Editing Polyrhythm (section)

== Sub-Saharan African music traditions ==

=== Comparing European and Sub-Saharan African meter ===
<blockquote>
In traditional European ("Western") rhythms, the most fundamental parts typically emphasize the primary beats. By contrast, in rhythms of sub-Saharan African origin, the most fundamental parts typically emphasize the secondary beats. This often causes the uninitiated ear to misinterpret the secondary beats as the primary beats, and to hear the true primary beats as cross-beats. In other words, the musical "background" and "foreground" may mistakenly be heard and felt in reverse—Peñalosa (2009: 21){{sfn|Peñalosa|2009|p=21}}
</blockquote>

=== 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}}

=== Adaptive instruments ===
Sub-Saharan instruments are constructed in a variety of ways to generate polyrhythmic melodies. Some instruments organize the pitches in a uniquely divided alternate array, not in the straight linear [[Bass (sound)|bass]] to [[Treble (sound)|treble]] structure that is so common to many western instruments such as the [[piano]], [[harp]], or [[marimba]].
[[File:TrebleKalimba.jpg|thumb|left|180px|Hugh Tracey Treble [[Kalimba]]]]

[[Lamellophone]]s including [[mbira]], mbila, mbira huru, mbira njari, mbira nyunga, marimba, karimba, [[kalimba]], likembe, and okeme. This family of instruments are found in several forms indigenous to different regions of Africa and most often have equal tonal ranges for right and left hands. 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 worldwide popularity.

[[File:Gravikord.JPG|150px|thumb|right|Signature Series [[Gravikord]]]]
[[Chordophone]]s, such as the West African [[kora (instrument)|kora]], and doussn'gouni, part of the [[harp-lute]] family of instruments, also have this African separated double tonal array structure.<ref name="Alves2013">{{cite book|author=William Alves|title=Music of the Peoples of the World|url=https://books.google.com/books?id=6fkJAAAAQBAJ&pg=PA63|date=12 April 2013|publisher=Cengage Learning|isbn=978-1-133-71230-5|page=63}}</ref>{{clarify|date=May 2012}}Another instrument, the [[Marovany]] from Madagascar is a double sided box zither which also employs this divided tonal structure. [[Trough zither]]s also have the ability to play polyrhythms.

The [[Gravikord]] is a new American instrument closely related to both the African kora and the kalimba was created in the latter 20th century to also exploit this adaptive principle in a modern electro-acoustic instrument.<ref>The Gravikord web site : http://www.gravikord.com/instrument.html#gravikord</ref>

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 of [[syncopation]]. 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-beat (music)|off beat]] pattern 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 to produce polyrhythmic music.