Polyrhythm is the simultaneous sounding of two or more independent rhythms. Polyrhythm in general is a nonspecific term for the simultaneous occurrence of two or more conflicting rhythms, of which cross-rhythm is a specific and definable subset.—Novotney (1998: 265)[2]
Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single part; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.
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The terms polyrhythm and cross-rhythm are often used interchangeably.
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.—New Harvard Dictionary of Music (1986: 216).[3]
The physical basis of cross-rhythms can be described in terms of interference of different periodicities.[4]
A simple example of a cross-rhythm is 3 evenly-spaced notes against 2 (3:2), with the 3-beat pattern being faster than the 2-beat pattern, so that they both take the same amount of time. Two simple and common ways to express this pattern in standard western musical notation would be 3 quarter notes over 2 dotted quarter notes within one bar of 6/8 time, quarter note triplets over 2 quarter notes within one bar of 2/4 time. Other cross-rhythms are 4:3 (with 4 dotted eight notes over 3 quarter notes within a bar of 3/4 time as an example in standard western musical notation), 5:2, 5:3, 5:4, etc.
There is a parallel between cross rhythms and musical intervals: in an audible frequency range, the 2:3 ratio produces the musical interval of a perfect fifth, the 3:4 ratio produces a perfect fourth, and the 4:5 ratio produces a major third. All these interval ratios are found in the harmonic series.
Another form of cross-rhythm would be phrasing to suggest a different meter than the one being played by the rest of the ensemble. A common example of this in jazz would be phrasing quarter notes in groupings of 3 to suggest 3/4 time while the ensemble plays in 4/4.
In some European art music cross-rhythm periodically contradicts the prevailing meter. For example, cross-rhythm is heard in the first few minutes of Beethoven's third Symphony and in the first movement of Brahms's Violin Concerto. Concerning the use of a two-over-three (2:3) cross-rhythm in Beethoven‘s sixth quartet in B flat, Ernest Walker says:
The vigorously effective Scherzo is in 3/4 time, but with a curiously persistent cross-rhythm that does its best to persuade us that it is really in 6/8 . . .—Walker (1905: 79)[5]
These polyrhythms are not cross-rhythms because they do not involve cross-beats. In Sub-Saharan 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 sub-Saharan rhythm in lectures by C.K. Ladzekpo and the writings of David Locke.
Cross-rhythm pervades southern Ewe music.—Locke (1982: 231)[6]
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)[7]
The ethnomusicological pioneer Arthur Morris Jones (1889–1980) observed that the shared rhythmic principles of Sub-Saharan African music traditions constitute one main system.[8] Similarly, Ewe master drummer and scholar C.K. Ladzekpo affirms the profound homogeneity of sub-Saharan African rhythmic principles.[9]
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 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)[10]
Cross rhythms can easily be produced by two or more musicians, however producing this effect on one instrument by one musician can be very challenging. Not many western instruments are capable of easily doing this. Because of the great importance of cross rhythms in African music several instruments have evolved there that are especially adaptive for accomplishing this. The structure of these instruments are made to facilitate the creation of cross rhythms. They organize the notes in a uniquely divided alternate array – not in the linear bass to treble structure that is common to so many western instruments such as the piano, harp, xylophone, etc.
Thumb piano type instruments including Mbira, Mbila, Mbira Huru, Mbira Njari, Mbira Nyunga, Marimba, Karimba, Kalimba, Likembe, Okeme, as well as marímbula (also called kalimba) in the Caribbean Islands have this quality.
The West African kora is another such cross rhythm adaptive instrument. It is in the double harp-lute family of instruments and it also has this separated double tonal array structure.
The Gravikord is an American instrument closely related to both the African kora and the kalimba that was created in the latter 20th century to also exploit this adaptive principle in a modern electro-acoustic instrument.[11]
Doussn'gouni is another adaptive African instrument similar to the kora but of lighter construction with fewer strings. It also has a double array structure of notes.
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 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 and produce polyrhythmic music of great beauty and complexity.
Three-over-two (3:2) The cross-rhythm three-over-two (3:2) or hemiola (also called sesquialtera), is the most significant rhythmic ratio found in sub-Saharan rhythm. 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.
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)[12]
. . . the 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics.— Novotney (1998: 201)[13]
3:2 is the generative or theoretic form of sub-Saharan rhythmic principles. Victor Kofi Agawu states very succinctly:
[The] resultant [3:2] rhythm holds the key to understanding . . . there is no independence here, because 2 and 3 belong to a single Gestalt.—Agawu (2003: 92)[14]
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." The only specific description offered is the statement that "triplet subdivisions contrast with duple subdivisions."[15] 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 systematic cross-rhythm in jazz did not occur until the second half of the twentieth century.
In 1959 Mongo Santamaria recorded Afro Blue, the first jazz standard built upon a typical African 3:2 cross-rhythm.[16] The song begins with the bass repeatedly playing 3 cross-beats per each measure of 6/8 (3:2).
The great jazz drummer Elvin Jones took the opposite approach, superimposing two cross-beats over every measure of a 3/4 jazz waltz (2:3). This swung 3/4 is perhaps the most common example of overt cross-rhythm in jazz.[17] In 1963 John Coltrane recorded Afro Blue with Elvin Jones on drums.[18][19] Coltrane reversed the metric hierarchy of Santamaria's composition, performing it instead in 3/4 swing (2:3).
In recent decades jazz has incorporated many different types of complex cross-rhythms, as well as other types of polyrhythms.
Nigerian percussion master Babatunde Olatunji arrived on the American music scene in 1959 with his album Drums of Passion, which was a collection of traditional Nigerian music for percussion and chanting. The album stayed on the charts for two years and had a profound impact on jazz and American popular music. Trained in the Yoruba sakara style of drumming, Olatunji would have a major impact on Western popular music. He went on to teach, collaborate and record with numerous jazz and rock artists, including Airto Moreira, Carlos Santana and Mickey Hart of the Grateful Dead. Olatunji reached his greatest popularity during the height of the Black Arts Movement of the 1960s and '70s.
Afro-Cuban music makes extensive use of polyrhythms. Cuban Rumba uses 3-based and 2-based rhythms at the same time, for example, the lead drummer (playing the quinto) might play in 6/8, while the rest of the ensemble keeps playing 2/2. Afro-Cuban conguero, or conga player, Mongo Santamaría was another percussionist whose polyrhythmic virtuosity helped transform both jazz and popular music. Santamaria fused Afro-Latin rhythms with R&B and jazz as a bandleader in the 1950s, and was featured in the 1994 album Buena Vista Social Club, which was the inspiration for the like-titled documentary released five years later.
Among the most sophisticated polyrhythmic music in the world is south Indian classical Carnatic music. A kind of rhythmic solfege called konnakol is used as a tool to construct highly complex polyrhythms and to divide each beat of a pulse into various subdivisions, with the emphasised beat shifting from beat cycle to beat cycle.
Common polyrhythms found in jazz are 3:2, which manifests as the quarter-note triplet; 2:3, usually in the form of dotted-quarter notes against quarter notes; 4:3, played as dotted-eighth notes against quarter notes (this one demands some technical proficiency to perform accurately, and was not at all common in jazz before Tony Williams used it when playing with Miles Davis); and finally 3/4 time against 4/4, which along with 2:3 was used famously by Elvin Jones and McCoy Tyner playing with John Coltrane.
The Beatles used polyrhythm in their 1968 song "Happiness Is a Warm Gun"(from the White Album).[20] The song also changes time-signature frequently. The Beatles use polyrhythm again on Abbey Road's "Mean Mr. Mustard".[21] Jimi Hendrix had the distinct ability to play polyrhythmic melodies on his guitar during live concerts and jam sessions. This ability was facilitated by the impressive length and size of his hands, and his unorthodox fretting method, in which he would maintain rhythm and lead melodies while using his thumb to fret underlying basslines. Examples are live concerts from 1968 to 1970, in particular a performance of "Killing Floor" live at Winterland 1968, an Improvisation during Woodstock 1969, a solo guitar jam for his song titled "Valleys of Neptune", among several other recordings.
Frank Zappa, especially towards the end of his career, experimented with complex polyrhythms, such as 11:17, and even nested polyrhythms. The metal bands Meshuggah, Nothingface, Periphery, Threat Signal, Lamb of God, Textures and TesseracT also use polyrhythms in their music. Contemporary progressive metal bands such as Tool, Animals as Leaders and Dream Theater also incorporate polyrhythms in their music, and polyrhythms have also been increasingly heard in techmetal bands such as Ion Dissonance and The Dillinger Escape Plan, Candiria and Textures. Much minimalist and totalist music makes extensive use of polyrhythms. Henry Cowell and Conlon Nancarrow created music with yet more complex polytempo and using irrational numbers like pi:e.
King Crimson used polyrhythms extensively in their 1981 album Discipline. Above all Bill Bruford used polyrhythmic drumming throughout his career.
The band Queen used polyrhythm in their 1974 song "The March of the Black Queen" with 8/8 and 12/8 time signatures.[1]
Nine Inch Nails front man Trent Reznor uses polyrhythm frequently. One notable appearance is in the song "La Mer" from the album The Fragile. The piano holds a 3/4 riff while the drums and bass back it with a standard 4/4 signature. Talking Heads' Remain in Light used dense polyrhythms throughout the album, most notably on the song "The Great Curve".
Megadeth frequently tends to use polyrhythm in its drumming, notably from songs such as "Sleepwalker" or the ending of "My Last Words", which are both played in 2:3.
Carbon Based Lifeforms have a song named "Polyrytmi", Finnish for polyrhythm, on their album Interloper. This song indeed does use polyrhythms in its melody. [2]
The Britney Spears single Till the World Ends (released March 2011) uses a 4:3 cross-rhythm in its hook.[22]
The following is an example of a 3 against 2 polyrhythm, given in time unit box system (TUBS) notation; each box represents a fixed unit of time; time progresses from the left of the diagram to the right. It is in bad form to teach a student to play 3/2 polyrhythms as simply quarter note, eighth note, eighth note, quarter note. The proper way is to establish sound bases for both the quarter-notes, and the triplet-quarters, and then to layer them upon each other, forming multiple rhythms. Beats are indicated with an X; rests are indicated with a blank.
| 3-beat rhythm | X | X | X | X | X | X | X | X | X | X | X | X | ||||||||||||
| 2-beat rhythm | X | X | X | X | X | X | X | X |
A common memory aid to help with the 3 against 2 polyrhythm is that it has the same rhythm as the phrase "not difficult"; the simultaneous beats occur on the word "not"; the second and third of the triple beat land on "dif" and "cult", respectively. The second 2-beat lands on the "fi" in "difficult." Try saying "not difficult" over and over in time with the sound file above. This will emphasize the "3 side" of the 3 against 2 feel. Now try saying the phrase "not a problem", stressing the syllables "not" and "prob-". This will emphasize the "2 side" of the 3 against 2 feel. More phrases with the same rhythm are "cold cup of tea", "four funny frogs", "come, if you please".
One of the best known examples of a 3 against 2 polyrhythm is the Ukrainian Bell Carol, "Carol of the Bells".
Similar phrases for the 4 against 3 polyrhythm are "pass the golden butter"[1] or "pass the goddamn butter"[23] and "what atrocious weather"; The 4 against 3 polyrhythm is shown below.
| 4-beat rhythm | X | X | X | X | X | X | X | X | ||||||||||||||||
| 3-beat rhythm | X | X | X | X | X | X |
As can be seen from above, the counting for polyrhythms is determined by the lowest common multiple, so if one wishes to count 2 against 3, one needs to count a total of 6 beats, as lcm(2,3) = 6 (123456 and 123456). However this is only useful for very simple polyrhythms, or for getting a feel for more complex ones, as the total number of beats rises quickly. To count 4 against 5, for example, requires a total of 20 beats, and counting thus slows the tempo considerably. However some players, such as classical Indian musicians, can intuitively play high polyrhythms such as 7 against 8. Polyrhythms are quite common in late Romantic Music and 20th century classical music. Works for keyboard often set odd rhythms against one another in separate hands. A good example is in the soloist's cadenza in Grieg's Concerto in A Minor; the left hand plays arpeggios of seven notes to a beat; the right hand plays an ostinato of eight notes per beat while also playing the melody in octaves, which uses whole notes, dotted eighth notes, and triplets. Other instances occur often in Rachmaninoff's Piano Concerto No. 2. The piano arpeggios that constitute much of the soloist's material in the first movement often have anywhere from four to eleven notes per beat. In the last movement, the piano's opening run, marked 'quasi glissando', fits 52 notes into the space of one measure, making for a glissando-like effect while keeping the mood of the music. Other instances in this movement include a scale that juxtaposes ten notes in the right hand against four in the left, and one of the main themes in the piano, which imposes an eighth-note melody on a triplet harmony. Another example is the fluid 7:3 polyrhythm at the beginning of Charles Griffes’ The White Peacock.
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