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Polyrhythm () is the simultaneous use of two or more that are not readily perceived as deriving from one another, or as simple manifestations of the same meter. New Harvard Dictionary of Music (1986: 646). Cambridge, Massachusetts: Harvard University Press. The rhythmic layers may be the basis of an entire piece of music (cross-rhythm), or a momentary section. 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. Concurrently in this context means within the same rhythmic cycle. The underlying pulse, whether explicit or implicit can be considered one of the concurrent rhythms. For example, the son clave is poly-rhythmic because its 3 section suggests a different meter from the pulse of the entire pattern.Novotney, Eugene D. (1998: 265). The 3:2 Relationship as the Foundation of Timelines in West African Musics, Urbana, Illinois: University of Illinois.
They are later joined by a third band, playing in time.
Polyrhythm is heard near the opening of Beethoven's Symphony No. 3. (See also syncopation.)
Chopin often explored the rhythmic possibilities inherent in the independence of a pianist's two hands. A spectacular example may be found in his Étude, Op, 10 No. 10. Alan Walker comments that while this piece is straightforward for listeners, "From the player’s point of view, however, nothing is straightforward. Chopin has placed him inside a veritable hornets’ nest of cross-rhythms and syncopations. The melody first emerges from a background of triplets, then of duplets. Accents are changed without warning, shifting the balance of the phrase sideways, so to speak, together with the place of each note within it."Walker, A. (2018, p. 325), Fryderyk Chopin, a Life and Times. London, Faber.
Polyrhythm is a particularly common feature of the music of Brahms. Writing about the Violin Sonata in G major, Op. 78, Jan Swafford (1997, p. 456) says "In the first movement Brahms plays elaborate games with the phrasing, switching the stresses of the meter back and forth between and , or superimposing both in violin and piano. These ideas gather at the climax at measure 235, with the layering of phrases making an effect that perhaps during the 19th century only Brahms could have conceived."Jan Swafford (1997) Johannes Brahms, a Biography. London, Macmillan.
In "The Snow Is Dancing" from his Children's Corner suite, Claude Debussy introduces a melody "on a static, repeated B-flat, cast in triplet-division cross rhythms which offset this stratum independently of the sixteenth notes comprising the two dancing-snowflake lines below it." "In this section great attention to the exactitude of rhythms is demanded by the polyrhythmic superposition of pedals, ostinato, and melody."Schmitz, E.R. (1966, 124) The Piano Works of Claude Debussy. New York, Dover.
However, the two beat schemes interact within a metric hierarchy (a single meter). The triple beats are primary and the duple beats are secondary; the duple beats are within a triple beat scheme.
Another example of polyrhythm can be found in measures 64 and 65 of the first movement of Mozart's Piano Sonata No. 12. Three evenly-spaced sets of three attack-points span two measures.
Another straightforward example of a cross-rhythm is 3 evenly spaced notes against 2 (3:2), also known as a hemiola. 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 time, quarter note triplets over 2 quarter notes within one bar of time. Other cross-rhythms are 4:3 (with 4 dotted eighth notes over 3 quarter notes within a bar of time as an example in standard western musical notation), 5:2, 5:3, 5:4, etc.
In auditory processing, rhythms are perceived as pitches once they have been sufficiently sped up. Furthermore, intervals of rhythms are perceived as intervals of pitch once sufficiently sped up. As such, 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 are found in the harmonic series. These are called harmonic polyrhythms.
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)
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).
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).Ladzekpo, C.K. (1995: webpage). "The Myth of Cross-Rhythm", Foundation Course in African Dance-Drumming.
Eugene Novotney observes: "The 3:2 relationship (and its permutations) is the foundation of most typical polyrhythmic textures found in West African musics."Novotney, Eugene D. (1998). The Three Against Two Relationship as the Foundation of Timelines in West African Musics Urbana, Illinois: University of Illinois. 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."Agawu, Kofi (2003: 92). Representing African Music: Postcolonial Notes, Queries, Positions New York: Routledge. .
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.
The music of African , 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. The cross-beats are written as quarter-notes for visual emphasis.
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.
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.
, 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.Another instrument, the Marovany from Madagascar is a double sided box zither which also employs this divided tonal structure. 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.The Gravikord web site : http://www.gravikord.com/instrument.html#gravikord
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 to produce polyrhythmic music.
/ref> Coltrane reversed the metric hierarchy of Santamaria's composition, performing it instead in swing (2:3).
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 rumba quinto) might play in , while the rest of the ensemble keeps playing . 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.
Another form of polyrhythmic music 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 time against , which along with 2:3 was used famously by Elvin Jones and McCoy Tyner playing with John Coltrane.
Frank Zappa, especially towards the end of his career, experimented with complex polyrhythms, such as 11:17, and even nested polyrhythms (see "The Black Page" for an example). The highly avant garde album produced by Frank Zappa, Trout Mask Replica by Captain Beefheart and his Magic Band found extensive use of polyrhythm and cross-rhythm. The metal bands Mudvayne, Nothingface, Threat Signal, Lamb of God, also use polyrhythms in their music. Contemporary progressive metal bands such as Meshuggah, Gojira, Periphery, Textures, TesseracT, Tool, Animals as Leaders, Between the Buried and Me and Dream Theater also incorporate polyrhythms in their music, and polyrhythms have also been increasingly heard in technical metal bands such as Ion Dissonance, The Dillinger Escape Plan, Necrophagist, Candiria, The Contortionist and Textures. Much minimalism 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 : e.Thomas, Margaret. "Nancarrow's 'Temporal Dissonance': Issues of Tempo Proportions, Metric Synchrony, and Rhythmic Strategies". Intégral 14/15 (2000–2001): p. 138.
Peter Magadini's album Polyrhythm, with musicians Peter Magadini, George Duke, David Young, and Don Menza, features different polyrhythmic themes on each of the six songs.
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 and time signatures.
Talking Heads' Remain in Light used dense polyrhythms throughout the album, most notably on the song "The Great Curve".Olwell, Greg. "BP Recommends: Talking Heads – Talking Heads Brick'". Bass Player 17:2 (February 2006): 73.
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 language for "polyrhythm", on their album Interloper. This song indeed does use polyrhythms in its melody.
Aphex Twin makes extensive use of polyrhythms in his electronic compositions.
Japanese girl group Perfume made use of the technique in their single, appropriately titled "Polyrhythm", included on their second album Game. The bridge of the song incorporates , in the vocals, common time () and in the drums.
The Britney Spears single "Till the World Ends" (released March 2011) uses a 4:3 cross-rhythm in its hook.Pellerin, Adrien (2011). Britney Spears is using Tuplets? http://adrienpellerin.tumblr.com/post/6274133096/britney-spears-is-using-tuplets.
The outro of the song "Animals" from the album The 2nd Law by the band Muse uses and time signatures for the guitar and drums respectively.
The Aaliyah song "Quit Hatin" uses against in the chorus.
The Japanese idol group 3776 makes use of polyrhythm in a number of their songs, most notably on their 2014 mini-album "Love Letter", which features five songs that all include several rhythmic references to the number 3776. A secret track on the album has the group's leader, Ide Chiyono, explain some of the uses of polyrhythm to the listener.
The National song "Fake Empire" uses a 4 over 3 polyrhythm.
The Cars' song "Touch and Go" has a rhythm in the drum and bass and a rhythm in the keys and vocals.
Harpist and pop folk musician Joanna Newsom is known for the use of polyrhythms on her albums The Milk-Eyed Mender and Ys.
King Gizzard & the Lizard Wizard used polyrhythms extensively throughout their discography, most notably on the album Polygondwanaland.
In Vietnam, bolero songs are composed with against .
The Britney Spears song "...Baby One More Time" contains a 16:9 polyrhythm in the beginning of the music video (the boot tapping 16 times every 9 times the clock ticks - a full cycle can be heard from 0:05 to 0:14).
The Sky Signals song "Amaterasu" is constructed around a 5:4 polyrhythm.
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+ 3 against 2 polyrhythm | ||||||||||||||||||||||||
| 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", and "ring, Christmas bells".
Similar phrases for the 4 against 3 polyrhythm are "pass the golden butter" or "pass the goddamn butter"Sep 2007. Guitar World, p.102. Vol. 28, No. 9. ISSN 1045-6295. and "what atrocious weather" (or "what a load of rubbish" in British English); the 4 against 3 polyrhythm is shown below.
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+ 4 against 3 polyrhythm | ||||||||||||||||||||||||
| 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 ( 12 34 56 and 123 456). 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.
| + !First rhythm !Second rhythm !Least common multiple | ||
| 2 | 3 | 6 |
| 2 | 5 | 10 |
| 3 | 4 | 12 |
| 2 | 7 | 14 |
| 3 | 5 | 15 |
| 2 | 9 | 18 |
| 4 | 5 | 20 |
| 3 | 7 | 21 |
| 3 | 8 | 24 |
| 4 | 6 | 12 |
| 4 | 7 | 28 |
| 5 | 6 | 30 |
| 5 | 7 | 35 |
| 4 | 9 | 36 |
| 5 | 8 | 40 |
| 6 | 7 | 42 |
| 5 | 9 | 45 |
| 6 | 8 | 24 |
| 6 | 9 | 18 |
| 7 | 8 | 56 |
| 7 | 9 | 63 |
| 7 | 11 | 77 |
| 8 | 9 | 72 |
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