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Polyrhythm
 Polyrhythm (/ˈpɒlirɪðəm/) is the simultaneous use of two or more rhythms that are not readily perceived as deriving from one another, or as simple manifestations of the same meter.[2] 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.[3] In western art musicIn some European art music, polyrhythm periodically contradicts the prevailing meter. For example, in Mozart's opera Don Giovanni, two orchestras are heard playing together in different metres (3  They are later joined by a third band, playing in 3 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."[4] 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 6  In "The Snow Is Dancing" from his Children's Corner suite, 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."[6] "In this section great attention to the exactitude of rhythms is demanded by the polyrhythmic superposition of pedals, ostinato, and melody."[7]  HemiolaConcerning the use of a two-over-three (2:3) hemiola in Beethoven's String Quartet No. 6, Ernest Walker states, "The vigorously effective Scherzo is in 3  Polyrhythm, not polymeterThe illusion of simultaneous 3  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 cross-beats within a triple beat scheme.  Composite hemiolaThe four-note ostinato pattern of Mykola Leontovych's "Carol of the Bells" (the first measure below) is the composite of the two-against-three hemiola (the second measure).  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. ![{ \new PianoStaff <<
\new Staff <<
\set Score.currentBarNumber = #62
\bar ""
\relative c' {
\set Score.tempoHideNote = ##t \tempo 4 = 160
\clef treble
\key f \major
\time 3/4
<d aes'>8 <d aes'> r <d aes'> r <d aes'>
<d g> <d g> r <d g> r <d g>
<c g'> <c g'> r <c g'> <c f>[ <c f>]
r <c f> <b f'>[ <b f'>] r <b f'>
}
>>
\new Staff <<
\relative c, {
\clef bass
\key f \major
\time 3/4
<bes bes'>4 d' f
<ees, ees'> g' bes
<aes,, aes'> aes'' <d,, d'>
d'' <g,,, g'> g''
}
>>
>> }](http://upload.wikimedia.org/score/1/d/1dl03gugvshnq8squvnc890gqzyf7ft/1dl03gug.png) Cross-rhythmCross-rhythm refers to systemic polyrhythm. The Concise Oxford Dictionary of Music defines it as “The Regular shift of some beats in a metric pattern to points ahead of or behind their normal positions.” [9] The finale of Brahms Symphony No. 2 features a powerful passage where the prevailing metre of four beats to the bar becomes disrupted. Here is the passage as notated in the score:  Here is the same passage re-barred to clarify how the ear may actually experience the changing metres:  “Polyrhythms run through Brahms’s music like an obsessive-compulsive streak...For Brahms, subdividing a measure of time into different units and layering different patterns on top of one another seemed to be almost a compulsion — as well as a compositional device and an engine of expression. ”[10] 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 6  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 interval ratios are found in the harmonic series. These are called harmonic polyrhythms. Sub-Saharan African music traditionsComparing European and Sub-Saharan African meter
The generating principleIn non-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 non-Saharan rhythm in lectures by C.K. Ladzekpo and the writings of David Locke.
Eugene Novotney observes: "The 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics."[13] 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."[14]  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. ![\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 }
}
>>](http://upload.wikimedia.org/score/e/3/e3wfbsqsub2sx95dyhn9kv3597wxgpy/e3wfbsqs.png) The music of African xylophones, 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.[15] 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.[16] Adaptive instrumentsSub-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 to treble structure that is so common to many western instruments such as the piano, harp, or marimba.  Lamellophones 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.  Chordophones, 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.[17][clarification needed]Another instrument, the Marovany from Madagascar is a double sided box zither which also employs this divided tonal structure. Trough zithers 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.[18] 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. Jazz3:2 cross-rhythmPolyrhythm is a staple of modern jazz. Although not as common, use of systemic cross-rhythm is also found in jazz. In 1959, Mongo Santamaria recorded "Afro Blue", the first jazz standard built upon a typical African 6:4 cross-rhythm (two cycles of 3:2).[19] The song begins with the bass repeatedly playing 6 cross-beats per each measure of 12  2:3 cross-rhythmThe famous jazz drummer Elvin Jones took the opposite approach, superimposing two cross-beats over every measure of a 3 In popular musicNigerian 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.[citation needed] Trained in the Yoruba sakara style of drumming, Olatunji would have a major impact on Western popular music.[citation needed] 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 1970s. 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 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 3 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.[citation needed] Contemporary progressive metal bands such as Meshuggah, Gojira,[23] 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.[citation needed] 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 π:e.[24] 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.[25] 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 Talking Heads' Remain in Light used dense polyrhythms throughout the album, most notably on the song "The Great Curve".[27] 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.[citation needed] Carbon Based Lifeforms have a song named "Polyrytmi", Finnish for "polyrhythm", on their album Interloper. This song indeed does use polyrhythms in its melody.[28][citation needed] 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 5 The Britney Spears single "Till the World Ends" (released March 2011) uses a 4:3 cross-rhythm in its hook.[30] The outro of the song "Animals" from the album The 2nd Law by the band Muse uses 5 The Aaliyah song "Quit Hatin" uses 9 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.[31] The Cars' song "Touch and Go" has a 5 Harpist and pop folk musician Joanna Newsom is known for the use of polyrhythms on her albums The Milk-Eyed Mender and Ys.[32] King Gizzard & the Lizard Wizard used polyrhythms extensively throughout their discography, most notably on the album Polygondwanaland. In Vietnam, bolero songs are composed with 3 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. ExamplesThe 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.
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"[1] or "pass the goddamn butter"[33] and "what atrocious weather" (or "what a load of rubbish" in British English); the 4 against 3 polyrhythm is shown below.
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.[citation needed] 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.[citation needed] 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. List of basic polyrhythms
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