Pentatonic scale

From HandWiki
Short description: Type of musical scale


The first two phrases of the melody from Stephen Foster's "Oh! Susanna" are based on the major pentatonic scale[1]File:'Oh, Susanna' pentatonic melody.mid

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

Pentatonic scales were developed independently by many ancient civilizations[2] 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."[3] There are two types of pentatonic scales: those with semitones (hemitonic) and those without (anhemitonic).

Types

Hemitonic and anhemitonic

Minyō scale on D,[4] equivalent to yo scale on D,[5] with brackets on fourthsFile:Min'yō scale.mid
Miyako-bushi scale on D, equivalent to in scale on D, with brackets on fourths[6]File:Miyako-bushi scale.mid

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).[7] (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.[1] One construction takes five consecutive pitches from the circle of fifths;[8] 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.

<score sound="1"> {

\override Score.TimeSignature #'stencil = ##f \relative c' { 

 \time 5/4
 c d e g a c

} } </score> 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.

<score sound="1"> {

\override Score.TimeSignature #'stencil = ##f \relative c { 

 \time 5/4
 ges aes bes des ees ges

} }

</score>

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.[1] (It may also be considered a gapped blues scale.)[9] 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.

<score sound="1"> {

\override Score.TimeSignature #'stencil = ##f \relative c { 

 \time 5/4
 a4 c d e g | a

} }

</score>

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.[10]

Japanese scale

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

<score sound="1"> {

\override Score.TimeSignature #'stencil = ##f \relative c' { 

 \time 5/4
 e f a b c | e

} }

</score>

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 – Bhoopali
Carnatic – Mohanam
Tamil - 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 – Megh
Carnatic – Madhyamavati
Tamil - Centurutti 		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 – Malkauns
Carnatic – Hindolam
Tamil - 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, ritsusen (ja), yo scale 徵 (zhǐ) mode Hindustani – Durga
Carnatic – Shuddha Saveri
Tamil - 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 – Dhani
Carnatic – Shuddha Dhanyasi
Tamil - 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.[11]

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:

Venn-like diagram showing the correspondence between each pentatonic scale and three different heptatonic modes.
Each pentatonic scale can be thought of as the five notes shared by three different heptatonic modes.
Pentatonic
scale 		Tonic
note 		Based on modes (Diatonic scale) Base scale
degrees 		Modifications Interval sequence
Major C
  • Lydian mode
  • Ionian mode (Major)
  • Mixolydian mode
 I–II–III–V–VI Omit 4 7 W–W–3/2–W–3/2
Blues major G
  • Ionian mode (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).

Chromatic circle diagrams comparing the pentatonic scale intervals to the heptatonic scale
The intervals used in the pentatonic scale compared to the heptatonic scale.
Pentatonic
scale 		Tonic
note 		Intervals with respect to the tonic
unison second
note 		third
note 		fourth
note 		fifth
note 		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:[12]

Note Solfege A C D E G A
Ratio ​1⁄1 ​32⁄27 ​4⁄3 ​3⁄2 ​16⁄9 ​2⁄1
Natural 54 64 72 81 96 108
Audio 1File:Unison on C.mid 3File:Pythagorean minor third on C.mid 4File:Just perfect fourth on C.mid 5File:Just perfect fifth on C.mid 7File:Lesser just minor seventh on C.mid 8File:Perfect octave on C.mid
Step Name   m3 T T m3 T  
Ratio ​32⁄27 ​9⁄8 ​9⁄8 ​32⁄27 ​9⁄8

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 = ​5⁄6–​1⁄1–​9⁄8–​5⁄4–​3⁄2).

Just intonation

Just pentatonic tuning of Lou Harrison's "American gamelan", Old Granddad.[13] This gives the proportions 24:27:30:36:40.File:Lou Harrison - Old Granddad pentatonic tuning.mid
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.

Slendro approximated in Western notation.[14]File:Slendro on C.mid

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,[15] but their tunings vary dramatically from gamelan to gamelan.[16]

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[17] (​1⁄1–​19⁄16–​21⁄16–​3⁄2–​7⁄4). They tuned the Mills gamelan so that the intervals between scale steps are 8:7–7:6–9:8–8:7–7:6[18] (​1⁄1–​8⁄7–​4⁄3–​3⁄2–​12⁄7–​2⁄1 = 42:48:56:63:72)

Use of pentatonic scales

Pentatonic scales occur in many musical traditions:

  • 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[19]
  • English folk music[20]
  • German folk music[21]
  • Nordic folk music[22]
  • Hungarian folk music[23]
  • Croatian folk music[23]
  • Berber music[24]
  • West African music[25]
  • African-American spirituals[26]
  • Gospel music[27]
  • Bluegrass music[28]
  • American folk music[29]
  • Music of Ethiopia[25]
  • Jazz[30]
  • Blues[31]
  • Rock music[32]
  • Sami joik singing[33]
  • Children's song[34]
  • The music of ancient Greece[35][36]
    • Greek traditional music and polyphonic songs from Epirus in northwest Greece[37]
  • Music of southern Albania[38]
  • Folk songs of peoples of the Middle Volga region (such as the Mari, the Chuvash and Tatars)[39]
  • The tuning of the Ethiopian krar[25] and the Indonesian gamelan[40]
  • Philippine kulintang[41]
  • Native American music, especially in highland South America (the Quechua and Aymara),[42] as well as among the North American Indians of the Pacific Northwest[citation needed]
  • Most Turkic,[43] Mongolic and Tungusic music of Siberia and the Asiatic steppe is written in the pentatonic scale[44]
  • Melodies of China , Korea, Laos, Thailand, Cambodia, Malaysia, Japan , and Vietnam (including the folk music of these countries)[44]
    • Traditional Japanese court music
    • Shōmyō chanting
  • Andean music[45]
  • Afro-Caribbean music[46]
  • Polish highlanders from the Tatra Mountains[47]


In classical music

Examples of its use include:

Beethoven, Quartet in F major, Op. 135, finale: File:Beethoven Quartet Op 135, finale bars 250-7.wav

Beethoven Quartet Op 135, finale bars 250-7

Chopin's Etude in G-flat major, op. 10, no. 5, the "Black Key" etude,[1] in the major pentatonic.File:Chopin Etude Op. 10 No. 5.wav

Chopin Etude Op. 10 No. 5

Western Impressionistic composers such as French composer Claude Debussy[48] and Maurice Ravel used the pentatonic scale extensively in their works.

Pentatonic scale in Debussy's Voiles, Preludes, Book I, no. 2, mm. 43–45.[49]File:Debussy Voiles, Preludes, Book I, no. 2, mm.43-45.mid

500px|thumb|center|Pentatonic scale in Ravel's Ma mère l'Oye III. "Laideronnette, Impératrice des Pagodes", mm. 9–13.[1]File:Ravel Ma Mere l'Oye Laideronnette Imperatricedes Pagodes m.9-13.mid

Giacomo Puccini used pentatonic scales in his operas Madama Butterfly and Turandot to imitate east Asian musical styles. Puccini also used whole-tone scales in the former to invoke similar ideas.

Indian ragas

Main page: Biology:Raga

Indian classical music has hundreds of ragas, of which many are pentatonic. Examples include Raag Abhogi Kanada (C, D, E-flat, F, A),[50] Raag Bhupali (C, D, E, G, A),[51] Raag Bairagi (C, D-flat, F, G, B-flat),[52] Raag Chandrakauns (C, E-flat, F, A-flat, B),[53] Raag Dhani (C, E-flat, F, G, B-flat),[50] Raag Durga (C, D, F, G, A),[54] Raag Gunakari (C, D-flat, F, G, A-flat),[55] Raag Hamsadhwani (C, D, E, G, B),[56] Raag Hindol (C, E, F#, A, B),[57] Raag Kalavati (C, E, G, A, B-flat),[50] Raag Katyayani (C, D, E-flat, G, A-flat),[58] Raag Malkauns (C, E-flat, F, A-flat, B-flat),[59] Raag Megh (C, D, F, G, B-flat),[50] Raag Shivaranjani (C, D, E-flat, G, A),[60] Raag Shuddha Sarang (C, D, F#, G, B),[61] Raag Tilang (C, E, F, G, B),[62] Raag Vibhas (C, D-flat, E, G, A-flat),[63] Raag Vrindavani Sarang (C, D, F, G, B), and others.[64]

(For Tamil Music System, See here - Ancient Tamil music#Evolution of panns )

Further pentatonic musical traditions

D Yo scaleFile:Yo scale on D.mid

The major pentatonic scale is the 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 as well as the indigenous Assamese ethnic groups.[citation needed] The pentatonic scale predominates most Eastern countries as opposed to Western countries where the heptatonic scale is more commonly used.[65] The fundamental tones (without meri or kari techniques) rendered by the five holes of the Japan ese shakuhachi 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[66] shown below, which is the fourth mode of the major pentatonic scale.

Javanese

File:Gamelan slendro.mid In Javanese gamelan music, the slendro scale has five tones, of which four are emphasized in classical music. 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.[67]

Somali

Somali music uses a distinct modal system that is pentatonic, with characteristically long intervals between some notes. As with many other aspects of Somali culture and tradition, tastes in music and lyrics are strongly linked with those in nearby Ethiopia, Eritrea, Djibouti and Sudan.[68][69]

Scottish

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" (although these two features are not in the same scale)[clarification needed].[70][failed verification] Roderick Cannon explains these pentatonic scales and their use in more detail, both in Piobaireachd and light music.[71] 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.[72]

Andean

File:Antara.mid 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 led with parallel fifths and fourths, so formally this music is hexatonic.[citation needed]

Jazz

File:Slow solo 20110108.ogg 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.[73] 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.[citation needed]

Other

U.S. military cadences, or jodies, which keep soldiers in step while marching or running, also typically use pentatonic scales.[74]

Hymns and other religious music sometimes use the pentatonic scale; for example, the melody of the hymn "Amazing Grace",[75] one of the most famous pieces in religious music.[citation needed]

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.[citation needed]

Most Tuareg songs are pentatonic, as is most other music from the Sahel and Sudan regions.

Role in education

The pentatonic scale plays a significant role in music education, particularly in Orff-based, Kodály-based, and Waldorf methodologies at the primary or elementary level.

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.[76]

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.[77]

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.[78]

See also

  • Jazz scale
  • Quartal and quintal harmony
  • Raga
  • Suspended chord
  • Traditional sub-Saharan African harmony

References

  1. ↑ 1.0 1.1 1.2 1.3 1.4 Bruce Benward and Marilyn Nadine Saker (2003), Music: In Theory and Practice, seventh edition (Boston: McGraw Hill), vol. I, pp. 36–37. ISBN:978-0-07-294262-0.
  2. ↑ John Powell (2010). How Music Works: The Science and Psychology of Beautiful Sounds, from Beethoven to the Beatles and Beyond. New York: Little, Brown and Company. p. 121. ISBN 978-0-316-09830-4. 
  3. ↑ Bernstein, L. (1976) The Unanswered Question, Cambridge Mass., Harvard University Press.
  4. ↑ Susan Miyo Asai (1999). Nōmai Dance Drama, p. 126. ISBN:978-0-313-30698-3.
  5. ↑ Minoru Miki, Marty Regan, Philip Flavin (2008). Composing for Japanese instruments, p. 2. ISBN:978-1-58046-273-0.
  6. ↑ Jeff Todd Titon (1996). Worlds of Music: An Introduction to the Music of the World's Peoples, Shorter Version. Boston: Cengage Learning. ISBN 978-0-02-872612-0. https://books.google.com/books?id=nWsHAAAAQBAJ.  p. 373.
  7. ↑ 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.
  8. ↑ Paul Cooper, Perspectives in Music Theory: An Historical-Analytical Approach(New York: Dodd, Mead, 1973), p. 18. . ISBN:0-396-06752-2.
  9. ↑ Steve Khan (2002). Pentatonic Khancepts. Alfred Music Publishing. ISBN 978-0-7579-9447-0. https://books.google.com/books?id=oPnBp74IN8UC.  p. 12.
  10. ↑ Serna, Desi (2013). Guitar Theory for Dummies. Hoboken, New Jersey: Wiley. p. 168. ISBN 978-1-118-64677-9. https://books.google.com/books?id=I5dtAwAAQBAJ. 
  11. ↑ Ramon Ricker (1999). Pentatonic Scales for Jazz Improvisation. Lebanon, Ind.: Studio P/R, Alfred Publishing Co.. ISBN 978-1-4574-9410-9. https://books.google.com/books?id=4pIIfRuiRpcC&pg=PA2.  cites Annie G. Gilchrist (1911). "Note on the Modal System of Gaelic Tunes". Journal of the Folk-Song Society 4 (16): 150–53.  (Subscription content?)
  12. ↑ 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 JSTOR 832482. (Subscription content?) Accessed 4 January 2009.
  13. ↑ Miller, Leta E.; Lieberman, Fredric (Summer 1999). "Lou Harrison and the American Gamelan". American Music 17 (2): 146–178 (158). doi:10.2307/3052712. 
  14. ↑ "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. ISBN:0-19-588582-1.
  15. ↑ Lindsay (1992), p. 38–39: "Slendro is made up of five equal, or relatively equal, intervals".
  16. ↑ "... 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.
  17. ↑ Miller & Lieberman 1999, p. 159.
  18. ↑ Miller & Lieberman 1999, p. 161.
  19. ↑ June Skinner Sawyers (2000). Celtic Music: A Complete Guide. United States: Da Capo Press. p. 25. ISBN 978-0-306-81007-7. [yes|permanent dead link|dead link}}]
  20. ↑ Ernst 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. ISBN:9780714527772.
  21. ↑ Judit 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. ISBN:978-963-89583-8-9.
  22. ↑ Blacking, John (November 1987). "A commonsense view of all music" : reflections on Percy Grainger's contribution to ethnomusicology and music education. Cambridge University Press. p. 161. ISBN 978-0-521-26500-3. https://books.google.com/books?id=Awo4AAAAIAAJ&q=nordic+folk+music+five+tone&pg=PA161. Retrieved 21 November 2019. 
  23. ↑ 23.0 23.1 Benjamin Suchoff, ed (1997). Béla Bartók Studies in Ethnomusicology. Lincoln: University of Nebraska Press. p. 198. ISBN 0-8032-4247-6. https://books.google.com/books?id=LKQuRowyjPcC&pg=PA198. 
  24. ↑ Alwan For The Arts. http://www.alwanforthearts.org/event/282. Retrieved 2021-01-23. [self-published source]
  25. ↑ 25.0 25.1 25.2 Richard Henry (n.d.). Culture and the Pentatonic Scale: Exciting Information On Pentatonic Scales. n.p.: World Wide Jazz. p. 4. https://books.google.com/books?id=uz1QYwA9t-oC&pg=PP4. 
  26. ↑ Erik Halbig (2005). Pentatonic Improvisation: Modern Pentatonic Ideas for Guitarists of All Styles (Book & CD). Van Nuys, California: Alfred Music. p. 4. ISBN 978-0-7390-3765-2. https://books.google.com/books?id=XalDz4xM6wEC&pg=PA4. 
  27. ↑ Lenard C. Bowie, DMA (2012). African American Musical Heritage: An Appreciation, Historical Summary, and Guide to Music Fundamentals. Philadelphia: Xlibris Corporation. p. 259. ISBN 978-1-4653-0575-6. https://books.google.com/books?id=lMeLfBO0kPsC&pg=PA259. [self-published source]
  28. ↑ Jesper Rübner-Petersen (2011). The Mandolin Picker's Guide to Bluegrass Improvisation. Pacific, Missouri: Mel Bay Publications. p. 17. ISBN 978-1-61065-413-5. https://books.google.com/books?id=hAKpyaL45uYC&pg=PA17. 
  29. ↑ William Duckworth (2009). A Creative Approach to Music Fundamentals. Boston: Schirmer / Cengage Learning. p. 203. ISBN 978-1-111-78406-5. https://books.google.com/books?id=SYsEAAAAQBAJ&pg=PA203. 
  30. ↑ Kurt Johann Ellenberger (2005). Materials and Concepts in Jazz Improvisation. Grand Rapids, Michigan: Keystone Publication / Assayer Publishing. p. 65. ISBN 978-0-9709811-3-4. https://books.google.com/books?id=H_o0aZFP93AC&pg=PA65. 
  31. ↑ Edward Komara, ed (2006). Encyclopedia of the Blues. New York: Routledge. p. 863. ISBN 978-0-415-92699-7. https://books.google.com/books?id=-w-uGwm_LhcC&pg=PA863. 
  32. ↑ Joe Walker (6 January 2012). "The World's Most-Used Guitar Scale: A Minor Pentatonic". https://deftdigits.com/2012/01/06/the-worlds-most-used-guitar-scale-a-minor-pentatonic/. 
  33. ↑ Kathryn Burke. "The Sami Yoik". http://www.laits.utexas.edu/sami/diehtu/giella/music/yoiksunna.htm. 
  34. ↑ Jeremy Day-O'Connell (2007). Pentatonicism from the Eighteenth Century to Debussy. Rochester: University Rochester Press. p. 54. ISBN 978-1-58046-248-8. https://books.google.com/books?id=2FSTvnnJWS0C&pg=PA54. 
  35. ↑ M. L. West (1992). Ancient Greek Music. Oxford: Clarendon Press. pp. 163–164. ISBN 0-19-814975-1. https://books.google.com/books?id=So-Qpz6WDS4C&pg=PA163. 
  36. ↑ A.-F. Christidis; Maria Arapopoulou; Maria Christi (2007). A History of Ancient Greek: From the Beginnings to Late Antiquity. Cambridge: Cambridge University Press. p. 1432. ISBN 978-0-521-83307-3. https://books.google.com/books?id=WJbd0m6YaFkC&pg=PA1432. 
  37. ↑ Meri-Sofia Lakopoulos (2015). The Traditional Iso-polyphonic song of Epirus[|permanent dead link|dead link}}]. The International Research Center for Traditional Polyphony. June 2015, issue 18. p. 10.
  38. ↑ Spiro J. Shetuni (2011). Albanian Traditional Music: An Introduction, with Sheet Music and Lyrics for 48 Songs. Jefferson, North Carolina: McFarland. p. 38. ISBN 978-0-7864-8630-4. https://books.google.com/books?id=SjasqxAeHXAC&pg=PA38. 
  39. ↑ Simon Broughton; Mark Ellingham; Richard Trillo (1999). World Music: Africa, Europe and the Middle East. London: Rough Guides. p. 160. ISBN 978-1-85828-635-8. https://books.google.com/books?id=ViwKAQAAMAAJ&q=middle+volga+pentatonic. 
  40. ↑ Mark Phillips (2002). GCSE Music. Oxford: Heinemann. p. 97. ISBN 978-0-435-81318-5. https://books.google.com/books?id=BDFb82vmI8AC&pg=PT104. 
  41. ↑ Willi Apel (1969). Harvard Dictionary of Music. Cambridge, Massachusetts: Harvard University Press. p. 665. ISBN 978-0-674-37501-7. https://books.google.com/books?id=TMdf1SioFk4C&pg=PA665. 
  42. ↑ Carmen Bernand (19 August 2009). "Musiques métisses, musiques populaires, musiques latines: genèse coloniale, identités républicaines et globalisation". Sorbonne University (France) 6 (11): 87–106. ISSN 1794-5887. http://www.scielo.org.co/scielo.php?script=sci_arttext&pid=S1794-58872009000200006. 
  43. ↑ Qian, Gong (19 June 1995). "A Common Denominator Music Links Ethnic Chinese with Hungarians". China Daily. 
  44. ↑ 44.0 44.1 Van Khe, Tran. "Is the Pentatonic Universal? A Few Reflections on Pentatonism." The World of Music 19, no. 1/2 (1977): 76–84. http://www.jstor.org/stable/43560446.
  45. ↑ The Garland Encyclopedia of World Music, Volume 2: South America, Mexico, Central America, and the Caribbean. New York: Taylor & Francis. 1998. p. 217. ISBN 0-8240-6040-7. https://books.google.com/books?id=Xb2ibVAXO9sC&pg=PA217.  (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 Malena Kuss, ed (2004). Music in Latin America and the Caribbean: an encyclopedic history. Austin: University of Texas Press. p. 141. ISBN 0-292-70298-1. https://books.google.com/books?id=SYuKB29_7qUC&pg=PA141. )
  46. ↑ Burton William Peretti (2009). Lift Every Voice: The History of African American Music. New York: Rowman & Littlefield Publishers. p. 39. ISBN 978-0-7425-5811-3. https://books.google.com/books?id=-1uasSvAnE4C&pg=PA39. 
  47. ↑ Anna Czekanowska; John Blacking (2006). Polish Folk Music: Slavonic Heritage – Polish Tradition – Contemporary Trends. Cambridge: Cambridge University Press. p. 189. ISBN 978-0-521-02797-7. https://books.google.com/books?id=czVkawHfw_UC&pg=PA189. 
  48. ↑ Jeremy Day-O'Connell (2009). "Debussy, Pentatonicism, and the Tonal Tradition". Music Theory Spectrum 31 (2): 225–261. doi:10.1525/mts.2009.31.2.225. https://www.skidmore.edu/music/documents/Day-OConnell_Debussy_Pentatonicism.pdf. 
  49. ↑ Bruce Benward and Marilyn Nadine Saker, Music in Theory and Practice, eighth edition (Boston: McGraw Hill, 2009): vol. II, p. 245. ISBN:978-0-07-310188-0.
  50. ↑ 50.0 50.1 50.2 50.3 Chaudhuri, A. (2021). Finding the Raga: An Improvisation on Indian Music. Faber & Faber. p. 52. ISBN 978-0-571-37076-4. https://books.google.com/books?id=N3oeEAAAQBAJ&pg=PT52. Retrieved 26 May 2021. 
  51. ↑ Menon, R.R. (1973). Discovering Indian Music. Somaiya Publications. p. 50. https://books.google.com/books?id=AuUXAQAAIAAJ. Retrieved 26 May 2021. "Some prefer the first Raga to be pentatonic in scale. Let us take for an example, the pentatonic Bhoopali. Its notes are: SA RI GA PA DHA SA up and down the scale." 
  52. ↑ Chib, S. K. S.; Khan, A. A. (2004). Companion to North Indian Classical Music. Munshiram Manoharlal Publishers. p. 337. ISBN 978-81-215-1090-5. https://books.google.com/books?id=ag4KAQAAMAAJ. Retrieved 26 May 2021. 
  53. ↑ Qureshi, R. B. (2016). Master Musicians of India: Hereditary Sarangi Players Speak. Taylor & Francis. p. 385. ISBN 978-1-135-87396-7. https://books.google.com/books?id=SxYfDAAAQBAJ&pg=PT385. Retrieved 26 May 2021. 
  54. ↑ Thatte, A.; Sabanīsa, M. P. (2000). Vande Mataram, Down the Memory Lane. Jayanti Samaroha Samitee Vande Mataram. p. 77. https://books.google.com/books?id=KsBjAAAAMAAJ. Retrieved 26 May 2021. "Named after the powerful Hindu goddess, Raga Durga is pentatonic, omitting the third and the seventh degrees, while emphasising the sixth and the second." 
  55. ↑ The Historical Development of Indian Music: A Critical Study. Firma K. L. Mukhopadhyay. 1973. p. 175. ISBN 978-0-88386-344-2. https://books.google.com/books?id=kowHAQAAMAAJ. Retrieved 26 May 2021. 
  56. ↑ O'Brien, J. P. (1977). Non-western Music and the Western Listener. Kendall/Hunt Publishing. p. 37. ISBN 978-0-8403-1755-1. https://books.google.com/books?id=Mr8ZAQAAIAAJ. Retrieved 26 May 2021. 
  57. ↑ Nizami, F.; Arshad, S.; Lakhvīrā, N. Ḥ. (1988). ABC of Music. Punjab Council of the Arts. p. 54. https://books.google.com/books?id=Guu5AAAAIAAJ. Retrieved 27 May 2021. 
  58. ↑ "Katyayani". 13 June 2009. http://kksongs.org/raga/list/katyayani.html. 
  59. ↑ Thom Lipiczky (1985). "Tihai Formulas and the Fusion of 'Composition' and 'Improvisation' in North Indian Music". The Musical Quarterly 71 (2): 157–171 (160). "They are set to one of the most widely performed ragas in North India, the pentatonic midnight raga Malkauns. The most important notes of Malkauns are Sa (the tonic) and Ma (the fourth). Both the gats and the tihais "cadence" on one of ...". 
  60. ↑ Chakraborty, S.; Mazzola, G.; Tewari, S.; Patra, M. (2014). Computational Musicology in Hindustani Music. Computational Music Science. Springer International Publishing. p. 3. ISBN 978-3-319-11472-9. https://books.google.com/books?id=0o2eBQAAQBAJ&pg=PA3. Retrieved 27 May 2021. 
  61. ↑ Karnani, C. (2005). Form in Indian Music: A Study in Gharanas. Rawat Publications. p. 81. ISBN 978-81-7033-921-2. https://books.google.com/books?id=dGIJAQAAMAAJ. Retrieved 27 May 2021. "Ghulam Ali showed unusual fondness for pentatonic modes like Gunkali, Malkauns, Kausi Dhani and Bhopali. Even Shudh Sarang and Megh Malhar are largely pentatonic." 
  62. ↑ Katz, J. (1992). The Traditional Indian Theory and Practice of Music and Dance. Panels of the VIIth World Sanskrit Conference / World Sanskrit Conference 7, 1987, Leiden: Panels of the VIIth World Sanskrit Conference. E. J. Brill. p. 19. ISBN 978-90-04-09715-5. https://books.google.com/books?id=HVjyfWPCO1wC&pg=PA19. Retrieved 27 May 2021. 
  63. ↑ Chib & Khan 2004, p. 39.
  64. ↑ "Raagabase – A collection of Indian Classical Music Raags (Aka Ragas)". https://www.swarganga.org/raagabase.php. 
  65. ↑ Graue, Jerald. "Scale". https://www.britannica.com/art/scale-music. 
  66. ↑ Japanese Music, Cross-Cultural Communication: World Music, University of Wisconsin – Green Bay.
  67. ↑ Sumarsam (1988) Introduction to Javanese Gamelan.
  68. ↑ Mohamed Diriye Abdullahi (2001). Culture and Customs of Somalia. Greenwood Publishing Group. p. 170. ISBN 0-313-31333-4. https://books.google.com/books?id=2Nu918tYMB8C&pg=PA170. "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." 
  69. ↑ Tekle, Amare (1994). Eritrea and Ethiopia: from conflict to cooperation. The Red Sea Press. p. 197. ISBN 0-932415-97-0. https://books.google.com/books?id=xbQTEF0rd7wC&pg=PA197. "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." 
  70. ↑ Seumas MacNeil and Frank Richardson Piobaireachd and its Interpretation (Edinburgh: John Donald Publishers, 1996): p. 36. ISBN:0-85976-440-0
  71. ↑ Roderick D. Cannon The Highland Bagpipe and its Music (Edinburgh: John Donald Publishers, 1995): pp. 36–45. ISBN:0-85976-416-8
  72. ↑ Bruno Nettl, Blackfoot Musical Thought: Comparative Perspectives (Ohio: The Kent State University Press, 1989): p. 43. ISBN:0-87338-370-2.
  73. ↑ "The Pentatonic and Blues Scale". How To Play Blues Guitar. 2008-07-09. http://how-to-play-blues-guitar.com/blues-concepts/the-pentatonic-and-blues-scale/. 
  74. ↑ "NROTC Cadences". http://www.lukeswartz.com/nrotc/cadences.html. 
  75. ↑ Steve Turner, Amazing Grace: The Story of America's Most Beloved Song (New York: HarperCollins, 2002): p. 122. ISBN:0-06-000219-0.
  76. ↑ 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. ISBN 978-0-940796-03-4. 
  77. ↑ Amanda Long. "Involve Me: Using the Orff Approach within the Elementary Classroom". Eastern Illinois University. p. 7. http://thekeep.eiu.edu/cgi/viewcontent.cgi?article=1003&context=lib_awards_2013_docs. 
  78. ↑ Andrea Intveen, Musical Instruments in Anthroposophical Music Therapy with Reference to Rudolf Steiner’s Model of the Threefold Human Being

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