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For psychoacoustic scale, see
Ascending and descending
  
Pattern of intervals in the C-major scale   
In , a scale is any set of musical
ordered by
or . A scale ordered by increasing pitch is an ascending scale, while descending scales are ordered by decreasing pitch. Some scales contain different pitches when ascending than when descending (for instance, see ).
Often, especially in the context of the , part or all of a
and/or , is built using the notes of a single scale, which can be conveniently represented on a
with a standard .
Due to the principle of
equivalence, scales are generally considered to span a single octave, with higher or lower octaves simply repeating the pattern. A musical scale represents a division of the octave space into a certain number of scale steps, a scale step being the recognizable distance (or ) between two successive notes of the scale.
A measure of the width of each scale step provides a method to classify scales. For instance, in a chromatic scale each scale step represents a
interval, while a
is defined by the interval pattern T–T–S–T–T–T–S, where T stands for
(an interval spanning two semitones), and S stands for semitone. Based on their interval patterns, scales are divided into categories including , , , , and others.
A specific scale is defined by its characteristic interval pattern and by a special note, known as its first
(or ). The tonic of a scale is the note selected as the beginning of the octave, and therefore as the beginning of the adopted interval pattern. Typically, the name of the scale specifies both its tonic and its interval pattern. For example,
indicates a major scale in which C is the tonic.
Diatonic scale in the
Scales are typically listed from low to high. Most scales are -repeating, meaning their pattern of notes is the same in every octave (the
is one exception). An octave-repeating scale can be represented as a circular arrangement of pitch classes, ordered by increasing (or decreasing) pitch class. For instance, the increasing C major scale is C–D–E–F–G–A–B–[C], with the bracket indicating that the last note is an octave higher than the first note, and the decreasing C major scale is C–B–A–G–F–E–D–[C], with the bracket indicating an octave lower than the first note in the scale.
The distance between two successive notes in a scale is called a .
The notes of a scale are numbered by their steps from the root of the scale. For example, in a C major scale the first note is C, the second D, the third E and so on. Two notes can also be numbered in relation to each other: C and E create an interval of a third (in this case a major third); D and F also create a third (in this case a minor third).
A single scale can be manifested at many different pitch levels. For example, a C major scale can be started at C4 (middle C; see ) and ascending an octave to C5; or it could be started at C6, ascending an octave to C7. As long as all the notes can be played, the
they take on can be altered.
Scales may be described according to the
they contain:
for example: , ,
or by the number of different pitch classes they contain:
(8 notes per octave): used in
(7 notes per octave): the most common modern Western scale
(6 notes per octave): common in Western folk music
(5 notes per octave): common in folk music, especial also known as the "black note" scale
(4 notes),
(3 notes), and
(2 notes): generally limited to
("primitive") music
(1 note): limited use in liturgy, and for effect in modern art music[]
"The number of the notes that make up a scale as well as the quality of the intervals between successive notes of the scale help to give the music of a culture area its peculiar sound quality." "The pitch distances or intervals among the notes of a scale tell us more about the sound of the music than does the mere number of tones."
The notes of a scale form intervals with each of the other notes of the chord in . A 5-note scale has 10 of these
intervals, a 6-note scale has 15, a 7-note scale has 21, an 8-note chord has 28. Though the scale is not a , and might never be heard more than one note at a time, still the absence, presence, and placement of certain key intervals plays a large part in the sound of the scale, the natural movement of melody within the scale, and the selection of
taken naturally from the scale.
A musical scale containing one without tritones is atritonic. A scale or
containing semitones one without semitones is . The significance of these categories lies in their bases of semitones and tritones being the severest of , avoidance of which is often desirable. The most used scales across the planet are anhemitonic.
The lydian mode   , middle, functions as an intermediary between the whole tone scale   , top, and the major scale   , bottom.
Scales can be abstracted from
or . They are also often used
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 's . To the right, 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.
generally consist of seven notes and repeat at the octave. Notes in the commonly used scales (see just below) are separated by
of tones and semitones. The harmonic minor scale includes a three- the pentatonic includes two of these.
Western music in the Medieval and Renaissance periods () tends to use the white-note
C–D–E–F–G–A–B.
are rare, and somewhat unsystematically used, often to avoid the .
Music of the common practice periods () uses three types of scale:
(seven notes)—this includes the major scale and the natural minor
The melodic and harmonic
(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 19th century (to a certain extent), but more in the 20th century, additional types of scales were explored:
(twelve notes)
(six notes)
The pentatonic scale (five notes)
The octatonic or
(eight notes)
A large variety of other scales exists, some of the more common being:
(actually, a mode of the harmonic minor scale)
scales (called echoi)
Scales such as the pentatonic scale may be considered gapped relative to the diatonic scale. An auxiliary scale is a scale other than the primary or original scale. See:
In many musical circumstances, a specific note of the scale will be chosen as the —the central and most stable note of the scale, also known as the root note. 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
(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 expression
refers to these numerical labels. Such labeling requires the choice of a "first" 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 major scale using A = 1, B = 2, C = 3, and so on. When we do so, we create a new scale called the A . See the
article for how the notes are customarily named in different countries.
The scale degrees of a heptatonic (7-note) scale can also be named using the terms , , , , , , . If the subtonic is a semitone away from the tonic, then it is usually called the
(or leading-note); otherwise the leading-tone refers to the raised subtonic. Also commonly used is the (movable do)
naming convention in which each scale degree is denoted by 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 major scale is written A–B–C?–D–E–F?–G? rather than A–B–D?–D–E–E–G?. However, it is impossible to do this with scales containing more than seven notes.
Scales may also be identified by using a binary system of twelve zeros or ones to represent each of the twelve notes of a . It is assumed that the scale is tuned using
(so that, for instance, C? is the same as D?), and that the tonic is in the leftmost position. For example the
, equivalent to the
2773, would represent any major scale (such as C–D–E–F–G–A–B). This system includes scales from
(4095), providing a total of 2048 possible , but only 352 unique scales containing from 1 to 12 notes.
Scales may also be shown as
(or fret positions) from the tonic. For instance, 0 2 4 5 7 9 11 denotes any major scale such as C–D–E–F–G–A–B, in which the first degree is, obviously, 0 semitones from the tonic (and therefore coincides with it), the second is 2 semitones from the tonic, the third is 4 semitones from the tonic, and so on. Again, this implies that the notes are drawn from a chromatic scale tuned with 12-tone equal temperament.
Composers often transform musical patterns by moving every note in the pattern by a constant number of scale steps: thus, in the
scale, the pattern C–D–E might be shifted up, or , a single scale step to become D–E–F. This process is called "scalar transposition" and can often be found in . 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.
Through the introduction of , jazz and
employ scale intervals smaller than a semitone. The blue note is an
that is technically neither
but "in the middle", giving it a characteristic flavour. For instance, in the
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
and scales are used, often within the same piece of music. Chromatic scales are common, especially in modern jazz.
In Western music, scale notes are often separated by
tones or semitones, creating 12 notes per octave. Many other musical traditions use scales that include other intervals or a different number of pitches. These scales originate within the derivation of the .
are complementary values of the
series. Many musical scales in the world are based on this system, except most of the musical scales from
Peninsulae, which are based on inharmonic resonance of the dominant metalophone and xylophone instruments. A common scale in Eastern music is the pentatonic scale, consisting of five notes. In the Middle Eastern , there are some intervals of three semitones.
music uses a small variety of scales including
and , none including equally tempered nor harmonic intervals.
uses a moveable . Indian
often use intervals smaller than a semitone.
intervals.[] In both rāgas and maqamat, the distance between a note and an inflection (e.g., ) of that same note may be less than a semitone.
This section does not
any . Please help improve this section by . Unsourced material may be challenged and . (June 2012)
usually refers to music with roots in traditional Western music that uses non-standard scales or scale intervals. Mexican composer
created in the late 19th century microtonal scales which he called "", The composer
to play compositions that employed a , and the American jazz
experimented with such scales in his Microtonal Blues Band in the 1970s.
has written compositions in all equal-tempered scales from 13 to 24 notes.
introduced concepts such as Combination Product Sets (), Moments of Symmetry and golden horagrams, used by many modern composers.[] Microtonal scales are also used in traditional Indian
music, which has a variety of modes which are used not only as
or scales but also as defining elements of the , or raga.
Benward, Bruce and Saker, Marilyn Nadine (2003). Music: In Theory and Practice, seventh edition: vol. 1, p.25. Boston: McGraw-Hill. .
Hewitt, Michael (2013). Musical Scales of the World, pp. 2–3. The Note Tree. .
Nzewi, Meki and Nzewi, Odyke (2007). A Contemporary Study of Musical Arts, p.34. .
Nettl, Bruno and Myers, Helen (1976). Folk Music in the United States, p.39. .
Hanson, Howard. (1960) Harmonic Materials of Modern Music, p.7ff. New York: Appleton-Century-Crofts. LOC 58-8138.
Hanson, Howard. (1960) Harmonic Materials of Modern Music, p.7ff. New York: Appleton-Century-Crofts. LOC 58-8138.
Dmitri Tymoczko, "Scale Networks and Debussy", Journal of Music Theory 48, no. 2 (Fall 2004): 219–94; citation on 254–64
Duncan, Andrew. , Journal of the Audio Engineering Society, vol. 39, pp. 427–448. (1991 June). AndrewDuncan.ws.
Burns, Edward M. 1998. "Intervals, Scales, and Tuning.", p.247. In The Psychology of Music, second edition, edited by Diana Deutsch, 215–64. New York: Academic Press. .
Zonis [Mahler], Ella. 1973. Classical Persian Music: An Introduction. Cambridge, MA: Harvard University Press.
. 2006. The Complete Thesaurus of Musical Scales, revised edition. New York: Masaya Music Services. .
Wikiquote has quotations related to:
Wikimedia Commons has media related to .
Barbieri, Patrizio. . (2008) Latina, Il Levante Libreria Editrice
This online tool helps you find a scale to fit a chord progression or some notes that are part of a scale.
Scale generator finder, over two thousand printable scales.
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