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Quintuple meter

Quintuple meter orquintuple time is a musicalmeter characterized by fivebeats in a measure, whether variably or equally stressed.

Like the more commonduple,triple, andquadruple meters, it may besimple, with each beat divided in half, orcompound, with each beat divided into thirds. The most commontime signatures for simple quintuple meter are5
4
and5
8
; compound quintuple meter is most often written in15
8
.

Notation

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15
8
as5
4
with 3 subdivisions
15
8
as3
4
with 5 subdivisions

Simple quintuple meter can be written in5
4
or5
8
time, but may also be notated by using regularlyalternating bars of triple and duple meters, for example2
4
+3
4
. Compound quintuple meter, with each of its five beats divided into three parts, can similarly be notated using a time signature of15
8
, by writing triplets on each beat of a simple quintuple signature, or by regularly alternating meters such as6
8
+9
8
.

Another notational variant involvescompound meters, in which two or three numerals take the place of the expected numerator. In simple quintuple meter, the 5 may be replaced as2+3
8
or2+1+2
8
for example.[1] A time signature of15
8
, however, does not necessarily mean the music is in a compound quintuple meter. It may, for example, indicate a bar of triple meter in which each beat is subdivided into five parts. In this case, the meter is sometimes characterized as "triple quintuple time".[2]

It is also possible for a15
8
time signature to be used for an irregular, oradditive, metrical pattern, such as groupings of3+3+3+2+2+2 eighth notes or, for example in theHymn to the Sun andHymn to Nemesis byMesomedes of Crete,2+2+2+2+2+3+2, which may alternatively be given the composite signature8+7
8
.[3]

Similarly, the presence of some bars with a5
4
or5
8
meter signature does not necessarily mean that the music is in quintuple meter overall. The regular alternation of5
4
and4
4
inBruce Hornsby's "The Tango King" (from the albumHot House), for example, results in an overall nonuple meter (5+4 = 9).[4]

History

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Transcription of the opening of theFirst Delphic Hymn, by Athenaeus, son of Athenaeus

Before the 20th century, quintuple time was rare in European concert music, but is more commonly found in other cultures.

Ancient Greek music

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Rhythm in ancient Greek music was closely tied to poetic meter, and included what are understood today as quintuple patterns. The twoDelphic Hymns from the second century BC both provide examples. The First Delphic Hymn, byAthenaeus, son of Athenaeus, is in the quintupleCretic meter throughout. The first nine of the ten sections of the Second Hymn, byLimenius, are also in Cretic meter.[5]

In addition to the Cretic meter, which consisted of along-short-long pattern, ancient Greek music had seven other quintuple meters: Bacchic (L-L-S), Palimbacchic (or antibacchic:S-L-L), four species of Paeanic (L-S-S-S,S-L-S-S,S-S-L-S—which is a composite ofpyrrhic andtrochee—andS-S-S-L), andhyporchematic (S-S-S-S-S).[6]

Asia, Transcaucasia, and the Middle East

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Arabic theorists already in the earlyAbbasid period (AD 750–900) describedmodal rhythmic cycles (īqā‘āt), that included quintuple meters, though taxonomies and terminology vary amongst writers. The first figure to describe these rhythms wasAbū Yūsuf Ya‘qūb al-Kindī (ca 801–ca 866), who divided them into two broad categories,ṯẖaqīl ("heavy", meaning slow) andkhafīf ("light", meaning quick). Two of hisṯẖaqīl modes—ṯẖaqīl thānī ("second heavy", S-S-L-S) andramal (L-S-L)—and onekhafīf mode are quintuple.[7] The most important writers of the later Abbasid period (AD 900–1258) wereAbū Naṣr al-Fārābī (d. 950) andIbn Sīnā (d. 1037). Al-Fārābī elaborated the rhythmic system established a century earlier by another important early Abbasid musician,Isḥāq al-Mawṣilī, who had based it on local traditions, without any knowledge of classical Greek music theory.[8] Isḥāq's and al-Fārābī's system consisted of eight rhythmic modes, the third and fourth of which were quintuple: calledṯẖaqīl thānī ("second heavy"), andkhafīf al-ṯẖaqīl thānī ("second light heavy"), both of which are short-short-short-long, in slow and fast tempo, respectively.[9] This terminology and these definitions continued to be found as late as the 12th century inMuslim Spain, for example in a document by Abd-Allāh ibn Muḥammad ib al-Ṣīd al-Baṭaliawsī.[10]

In the MoroccanMalḥūn repertory (an urban song style closely associated withAndalusian music),5
8
rhythms are sometimes introduced into the basic meter of2
4
.[11] Turkish classical music employs a system of rhythmic modes (calledusul), which include units ranging from two to ten time units. The five-beat meter is calledtürk aksağı.[12]

The traditional music ofAdjara in Western Georgia includes an ancient war-dance calledKhorumi, which is in quintuple meter.[13]

The cyclically repeating fixed time cycles ofCarnatic andHindustani classical music, calledtālas, include both fast and slow quintuple patterns, as well as binary, ternary, and septenary cycles.[14] In the Carnatic system, there is a complex "formal" system of tālas which is of great antiquity, and a more recent, rather simpler "informal" system, comprising selected tālas from the "formal" system, plus two fast tālas calledCāpu. The slow quintuple tāla, calledJhampā is from the formal system, and consists of a pattern of7+1+2 beats; the fast quintuple tāla is calledkhaṇḍa Cāpu orara Jhampā, and consists of2+1+2 beats. However, the pattern of beats marking the rotation of the cycle does not necessarily indicate the internal rhythmic organization. For example, although theJhampā tāla, in its most commonmiśra variety, is governed by2+1+2, the most characteristic rhythm of melodies in this tāla is(2+3) + (2+3).[15]

The tālas in Hindustani music are somewhat more complicated. To begin with, they are not systematically codified, but rather comprise a miscellany of patterns from a number of different repertories. Secondly, the counting units (mātrā) of each tāla are grouped into segments calledvibhāg, which constitute slower "beats" of from1+12 to 5 of those counting units. Third, in addition to the soundedvibhāg, marked by hand-claps (tālī), there are alsovibhāg marked only by a wave of the hand—the so-calledkhālī beats. The two quintuple tālas in these repertories areJhaptāl2+3+(2)+3—andSūltāl2+(2)+2+2+(2). Both are measured by tenmātrā units, butJhaptāl is divided into four unequalvibhāg (the third being akhālī beat) in two halves of fivemātrā each, andSūltāl is divided into five equalvibhāg, the second and fifth of which arekhālī.[16]

Thekasa repertory of traditionalKorean court music often employs cycles in quintuple time, even though Korean traditional music terminology has no specific term for it. This repertory can be traced back in some cases to the fifteenth century. Quintuple meter is also occasionally found in folk music, with perhaps the most well-known example being theEotmori (엇모리) rhythm (장단) often employed inSanjo.[17] Quintuple is the oldest surviving traditional Korean meter.[18]

Australia

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Quintuple meter occurs as a variation in some women's dance songs ofindigenous Australians, where a5
8
measure is occasionally inserted into songs with a basic duple or four-beat pattern.[19]

The Americas

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Traditional dance songs of theYupik of Alaska are accompanied by frame drums, beaten with a long thin wand, most commonly in a5
8
crotchet–dotted crotchet (quarter–dotted quarter) pattern.[20]

European folk music

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Many European folk and traditional repertories also feature quintuple meter. This is particularly true of Slavic cultural groups. The Bulgarian "paidushko" dance, for example, is in a fast5, counted2+3.[21] In north-eastern Poland (especially inKurpie,Masuria, and northernPodlaskie), five-beat bars are frequently found in wedding songs, with rather slow tempos and not accompanied by dancing. Traditional Russian wedding songs also are in quintuple time.[22] The Poles and Russians share this proclivity for quintuple meter with the Finns,Sami people, Estonians, and Latvians.[23] In Finland, theKalevalaic "runometric" songs are the most distinctive feature of folk music, and the most common melody of these epic songs is in quintuple meter. This melody was described in the oldest study of runo singing in 1766, but first published in a musical transcription only about 20 years later.[24] One South Slavic example is recorded in a manual published in 1714 by the Venetian dancing master Gregorio Lambranzi. It is aforlana titled "Polesana", probably meaning "FromPola", a city inIstria—today a part of Croatia but a Venetian possession until 1947. Although Lambranzi notated this dance in6
8
time, its recurring phrase structure shows it to be in compound-quintuple time, so that its correct form is actually written in15
8
.[25]

Greek folk music is also characterized by rhythms in asymmetrical meters. The repertory of thePeloponnese, for example, includes the Dorictsakonikos from Doric-speaking (seeTsakonian language)Kynouria in5
4
time.[26] TheEpirus region of Northern Greece also has dance melodies in a slow 5 (2–3).[27]

Spanish folk music is also noted for the use of quintuple meter, particularly well-known examples being theCastilianrueda and theBasquezortziko, but it is also found in the music ofExtremadura,Aragon,Valencia, andCatalonia.[28] Some types of the folk dances collectively referred to asgavottes, and stemming fromLower Brittany in France are in5
8
meter, though4
4
,2
4
, and9
8
are also found.[29] In theAlsatian region ofKochersberg, a peasant dance called theKochersberger Tanz is in5
8
time, and is similar to a dance of theUpper Palatinate inBavaria calledDer Zwiefache orGerad und Ungerad, because it alternates even and uneven bars (2
8
and3
8
).[30]

European art music

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Medieval and Renaissance

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In European art music it became possible only in the 14th century to notate quintuple rhythms unambiguously, through the use of minor or reversedcoloration.[31] In some instances from the late-14th-centuryArs subtilior period, quintuple passages occur which are long enough to regard as an established meter. For example, in thesecunda pars of an anonymous two-voiceFortune (MS Paris, Bibliothèque Nationaleital. 568, fol. 3), a "clear and definite rhythm" in the upper part creates a5
8
meter set against the6
8
of the lower part.[32] The earliestcomplete European compositions in quintuple time, however, appear to be seven villancicos in theCancionero Musical de Palacio, which were composed between 1516 and 1520.[33] Notation of the quintuple meter in these seven pieces is achieved in various ways:[34]

  • Juan del Encina uses the mensuration 5
    1
    in "Amor con fortuna", but in "Tan buen ganadico", he uses a signature of
    (1496).[clarification needed]
  • Juan de Anchieta uses 5
    1
    (tempus perfectum,proportio quintupla), in both "Con amores, mi madre" (1465), and "Dos ánades, madre".
  • The anonymous "Pensad ora'n al" uses the mensuration 5
    2
    .
  • "Las mis penas madre" byPedro de Escobar and "De ser mal casada" by Diego Fernández (d. 1551) both use just the proportion sign5
    2
    .

Other examples from the 16th century include theIn Nomine "Trust" byChristopher Tye,[35] the "Qui tollis" section ofJacob Obrecht's Missa "Je ne demande", the "Sanctus" from theMissa Paschalis byHeinrich Isaac,[31] and the final "Agnus Dei" ofAntoine Brumel's Missa "Bon temps".[36] Keyboard examples from this period include the first half of an English setting of the offertoryFelix namque from about 1530, and a passage in no. 41 of theLibro de tientos (1626) byFrancisco Correa de Arauxo.[31]

Baroque and Classical

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In theBaroque andClassical eras quintuple meter is, if anything, even less frequently encountered than in theRenaissance. One possible example is the ritornello that precedes and follows Orfeo's aria "Vi ricorda" in act 2 ofClaudio Monteverdi'sL'Orfeo. The notation is problematic, however, and while several editors (Robert Eitner,Vincent d'Indy,Hugo Leichtentritt, andCarl Orff) have transcribed it in quintuple meter, others interpret it differently.[37] The verses ofGiovanni Valentini'smadrigalCon guardo altero, published inMusiche a doi voci (1621) is composed in5
4
.[38]Johann Heinrich Schmelzer included a5
4
section of 27 measures in hisHarmonia à 5, composed by at least 1668.[39] Two brief passages of5
8
occur in the "mad scene" (act 2, scene 11) fromHandel's operaOrlando (1732), first at the words "Già solco l'onde" ("Already I am cleaving the waves") when the demented hero believes he has embarked onCharon's boat on theStyx, and then again two bars later.[31]Charles Burney found this whole scene admirable, as a portrait of Orlando's madness, but observed that "Handel has endeavoured to describe the hero's perturbation of intellect by fragments of symphony in5
8
, a division of time which can only be borne in such a situation".[40] Burney's German contemporary,Johann Kirnberger, also felt that "No one can repeat groups of five and even less of seven equal pulses in succession without wearisome strain".[41]

Another exceptional 18th-century example is an entire aria composed in5
4
time, "Se la sorte mi condanna" found inAndrea Adolfati's operaArianna (1750),[42] but the English theater composerWilliam Reeve, with the last movement of hisGypsy's Glee (1796), to the words "Come, stain your cheeks with nut or berry" (in5
4
time) is credited with having composed an example in true quintuple time, "for instead of the usual division of the bar into two parts, such as might be expressed by alternate bars of3
4
and2
4
, or2
4
and3
4
, there are five distinct beats in every bar, each consisting of an accent and a non-accent. This freedom from the ordinary alternation of two and three is well expressed by the grouping of the accompaniment, which varies throughout the movement…".[43]

19th century

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There appear to have been several motivations for composers to use quintuple time: firstly to demonstrate technical skill, as in the Tye and Correa de Arauxo examples, and secondly to produce an atmospheric effect, or to suggest unease or unusual excitement, as in Handel'sOrlando. In the 19th century, a third motivation arises with the rise ofnationalistic music, which often invokes folk-music elements.[31] In any case, quintuple time becomes much more frequent (though still not common) in the 19th century. Early examples include Fugue 20 (Allegretto) fromAnton Reicha'sTrente-six fugues for piano (1805),[44] the tenor aria "Viens, gentille dame" from act 2 ofFrançois-Adrien Boieldieu's operaLa dame blanche (1825),[45] and the third movement (Larghetto, con molta espressione), fromFrédéric Chopin'sPiano Sonata No. 1 in C minor, Op. 4 (1828).[46] Although Reicha's fugue probably falls into the category of technical skill, the composer does mention taking as a model for the meter the AlsatianKochersberger Tanz.

Nationalistic influence is clearer in the operas of the Russian composerMikhail Glinka: the "Nuptial chorus and scene" from act 3 of the operaA Life for the Tsar (1834–1836) was the first time a composer of art music set the pentasyllabichemistichs of Russian wedding songs in quintuple meter instead of adapting it to a more conventional one.[47] In his next opera,Ruslan and Ludmila (1837–1842) Glinka repeated the effect in the opening of act 1, where the chorus sings an epithalamium to Lel', the Slavonic god of love, once again in quintuple time.[48] Later Russian examples are found inTchaikovsky's folk-song settings:Fifty Russian Folk Songs for piano four-hands (1868–1869),Children's Ukrainian and Russian Folksongs (book 1: 1872, book 2: 1877), andSixty-Six Russian Folk Songs for voice and piano (1872), where quintuple meter is notated by regularly alternating signatures, usually3
4
and2
4
.[49] AlsoNikolai Rimski-Korsakov'sRussian Easter Festival Overture initial theme is in5
2
.

Shorter passages also occur in the music ofHector Berlioz:La tempête (1830), later incorporated intoLélio as the finale, has "quintuple metre for a whole section, notated in compound duple; 'bars' of15
4
are defined by a recurring rhythmic pattern and by accents (six 'bars' covering bars 289–306 in the6
4
notation)",[50] and the "Combat de ceste" (No. 5), fromLes Troyens (1856–1858), has "an attractive5
8
section, only eight bars long".[50] The outer sections of thescherzo fromAlexander Borodin's unfinished Third Symphony are in5
8
time, interrupted six times in bars 36–38, 69–71, 180–182, 218–220, 352–354, and 392–394 with a three-bar group in2
4
. The central trio section, b. 235–313 is in3
4
time.[51]

From around the middle of the century, there isCarl Loewe's ballad for voice and piano, "Prinz Eugen, der edle Ritter", Op. 92 (to the poem byFerdinand Freiligrath, 1844), which is in5
4
time throughout,[52]Ferdinand Hiller's Piano Trio No. 4, Op. 64 (1855) andRhythmische Studien for piano,[31] a String Trio by K. J. Bischoff, which was awarded a prize by the Deutsche Tonhalle in 1853,[53] andBenjamin Godard's Violin Sonata No. 4, Op. 12 (1872) which includes ascherzo in5
4
time throughout.[54] The piano virtuosoCharles-Valentin Alkan showed an interest in unusual rhythmic devices, and composed at least four keyboard pieces in quintuple time: the first three of theDeuxième recueil d'impromptus, Op. 32, no. 2 (1849), Andantino, Allegretto, and Vivace (the fourth and last piece in this collection is inseptuple meter),[55] and a5
4
"Zorzico dance" episode in thePetit Caprice, réconciliation, Op. 42 (1857).[56] In opera,Wagner, inserted several5
4
bars in "Tristan, der Held, in jubelnder Kraft", in act 3 ofTristan und Isolde (1856–1859).[57] Another instance from around this same time is found inAnton Rubinstein's "sacred opera"Der Thurm zu Babel (The Tower of Babel), Op. 80 (1868–1869).[31] InJohannes Brahms's late collection of six vocal quartets, Op. 112, the second piece, "Nächtens", is entirely in5
4
.[58] At the very end of the century,Alban Berg used5
4
meter throughout his song-setting ofTheodor Storm's poem, "Schließe mir die Augen beide" (1900).[59]

Three of the best-known examples of quintuple meter in thesymphonic repertoire are from late in theneoromantic (orpost-romantic) period, which reaches from the mid-19th century through World War I: the second movement ofTchaikovsky'sSymphony No. 6 in B minor, "Pathétique", Op. 74 (1893)[60] (described by one author as the very first example of quintuple meter in Western classical music),[61]Rachmaninoff'sThe Isle of the Dead, Op. 29 (1908),[62] and the opening movement, "Mars, the Bringer of War" ofThe Planets (1914–1916) byGustav Holst. (The final movement, "Neptune, the Mystic", is also in quintuple meter, but this is less well known.)[63] The first theme of Tchaikovsky's Symphony No. 6, mvmt. II is shown below.

The Finnish composerJean Sibelius used a pattern of quintuple meter in the third movement ofKullervo (1891–1892), where "the orchestra maintains a pattern of five beats in a bar, while the chorus elongates its lines to phrases of fifteen, ten, eight, and twelve beats, respectively".[64] These areKarelian rhythms, reflecting nationalism in Sibelius's music. He used these quintuple meters as well in several male-chorus works: "Venematka" (no. 3 fromSix Partsongs, Op. 18, 1893), the third movement, "Hyvää iltaa, lintuseni", fromRakastava, Op. 14 (1894), and "Sortunut ääni" (no. 1 fromSix Partsongs, Op. 18, 1898).[65]

In 1895, the British composerSamuel Coleridge-Taylor wrote the second movement, "Serenade", of hisFantasiestücke, Op. 5, for string quartet in5
4
time.[66] A little more than ten years later, the Scottish composer Robert Ernest Bryson wrote a string-orchestra fantasy titledVaila in5
4
time.[67]

In the piano repertoire, the "Promenade", fromModest Mussorgsky'sPictures at an Exhibition (1874), has five versions, in each of which5
4
is mixed with other meters, regularly or irregularly:

  1. 5
    4
    alternates with6
    4
    for eight bars, then two of6
    4
    and one pair of5
    4
    +6
    4
    , ending with twelve bars of6
    4
  2. 5
    4
    alternates regularly with6
    4
    throughout (effectively11
    4
    )
  3. regular alternation of5
    4
    and6
    4
    until the final two bars, which are5
    4
    and C
  4. irregular mixture of5
    4
    ,6
    4
    , and7
    4
    , with a single3
    4
    bar at the end
  5. four pairs of regularly alternating5
    4
    and6
    4
    , then an irregular mixture of5
    4
    ,6
    4
    , and7
    4
    to the end.[68]

The opening measures are shown below:

To this same period (and to the Russian tradition) also belongs "Prizrak" (Phantom), in5
8
time, which is No. 4 ofSergei Prokofiev's Four Pieces for Piano, Op. 3 (1911).[69]

These examples are all simple quintuple time. Compound quintuple meter is less frequent, but an instance is found in the middle section of the third movement, "Andante grazioso", of Brahms'sPiano Trio No. 3 in C minor, Op. 101 (1886), which is in15
8
with9
8
turnarounds.[70] "Fêtes", the second movement ofClaude Debussy'sNocturnes for orchestra (1892–1899), also has a recurring passage of two15
8
bars, embedded in a context of mainly compound triple (9
8
) bars.[71] The seventh ofFlorent Schmitt'sEight Short Pieces for piano four-hands (1907–1908), "Complainte", is in15
8
with occasional bars of9
8
inserted.[72] The first section ofNikolai Medtner's Piano Sonata Op. 25 No. 2 in E minor ("Night Wind"), which is from 1911, is "perhaps the most extended piece of music in15
8
time in existence".[73]

20th century

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The common occurrence of quintuple meter in many folk-music traditions caused an increase in its appearance in the works of composers with nationalistic tendencies in the early 20th century.[31] Examples are the Prelude in the Unison fromGeorge Enescu's Orchestral Suite No. 1, Op. 9 (1903),[74] "In Mixolydian Mode", "Bulgarian Rhythm (2)", and the third of "Six Dances in Bulgarian Rhythm", nos. 48, 115, and 150 fromBéla Bartók'sMikrokosmos (1926, 1932–1939),[75] the "Chanson épique", no. 2 fromMaurice Ravel's song cycleDon Quichotte à Dulcinée (1932–1933),[76] and the first theme group ofCarlos Chávez'sSinfonía india (1935–1936), which is predominantly in5
8
time, but mixed with other meters.[77] Another impulse for the use of quintuple meter was to evoke pagan and specifically Ancient Greek culture. The5
4
meter of thebacchanalian "Danse générale" concluding Ravel's balletDaphnis et Chloé (1909–1912) is a particularly well-known example.[78] In his First Symphony, theSinfonía de Antígona (1933), Carlos Chávez reworked incidental music he had composed in 1932 for a production ofSophocles'Antigone in the adaptation byJean Cocteau. In this symphony Chávez made extensive use of the Greek paeonic (or cretic) meter, notated in5
8
time in the score.[79] The fourth and last movement of Ravel'sString Quartet is mostly in5
8
and5
4
time, alternating several times with3
4
time.[80]

A fourth example from Ravel is a particularly intense, if brief use of quintuples for symbolic purposes. This isFrontispice for two pianos (1918), written at the request ofRicciotto Canudo to accompany a philosophical meditation onWorld War I, titledS.P. 503, le poème du Vardar. Canudo's title bears the numerical designation of the postal sector of his combat division, and Ravel used the numbers as the basis of his composition. Five staves of music, "'progressing' vertically from flats through naturals to sharps, are played by five hands (three players) in meters of15
8
(i.e.,(3×5)
(3+5)
) and5
4
".[81]

The Basque setting ofPierre Loti's playRamuntcho made the inclusion of Basque traditional melodies in the incidental music composed for it in 1907 byGabriel Pierné a natural choice. Pierné included at the end of act 2 an arrangement of the Basque anthemGernikako Arbola byJosé María Iparraguirre, which is inzortziko rhythm,[82] but he also quotes traditionalzortziko melodies, as well as imitating their quintuple rhythms, in the opening "Ouverture sur des thèmes populaires basques"[83] as well as in the "Rapsodie basque" that serves as an interlude between the first and second tableaux of act 2.[84] Pierné, who was attracted to quintuple meter as part of a broader taste for exoticism,[85] also employed quintuple meter in his Piano Quintet, Op. 41 (1917), and in theFantaisie basque, Op. 49 (1927), for violin and orchestra. The outer sections of the second movement of the Quintet are in5
8
time, and marked "Sur une rythme de Zortzico",[86] while the contrasting central section superimposes20
8
on4
2
time, in "quadruple quintuple" meter.[87] In theFantaisie, a long section near the beginning is in5
8
time, and is marked "Rythme de Zortzico".[88]

Igor Stravinsky's name is often associated with rhythmic innovation in the 20th century, and quintuple meter is sometimes found in his music—for example, the fugato variation in the second movement of hisOctet (1922–1923) is written almost uniformly in5
8
time.[89] Much more characteristically, however, quintuple bars in Stravinsky's scores are found in a context of constantly changing meters, as for example in his balletThe Rite of Spring (1911–1913), where the object appears to be the combination of two- and three-note subdivisions in irregular groupings.[90]

 
Stravinsky, "Sacrificial Dance" (excerpt), fromThe Rite of Spring

This treatment of rhythm subsequently became so habitual for Stravinsky that, when he composed hisSymphony in C in 1938–1940, he found it worth observing that the first movement had no changes of meter at all (though the metrical irregularities in the third movement of the same work were amongst the most extreme in his entire output).[citation needed]

So many other composers followed Stravinsky's example in the use of irregular meters that the occasional occurrence of quintuple-time bars becomes unremarkable from the 1920s onward.[31] Entire movements with a constant five-to-a-bar rhythm are less-often encountered. An example is the second-movement "Lament" of theDouble Concerto for Two Violins and Orchestra, Op. 49 (1929), by Gustav Holst.[91] One particularly notable pre–World War II quintuple-meter composition is the popular first movement, "Aria (Cantilena)" (1938), of theBachianas Brasileiras no. 5 byHeitor Villa-Lobos (the second movement was added only in 1945). The opening and closing parts of this aria for soprano and orchestra of cellos is predominantly in5
4
, and the middle section is entirely in that meter.[92]

Written during the war, the third movement,Andante calmo, ofBenjamin Britten'sString Quartet No. 1 (1941) is in5
4
.[93] TheLudus Tonalis byHindemith (1942) has several instances of quintuple meter: itsPreludium and retrograde-invertedPostludium each have aSolenne, largo section in15
8
;[94] Fugue II in G is in5
8
;[95] and though Fugue VIII in D[96] is notated in4
4
, itsmusic is predominantly in5
4
, so shifts one beat forward each measure with respect to its notated meter.[original research?] ThePassacaglia for piano (1943) byWalter Piston is in quintuple meter.[97]

In the post-war period,Gian Carlo Menotti used a quintuple-meter funeral march as an instrumental transition to the final scene of his operaThe Consul (1950),[98] and Britten set "Green Leaves Are We, Red Rose Our Golden Queen", the opening chorus from his operaGloriana, Op. 53 (1952–1953, rev. 1966), in5
4
time.[99]Dmitri Shostakovich set Fugues 12, 17, and 19 from hisTwenty-Four Preludes and Fugues for piano, Op. 87 (1950–1951) entirely in5
4
time, and also interspersed this time signature with other meters in Preludes 9, 20, and 24, and in Fugues 15 and 16 from the same collection.[100] Fugue No 17 in A major follows in the Slavic tradition of "naturally" flowing music in five time.[101]

Quintuple meter is sometimes employed to characterize particular variations of works invariation form. Examples include the third movement, "Variations on a Ground", from the Double Concerto for Two Violins and Orchestra, Op. 49 (1929), by Gustav Holst (11th and 18th variations in5
4
),[102] "Variation IV: Più mosso" (in5
8
time), in Part I ofThe Age of Anxiety: Symphony No. 2 (1949) byLeonard Bernstein.[103] Britten composed hisCanticle III ("Still Falls the Rain"), Op. 55 (1954), in variation form, with the "Theme", "Variation IV", and "Variation VI" all in5
4
.[104] In a similar fashion, extended single-movement compositions may set off large sections by using contrasting meters. Quintuple meter is used in this way byRob du Bois in his Concerto for Two Violins and Orchestra (1979), where bars 160–175 and 227–277 are in5
8
.[105]

In theminimal music that emerged in the late 1960s, quintuple meter is not often encountered. A rare exception is found in an early work bySteve Reich,Reed Phase (1966), which is built on the constant repetition of a five-note basic unit in steady eighth notes.[106]

Reich was not satisfied with the result, largely because of the failure of the meter to produce the kind of rhythmic ambiguity found in the 12-beat patterns he came to favour:

which can divide up in very different ways; and that ambiguity as to whether you're in duple or triple time is, in fact, the rhythmic life-blood of much of my music. In this way, one's listening mind can shift back and forth within the musical fabric, because the fabricencourages that. But if you don't build in that flexibility of perspective, then you wind up with something extremely flat-footed and boring.[107]

Reich's 1979 Octet (originally scored for two pianos, string quartet, and two wind players who perform on both flutes and clarinets), revised and rescored asEight Lines) is entirely in quintuple time.[108]

Jazz and popular music

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A survey of American popular music found that the most common accent pattern used in quintuple meter isstrong-weak-weak-medium-weak.[109]

Musical theatre

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Until after the Second World War, quintuple time was virtually unheard of in the American genres ofjazz and popular music. When in 1944, Stravinsky was commissioned byBilly Rose to compose a fifteen-minute dance component to be incorporated into his Broadway revue,The Seven Lively Arts, Stravinsky composedScènes de ballet, to be choreographed byAnton Dolin. Rose was enthusiastic about the new score when initially he saw the piano reduction made byIngolf Dahl, but later was dismayed by the sound of the orchestra, and offended the composer by telegraphing the suggestion that Stravinsky should allow the scoring to be "retouched" byRobert Russell Bennett, who "orchestrates even the works ofCole Porter".[110] Whole sections of the score had to be cut for the Philadelphia premiere, because the New Yorkpit musicians, accustomed to the conventions ofBroadway musicals of that period, were unable to manage the5
8
bars that feature in Stravinsky's score.[111]

A dozen years later, things were changing in musical theater in New York.Leonard Bernstein'sCandide opened on Broadway in December 1956, and featured a variety of meters that Billy Rose's musicians would have found as impossible as Stravinsky's. In act 1, the quartet "Universal Good" is a chorale in5
4
time, and the main verses of "Ballad of Eldorado" in act 2 are in5
8
, with turnarounds in7
8
or3
4
+7
8
.[112]Mary Rodgers's 1959Once Upon a Mattress featured the5
4
song "Sensitivity".[113] Later examples in musical theater include the song "Everything's Alright", fromJesus Christ Superstar (1971), byAndrew Lloyd Webber, which is mainly in5
4
,[114] and "Ladies in Their Sensitivities" fromStephen Sondheim'sSweeney Todd (1979), which is in5
8
.[115] Sondheim also alternates5
4
with4
4
(at the passage beginning "Living like a shut-in") and5
4
and6
4
(at "All I ever dreamed I'd be") in the song "In Buddy's Eyes' fromFollies (1971).[116]

Jazz

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In 1914, American ragtime composersJames Reese Europe andFord Dabney composed and recorded a dance tune in5
4
called "Castles' Half and Half", based on a dance created byVernon and Irene Castle (described as a "hesitation waltz"). Additional tunes in5
4
were also composed by others in 1914 to accompany the dance.[117][118][119]

In 1959, theDave Brubeck Quartet releasedTime Out, a jazz album with music in unusual meters. It includedPaul Desmond's "Take Five", in5
4
time.[120] Brubeck had studied with the French composerDarius Milhaud, who in turn had been strongly influenced by Stravinsky, and is credited with the systematic introduction of asymmetrical and shifting rhythms that sparked a far-reaching surge of interest in jazz and popular music in the 1960s.[121]

The 1960Max Roach albumWe Insist! contains three tracks making use of5
4
.[122]

Starting in 1964, the trumpeter and band leaderDon Ellis sought to fuse traditional big-band styles with rhythms borrowed from Indian and Near Eastern music; this was largely initiated by his UCLA ethnomusicology studies with Indian percussionist and sitar playerHarihar Rao and his contact with Turkish-American music producerArif Mardin.[123][124] For example, one of his largest works,Variations for Trumpet, is divided into six sections with meters including5
4
,9
4
,7
4
, and32
8
.[123] Two other Ellis compositions are entirely in5
4
time: "Indian Lady" and "5/4 Getaway".[125]

In 1966, the popular American television drama seriesMission: Impossible began a seven-season run with the5
4
"Theme from Mission: Impossible" byLalo Schifrin.[126] Schifrin said he wrote several compositions usingMorse code as the rhythmic basis. Morse code for the initials of Mission Impossible (M.I.) is "_ _ .."; if a dot is one beat and a dash is one and a half beats, then this gives a bar of five beats, exactly matching the underlying rhythm.[127]

In 1968,Leonard Feather interviewed pianistJohnny Guarnieri inDownBeat magazine;[128] Guarnieri had spent the last few years working up arrangements of jazz standards changed to a5
4
rhythm. Guarnieri stated "I can forsee 5/4, within the next few years, sweeping the world completely". Shortly afterwards, Guarnieri released an album on BET records calledBreakthrough in 5/4, which consisted of original compositions in5
4
, jazz standards changed to5
4
, as well as a version ofYesterday in5
4
.[129]

Rock

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In the late 1960s, quintuple meters began to appear with some frequency in rock-music contexts as well, where exploration of meters other than4
4
became one of the hallmarks ofprogressive rock. One of the earliest examples is "Grim Reaper of Love" byThe Turtles (May 1966).[130] Another early example is the instrumental that ends theGeorge Harrison song "Within You Without You" (from the 1967Beatles' LP "Sgt. Pepper's Lonely Hearts Club Band");[131] isolated5
4
bars also occur in the Beatles' songs "Happiness Is a Warm Gun" and "Across the Universe".[132][133] TheByrds' LPThe Notorious Byrd Brothers (recorded in the second half of 1967, and released in January 1968) contained two songs using quintuple meter, "Get to You" and "Tribal Gathering".[134]

Under the influence of Brubeck,Keith Emerson ofEmerson, Lake & Palmer began exploring unusual meters at about this same time. His first quintuple-meter piece was "Azrael, the Angel of Death", written in 1968, and the meter cropped up again three years later in the opening instrumental section, "Eruption", of thetitle track and some later passages from the albumTarkus.[135]

Frank Zappa frequently played in 5; two specific documented examples are "Flower Punk" from 1968 (a repeating pattern of 4 bars of 5 followed by 4 bars of 7)[136] and "Five Five Five" (bars of5
8
combined with bars of5
4
).[137] Zappa even had a hand signal with which he could cue the band to quickly switch into a quintuple meter at any time during a live performance.[138]

Examples in popular music

edit
TitleArtistYearNotes
"Aliens"Coldplay2017
"Azrael (Angel of Death)"The Nice1967written byKeith Emerson, released as a bonus track on the 1999 release ofThe Thoughts of Emerlist Davjack
"Bahlawan"Mira Awad20155
8
[139][140]
"Bane's theme" (fromThe Dark Knight Rises)Hans Zimmer[141]2012
"Black Widow Spider"Dr. John1969from the albumBabylon. Described as inspired by Dave Brubeck's "Take Five".[142]
"Caesar's Palace Blues"U.K.19795
4
; from the albumDanger Money.[143]
"Closure"Taylor Swift2020from the albumEvermore.[144]
"Countdown"Dave Brubeck[145]1962
"Dance of the Little Fairies"Sky1980[146]
"Do What You Like"Blind Faith19695
4
[145]
"Donkey Carol"John Rutter19765
8
; aChristmas carol.[147]
"English Roundabout"XTC[145]1982fromEnglish Settlement
"Face Dances, Pt. 2"Pete Townshend19825
4
[148]
"15 Step"Radiohead2007fromIn Rainbows[149]
"5/4"Gorillaz20015
4
[150]
"5-4=Unity"Pavement2001
"Morning Bell"Radiohead2000fromKid A
"Five"Lamb1999fromFear of Fours[151]
"Five Five Five"Frank Zappa1981bars of5
8
combined with bars of5
4
"From Eden"Hozier20145
4
[152]
"Get to You"The Byrds1968recorded late 1967, forThe Notorious Byrd Brothers
"Grim Reaper of Love"The Turtles1966
"Halloween Theme (main title)"John Carpenter[153]1978fromHalloween
"Happiness Is a Warm Gun"The Beatles1968written byJohn Lennon andPaul McCartney
"Here Come The Bastards"Primus199115
8
;[154] fromSailing the Seas of Cheese
"Icon"OHMME20185
4
[155]
"In Her Eyes"Josh Groban20065
4
;[156] from theAwake
"The Incredits"Michael Giacchino2004main theme forThe Incredibles5
4
[157]
"Isengard Theme" (fromThe Lord of the Rings film trilogy)Howard Shore2002[158]
"Kamisama no Shitauchi"Akeboshi20055
4
[159]
"Last Night"Vanessa Hudgens2008[160]
"Living in the Past"Jethro Tull19695
4
[161]
"River Man"Nick Drake19695
4
[162]
"Seven Days"Sting19933+2
4
[163]
"Soft Mistake"Lamb[151]1999fromFear of Fours
"Turn the World Around"Harry Belafonte19775
4
[164]
"Tribal Gathering"The Byrds1968recorded late 1967, forThe Notorious Byrd Brothers
"Wind"Akeboshi20025
4
[159]
"Within You Without You"The Beatles1967written byGeorge Harrison; recorded onSgt. Pepper's Lonely Hearts Club Band
"WTF?"OK Go20105
4
[165]

Partially in quintuple time

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Notes

edit
  1. ^Read 1964, 161 and 164–165.
  2. ^Read 1964, 152.
  3. ^West 1992, 304–307.
  4. ^Hornsby 1995.
  5. ^Pöhlmann and West 2001, 70–71 and 85.
  6. ^Salinas 1577, 251–253.
  7. ^Wright and Poché 2001, 2 (iv).
  8. ^Neubauer 2001.
  9. ^Sawa 2004, 164–166.
  10. ^Sawa 2004, 151–154;Neubauer 2001.
  11. ^Schuyler 2001.
  12. ^Reinhard and Stokes 2001.
  13. ^Dolidze, et al. 2001, III, 1 (ii).
  14. ^Powers 2001, (i).
  15. ^Powers 2001, (iii).
  16. ^Powers 2001, (iv).
  17. ^"Eotmori".Encyclopedia of Korean Folk Culture (in Korean). Retrieved3 April 2021.
  18. ^Condit 1978, 3 and 7;Lee 1981, 119 and 123.
  19. ^May and Wild 1967, 210, 216.
  20. ^Johnston 1989, 424, 431.
  21. ^Rice 1994, 73–74.
  22. ^Taruskin 1992a;Taruskin 1992b.
  23. ^Stęszewski 2001.
  24. ^Asplund 1985, 28.
  25. ^Heartz 1999, 144–146.
  26. ^Chianis and Brandl 2001.
  27. ^Peristeres 1956.
  28. ^Cunningham and Aiats 2001, 2(ii)(a).
  29. ^Little 2001.
  30. ^Engel 1876, 12.
  31. ^abcdefghiHiley 2001.
  32. ^Apel 1961, 401.
  33. ^Hiley 2001;Schmitt 1995.
  34. ^Hiley 2001;Pope and Knighton 2001
  35. ^Tye 1967, 39–42, transcribed in5
    4
    throughout by the editor, Robert W. Weidner. PaulDoe (1988, 105–107), transcribes the same piece in5
    4
    except for one passage of 40 beats, which he renders as ten bars of4
    4
    instead of eight bars of5
    4
    , on the grounds that "repeated notes in theCF permit a harmonic structure based on a normal duple metre" (Doe 1988, 150).
  36. ^Hudson 2001.
  37. ^Apel 1951, 216–219.
  38. ^Paxman 2014, 89.
  39. ^Manuscript copied byChristian Geist in theDüben collection ofUppsala University Library. Seedigital scan at website ofUppsala Universitet.
  40. ^Burney 1789, 4:364.
  41. ^Kirnberger & [1776] 1982, 383.
  42. ^Hansell and Steffan 2001;Hiley 2001.
  43. ^Taylor 1890, 3:61.
  44. ^Reicha 1973, 2:35–40.
  45. ^Helmore 1879, 15;Hiley 2001.
  46. ^Chopin 1976, 19–21.
  47. ^Taruskin 1992a;Glinka 1907, 262–264.
  48. ^Taruskin 1992b.
  49. ^Kroetsch 1996, 18.
  50. ^abRushton 1983, 128
  51. ^Borodin n.d., 32–76.
  52. ^Loewe & [ca. 1900].
  53. ^Taylor 1890.
  54. ^Godard 1880, pp. 13–19.
  55. ^Eddie 2007, 104;MacDonald 2001.
  56. ^Eddie 2007, 110.
  57. ^Wiehmayer 1917, 79.
  58. ^Brahms 1891, 1015.
  59. ^Berg 1955, 1.
  60. ^Tschaikowsky n.d., 58–87;Hiley 2001.
  61. ^Gutmann 2003.
  62. ^Rachmaninoff 2003.
  63. ^Holst 1979, 1–31, 162–187.
  64. ^Ross 2007.
  65. ^Hepokoski 2001.
  66. ^Richards 1987, 568.
  67. ^Young and Montagu 1975, 79.
  68. ^Mussorgsky 1914, 2–3, 7, 12, 18, 24–25.
  69. ^Prokofiev 1926, 8–9;Nice 2003, 50;first 24 bars.
  70. ^Brahms 1972, 134–137 of the score (= piano part).
  71. ^Debussy 1941, 74–83.
  72. ^Schmitt 1909.
  73. ^Martyn 1998, 7.
  74. ^Voicana, et al. 1971, 1:231.
  75. ^Bartók 1940, 2:13, 4:36–37, and 6:42–44.
  76. ^Ravel 1934.
  77. ^Chávez 1950, 2–7;García Morillo 1960, 90–92, 186
  78. ^Mawer 2000b, 144, 149.
  79. ^García Morillo 1960, 76;Chávez 1948, 8–10, 13, 20–22
  80. ^Ravel 1905, pp. 34–47.
  81. ^Mawer 2000a, 52–53;Ravel 1975
  82. ^Pierné 1908c, 62–63.
  83. ^Pierné 1908b;Pierné 1908c, 1–15
  84. ^Pierné 1908a, 7–25, specifically 15–18;Pierné 1908c, 48–61
  85. ^Masson 2001.
  86. ^Pierné 1919, 24–34, 38–47.
  87. ^Pierné 1919, 34–38.
  88. ^Pierné 1928, 12–20.
  89. ^White 1979, 311.
  90. ^White 1979, 212–213.
  91. ^Holst 1973, 13–14.
  92. ^Villa-Lobos 1947.
  93. ^Parker 2013, §11.
  94. ^Hindemith 1942, 4, 57.
  95. ^Hindemith 1942, 9–11.
  96. ^Hindemith 1942, 36–38.
  97. ^Piston 1942.
  98. ^Archibald 1992.
  99. ^Howard 1969, 108.
  100. ^Kroetsch 1996, 69–70.
  101. ^Woodward
  102. ^Holst 1973, 17–18, 22.
  103. ^Bernstein 1993, 12–16.
  104. ^Britten 1956, 1, 9, and 15.
  105. ^Bois 1979, 28–30 and 39–42.
  106. ^Potter 2000, 181.
  107. ^Reich 2002, 130.
  108. ^Reich 1979;Reich 1998
  109. ^Murphy 2016.
  110. ^White 1979, 420–21.
  111. ^Craft 2007, 6.
  112. ^Bernstein 1994, 40, 180–185.
  113. ^Rodgers, Mary 1967,[page needed].
  114. ^Lloyd Webber and Rice 1970, 12–17.
  115. ^Horowitz and Sondheim 2010, 141.
  116. ^Horowitz and Sondheim 2010, 206.
  117. ^Suwannakit 2014, 31.
  118. ^Sandke 2012.
  119. ^Saull 2014, 117.
  120. ^Kernfeld 2002, §1: Meter.
  121. ^Macan 1997, 47.
  122. ^Bowden 2018, 16.
  123. ^abDickow 2002.
  124. ^Fenlon 2002, 37.
  125. ^Fenlon 2002, 35, 87–88.
  126. ^Karger 1996.
  127. ^Schifrin, Lalo (2011).Music Composition for Film and Television. Berklee Press.
  128. ^Feather 1968.
  129. ^Anon. & n.d.(f).
  130. ^Anon. 2009b;Everett 2008, 308
  131. ^Fujita, Hagino, Kubo, and Sato 1993, 1037–1048;Macan 1997, 47–48.
  132. ^Fujita, Hagino, Kubo, and Sato 1993, 353–358.
  133. ^Fujita, Hagino, Kubo, and Sato 1993, 12–17.
  134. ^Menck 2007, 105, 119.
  135. ^Macan 1997, 48;Emerson, Lake, and Palmer 1980.
  136. ^Ulrich 2018, 604.
  137. ^Vai 1982.
  138. ^Butcher 2011, 131;Chevalier 1986, 15
  139. ^My TEDx talk, Mira Awad, 8 May 2014. "When I put 'Bahlawan' to music, I chose a very specific beat, the five eighths."
  140. ^Reply, Mira Awad's Facebook page, 22 March 2020. "the song is definitely in 5/8"
  141. ^Film Score Junkie 2013.
  142. ^Rebennack 1993.
  143. ^Stringer n.d.
  144. ^Shaffer 2020.
  145. ^abcKatzif 2008.
  146. ^Sliwa 2005.
  147. ^Rutter 1976.
  148. ^Townshend n.d.
  149. ^Fishko 2008.
  150. ^abAnon. & n.d.(b).
  151. ^abFuture Music 2016.
  152. ^Anon. 2016.
  153. ^Spencer 2008, 245.
  154. ^Primus 2000, 1:43–46.
  155. ^Thiessen, Christopher (2018-12-12)."The 10 Best Indie Rock Albums of 2018".Pop Matters. Retrieved2020-12-07.
  156. ^Ochs, Cohen, Selby, and Groban 2008.
  157. ^Michael 2007.
  158. ^Shore 2002.
  159. ^abKkunurashima 2006.
  160. ^Anon. 2008.
  161. ^Macan 1997, 48.
  162. ^Anon. & n.d.(d);Katzif 2008
  163. ^IrishDrummerGuy 2011.
  164. ^Belafonte & Freedman 1975.
  165. ^Kulash & Go 2010.
  166. ^"Undertale – 048 "Alphys"". Archived fromthe original on 2018-04-01.
  167. ^Anon. & n.d.(c).
  168. ^Heisel 2014.
  169. ^Holmes 2016.
  170. ^Banks, Collins, and Rutherford 1978.
  171. ^"fallen shepherd ft. RabbiTon Strings (ARM, IOSYS) - ENDYMION".
  172. ^Anon. 2009a.
  173. ^"Vs. Ridley - Super Metroid (arranged by Nate Alberda)".Musescore. 24 September 2022.
  174. ^Cohen 2009.
  175. ^Led Zeppelin 1973, 118–23.
  176. ^"Five Magics".SheetMusicPlus.
  177. ^"The first riff in5
    4
    is driving, but it's almost like a straight4
    4
    line to me" (Shiraki and Bradman 2001, 6).
  178. ^"The Hammer".Musicnotes. 9 January 2013.
  179. ^Townshend 1966.
  180. ^Anon. 2007–2015.
  181. ^Riccio 2004.
  182. ^Browne 2001.
  183. ^Dibben 2011.
  184. ^Waters 1999.
  185. ^Drozdowski 2011.
  186. ^Thompson 2018.
  187. ^Picton, Cameron."953". Retrieved9 November 2021.
  188. ^Harris 1982.
  189. ^Lilholt n.d.
  190. ^"stereolab | **Stereolab alternative titles:**".www.facebook.com. Retrieved2023-05-19.
  191. ^Beyoncé, Blake, and Garrett 2016.
  192. ^Mills 2014.
  193. ^Anon. & n.d.(e).
  194. ^"I think "Red" [from the Crimson LP of the same name] was a beautiful piece of Heavy metal—in 5 [the unusual time signature5
    8
    ]. I mean, I hadn't heard heavy metal in 5 before, but for me that was it."(Fripp and Mandl 1991,[page needed]).
  195. ^Musescore."The River - King Gizzard and the Lizard Wizard".Musescore.com. Retrieved2021-07-13.
  196. ^Pickard, Joshua (2 September 2022)."Turning 25: Musicians discuss some of their favorite records from 1997".Beats Per Minute. Retrieved28 April 2023.
  197. ^Bennett 2008, 105.
  198. ^Yes 1981,[page needed].
  199. ^Anon. & n.d.(a).
  200. ^Tiemann 2014.
  201. ^NatuMz n.d.
  202. ^Reuland 2011, 61, 66.

Sources

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Further reading

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  • Arlin, Mary I. 2000. "Metric Mutation and Modulation: The Nineteenth-Century Speculations of F.-J. Fétis".Journal of Music Theory 44, no. 2 (Autumn): 261–322.
  • Barber, Samuel. 1943.String Quartet, Op. 11. G. Schirmer's Edition of Study Scores of Orchestral Works and Chamber Music 28. New York: G. Schirmer.
  • Bartók, Béla. 1942.Sonata for Two Pianos and Percussion. London: Hawkes & Son (Ltd.).
  • Britten, Benjamin. 1946.Quartet No. 2 in C, Op. 36. London: Boosey & Hawkes.
  • Buchanan, Donna A. 2001. "Bulgaria: II. Traditional Music".The New Grove Dictionary of Music and Musicians, second edition, edited byStanley Sadie andJohn Tyrrell. London: Macmillan Publishers.
  • Cronshaw, Andrew. 1990. "Trikitixa!".Folk Roots 11, no. 10:82 (April): 28–29, 31.
  • Flashkirby. 2015. "Wild Woods (Mario Kart 8 Transcription)", uploaded 10 May. Musescore.com (accessed 5 April 2019).
  • Frampton, John Ross. 1926. "Some Evidence for the Naturalness of the Less Usual Rhythms".The Musical Quarterly 12, no. 3 (July): 400–405.
  • Howes, Frank. 1945. "Anthropology and Music".Man 45 (September–October): 107–108.
  • Laborde, Denis. 2001. "Basque Music".The New Grove Dictionary of Music and Musicians, second edition, edited byStanley Sadie andJohn Tyrrell. London: Macmillan Publishers.
  • Mathis-Lilley, Ben. 2006. "Secrets of the Radiohead Set List".New York 39, no. 23 (26 June): 88–89 (accessed 23 March 2008).
  • Nettl, Bruno. 1953. "Stylistic Variety in North American Indian Music".Journal of the American Musicological Society 6, no. 2 (Summer): 160–168.
  • Nettl, Bruno. 1965. "The Songs of Ishi: Musical Style of the Yahi Indians".The Musical Quarterly 51, no. 3 (July): 460–477.
  • Miner, Ansorena, and José Ignacio. 1993. "El zortziko: La frase de ocho compases y el compás de cinco por ocho".Txistulari, no. 155 (July–September).
  • Sánchez Ekiza, Carlos. 1991a. "En torno al zortziko".Txistulari, no. 146 (July): 44–53.
  • Sánchez Ekiza, Carlos. 1991b. "En torno al zortziko".Cuadernos de etnología y etnografía de Navarra 23, no. 57 (January–June): 89–103.

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