Editing Polyrhythm (section)

=== The generating principle ===
In non-Saharan [[music of Africa|African music traditions]], cross-rhythm is the generating principle; the meter is in a permanent state of contradiction. Cross-rhythm was first explained as the basis of non-Saharan rhythm in lectures by C.K. Ladzekpo and the writings of David Locke.

<blockquote>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 non-Saharan languages do not have a word for ''rhythm'', or even ''music''. 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—Peñalosa (2009: 21).{{sfn|Peñalosa|2009|p=21}}</blockquote>

<blockquote>At the center of a core of rhythmic traditions within which the composer conveys his ideas 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 (1995).<ref>Ladzekpo, C.K. (1995: webpage). [https://home.comcast.net/~dzinyaladzekpo/Myth.html "The Myth of Cross-Rhythm"], ''Foundation Course in African Dance-Drumming''.</ref></blockquote>

Eugene Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics."<ref>Novotney, Eugene D. (1998). ''The Three Against Two Relationship as the Foundation of Timelines in West African Musics'' Urbana, Illinois: University of Illinois.</ref> 3:2 is the ''generative'' or ''theoretic form'' of non-Saharan rhythmic principles. [[Victor Kofi 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."<ref>Agawu, Kofi (2003: 92). ''Representing African Music: Postcolonial Notes, Queries, Positions New York: Routledge''. {{ISBN|0-415-94390-6}}.</ref>

{{Block indent|<score sound="1">
    \new DrumStaff <<
       \new voice \drummode { 
           \set Score.tempoHideNote = ##t \tempo 4 = 120
           \time 6/8
           \stemUp \repeat volta 2 { tommh4 tommh tommh }
       }
       \new voice \drummode {
           \stemDown \repeat volta 2 { tomfh4. tomfh }
       }
   >>
</score>}}

The two beat schemes interact within the hierarchy of a single meter. The duple beats are primary and the triple beats are secondary. The example below shows the African 3:2 cross-rhythm within its proper metric structure.

{{Block indent|<score sound="1">
    \new DrumStaff <<
       \new voice \drummode { 
           \set Score.tempoHideNote = ##t \tempo 4 = 120
           \time 6/8
           \stemUp \repeat volta 2 { tommh8[ r tommh] r[ tommh r] }
       }
       \new voice \drummode {
           \stemDown \repeat volta 2 { tomfh4. tomfh }
       }
   >>
</score>}}

The music of African [[xylophone]]s, such as the [[balafon]] and [[gyil]], is often based on cross-rhythm. In the following example, a Ghanaian gyil sounds a 3:2-based [[ostinato]] melody. The left hand (lower notes) sounds the two main beats, while the right hand (upper notes) sounds the three cross-beats.{{sfn|Peñalosa|2009|p=22}} The cross-beats are written as quarter-notes for visual emphasis.

{{Block indent|<score sound="1" override_midi="Ghanaian gyil.mid">
    \new Staff <<
       \clef treble
       \time 6/8
       \new Voice \relative c' {
           \stemUp \repeat volta 2 { fis4 fis a }
       }
       \new Voice {
           \stemDown \repeat volta 2 { b4. d' }
       }
   >>
</score>}}

The following notated example is from the [[kushaura]] part of the traditional [[mbira]] piece "Nhema Mussasa". The mbira is a [[lamellophone]]. The left hand plays the ostinato bass line while the right hand plays the upper melody. The composite melody is an embellishment of the 3:2 cross-rhythm.{{sfn|Peñalosa|2009|p=35}}