Inmusic,across-beatorcross-rhythmis a specific form ofpolyrhythm.The termcross rhythmwas introduced in 1934 by themusicologistArthur Morris Jones(1889–1980). It refers to a situation where the rhythmic conflict found in polyrhythms is the basis of an entire musical piece.[1]
Etymology
editThe term "cross rhythm" was introduced in 1934 by themusicologistArthur Morris Jones(1889–1980), who, withKlaus Wachsmann,took-up extended residence inZambiaandUganda,respectively, asmissionaries,educators,musicologists,andmuseologists.
Cross-rhythm.A rhythm in which the regular pattern of accents of the prevailing meter is contradicted by a conflicting pattern and not merely a momentary displacement that leaves the prevailing meter fundamentally unchallenged.
— The New Harvard Dictionary of Music(1986: 216)[2]
African music
editOne main system
editAfrican cross-rhythm is most prevalent within the greater Niger-Congo linguistic group, which dominates the continent south of the Sahara Desert. (Kubik, p. 58)[3]Cross-rhythm was first identified as the basis of sub-Saharan rhythm by A.M. Jones. Later, the concept was more fully explained in the lectures ofEwemaster drummer and scholar C.K. Ladzekpo, and in the writings of David Locke.[4]Jones observes that the shared rhythmic principles of Sub-Saharan African music traditions constituteone main system.[5]Similarly, Ladzekpo affirms theprofound homogeneityof sub-Saharan African rhythmic principles.[6]InSub-Saharan African music traditions(and many of thediasporamusics) cross-rhythm is the generating principle; the meter is in a permanent state of contradiction.
An embodiment of the people
editAt the center of a core of rhythmic traditions and composition is the technique of cross-rhythm. The technique of cross-rhythm is a simultaneous use of contrasting rhythmic patterns within the same scheme of accents or meter... By the very nature of the desired resultant rhythm, the main beat scheme cannot be separated from the secondary beat scheme. It is the interplay of the two elements that produces the cross-rhythmic texture.
— Ladzekpo, a: "Myth"[6]
From the philosophical perspective of the African musician, cross-beats can symbolize the challenging moments or emotional stress we all encounter. Playing cross-beats while fully grounded in the main beats, prepares one for maintaining a life-purpose while dealing with life’s challenges. Many sub-Saharan languages do not have a word forrhythm,or evenmusic.From the African viewpoint, the rhythms represent the very fabric of life itself; they are an embodiment of the people, symbolizing interdependence in human relationships.
— Clave Matrix,p. 21[7]
Cross-rhythmic ratios
edit3:2
editThe cross-rhythmicratiothree-over-two(3:2) or verticalhemiola,is the most significant rhythmiccellfound in sub-Saharan rhythms. The following measure is evenly divided by three beats and two beats. The twocyclesdo not share equal status though. The two bottom notes are the primary beats, the ground, the main temporal referent. The three notes above are the secondary beats. Typically, the dancer's feet mark the primary beats, while the secondary beats are accented musically.
Watch: Stepping to the main beats within 3:2 cross-rhythm. Afro-Cuban "Obatalá Dance" (Marta Ruiz)onYouTube
We have to grasp the fact that if from childhood you are brought up to regard beating 3 against 2 as being just as normal as beating in synchrony, then you develop a two dimensional attitude to rhythm... This bi-podal conception is... part of the African's nature
— Jones (1959: 102)[5]
Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics."[8]3:2 is thegenerativeortheoretic formof sub-Saharan rhythmic principles.Agawusuccinctly states: "[The] resultant [3:2] rhythm holds the key to understanding... there is no independence here, because 2 and 3 belong to a single Gestalt."[9]
AfricanXylophonessuch as thebalafonandgyilplay cross-rhythms, which are often the basis ofostinatomelodies. In the following example, a Ghanaiangyilsounds the three-against-two cross-rhythm. The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats.(Clave Matrixp. 22)[7]
6:4
editThe primary cycle of four beats
A great deal of African music is built upon acycleof four main beats. This basicmusical periodhas a bipartite structure; it is made up of twocells,consisting of two beats each. Ladzekpo states: "The first most useful measure scheme consists of four main beats with each main beat measuring off three equal pulsations [12
8] as its distinctive feature... The next most useful measure scheme consists of four main beats with each main beat flavored by measuring off four equal pulsations [4
4]. "(b:" Main Beat Schemes ")[6]The four-beat cycle is a shorter period than what is normally heard in European music. This accounts for the stereotype of African music as "repetitive." (Kubik, p. 41)[3]A cycle of only two main beats, as in the case of 3:2, does not constitute a complete primary cycle. (Kubik, Vol. 2, p. 63)[3]Within the primary cycle there are two cells of 3:2, or, a single cycle of six-against-four (6:4). The six cross-beats are represented below as quarter-notes for visual emphasis.
Interacting the four recurrent triple structure main beat schemes (four beat scheme) simultaneously with the six recurrent two pulse beat schemes (six beat scheme) produces the first most useful cross rhythmic texture in the development ofAnlo-Ewedance-drumming.
— Ladzekpo (c: "Six Against Four" )[6]
The following notated example is from thekushaurapart of the traditional mbira piece "Nhema Mussasa." The left hand plays theostinato"bass line," built upon the four main beats, while the right hand plays the upper melody, consisting of six cross-beats. The composite melody is an embellishment of the 6:4 cross-rhythm.(Clave Matrixp. 35)[7]
3:4
editIf every other cross-beat is sounded, the three-against-four (3:4) cross-rhythm is generated. The "slow" cycle of three beats is more metrically destabilizing and dynamic than the six beats. The Afro-Cuban rhythmabakuá(Havana-style) is based on the 3:4 cross-rhythm.[10]The three-beat cycle is represented as half-notes in the following example for visual emphasis.
In contrast to the four main beat scheme, the rhythmic motion of the three beat scheme is slower. A simultaneous interaction of these two beat schemes with contrasting rhythmic motions produces the next most useful cross rhythmic texture in the development of sub-Saharan dance-drumming. The composite texture of the three-against-four cross rhythm produces a motif covering a length of themusical period.The motif begins with the component beat schemes coinciding and continues with the beat schemes in alternate motions thus showing a progression from a "static" beginning to a "dynamic" continuation
— Ladzekpo ( "Three Against Four" )[6]
The following pattern is an embellishment of the three-beat cycle, commonly heard in African music. It consists of three sets of three strokes each.
1.5:4 (or 3:8)
editEven more metrically destabilizing and dynamic than 3:4, is theone and a half beat-against-four(1.5:4) cross-rhythm. Another way to think of it is as three "very slow" cross-beats spanning two main beatcycles(of four beats each), or three beats over twoperiods(measures), a type of macro "hemiola."In terms of the beat scheme comprising the complete 24-pulse cross-rhythm, theratiois 3:8. The three cross-beats are shown as whole notes below for visual emphasis.
The 1.5:4 cross-rhythm is the basis for the open tone pattern of the enú (largebatádrum head) for theAfro-Cubanrhythm changó (Shango).[a]It is the same pattern as the previous figure, but the strokes occur at half the rate.
The followingbell patternis used in theEwerhythm kadodo.[11]The pattern consists of three modules—two pairs of strokes, and a single stroke. The three single stroke are muted. The pattern is another embellishment of the 1.5:4 cross-rhythm.
4:3
editWhen duple pulses (4
4) are grouped in sets of three, the four-against-three (4:3) cross-rhythm is generated. The four cross-beats cycle every three main beats. In terms of cross-rhythm only, this is the same as having duple cross-beats in a triple beat scheme, such as3
4or6
4.The pulses on the top line are grouped in threes for visual emphasis.
However, this 4:3 is within a duple beat scheme, with duple (quadruple) subdivisions of the beats. Since themusical periodis acycleof four main beats, the 4:3 cross-rhythm significantly contradicts the period by cycling every three main beats. The complete cross-beat cycle is shown below in relation to thekey patternknown in Afro-Cuban music asclave.(Rumba,p. xxxi)[12]The subdivisions are grouped (beamed) in sets of four to reflect the proper metric structure. The complete cross-beat cycle is three claves in length. Within the context of the complete cross-rhythm, there is a macro 4:3—four4:3 modules-against-threeclaves.Continuous duple-pulse cross-beats are often sounded by thequinto,the lead drum in the Cuban genresrumbaandconga.(Rumba,pps. 69–86)[12][b][c]
While 3:2 pervades ternary music, quaternary music seldom uses tuplets; instead, a set of dotted notes may temporarily make 2:3 and 4:3 temporal structures.
— Locke ( "Metric Matric" )[13]
Duple-pulse correlative of 3:2
editIn sub-Saharan rhythm the four main beats are typically divided into three or four pulses, creating a 12-pulse (12
8), or 16-pulse (4
4)cycle.(Ladzekpo, b: "Main Beat Scheme" )[6]Every triple-pulse pattern has its duple-pulse correlative; the two pulse structures are two sides of the same coin. Cross-beats are generated by grouping pulses contrary to their given structure, for example: groups of two or four in12
8or groups of three or six in4
4.(Rumba,p. 180)[12]The duple-pulse correlative of the three cross-beats of thehemiola,is a figure known in Afro-Cuban music astresillo.Tresillo is aSpanishword meaning ‘triplet’—three equal notes within the same time span normally occupied by two notes. As used in Cuban popular music, tresillo refers to the most basic duple-pulse rhythmiccell.[14]The pulse names of tresillo and the three cross-beats of the hemiola are identical: one, one-ah, two-and.
The composite pattern of tresillo and the main beats is commonly known as thehabanera,[15]congo,[16]tango-congo,[17]ortango.[18]The habanera rhythm is the duple-pulse correlative of the verticalhemiola(above). The three cross-beats of the hemiola are generated by grouping triple pulses in twos: 6 pulses ÷ 2 = 3 cross-beats. Tresillo is generated by grouping duple pulses in threes: 8 pulses ÷ 3 = 2 cross-beats (consisting of three pulses each), with a remainder of a partial cross-beat (spanning two pulses). In other words, 8 ÷ 3 = 2, r2. Tresillo is a cross-rhythmic fragment. It contains the first three cross-beats of 4:3.(Rumba,p. xxx)[12]
Tresilloover two Video
Cross-rhythm, not polymeter
editEarly ethnomusicological analysis often perceived African music aspolymetric.Pioneers such asA.M. Jonesand Anthony King identified the prevailing rhythmic emphasis as metrical accents (main beats), instead of the contrametrical accents (cross-beats) they in fact are. Some of their music examples are polymetric, with multiple and conflicting main beat cycles, each requiring its own separate time signature. King shows twoYorubadundun pressure drum ( "talking drum") phrases in relation to the five-strokestandard pattern,or "clave,"played on the kagano dundun (top line).[19]The standard pattern is written in a polymetric7
8+5
8time signature. One dundun phrase is based on a grouping of three pulses written in3
8,and the other, a grouping of four pulses written in4
8.Complicating the transcription further, one polymetric measure is offset from the other two.
African music is often characterized as polymetric, because, in contrast to most Western music, African music cannot be notated without assigning different meters to the different instruments of an ensemble
— Chernoff (1979: 45).[20]
More recent writings represent African music as cross-rhythmic, within a single meter.
Of the many reasons why the notion of polymeter must be rejected, I will mention three. First, if polymeter were a genuine feature of African music, we would expect to find some indication of its pertinence in the discourses and pedagogical schemes of African musicians, carriers of the tradition. As far as I know, no such data is available...Second, because practically all the ensemble music in which polymeter is said to be operative in dance music, and given the grounding demanded by choreography, it is more likely that these musics unfold within polyrhythmic matrices in single meters rather than in... "mixed" meters... Third, decisions about how to represent drum ensemble music founder on the assumption, made most dramatically by Jones, that accents are metrical rather than phenomenal...phenomenal accents play a more important role in African music than metrical accents. Because meter and grouping are distinct, postulating a single meter in accordance with the dance allows phenomenal or contrametric accents to emerge against a steady background. Polymeter fails to convey the true accentual structure of African music insofar as it creates the essential tension between a firm and stable background and a fluid foreground
— Agawu (2003: 84, 85).[21]
[The] term ‘polymetric’ is only applicable to a very special kind of phenomenon. If we take "metre" in its primary sense of metrum (the metre being the temporal reference unit), ‘polymetric’ would describe the simultaneous unfolding of several parts in a single work at different tempos so as not to be reducible to a single metrum. This happens in some modern music, such as some ofCharles Ives' works,Elliott Carter’s Symphony,B.A. Zimmermann’s opera "Die Soldaten," andPierre Boulez’s "Rituel." Being polymetric in the strict sense, these works can only be performed with several simultaneous conductors
— Arom (1991: 205).[22]
When written within a single meter, we see that the dundun in the second line sounds the main beats, and the subdivision immediately preceding it. The firstcell(halfmeasure) of the top line is ahemiola.The two dunduns shown in the second and third lines sound an embellishment of the three-over-four (3:4) cross-rhythm—expressed as three pairs of strokes against four pairs of strokes.(Clave Matrixp. 216)[7]
Adaptive instruments
editSub-Saharan instruments are constructed in a variety of ways to generate cross-rhythmic melodies. Some instruments organize the pitches in a uniquely divided alternate array – not in the straight linearbasstotreblestructure that is so common to many western instruments such as thepiano,harp,andmarimba.
Lamellophonesincludingmbira,mbila, mbira huru, mbira njari, mbira nyunga, marimba, karimba,kalimba,likembe, and okeme. These instruments are found in several forms indigenous to different regions of Africa and most often have equal tonal ranges for right and left hands. Thekalimbais a modern version of these instruments originated by the pioneer ethnomusicologistHugh Traceyin the early 20th century which has over the years gained world-wide popularity.
Chordophones,such as the West Africankora,and Doussn'gouni, part of theharp-lutefamily of instruments, also have this African separated double tonal array structure. Another instrument, theMarovanyfrom Madagascar is a double sided box zither which also employs this divided tonal structure. TheGravikordis a new American instrument closely related to both the African kora and the kalimba. It was created to exploit this adaptive principle in a modern electro-acoustic instrument.[23]
On these instruments one hand of the musician is not primarily in the bass nor the other primarily in the treble, but both hands can play freely across the entire tonal range of the instrument. Also the fingers of each hand can play separate independent rhythmic patterns and these can easily cross over each other from treble to bass and back, either smoothly or with varying amounts ofsyncopation.This can all be done within the same tight tonal range, without the left and right hand fingers ever physically encountering each other. These simple rhythms will interact musically to produce complex cross rhythms including repeating on beat/off beatpattern shifts that would be very difficult to create by any other means. This characteristically African structure allows often simple playing techniques to combine with each other and produce cross-rhythmic music of great beauty and complexity.
Jazz
editThe New Harvard Dictionary of Musiccallsswing"an intangible rhythmic momentum in jazz," adding that "swing defies analysis; claims to its presence may inspire arguments." The only specific description offered is the statement that "triplet subdivisions contrast with duple subdivisions."[24]The argument could be made that by nature of its simultaneous triple and duple subdivisions, swing is fundamentally a form of polyrhythm. However, the use of true systematic cross-rhythm injazzdid not occur until the second half of the twentieth century.
3:2 (or 6:4)
editIn 1959Mongo Santamariarecorded "Afro Blue,"the first jazz standard built upon a typical African 3:2 cross-rhythm.[d]The song begins with the bass repeatedly playing 3 cross-beats per each measure of6
8(3:2), or 6 cross-beats per12
8measure (6:4). The following example shows the originalostinato"Afro Blue" bass line. The slashed noteheads are not bass notes, but are shown to indicate the mainbeats,where you would normally tap your foot to "keep time."
3:4
editOn the original "Afro Blue," drummerWillie Boboplayed anabakuábell patternon a snare drum, using brushes. This cross-rhythmic figure divides the twelve-pulse cycle into three sets of four pulses. Since the main beats (four sets of three pulses) are present whether sounded or not, this bell pattern can be considered an embellishment of the three-against-four (3:4) cross-rhythm. Bobo used this same pattern and instrumentation on theHerbie Hancockjazz-descarga "Succotash."[e]
2:3
editIn 1963John Coltranerecorded "Afro Blue"with the jazz drummerElvin Jones.[f]Jones inverted the metric hierarchy of Santamaria's composition, performing it instead as duple cross-beats over a3
4"jazz waltz" (2:3). This 2:3 in a swung3
4is perhaps the most common example of overt cross-rhythm in jazz.[g]
Duple-pulse correlative of 3:2
editTheWayne Shortercomposition "Footprints"may have been the first overt expression of the 6:4 cross-rhythm (two cycles of 3:2) used by a straight ahead jazz group.[h]On the version recorded onMiles SmilesbyMiles Davis,the bass switches to4
4at 2:20. The4
4figure is known astresilloin Latin music and is the duple-pulse correlative of the cross-beats in triple-pulse. Throughout the piece, the four main beats are maintained. In the example below, the main beats are indicated by slashed noteheads. They are shown here for reference and do not indicate bass notes.
In recent decades, jazz has incorporated many different types of complex cross-rhythms, as well as other types of polyrhythms.
See also
editReferences
editAudio-visual samples and references to recordings
- ^"Changó," Ilu Aña and Regino Jiménez
- ^"Cantar Maravilloso" ( "Wonderful Song" ) (at 2:24),Los Muñequitos de Matanzas(originally known as Grupo Guaguancó Matancero)
- Album:GuaguancóVol. 2, Grupo Guaguancó Matancero, Antilla MLP 595 (1958)
- Original release: Puchito SP 103 (LP)
- ^"Los Beodos" ( "The Drunk" ) (side A, 2nd track, at 2:11),Los Muñequitos de Matanzas(originally known as Grupo Guaguancó Matancero)
- ^"Afro Blue,"Mongo Santamaria
- ^"Succotash,"Herbie Hancock
- Album:Inventions and DimensionsBlue NoteCD 84147-2 (1963)
- OCLC20227090,874388051
- Recorded at theVan Gelder Studio,Englewood Cliffs, New Jersey,August 30, 1963
- Herbie Hancock(piano),Paul Chambers(bass),Willie Bobo(drums,timbales), Osvaldo "Chihuahua" Martinez (conga, bongo)
- ^"Afro Blue",YouTube,John Coltrane Quartet
- Album:Afro Blue Impressions
- Pablo-Live(G)PL2620-101 (1977)
- OCLC173207839
- Live, Auditorium Maximum,Free University of Berlin,November 2, 1963
- John Coltrane(soprano & tenor sax),McCoy Tyner(piano),Jimmy Garrison(bass),Elvin Jones(drums)ArchivedFebruary 17, 2007, at theWayback Machine
- ^"Jazz Drumming in3
4"(part 2), by Conor Guilfoyle,YouTube- Guilfoyle demonstrates 2:3 cross-rhythm in3
4swing.
- Guilfoyle demonstrates 2:3 cross-rhythm in3
- ^"Footprints,"Miles Davis Quintet
- Album:Miles Smiles,ColumbiaCS 9401; CD (1967)
- OCLC872563570,41265755,872667474
- Recorded 1966 October 24–25, 1966,Columbia 30th Street Studio,New York City
- Miles Davis(trumpet),Wayne Shorter(tenor sax),Herbie Hancock(piano),Ron Carter(bass),Tony Williams(drums)
Inline citations
- ^New Harvard Dictionary of Music(1986: 216). Cambridge, MA: Harvard University Press.
- ^The New Harvard Dictionary of Music,Don Michael Randel(ed.),Belknap Press,Harvard University Press(1986), pg. 216;OCLC13333674
- ^abcKubik, Gerhard(1999). Africa and the Blues.Jackson, Mississippi:University Press of Mississippi;OCLC44959610
- ^Locke, David Laurence (1982). "Principles of Off-Beat Timing and Cross-Rhythm in Southern Ewe Dance Drumming,"Ethnomusicology,Society for Ethnomusicology,November 11;ISSN0014-1836
- ^abJones, A.M.(1959).Studies in African Music(vol. 1 of 2). London:Oxford University Press.1978 edition, pg. 102;ISBN0-19-713512-9;OCLC611586.
- ^abcdefLadzekpo, C.K. (1995).
- a: "The Myth of Cross-Rhythm"
- b: "Main Beat Schemes"
- c: "Six Against Four Cross-Rhythm"
- d: "Three Against Four Cross-Rhythm"
- ^abcdPeñalosa, David (2009).The Clave Matrix, Afro-Cuban Rhythm: Its Principles and African Origins.Redway, California:Bembe Inc., pps. 21, 22, 35, 216;ISBN1-886502-80-3;OCLC466422227
- ^Novotney, Eugene D. (1998).The Three Against Two Relationship as the Foundation of Timelines in West African MusicsUrbana, IL: University of Illinois. UnlockingClave.com.
- ^Agawu, Kofi (2003: 92).Representing African Music: Postcolonial Notes, Queries, Positions New York: Routledge.ISBN0-415-94390-6.
- ^Coburg, Adrian (2004). "6
8toque de la rama efí, "Percusion Afro-Cubana(vol. 1 of 2:Muisca Folklorico)Bern: Coburg Percussion Publishing, p. 1;OCLC823726876 - ^"Kadodo,"Ritual Music of the Yeve,(Ladzekpo brothers). Makossa phonorecord 86011 (1982).
- ^abcdPeñalosa, David (2010).Rumba Quinto,Redway, California:Bembe Books;ISBN1-4537-1313-1;OCLC806336780
- ^Locke, David Laurence (2011)."The Metric Matrix: Simultaneous Multidimensionality in African Music,"Analytical Approaches To World Music,Vol. 1, No. 1 (p. 56; out of pps. 48–72);ISSN2158-5296
- ^Mauleón, Rebeca (1993: 51).Salsa Guidebook for Piano and Ensemble.Petaluma, California: Sher Music.ISBN0-9614701-9-4.
- ^Roberts, John Storm (1979: 6).The Latin tinge: the impact of Latin American music on the United States.Oxford.
- ^Manuel, Peter (2009: 69).Creolizing Contradance in the Caribbean.Philadelphia: Temple University Press.
- ^Acosta, Leonardo (2003: 5).Cubano Be Cubano Bop; One Hundred Years of Jazz in Cuba.Washington D.C.: Smithsonian Books.
- ^Mauleón (1999: 4)Salsa Guidebook for Piano and Ensemble.Petaluma, California: Sher Music.ISBN0-9614701-9-4.
- ^King, Anthony (1961).Yoruba Sacred Music from Ekitip. 15. Ibadan: University Press.
- ^Chernoff, John Miller (1979).African Rhythms and Sensibilitiesp. 45. Chicago: University Press.
- ^Agawu, Kofi (2003).Representing African Music: Postcolonial Notes, Queries, Positions.New York: Routledge.
- ^Arom, Sinmha (1991).African Polyphony and Polyrhythm: Musical Structure and Methodologyp. 205. Cambridge University Press.
- ^"The 'Gravikord,'"(www
.gravikord .com /instrument .html #gravikord) - ^The New Harvard Dictionary of Music(1986: 818). Cambridge, MA: Harvard University Press.