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This article is about music. Cross-beat_sentence_0

For the use in horology, see Cross-beat escapement. Cross-beat_sentence_1

For cross-beat tonguing, see Tonguing. Cross-beat_sentence_2

"Cross-rhythm" redirects here. Cross-beat_sentence_3

For the Christian media organization, see Cross Rhythms Cross-beat_sentence_4

In music, a cross-beat or cross-rhythm is a specific form of polyrhythm. Cross-beat_sentence_5

The term cross rhythm was introduced in 1934 by the musicologist Arthur Morris Jones (1889–1980). Cross-beat_sentence_6

It refers to when the rhythmic conflict found in polyrhythms is the basis of an entire musical piece. Cross-beat_sentence_7

Etymology Cross-beat_section_0

The term "cross rhythm" was introduced in 1934 by the musicologist Arthur Morris Jones (1889–1980), who, with Klaus Wachsmann, took-up extended residence in Zambia and Uganda, respectively, as missionaries, educators, musicologists, and museologists. Cross-beat_sentence_8

African music Cross-beat_section_1

One main system Cross-beat_section_2

African cross-rhythm is most prevalent within the greater Niger-Congo linguistic group, which dominates the continent south of the Sahara Desert. Cross-beat_sentence_9

(Kubik, p. 58) Cross-rhythm was first identified as the basis of sub-Saharan rhythm by A.M. Jones. Cross-beat_sentence_10

Later, the concept was more fully explained in the lectures of Ewe master drummer and scholar C.K. Cross-beat_sentence_11

Ladzekpo, and in the writings of David Locke. Cross-beat_sentence_12

Jones observes that the shared rhythmic principles of Sub-Saharan African music traditions constitute one main system. Cross-beat_sentence_13

Similarly, Ladzekpo affirms the profound homogeneity of sub-Saharan African rhythmic principles. Cross-beat_sentence_14

In Sub-Saharan African music traditions (and many of the diaspora musics) cross-rhythm is the generating principle; the meter is in a permanent state of contradiction. Cross-beat_sentence_15

An embodiment of the people Cross-beat_section_3

Cross-rhythmic ratios Cross-beat_section_4

3:2 Cross-beat_section_5

The cross-rhythmic ratio three-over-two (3:2) or vertical hemiola, is the most significant rhythmic cell found in sub-Saharan rhythms. Cross-beat_sentence_16

The following measure is evenly divided by three beats and two beats. Cross-beat_sentence_17

The two cycles do not share equal status though. Cross-beat_sentence_18

The two bottom notes are the primary beats, the ground, the main temporal referent. Cross-beat_sentence_19

The three notes above are the secondary beats. Cross-beat_sentence_20

Typically, the dancer's feet mark the primary beats, while the secondary beats are accented musically. Cross-beat_sentence_21

on YouTube Cross-beat_sentence_22

Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." Cross-beat_sentence_23

3:2 is the generative or theoretic form of sub-Saharan rhythmic principles. Cross-beat_sentence_24

Agawu succinctly 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." Cross-beat_sentence_25

African Xylophones such as the balafon and gyil play cross-rhythms, which are often the basis of ostinato melodies. Cross-beat_sentence_26

In the following example, a Ghanaian gyil sounds the three-against-two cross-rhythm. Cross-beat_sentence_27

The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats. Cross-beat_sentence_28

(Clave Matrix p. 22) Cross-beat_sentence_29

6:4 Cross-beat_section_6

The primary cycle of four beats Cross-beat_sentence_30

A great deal of African music is built upon a cycle of four main beats. Cross-beat_sentence_31

This basic musical period has a bipartite structure; it is made up of two cells, consisting of two beats each. Cross-beat_sentence_32

Ladzekpo states: "The first most useful measure scheme consists of four main beats with each main beat measuring off three equal pulsations [ 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]." Cross-beat_sentence_33

(b: "Main Beat Schemes") The four-beat cycle is a shorter period than what is normally heard in European music. Cross-beat_sentence_34

This accounts for the stereotype of African music as "repetitive." Cross-beat_sentence_35

(Kubik, p. 41) A cycle of only two main beats, as in the case of 3:2, does not constitute a complete primary cycle. Cross-beat_sentence_36

(Kubik, Vol. 2, p. 63) Within the primary cycle there are two cells of 3:2, or, a single cycle of six-against-four (6:4). Cross-beat_sentence_37

The six cross-beats are represented below as quarter-notes for visual emphasis. Cross-beat_sentence_38

The following notated example is from the kushaura part of the traditional mbira piece "Nhema Mussasa." Cross-beat_sentence_39

The left hand plays the ostinato "bass line," built upon the four main beats, while the right hand plays the upper melody, consisting of six cross-beats. Cross-beat_sentence_40

The composite melody is an embellishment of the 6:4 cross-rhythm. Cross-beat_sentence_41

(Clave Matrix p. 35) Cross-beat_sentence_42

3:4 Cross-beat_section_7

If every other cross-beat is sounded, the three-against-four (3:4) cross-rhythm is generated. Cross-beat_sentence_43

The "slow" cycle of three beats is more metrically destabilizing and dynamic than the six beats. Cross-beat_sentence_44

The Afro-Cuban rhythm abakuá (Havana-style) is based on the 3:4 cross-rhythm. Cross-beat_sentence_45

The three-beat cycle is represented as half-notes in the following example for visual emphasis. Cross-beat_sentence_46

The following pattern is an embellishment of the three-beat cycle, commonly heard in African music. Cross-beat_sentence_47

It consists of three sets of three strokes each. Cross-beat_sentence_48

1.5:4 (or 3:8) Cross-beat_section_8

Even more metrically destabilizing and dynamic than 3:4, is the one and a half beat-against-four (1.5:4) cross-rhythm. Cross-beat_sentence_49

Another way to think of it is as three "very slow" cross-beats spanning two main beat cycles (of four beats each), or three beats over two periods (measures), a type of macro "hemiola." Cross-beat_sentence_50

In terms of the beat scheme comprising the complete 24-pulse cross-rhythm, the ratio is 3:8. Cross-beat_sentence_51

The three cross-beats are shown as whole notes below for visual emphasis. Cross-beat_sentence_52

The 1.5:4 cross-rhythm is the basis for the open tone pattern of the enú (large batá drum head) for the Afro-Cuban rhythm changó (Shango). Cross-beat_sentence_53

It is the same pattern as the previous figure, but the strokes occur at half the rate. Cross-beat_sentence_54

The following bell pattern is used in the Ewe rhythm kadodo. Cross-beat_sentence_55

The pattern consists of three modules—two pairs of strokes, and a single stroke. Cross-beat_sentence_56

The three single stroke are muted. Cross-beat_sentence_57

The pattern is another embellishment of the 1.5:4 cross-rhythm. Cross-beat_sentence_58

4:3 Cross-beat_section_9

When duple pulses ( 4) are grouped in sets of three, the four-against-three (4:3) cross-rhythm is generated. Cross-beat_sentence_59

The four cross-beats cycle every three main beats. Cross-beat_sentence_60

In terms of cross-rhythm only, this is the same as having duple cross-beats in a triple beat scheme, such as 4 or 4. Cross-beat_sentence_61

The pulses on the top line are grouped in threes for visual emphasis. Cross-beat_sentence_62

However, this 4:3 is within a duple beat scheme, with duple (quadruple) subdivisions of the beats. Cross-beat_sentence_63

Since the musical period is a cycle of four main beats, the 4:3 cross-rhythm significantly contradicts the period by cycling every three main beats. Cross-beat_sentence_64

The complete cross-beat cycle is shown below in relation to the key pattern known in Afro-Cuban music as clave. Cross-beat_sentence_65

(Rumba, p. xxxi) The subdivisions are grouped (beamed) in sets of four to reflect the proper metric structure. Cross-beat_sentence_66

The complete cross-beat cycle is three claves in length. Cross-beat_sentence_67

Within the context of the complete cross-rhythm, there is a macro 4:3—four 4:3 modules-against-three claves. Cross-beat_sentence_68

Continuous duple-pulse cross-beats are often sounded by the quinto, the lead drum in the Cuban genres rumba and conga. Cross-beat_sentence_69

(Rumba, pps. Cross-beat_sentence_70

69–86) Cross-beat_sentence_71

Duple-pulse correlative of 3:2 Cross-beat_section_10

In sub-Saharan rhythm the four main beats are typically divided into three or four pulses, creating a 12-pulse ( 8), or 16-pulse ( 4) cycle. Cross-beat_sentence_72

(Ladzekpo, b: "Main Beat Scheme") Every triple-pulse pattern has its duple-pulse correlative; the two pulse structures are two sides of the same coin. Cross-beat_sentence_73

Cross-beats are generated by grouping pulses contrary to their given structure, for example: groups of two or four in 8 or groups of three or six in 4. Cross-beat_sentence_74

(Rumba, p. 180) The duple-pulse correlative of the three cross-beats of the hemiola, is a figure known in Afro-Cuban music as tresillo. Cross-beat_sentence_75

Tresillo is a Spanish word meaning ‘triplet’—three equal notes within the same time span normally occupied by two notes. Cross-beat_sentence_76

As used in Cuban popular music, tresillo refers to the most basic duple-pulse rhythmic cell. Cross-beat_sentence_77

The pulse names of tresillo and the three cross-beats of the hemiola are identical: one, one-ah, two-and. Cross-beat_sentence_78


The composite pattern of tresillo and the main beats is commonly known as the habanera, congo, tango-congo, or tango. Cross-beat_sentence_79

The habanera rhythm is the duple-pulse correlative of the vertical hemiola (above). Cross-beat_sentence_80

The three cross-beats of the hemiola are generated by grouping triple pulses in twos: 6 pulses ÷ 2 = 3 cross-beats. Cross-beat_sentence_81

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). Cross-beat_sentence_82

In other words, 8 ÷ 3 = 2, r2. Cross-beat_sentence_83

Tresillo is a cross-rhythmic fragment. Cross-beat_sentence_84

It contains the first three cross-beats of 4:3. Cross-beat_sentence_85

(Rumba, p. xxx) Cross-beat_sentence_86


  • Cross-beat_item_1_0

Cross-rhythm, not polymeter Cross-beat_section_11

Early ethnomusicological analysis often perceived African music as polymetric. Cross-beat_sentence_87

Pioneers such as A.M. Cross-beat_sentence_88 Jones and Anthony King identified the prevailing rhythmic emphasis as metrical accents (main beats), instead of the contrametrical accents (cross-beats) they in fact are. Cross-beat_sentence_89

Some of their music examples are polymetric, with multiple and conflicting main beat cycles, each requiring its own separate time signature. Cross-beat_sentence_90

King shows two Yoruba dundun pressure drum ("talking drum") phrases in relation to the five-stroke standard pattern, or "clave," played on the kagano dundun (top line). Cross-beat_sentence_91

The standard pattern is written in a polymetric 8 + 8 time signature. Cross-beat_sentence_92

One dundun phrase is based on a grouping of three pulses written in 8, and the other, a grouping of four pulses written in 8. Cross-beat_sentence_93

Complicating the transcription further, one polymetric measure is offset from the other two. Cross-beat_sentence_94

More recent writings represent African music as cross-rhythmic, within a single meter. Cross-beat_sentence_95

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. Cross-beat_sentence_96

The first cell (half measure) of the top line is a hemiola. Cross-beat_sentence_97

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. Cross-beat_sentence_98

(Clave Matrix p. 216) Cross-beat_sentence_99

Adaptive instruments Cross-beat_section_12

Sub-Saharan instruments are constructed in a variety of ways to generate cross-rhythmic melodies. Cross-beat_sentence_100

Some instruments organize the pitches in a uniquely divided alternate array – not in the straight linear bass to treble structure that is so common to many western instruments such as the piano, harp, and marimba. Cross-beat_sentence_101

Lamellophones including mbira, mbila, mbira huru, mbira njari, mbira nyunga, marimba, karimba, kalimba, likembe, and okeme. Cross-beat_sentence_102

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. Cross-beat_sentence_103

The kalimba is a modern version of these instruments originated by the pioneer ethnomusicologist Hugh Tracey in the early 20th century which has over the years gained world-wide popularity. Cross-beat_sentence_104

Chordophones, such as the West African kora, and Doussn'gouni, part of the harp-lute family of instruments, also have this African separated double tonal array structure. Cross-beat_sentence_105

Another instrument, the Marovany from Madagascar is a double sided box zither which also employs this divided tonal structure. Cross-beat_sentence_106

The Gravikord is a new American instrument closely related to both the African kora and the kalimba. Cross-beat_sentence_107

It was created to exploit this adaptive principle in a modern electro-acoustic instrument. Cross-beat_sentence_108

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. Cross-beat_sentence_109

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 of syncopation. Cross-beat_sentence_110

This can all be done within the same tight tonal range, without the left and right hand fingers ever physically encountering each other. Cross-beat_sentence_111

These simple rhythms will interact musically to produce complex cross rhythms including repeating on beat/off beat pattern shifts that would be very difficult to create by any other means. Cross-beat_sentence_112

This characteristically African structure allows often simple playing techniques to combine with each other and produce cross-rhythmic music of great beauty and complexity. Cross-beat_sentence_113

Jazz Cross-beat_section_13

The New Harvard Dictionary of Music calls swing "an intangible rhythmic momentum in jazz," adding that "swing defies analysis; claims to its presence may inspire arguments." Cross-beat_sentence_114

The only specific description offered is the statement that "triplet subdivisions contrast with duple subdivisions." Cross-beat_sentence_115

The argument could be made that by nature of its simultaneous triple and duple subdivisions, swing is fundamentally a form of polyrhythm. Cross-beat_sentence_116

However, the use of true systematic cross-rhythm in jazz did not occur until the second half of the twentieth century. Cross-beat_sentence_117

3:2 (or 6:4) Cross-beat_section_14

In 1959 Mongo Santamaria recorded "Afro Blue," the first jazz standard built upon a typical African 3:2 cross-rhythm. Cross-beat_sentence_118

The song begins with the bass repeatedly playing 3 cross-beats per each measure of 8 (3:2), or 6 cross-beats per 8 measure (6:4). Cross-beat_sentence_119

The following example shows the original ostinato "Afro Blue" bass line. Cross-beat_sentence_120

The slashed noteheads are not bass notes, but are shown to indicate the main beats, where you would normally tap your foot to "keep time." Cross-beat_sentence_121


3:4 Cross-beat_section_15

On the original "Afro Blue," drummer Willie Bobo played an abakuá bell pattern on a snare drum, using brushes. Cross-beat_sentence_122

This cross-rhythmic figure divides the twelve-pulse cycle into three sets of four pulses. Cross-beat_sentence_123

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. Cross-beat_sentence_124

Bobo used this same pattern and instrumentation on the Herbie Hancock jazz-descarga "Succotash." Cross-beat_sentence_125

2:3 Cross-beat_section_16

In 1963 John Coltrane recorded "Afro Blue" with the great jazz drummer Elvin Jones. Cross-beat_sentence_126

Jones inverted the metric hierarchy of Santamaria's composition, performing it instead as duple cross-beats over a 4 "jazz waltz" (2:3). Cross-beat_sentence_127

This 2:3 in a swung 4 is perhaps the most common example of overt cross-rhythm in jazz. Cross-beat_sentence_128

Duple-pulse correlative of 3:2 Cross-beat_section_17

The Wayne Shorter composition "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. Cross-beat_sentence_129

On the version recorded on Miles Smiles by Miles Davis, the bass switches to 4 at 2:20. Cross-beat_sentence_130

The 4 figure is known as tresillo in Latin music and is the duple-pulse correlative of the cross-beats in triple-pulse. Cross-beat_sentence_131

Throughout the piece, the four main beats are maintained. Cross-beat_sentence_132

In the example below, the main beats are indicated by slashed noteheads. Cross-beat_sentence_133

They are shown here for reference and do not indicate bass notes. Cross-beat_sentence_134


In recent decades, jazz has incorporated many different types of complex cross-rhythms, as well as other types of polyrhythms. Cross-beat_sentence_135

See also Cross-beat_section_18


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