In music, a scale is a collection of musical notes that provides material for part or all of a musical work. Scales are ordered in pitch or pitch class, with their ordering providing a measure of musical distance. Scales differ from modes in that scales do not have a primary or "tonic" note. Thus a single scale can have many different modes, depending on which of its notes is chosen as primary.
The distance between two successive notes in a scale is called a "scale step." Composers often transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the C major scale, the pattern C-D-E ("doe, a deer") might be shifted up a single scale step to become D-E-F ("ray, a drop"). This process is called ''scalar transposition''. Since the steps of a scale can have various sizes, this process introduces subtle melodic and harmonic variation into the music. This variation is what gives scalar music much of its complexity.

Background

Scales are typically listed from low to high, or, alternatively and more rarely, from high to low. A scale is ''octave-repeating'' when every pitch in the scale appears in every possible octave. An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the C major scale can be represented as the circular ordering C-D-E-F-G-A-B-C, with the bracket indicating that the ordering returns to its starting point.

This single scale can be manifested at many different pitch levels. For example a C major scale can be started at C4 (middle C; see scientific pitch notation) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7.

Scales may be described according to the intervals they contain:

for example: diatonic, chromatic, whole tone

or by the number of different pitch classes they contain:

very common: pentatonic, hexatonic, heptatonic have five, six, and seven tone scales, respectively.

used in prehistoric music: ''ditonic'' or two, ''tritonic'' or three, ''tetratonic'' or four

used in jazz and modern classical music: octatonic or eight.

Scales can be abstracted from performance or composition. They are also often used precompositionally to guide or limit a composition. Explicit instruction in scales has been part of compositional training for many centuries. One or more scales may be used in a composition, such as in Claude Debussy's ''L'Isle Joyeuse''. Below, the first scale is a whole tone scale, while the second and third scales are diatonic scales. All three are used in the opening pages of Debussy's piece.

Terminological note

Musicians use the term "scale" in several incompatible senses.

Scale vs. Mode. Sometimes the term refers to an ordered collection in which no element has been chosen as primary. Thus musicians will talk about the "diatonic scale," the "octatonic scale," or the "whole tone scale." However, the term is sometimes used to mean "mode," indicating that an element of the scale has been chosen as most important. Thus the "C major scale" and used to refer to ''types'' of scale related by transposition. In this sense, musicians will talk about ''the'' diatonic scale, considering the C diatonic scale and G diatonic scale to be instances of a single, larger category. Consistency suggests distinguishing a "scale" (such as C or G diatonic) from "scale type" (''the'' diatonic scale-type"). To avoid neologisms, however, we will follow traditional musical practice, using the term "scale" in both senses. Context should allow readers to distinguish between particular scales and the larger types to which they belong.

In addition, the term "scale" is used in psychoacoustics to refer to various ways of measuring distances between pitches. See bark scale and mel scale.

Scales in Western music

Scales in traditional Western music generally consist of seven notes and repeat at the 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 includes a three-semitone step; the pentatonic includes two of these.

Western music in the Medieval and Renaissance periods (1100-1600) tends to use the white-note diatonic scale C-D-E-F-G-A-B. Accidentals are rare, and somewhat unsystematically used, often to avoid the tritone.

Music of the common practice periods (1600-1900) uses three types of scale:

The diatonic scale (seven notes)

The melodic and harmonic minor scales (seven notes)

These scales are used in all of their transpositions. The music of this period introduces ''modulation,'' which involves systematic changes from one scale to another. Modulation occurs in relatively conventionalized ways. For example, major-mode pieces typically begin in a "tonic" diatonic scale and modulate to the "dominant" scale a fifth above.

In the nineteenth and twentieth century, additional types of scale are explored:

The chromatic scale (twelve notes)

The whole tone scale (six notes)

The pentatonic scale (five notes)

The octatonic or diminished scales

A large — indeed, virtually endless — variety of other scales exists:

The Phrygian dominant scales (actually, a mode of the harmonic minor scale)

The Arabic scales

The Hungarian minor scale

Naming the notes of a scale

In many musical circumstances, a specific note of the scale will be chosen as the "tonic"--the central and most stable note of the scale. Relative to a choice of tonic, the notes of a scale are often labeled with numbers recording how many scale steps above the tonic they are. For example, the notes of the C diatonic scale (C, D, E, F, G, A, B) can be labeled {1, 2, 3, 4, 5, 6, 7}, reflecting the choice of C as tonic. The term "scale degree" refers to these numerical labels. In the C diatonic scale, with C chosen as tonic, C is the first scale degree, D is the second scale degree, and so on.

Note that such labeling requires the choice of a "first" note; hence scale-degree labels are not intrinsic to the scale itself, but rather to its modes. For example, if we choose A as tonic, then we can label the notes of the C diatonic scale using A = 1, B = 2, C = 3, D = 4, and so on. However, the ''difference'' between two scale degrees is independent of the choice of scale degree 1. Thus whether two notes are adjacent in a scale, or separated by one note, does not depend on the mode under discussion.

The scale degrees of the traditional major scale can also be named using the terms 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 (or Sol), La, Ti (or Si), Do (or Ut).

In naming the notes of a scale, it is customary that each scale degree be assigned its own letter name: for example, the A diatonic scale is written A - B - C♯ - D - E - F♯ - G♯ rather than A - B - D♭ - D - F♭ - E♯♯ - G♯. However, it is impossible to do this with scales containing more than seven notes.

Non-Western scales

In traditional Western music, scale notes are most often separated by equally-tempered tones or semitones, creating, at most, twelve pitches per octave. Many other musical traditions employ scales that include other intervals or a different number of pitches. A common scale in Eastern music is the pentatonic scale, consisting of five tones, in a pattern equivalent to the black keys on a piano. 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. Ragas in Indian classical music often employ intervals smaller than a semitone (Burns 1998, 247). Arabic music maqamat may use quarter tone intervals (Zonis, 1973). In both ragas and maqamat, the distance between a note and an inflection (e.g., śruti) of that same note may be less than a semitone.

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. Easley Blackwood has written microtonal but equal-tempered composition. 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. The blue note is an interval that is technically neither major nor 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, patterns, and scalar transposition

As discussed above, musicians often utilize scales by shifting (transposing) a musical pattern by some constant number of scale steps. This process is known as ''scalar transposition''.

The harmonies of traditional tonal music are constructed in this way. Western tonal chords are stacks of thirds, with or without accidentals, built above a particular scale degree, which is called the root of the harmony. Thus in a C diatonic scale: CDEFGAB, a three-note chord built on C will consist of the notes C-E-G. The same pattern, built on the note G, produces the chord G-B-D.