading-note). Also commonly used is the "movable do" solfege naming convention in which each scale degree is given a syllable. In the major scale, the solfege syllables are: Do, Re, Mi, Fa, So, La, Ti (or Si), Do (or Ut).

Non-Western scales

In traditional Western music, scale degrees are most often separated by equally tempered tones or semitones, creating at most, twelve pitches. Many other musical traditions employ scales that include other intervals or a different number of pitches. In the middle eastern Hejaz scale, there are some intervals of three semitones. Gamelan music uses a small variety of scales including Pélog and Sléndro, none including equally tempered intervals. The music of India includes some excellent examples, as some ragas employ scale intervals smaller than a semitone, up to twenty two pitches, though many of these are shrutis or inflections of the twelve main notes (Callow & Sheperd, 1972; Jhairazbhoy & Stone, 1963). Arab music maqams may use quarter tones and thus from fifteen to the max of twenty-four pitches, though these may similarly be inflecions (Zonis, 1973). Neither Indian nor Arab scales are chromatically microtonal (Burns, 1999).

Microtonal scales

The term microtonal music usually refers to music with roots in traditional Western music that employs non-standard scales or scale intervals. The composer Harry Partch made custom musical instruments to play compositions that employed a 43-note scale system, and the American jazz vibraphonist Emil Richards experimented with such scales in his 'Microtonal Blues Band' in the 1970s. John Cage, the American experimental composer also created works for prepared piano which use varied, sometimes random, scales. Microtonal scales are also used in traditional Indian Raga music, which has a variety of modes which are used not only as modes or scales but also as defining elements of the song, or raga.

Jazz and blues

Through the introduction of blue notes, jazz and blues employ scale intervals smaller than a semitone. See also: jazz scales. The blue note is an interval that is technically neither major or minor but 'in-between', giving it a characteristic flavour. For instance, in the key of E, the blue note would be either, a note between g and g# or a note moving between both. In blues a pentatonic scale is often used. In jazz many different modes and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz.

Chords

The notes in a chord are usually a subset of a particular scale, in the common practice period being built upward by thirds from a particular scale degree. Thus in a C major scale: CDEFGAB, a chord built on C is the notes CEG.

Psychoacoustical scales

The bark scale and the mel scale are two psychoacoustical scales.

Source

• Burns, Edward M. (1999). "Intervals, Scales, and Tuning", The Psychology of Music second edition. Deutsch, Diana, ed. San Diego: Academic Press. ISBN 0122135644.
• Zonis, E. (1973). Classical Persian music: An Introduction. Cambridge, MA: Harvard University Press.