Musical scale

In music, a scale is a set of musical notes that provides material for part or all of a musical work. Scales are typically ordered in pitch, with their ordering providing a measure of musical distance. Scales differ from modes in that scales do not have a primary or "tonic" pitch. 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"). 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.

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:

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
most commonly in jazz and 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. 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 the "A natural minor scale" contain the same notes; the difference between them consists only in which note is assigned primacy. Similarly, jazz musicians use the term altered scale to refer to the seventh mode of the ascending melodic minor scale. For consistency, this article will use the term "scale" to refer to an ordered collection with no "primary" or "tonic" note.

Scale vs. Scale Type. Sometimes the term "scale" refers to a specific ordered collection of pitches. For instance, the "C diatonic scale" contains the pitch classes C-D-E-F-G-A-B and no others, while the "G diatonic scale" contains the pitch classes G-A-B-C-D-E-F# and no others. However, the term "scale" is also 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 including a three-semitone interval; the pentatonic including two of these). Notes with one note between them are separated by three or four semitones.

Traditional Western classical music uses just three types of scale:

The diatonic scale (seven notes)
The melodic and harmonic minor scales (seven notes)

In the nineteenth and twentieth century, additional types of scale become common:

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 exist:

The Phrygian dominant scales (this is in fact a mode of the harmonic minor scale)
The Arabic scales

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 doh" 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).

Non-Western scales

In traditional Western music, scale notes 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. Ragas in Indian classical music often employ intervals smaller than a semitone (Callow & Sheperd, 1972; Jhairazbhoy & Stone, 1963). Arab music maqams may use quarter tone intervals (Zonis, 1973). In both ragas and maqams, 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. 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, 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 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 harmony G-B-D.

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.

External links

http://musicianswiki.com/index.php/scales Lots of scales (including exotic ones) with midi examples.
Piano Scales
Jazz Scales
http://www.skytopia.com/project/scale.html
http://home.austin.rr.com/jmjensen/musicTheory.html
http://www.greenwych.ca/natbasis.htm (Evolution of Scales)
http://www.greenwych.ca/cycl-5-2.htm (7-Note Solution -- why history & archaeologists turns up so many 5 and 7 note scales)
http://www.greenwych.ca/fl-compl.htm (Oldest known "Neanderthal flute" plays do-re-mi-fa scale notes.)
Guitar scales at GOSK.com

Music theory

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