Pentatonic scale

A pentatonic scale is a musical scale with five notes per octave, in contrast to heptatonic scales, which have seven notes per octave (such as the major scale and minor scale).

Pentatonic scales were developed independently by many ancient civilizations and are still used in various musical styles to this day. As Leonard Bernstein put it: "The universality of this scale is so well known that I'm sure you could give me examples of it, from all corners of the earth, as from Scotland, or from China, or from Africa, and from American Indian cultures, from East Indian cultures, from Central and South America, Australia, Finland ... now, that is a true musico-linguistic universal."Bernstein, L. (1976) The Unanswered Question, Cambridge Massachusetts: Harvard University Press. There are two types of pentatonic scales: those with semitones (hemitonic) and those without (anhemitonic).

Types

Hemitonic and anhemitonic

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).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. (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, using scale tones 1, 2, 3, 5, and 6 of the major scale. One construction takes five consecutive pitches from the circle of fifths;Paul Cooper, Perspectives in Music Theory: An Historical-Analytical Approach(New York: Dodd, Mead, 1973), p. 18. . . starting on C, these are C, G, D, A, and E. Rearranging the pitches to fit into one octave creates 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 make 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 (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.) p. 12. The C minor pentatonic scale, the relative minor of the E-flat pentatonic scale, is C, E-flat, F, G, B-flat. The A minor pentatonic, the relative minor of C pentatonic, 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.

The standard tuning of a guitar uses the notes of an E minor pentatonic scale: E–A–D–G–B–E, contributing to its frequency in popular music. Stevie Wonder employed the minor pentatonic for the funky clavinet riff on the track "Superstition" (1972).

Japanese scale

The Japanese mode is based on the Phrygian mode, but uses scale tones 1, 2, 4, 5, and 6 instead of scale tones 1, 3, 4, 5, and 7.

Modes of the pentatonic scale

The pentatonic scale (containing notes C, D, E, G, and A) has five modes, which are derived by treating a different note as the tonic:

Tonic Name(s) Chinese pentatonic scale Indian pentatonic scale On C White key transpositions Black key transposition C major pentatonic F major pentatonic G major pentatonic F/G major pentatonic 1 (C) Major pentatonic 宮 (gōng) mode Hindustani – BhoopaliCarnatic – MohanamTamil – Mullaittīmpāṇi C–D–E–G–A–C C–D–E–G–A–C F–G–A–C–D–F G–A–B–D–E–G G–A–B–D–E–G 2 (D) Suspended, Egyptian 商 (shāng) mode Hindustani – MeghCarnatic – MadhyamavatiTamil – Centurutti C–D–F–G–B–C D–E–G–A–C–D G–A–C–D–F–G A–B–D–E–G–A A–B–D–E–G–A 3 (E) Blues minor, Man Gong (Guqin tunings) 角 (jué) mode Hindustani – MalkaunsCarnatic – HindolamTamil – Intaḷam C–E–F–A–B–C E–G–A–C–D–E A–C–D–F–G–A B–D–E–G–A–B B–D–E–G–A–B 5 (G) Blues major, , yo scale 徵 (zhǐ) mode Hindustani – DurgaCarnatic – Shuddha SaveriTamil – Koṉṟai C–D–F–G–A–C G–A–C–D–E–G C–D–F–G–A–C D–E–G–A–B–D D–E–G–A–B–D 6 (A) Minor pentatonic 羽 (yǔ) mode Hindustani – DhaniCarnatic – Shuddha DhanyasiTamil – āmpal C–E–F–G–B–C A–C–D–E–G–A D–F–G–A–C–D E–G–A–B–D–E E–G–A–B–D–E

Ricker assigned the major pentatonic scale mode I while Gilchrist assigned it mode III. cites

Relationship to diatonic modes Each mode of the pentatonic scale (containing notes C, D, E, G, and A) can be thought of as the five scale degrees shared by three different diatonic modes with the two remaining scale degrees removed:

Pentatonicmode Tonicnote Based on modes (Diatonic scale) Base scaledegrees Modifications Interval sequence Major C Lydian mode Ionian mode (Natural Major) Mixolydian mode I–II–III–V–VI Omit 4 7 W–W–3/2–W–3/2 Blues major G Ionian mode (Natural Major) Mixolydian mode Dorian mode I–II–IV–V–VI Omit 3 7 W–3/2–W–W–3/2 Suspended D Mixolydian mode Dorian mode Aeolian mode (Natural minor) I–II–IV–V–VII Omit 3 6 W–3/2–W–3/2–W Minor A Dorian mode Aeolian mode (Natural minor) Phrygian mode I–III–IV–V–VII Omit 2 6 3/2–W–W–3/2–W Blues minor E Aeolian mode (Natural minor) Phrygian mode Locrian mode I–III–IV–VI–VII Omit 2 5 3/2–W–3/2–W–W

Intervals from tonic

Each mode of the pentatonic scale (containing notes C, D, E, G, and A) features different intervals of notes from the tonic according to the table below. Note the omission of the semitones above (m2) and below (M7) the tonic as well as the tritone (TT).

Pentatonicmode Tonicnote Intervals with respect to the tonic unison secondnote thirdnote fourthnote fifthnote octave Major C P1 M2 M3 P5 M6 P8 Blues major G P4 Suspended D m7 Minor A m3 Blues minor E m6

Tuning Pythagorean tuning

Ben Johnston gives the following Pythagorean tuning for the minor pentatonic scale: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 .

Note Solfege A C D E G A Ratio Natural 54 64 72 81 96 108 Audio 1 3 4 5 7 8 Step Name   m3 T T m3 T   Ratio

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 = ––––).

Just intonation

Modes Ratios (just) Major 24:27:30:36:40 Blues major 24:27:32:36:40 Suspended 24:27:32:36:42 Minor 30:36:40:45:54 Blues minor 15:18:20:24:27 (A minor seventh can be 7:4, 16:9, or 9:5; a major sixth can be 27:16 or 5:3. Both were chosen to minimize ratio parts.)

Other 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,Lindsay (1992), p. 38–39: "Slendro is made up of five equal, or relatively equal, intervals". but their tunings vary dramatically from gamelan to gamelan."... 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.

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)

Use of pentatonic scales Overview Pentatonic scales occur in many musical traditions:

Stone Age flutes Indian classical music, both Hindustani and Carnatic traditions Ancient Tamil music, see the Section "Evolution of panns". Peruvian Chicha cumbia Indigenous ethnic folk music of Assam Sudanese Music Celtic folk music English folk musicErnst H. Meyer, Early English Chamber Music: From the Middle Ages to Purcell, second edition, edited by Diana Poulton (Boston: Marion Boyars Publishers, Incorporated, 1982): p. 48. . German folk musicJudit Frigyesi (2013). "Is there such a thing as Hungarian-Jewish music?" in Pál Hatos & Attila Novák (eds.) (2013). Between Minority and Majority: Hungarian and Jewish/Israeli ethnical and cultural experiences in recent centuries. Budapest: Balassi Institute. p. 129. . Nordic folk music Hungarian folk music Croatian folk music Berber music West African music African-American spirituals Gospel music Bluegrass music American folk music Music of Ethiopia Jazz Blues Rock music Sami joik singing Children's song The music of ancient Greece Greek traditional music and polyphonic songs from Epirus in northwest GreeceMeri-Sofia Lakopoulos (2015). The Traditional Iso-polyphonic song of Epirus . The International Research Center for Traditional Polyphony. June 2015, issue 18. p. 10. Music of southern Albania Folk songs of peoples of the Middle Volga region (such as the Mari, the Chuvash and Tatars) The tuning of the Ethiopian krar and the Indonesian gamelan Philippine kulintang Native American music, especially in highland South America (the Quechua and Aymara), as well as among the North American Indians of the Pacific Northwest Most Turkic, Mongolic and Tungusic music of Siberia and the Asiatic steppe is written in the pentatonic scaleTran Van Khe. "Is the Pentatonic Universal? A Few Reflections on Pentatonicism." The World of Music 19, no. 1/2 (1977): 76–84. http://www.jstor.org/stable/43560446. Melodies of Eastern Asia: China, Korea, Laos, Thailand, Cambodia, Malaysia, Japan, and Vietnam (including the folk music of these countries) Traditional Japanese court music Shōmyō chanting Andean music (Thomas Turino (2004) points out that the pentatonic scale, although widespread, cannot be considered to be predominant in the Andes: Local practices among the Aymara and Kechua in Conima and Canas, Southern Peru in ) Afro-Caribbean music Polish highlanders from the Tatra Mountains

Example details

In classical music Examples of its use include:

Beethoven, Quartet in F major, Op. 135, finale:

Chopin's Etude in G-flat major, Op. 10, No. 5, the "Black Key" etude, in the major pentatonic.

Western Impressionistic composers such as French composer Claude Debussy and Maurice Ravel used the pentatonic scale extensively in their works.