In music, a cross-beat or cross-rhythm is a specific form of polyrhythm. The term cross rhythm was introduced in 1934 by the musicologist Arthur Morris Jones (1889–1980). It refers to a situation where the rhythmic conflict found in polyrhythms is the basis of an entire musical piece.
Etymology
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.
African music
One main system
African cross-rhythm is most prevalent within the greater Niger-Congo linguistic group, which dominates the continent south of the Sahara Desert. (Kubik, p. 58) 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 of Ewe master drummer and scholar C.K. Ladzekpo, and in the writings of David Locke. Jones observes that the shared rhythmic principles of Sub-Saharan African music traditions constitute one main system. Similarly, Ladzekpo affirms the profound homogeneity of sub-Saharan African rhythmic principles. 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.
An embodiment of the people
Cross-rhythmic ratios
3:2
The cross-rhythmic ratio three-over-two (3:2) or vertical hemiola, is the most significant rhythmic cell found in sub-Saharan rhythms. The following measure is evenly divided by three beats and two beats. The two cycles do 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.
Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics." 3:2 is the generative or theoretic form of sub-Saharan rhythmic principles. 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."
African Xylophones such as the balafon and gyil play cross-rhythms, which are often the basis of ostinato melodies. In the following example, a Ghanaian gyil sounds 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 Matrix p. 22)
6:4
The primary cycle of four beats
A great deal of African music is built upon a cycle of four main beats. This basic musical period has a bipartite structure; it is made up of two cells, 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 [] 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 []." (b: "Main Beat Schemes") 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) 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) 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.
The following notated example is from the kushaura part of the traditional mbira piece "Nhema Mussasa." 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. The composite melody is an embellishment of the 6:4 cross-rhythm. (Clave Matrix p. 35)
3:4
If 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 rhythm abakuá (Havana-style) is based on the 3:4 cross-rhythm. The three-beat cycle is represented as half-notes in the following example for visual emphasis.
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.