Pentatonic scales were developed independently by many ancient civilizations--an indication that pentatonic scales are based upon a naturally occurring phenomenon. They are still used all over the world, for example (just to name a few) Chinese traditional music and US country music and blues.
There are two types of pentatonic scales: those with semitones (hemitonic) and those without (anhemitonic).
Pentatonic scales occur in the following traditions:
Miyako-bushi scale on D, equivalent to in scale on D, with brackets on fourthsPlay (help·info).
Musicology commonly classifies pentatonic scales as either hemitonic or anhemitonic. Hemitonic scales contain one or more semitones and anhemitonic scales do not contain semitones. (For example, in Japanese music the anhemitonic yo scale is contrasted with the hemitonic in scale.) Hemitonic pentatonic scales are also called "ditonic scales", because the largest interval in them is the ditone (e.g., in the scale C-E-F-G-B-C, the interval found between C-E and G-B). This should not be confused with the identical term also used by musicologists to describe a scale including only two notes.
Major pentatonic scale
Anhemitonic pentatonic scales can be constructed in many ways. The major pentatonic scale may be thought of as a gapped or incomplete major scale. However, the pentatonic scale has a unique character and is complete in terms of tonality. One construction takes five consecutive pitches from the circle of fifths; starting on C, these are C, G, D, A, and E. Transposing the pitches to fit into one octave rearranges the pitches into the major pentatonic scale: C, D, E, G, A.
Another construction works backward: It omits two pitches from a diatonic scale. If one were to begin with a C major scale, for example, one might omit the fourth and the seventh scale degrees, F and B. The remaining notes then makes up the major pentatonic scale: C, D, E, G, and A.
Omitting the third and seventh degrees of the C major scale obtains the notes for another transpositionally equivalent anhemitonic pentatonic scale: F, G, A, C, D. Omitting the first and fourth degrees of the C major scale gives a third anhemitonic pentatonic scale: G, A, B, D, E.
The black keys on a piano keyboard comprise a G-flat major (or equivalently, F-sharp major) pentatonic scale: G-flat, A-flat, B-flat, D-flat, and E-flat, which is exploited in Chopin's black key étude.
Minor pentatonic scale
Although various hemitonic pentatonic scales might be called minor, the term is most commonly applied to the relative minor pentatonic derived from the major pentatonic, using scale tones 1, 3, 4, 5, and 7 of the natural minor scale. It may also be considered a gapped blues scale. The C minor pentatonic is C, E-flat, F, G, B-flat. The A minor pentatonic, the relative minor of C, comprises the same tones as the C major pentatonic, starting on A, giving A, C, D, E, G. This minor pentatonic contains all three tones of an A minor triad.
Five black-key pentatonic scales of the piano
Each "black-key" pentatonic scale can be thought of as a selection of 5 notes from 3 different heptatonic modes.
The five pentatonic scales found by running up the black keys on the piano are:
Naturals in that table are not the alphabetic series A to G without sharps and flats: Naturals are reciprocals of terms in the Harmonic series (mathematics), which are in practice multiples of a fundamental frequency. This may be derived by proceeding with the principle that historically gives the Pythagorean diatonic and chromatic scales, stacking perfect fifths with 3:2 frequency proportions (C-G-D-A-E). Considering the anhemitonic scale as a subset of a just diatonic scale, it is tuned thus: 20:24:27:30:36 (A-C-D-E-G = ----). Assigning precise frequency proportions to the pentatonic scales of most cultures is problematic as tuning may be variable.
For example, the slendro anhemitonic scale and its modes of Java and Bali are said to approach, very roughly, an equally-tempered five-note scale, but their tunings vary dramatically from gamelan to gamelan.
Composer Lou Harrison has been one of the most recent proponents and developers of new pentatonic scales based on historical models. Harrison and William Colvig tuned the slendro scale of the gamelan Si Betty to overtones 16:19:21:24:28  (----). They tuned the Mills gamelan so that the intervals between scale steps are 8:7-7:6-9:8-8:7-7:6 (----- = 42:48:56:63:72)
Further pentatonic musical traditions
The major pentatonic scale is the Raag Bhimpalsi in Hindustani classical music of India and basic scale of the music of China and the music of Mongolia as well as many Southeast Asian musical traditions such as that of the Karen people (whose music has sometimes been described as sounding "Scottish"). The fundamental tones (without meri or kari techniques) rendered by the five holes of the Japaneseshakuhachi flute play a minor pentatonic scale. The yo scale used in Japanese shomyo Buddhist chants and gagaku imperial court music is an anhemitonic pentatonic scale shown below, which is the fourth mode of the major pentatonic scale.
In Javanesegamelan music, the slendro scale has five tones, of which four are emphasized in classical music(MIDI sample (help·info)). Another scale, pelog, has seven tones, and is generally played using one of three five-tone subsets known as pathet, in which certain notes are avoided while others are emphasized.
In Scottish music, the pentatonic scale is very common. Seumas MacNeill suggests that the Great Highland bagpipe scale with its augmented fourth and diminished seventh is "a device to produce as many pentatonic scales as possible from its nine notes". Roderick Cannon explains these pentatonic scales and their use in more detail, both in Piobaireachd and light music. It also features in Irish traditional music, either purely or almost so. The minor pentatonic is used in Appalachian folk music. Blackfoot music most often uses anhemitonic tetratonic or pentatonic scales.
In Andean music, the pentatonic scale is used substantially minor, sometimes major, and seldom in scale. In the most ancient genres of Andean music being performed without string instruments (only with winds and percussion), pentatonic melody is often leaded with parallel fifths and fourths, so formally this music is hexatonic. Hear example: Pacha Siku (help·info).
Jazz music commonly uses both the major and the minor pentatonic scales. Pentatonic scales are useful for improvisers in modern jazz, pop, and rock contexts because they work well over several chords diatonic to the same key, often better than the parent scale. For example, the blues scale is predominantly derived from the minor pentatonic scale, a very popular scale for improvisation in the realms of blues and rock alike.Rock guitar solo almost all over B minor pentatonic (help·info) For instance, over a C major triad (C, E, G) in the key of C major, the note F can be perceived as dissonant as it is a half step above the major third (E) of the chord. It is for this reason commonly avoided. Using the major pentatonic scale is an easy way out of this problem. The scale tones 1, 2, 3, 5, 6 (from the major pentatonic) are either major triad tones (1, 3, 5) or common consonant extensions (2, 6) of major triads. For the corresponding relative minor pentatonic, scale tones 1, ♭3, 4, 5, ♭7 work the same way, either as minor triad tones (1, ♭3, 5) or as common extensions (4, ♭7), as they all avoid being a half step from a chord tone.
U.S. military cadences, or jodies, which keep soldiers in step while marching or running, also typically use pentatonic scales.
Hymns and other religious music sometimes use the pentatonic scale; for example, the melody of the hymn "Amazing Grace", one of the most famous pieces in religious music.
The common pentatonic major and minor scales (C-D-E-G-A and C-E♭-F-G-B♭, respectively) are useful in modal composing, as both scales allow a melody to be modally ambiguous between their respective major (Ionian, Lydian, Mixolydian) and minor (Aeolian, Phrygian, Dorian) modes (Locrian excluded). With either modal or non-modal writing, however, the harmonization of a pentatonic melody does not necessarily have to be derived from only the pentatonic pitches.
The Orff system places a heavy emphasis on developing creativity through improvisation in children, largely through use of the pentatonic scale. Orff instruments, such as xylophones, bells and other metallophones, use wooden bars, metal bars or bells, which can be removed by the teacher, leaving only those corresponding to the pentatonic scale, which Carl Orff himself believed to be children's native tonality.
Children begin improvising using only these bars, and over time, more bars are added at the teacher's discretion until the complete diatonic scale is being used. Orff believed that the use of the pentatonic scale at such a young age was appropriate to the development of each child, since the nature of the scale meant that it was impossible for the child to make any real harmonic mistakes.
In Waldorf education, pentatonic music is considered to be appropriate for young children due to its simplicity and unselfconscious openness of expression. Pentatonic music centered on intervals of the fifth is often sung and played in early childhood; progressively smaller intervals are emphasized within primarily pentatonic as children progress through the early school years. At around nine years of age the music begins to center on first folk music using a six-tone scale, and then the modern diatonic scales, with the goal of reflecting the children's developmental progress in their musical experience. Pentatonic instruments used include lyres, pentatonic flutes, and tone bars; special instruments have been designed and built for the Waldorf curriculum.
^Anon., "Ditonus", The New Grove Dictionary of Music and Musicians, second edition, edited by Stanley Sadie and John Tyrrell (London: Macmillan Publishers, 2001); Bence Szabolcsi, "Five-Tone Scales and Civilization", Acta Musicologica 15, nos. 1-4 (January-December 1943): pp. 24-34, citation on p. 25.
^Ben Johnston, "Scalar Order as a Compositional Resource", Perspectives of New Music 2, no. 2 (Spring-Summer 1964): pp. 56-76. Citation on p. 64 . (subscription required) Accessed 4 January 2009.
^Leta E. Miller and Fredric Lieberman (Summer 1999). "Lou Harrison and the American Gamelan", p. 158, American Music, Vol. 17, No. 2, pp. 146-78.
^"The representations of slendro and pelog tuning systems in Western notation shown above should not be regarded in any sense as absolute. Not only is it difficult to convey non-Western scales with Western notation ..." Jennifer Lindsay, Javanese Gamelan (Oxford and New York: Oxford University Press, 1992), pp. 39-41. ISBN0-19-588582-1.
^Lindsay (1992), p. 38-39: "Slendro is made up of five equal, or relatively equal, intervals".
^"... in general, no two gamelan sets will have exactly the same tuning, either in pitch or in interval structure. There are no Javanese standard forms of these two tuning systems." Lindsay (1992), pp. 39-41.
^Mohamed Diriye Abdullahi (2001). Culture and Customs of Somalia. Greenwood Publishing Group. p. 170. ISBN0-313-31333-4. Somali music, a unique kind of music that might be mistaken at first for music from nearby countries such as Ethiopia, the Sudan, or even Arabia, can be recognized by its own tunes and styles.
^Tekle, Amare (1994). Eritrea and Ethiopia: from conflict to cooperation. The Red Sea Press. p. 197. ISBN0-932415-97-0. Djibouti, Eritrea, Ethiopia, Somalia and Sudan have significant similarities emanating not only from culture, religion, traditions, history and aspirations[...] They appreciate similar foods and spices, beverages and sweets, fabrics and tapestry, lyrics and music, and jewelry and fragrances.
^Seumas MacNeil and Frank Richardson Piobaireachd and its Interpretation (Edinburgh: John Donald Publishers Ltd, 1996): p. 36. ISBN0-85976-440-0
^Roderick D. Cannon The Highland Bagpipe and its Music (Edinburgh: John Donald Publishers Ltd, 1995): pp. 36-45. ISBN0-85976-416-8
^Bruno Nettl, Blackfoot Musical Thought: Comparative Perspectives (Ohio: The Kent State University Press, 1989): p. 43. ISBN0-87338-370-2.
^Steve Turner, Amazing Grace: The Story of America's Most Beloved Song (New York: HarperCollins, 2002): p. 122. ISBN0-06-000219-0.
^Beth Landis; Polly Carder (1972). The Eclectic Curriculum in American Music Education: Contributions of Dalcroze, Kodaly, and Orff. Washington D.C.: Music Educators National Conference. p. 82. ISBN978-0-940796-03-4.
Jeremy Day-O'Connell, Pentatonicism from the Eighteenth Century to Debussy (Rochester: University of Rochester Press 2007) - the first comprehensive account of the increasing use of the pentatonic scale in 19th-century Western art music, including a catalogue of over 400 musical examples.