Polyrhythm is the simultaneous sounding of two or more independent
rhythmRhythm may be generally defined as a "movement marked by the regulated succession of strong and weak elements, or of opposite or different conditions." This general meaning of regular recurrence or pattern in time may be applied to a wide variety of cyclical natural phenomena having a periodicity or...
s.
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)
Polyrhythms can be distinguished from irrational rhythms, which can occur within the context of a single
part1) A part is a strand or melody of music played by an individual instrument or voice within a larger work. Parts may be referred to as an outer part or an inner part . Part-writing is the composition of parts in consideration of harmony and counterpoint...
; polyrhythms require at least two rhythms to be played concurrently, one of which is typically an irrational rhythm.
Cross-rhythm
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).
The physical basis of cross-rhythms can be described in terms of interference of different periodicities.
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 fifthIn classical music from Western culture, a fifth is a musical interval encompassing five staff positions , and the perfect fifth is a fifth spanning seven semitones, or in meantone, four diatonic semitones and three chromatic semitones...
, the 3:4 ratio produces a
perfect fourthIn classical music from Western culture, a fourth is a musical interval encompassing four staff positions , and the perfect fourth is a fourth spanning five semitones. For example, the ascending interval from C to the next F is a perfect fourth, as the note F lies five semitones above C, and there...
, and the 4:5 ratio produces a
major thirdIn classical music from Western culture, a third is a musical interval encompassing three staff positions , and the major third is one of two commonly occurring thirds. It is qualified as major because it is the largest of the two: the major third spans four semitones, the minor third three...
. All these
interval ratioIn music, an interval ratio is a ratio of the frequencies of the pitches in a musical interval. For example, a just perfect fifth is 3:2 , 1.5, and may be approximated by an equal tempered perfect fifth which is 27/12, 1.498...
s are found in the
harmonic seriesPitched musical instruments are often based on an approximate harmonic oscillator such as a string or a column of air, which oscillates at numerous frequencies simultaneously. At these resonant frequencies, waves travel in both directions along the string or air column, reinforcing and canceling...
.
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
jazzJazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...
would be phrasing quarter notes in groupings of 3 to suggest 3/4 time while the ensemble plays in 4/4.
European (Western) art music
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)
Sub-Saharan African music
These polyrhythms are not cross-rhythms because they do not involve
cross-beatIn music, a cross-beat or cross-rhythm is a form of polyrhythm.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...
s.
In
Sub-Saharan African music traditionsSub-Saharan African music traditions exhibit so many common features that they may in some respects be thought of as constituting a single musical system. While some African music is clearly contemporary-popular music and some is art-music, still a great deal is communal and orally transmitted...
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 musicEwe music is the music of the Ewe people of West Africa. Instrumentation is primarily percussive and rhythmically the music features great metrical complexity. Its highest form is in dance music including a drum orchestra, but there are also work, play, and other songs. Despite his title Ewe music...
.—Locke (1982: 231)
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)
The ethnomusicological pioneer
Arthur Morris JonesArthur Morris Jones , was a missionary and musicologist who worked in Zambia during the early 20th century. He was stationed at St Mark's School in Mapanza in the Southern Province of present-day Zambia . He is best known for his ethnomusicological work, particularly his two-volume Studies in...
(1889–1980) observed that the shared rhythmic principles of Sub-Saharan African music traditions constitute
one main system. Similarly, Ewe master drummer and scholar C.K. Ladzekpo affirms the
profound homogeneity of sub-Saharan African rhythmic principles.
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)
Adaptive instruments
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
trebleTreble refers to tones of high frequency or range. In music this corresponds to high notes, and for this reason the treble clef is often used for instruments with higher pitch. Examples of treble sounds are guitar tones, female voice , young boy voice, etc. They have frequencies above 9 KHz. Treble...
structure that is common to so many western instruments such as the
pianoThe piano is a musical instrument played by means of a keyboard. It is one of the most popular instruments in the world. Widely used in classical and jazz music for solo performances, ensemble use, chamber music and accompaniment, the piano is also very popular as an aid to composing and rehearsal...
,
harpThe harp is a multi-stringed instrument which has the plane of its strings positioned perpendicularly to the soundboard. Organologically, it is in the general category of chordophones and has its own sub category . All harps have a neck, resonator and strings...
,
xylophoneThe xylophone is a musical instrument in the percussion family that consists of wooden bars struck by mallets...
, etc.
Thumb pianoThe thumb piano is an African musical instrument, a type of plucked idiophone common throughout Sub-Saharan Africa.-Description:Each note of a kalimba, mbira, etc. is a separate idiophone, and in orchestral terms, the instrument as a whole belongs in the bar percussion family...
type instruments including MbiraIn African music, the mbira is a musical instrument that consists of a wooden board to which staggered metal keys have been attached. It is often fitted into a resonator...
, Mbila, Mbira Huru, Mbira Njari, Mbira Nyunga, Marimba, Karimba, Kalimba, Likembe, Okeme, as well as marímbulaA marímbula is a folk musical instrument of the Caribbean Islands . The marímbula is usually classified as part of the lamellophone family of musical instruments. With its roots in African instruments, marimbula originated in the province of Oriente, Cuba in the 19th century...
(also called kalimba) in the Caribbean Islands have this quality.
The West African koraThe kora is a 21-string bridge-harp used extensively in West Africa.-Description:A kora is built from a large calabash cut in half and covered with cow skin to make a resonator, and has a notched bridge. It does not fit well into any one category of western instruments and would have to be...
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 GravikordThe gravikord is an electric double bridge-harp invented by Robert Grawi in 1986.- Description :The gravikord is a new instrument developed on the basis of the West African kora. It is made of welded stainless steel tubing, with 24 nylon strings but no resonating gourd or skin. The bridge is made...
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.
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
syncopationIn music, syncopation includes a variety of rhythms which are in some way unexpected in that they deviate from the strict succession of regularly spaced strong and weak but also powerful beats in a meter . These include a stress on a normally unstressed beat or a rest where one would normally be...
. 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.
Simple examples
Three-over-two (3:2) The cross-rhythm
three-over-two (3:2) or
hemiolaIn modern musical parlance, a hemiola is a metrical pattern in which two bars in simple triple time are articulated as if they were three bars in simple duple time...
(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)
. . . the 3:2 relationship (and [its] permutations) is the foundation of most typical polyrhythmic textures found in West African musics.— Novotney (1998: 201)
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 GestaltDie Gestalt is a German word for form or shape. It is used in English to refer to a concept of 'wholeness'. Gestalt may also refer to:* Gestalt psychology , a theory of mind and brain, describing the Gestalt effect....
.—Agawu (2003: 92)
Jazz
The New Harvard Dictionary of Music calls
swingIn jazz and related musical styles, the term swing is used to describe the sense of propulsive rhythmic "feel" or "groove" created by the musical interaction between the performers, especially when the music creates a "visceral response" such as feet-tapping or head-nodding...
"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." 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
jazzJazz is a musical style that originated at the beginning of the 20th century in African American communities in the Southern United States. It was born out of a mix of African and European music traditions. From its early development until the present, jazz has incorporated music from 19th and 20th...
did not occur until the second half of the twentieth century.
In 1959
Mongo SantamariaRamón "Mongo" Santamaría Rodríguez was an Afro-Cuban Latin jazz percussionist. He is most famous for being the composer of the jazz standard "Afro Blue," recorded by John Coltrane among others. In 1950 he moved to New York where he played with Perez Prado, Tito Puente, Cal Tjader, Fania All...
recorded
Afro Blue"Afro Blues" is a jazz standard composed by Mongo Santamaría, perhaps best known in its arrangement by John Coltrane.Coltrane's recordings of the piece have several features in common with his versions of "My Favorite Things", including a pulsating 3/4 jazz waltz rhythm, and a simple, almost...
, the first jazz standard built upon a typical African 3:2 cross-rhythm. The song begins with the bass repeatedly playing 3 cross-beats per each measure of 6/8 (3:2).
The great jazz drummer
Elvin JonesElvin Ray Jones was a jazz drummer of the post-bop era. He showed interest in drums at a young age, watching the circus bands march by his family's home in Pontiac, Michigan....
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. In 1963
John ColtraneJohn William Coltrane was an American jazz saxophonist and composer. Working in the bebop and hard bop idioms early in his career, Coltrane helped pioneer the use of modes in jazz and later was at the forefront of free jazz...
recorded Afro Blue with Elvin Jones on drums. 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.
Usage and history
Nigerian percussion master
Babatunde OlatunjiBabatunde Olatunji was a Nigerian drummer, educator, social activist and recording artist.- Biography :Olatunji was born in the village of Ajido, a small town near Badagry, Lagos State, in southwestern Nigeria. A member of the Yoruba people, Olatunji was introduced to traditional African music at...
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
YorubaThe music of the Yoruba people of Nigeria is best known for an extremely advanced drumming tradition, especially using the dundun hourglass tension drums. Yoruba folk music became perhaps the most prominent kind of West African music in Afro-Latin and Caribbean musical styles...
sakaraThe Sakara drum is one of the four major families of Yoruba drums of Nigeria. The other families are the Dundun/Gangan or talking drum, the Batá drum and the Gbedu drum....
style of drumming, Olatunji would have a major impact on
WesternThe Western world, also known as the West and the Occident , is a term referring to the countries of Western Europe , the countries of the Americas, as well all countries of Northern and Central Europe, Australia and New Zealand...
popular music. He went on to teach, collaborate and record with numerous jazz and rock artists, including
Airto MoreiraAirto Moreira is a Brazilian jazz drummer and percussionist. Airto is married to jazz singer Flora Purim, and their daughter Diana Moreira is also a singer. He currently resides in Los Angeles.-Biography:...
,
Carlos SantanaCarlos Augusto Alves Santana is a Mexican rock guitarist. Santana became famous in the late 1960s and early 1970s with his band, Santana, which pioneered rock, salsa and jazz fusion...
and
Mickey HartMickey Hart is an American percussionist and musicologist. He is best known as one of the two drummers of the rock band the Grateful Dead. He was a member of the Grateful Dead from September 1967 to February 1971, and from October 1974 to August 1995...
of the
Grateful DeadThe Grateful Dead was an American rock band formed in 1965 in the San Francisco Bay Area. The band was known for its unique and eclectic style, which fused elements of rock, folk, bluegrass, blues, reggae, country, improvisational jazz, psychedelia, and space rock, and for live performances of long...
. Olatunji reached his greatest popularity during the height of the
Black Arts MovementThe Black Arts Movement or BAM is the artistic branch of the Black Power movement. It was started in Harlem by writer and activist Amiri Baraka...
of the 1960s and '70s.
Afro-Cuban music makes extensive use of polyrhythms.
Cuban RumbaIn Cuban music, Rumba is a generic term covering a variety of musical rhythms and associated dances. The rumba has its influences in the music brought to Cuba by Africans brought to Cuba as slaves as well as Spanish colonizers...
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-CubanThe term Afro-Cuban refers to Cubans of Sub Saharan African ancestry, and to historical or cultural elements in Cuba thought to emanate from this community...
conguero, or
congaThe conga, or more properly the tumbadora, is a tall, narrow, single-headed Cuban drum with African antecedents. It is thought to be derived from the Makuta drums or similar drums associated with Afro-Cubans of Central African descent. A person who plays conga is called a conguero...
player,
Mongo SantamaríaRamón "Mongo" Santamaría Rodríguez was an Afro-Cuban Latin jazz percussionist. He is most famous for being the composer of the jazz standard "Afro Blue," recorded by John Coltrane among others. In 1950 he moved to New York where he played with Perez Prado, Tito Puente, Cal Tjader, Fania All...
was another percussionist whose polyrhythmic virtuosity helped transform both jazz and popular music. Santamaria fused Afro-Latin rhythms with
R&BRhythm and blues, often abbreviated to R&B, is a genre of popular African American music that originated in the 1940s. The term was originally used by record companies to describe recordings marketed predominantly to urban African Americans, at a time when "urbane, rocking, jazz based music with a...
and jazz as a bandleader in the 1950s, and was featured in the 1994 album
Buena Vista Social Club- Music :"Chan Chan", the first song on the album, is a Cuban song composition by Compay Segundo, revolving around two central characters, Juanita and Chan Chan. The song was one of Segundo's last compositions and was written in 1987, already having been recorded by Segundo himself various...
, which was the inspiration for
the like-titled documentaryBuena Vista Social Club is a documentary film by Wim Wenders about the music of Cuba. It is named for a danzón that became the title piece of the album Buena Vista Social Club.-Synopsis:...
released five years later.
Among the most sophisticated polyrhythmic music in the world is south Indian classical
Carnatic musicCarnatic music is a system of music commonly associated with the southern part of the Indian subcontinent, with its area roughly confined to four modern states of India: Andhra Pradesh, Karnataka, Kerala, and Tamil Nadu...
. A kind of rhythmic
solfegeIn music, solfège is a pedagogical solmization technique for the teaching of sight-singing in which each note of the score is sung to a special syllable, called a solfège syllable...
called
konnakolKonnakol is the art of performing percussion syllables vocally in South Indian music, the Carnatic music - South Indian classical - performance art of vocal percussion. It is comparable in some respects to bol in Hindustani music, but allows the composition, performance or communication of rhythms...
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 DavisMiles Dewey Davis III was an American jazz musician, trumpeter, bandleader, and composer. Widely considered one of the most influential musicians of the 20th century, Miles Davis was, with his musical groups, at the forefront of several major developments in jazz music, including bebop, cool jazz,...
); and finally 3/4 time against 4/4, which along with 2:3 was used famously by
Elvin JonesElvin Ray Jones was a jazz drummer of the post-bop era. He showed interest in drums at a young age, watching the circus bands march by his family's home in Pontiac, Michigan....
and
McCoy TynerMcCoy Tyner is a jazz pianist from Philadelphia, Pennsylvania, known for his work with the John Coltrane Quartet and a long solo career.-Early life:...
playing with
John ColtraneJohn William Coltrane was an American jazz saxophonist and composer. Working in the bebop and hard bop idioms early in his career, Coltrane helped pioneer the use of modes in jazz and later was at the forefront of free jazz...
.
The BeatlesThe Beatles were an English rock band, active throughout the 1960s and one of the most commercially successful and critically acclaimed acts in the history of popular music. Formed in Liverpool, by 1962 the group consisted of John Lennon , Paul McCartney , George Harrison and Ringo Starr...
used polyrhythm in their 1968 song "
Happiness Is a Warm Gun"Happiness Is a Warm Gun" is a song by The Beatles, featured on the eponymous double-disc album The Beatles, also known as The White Album...
"(from the
White AlbumThe Beatles is the ninth official album by the English rock group The Beatles, a double album released in 1968. It is also commonly known as "The White Album" as it has no graphics or text other than the band's name embossed on its plain white sleeve.The album was written and recorded during a...
). The song also changes time-signature frequently. The Beatles use polyrhythm again on Abbey Road's "
Mean Mr. Mustard"Mean Mr. Mustard" is a song written by John Lennon, and performed by The Beatles on their album Abbey Road...
".
Jimi HendrixJames Marshall "Jimi" Hendrix was an American guitarist and singer-songwriter...
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 ZappaFrank Vincent Zappa was an American composer, singer-songwriter, electric guitarist, record producer and film director. In a career spanning more than 30 years, Zappa wrote rock, jazz, orchestral and musique concrète works. He also directed feature-length films and music videos, and designed...
, especially towards the end of his career, experimented with complex polyrhythms, such as 11:17, and even nested polyrhythms. The
metalHeavy metal is a genre of rock music that developed in the late 1960s and early 1970s, largely in the Midlands of the United Kingdom and the United States...
bands
MeshuggahMeshuggah is an extreme metal band from Umeå, Sweden, formed in 1987. Meshuggah's line-up has primarily consisted of founding members vocalist Jens Kidman and lead guitarist Fredrik Thordendal, drummer Tomas Haake, who joined in 1990, and rhythm guitarist Mårten Hagström, who joined in 1992...
,
NothingfaceNothingface was a four-piece metal band from Washington, D.C. noted for having graphic lyrics and occasionally using political themes in their later works, as well as polyrhythmic songs.-First Run:...
,
PeripheryPeriphery is an American metal band from Bethesda, Maryland , formed in 2005.- Formation and lineup changes :Periphery was formed by guitarist Misha Mansoor in 2005...
,
Threat SignalThreat Signal is a Canadian Melodic death metal band hailing from the city of Hamilton. However, different members of the band hail from other parts of the Ontario province...
,
Lamb of GodLamb of God is an American heavy metal band from Richmond, Virginia. Formed in 1994, the group consists of vocalist Randy Blythe, guitarists Mark Morton and Willie Adler, bassist John Campbell, and drummer Chris Adler...
,
TexturesTextures is a metal band from the Netherlands, formed in 2001. Textures' lineup revolves around founding members Jochem Jacobs, Stef Broks, Bart Hennephof, and bassist Remko Tielemans who joined in 2007...
and
TesseracTIn geometry, the tesseract, also called an 8-cell or regular octachoron or cubic prism, is the four-dimensional analog of the cube. The tesseract is to the cube as the cube is to the square. Just as the surface of the cube consists of 6 square faces, the hypersurface of the tesseract consists of 8...
also use polyrhythms in their music. Contemporary
progressive metalProgressive metal is a subgenre of heavy metal originating in the United Kingdom and North America in the late 1980s...
bands such as
ToolTool is an American rock band from Los Angeles, California. Formed in 1990, the group's line-up has included drummer Danny Carey, guitarist Adam Jones, and vocalist Maynard James Keenan. Since 1995, Justin Chancellor has been the band's bassist, replacing their original bassist Paul D'Amour...
,
Animals as LeadersAnimals as Leaders is an American, Washington, D.C.–based instrumental progressive metal band, formed by guitarist Tosin Abasi in 2007 which now includes guitarist Javier Reyes and drummer Navene Koperweis. The self-titled debut album was released in April 2009 by Prosthetic Records...
and
Dream TheaterDream Theater is an American progressive metal band formed in 1985 under the name Majesty by John Petrucci, John Myung, and Mike Portnoy while they attended Berklee College of Music in Massachusetts. They subsequently dropped out of their studies to further concentrate on the band that would...
also incorporate polyrhythms in their music, and polyrhythms have also been increasingly heard in techmetal bands such as
Ion DissonanceIon Dissonance is a Canadian mathcore/deathcore band from Montreal, Quebec, Canada. They're known for their technical mathcore style but changed to a more heavy, groove based style with the release of their 2007 album Minus the Herd.-History:...
and
The Dillinger Escape PlanThe Dillinger Escape Plan is an American mathcore band from Morris Plains, New Jersey. The group originated in 1997 after the disbanding of Arcane, a hardcore punk trio consisting of Ben Weinman, Dimitri Minakakis, and Chris Pennie. The band's current line-up consists of guitarist Ben Weinman,...
,
CandiriaCandiria are an American band from Brooklyn, New York. They blend various styles of music, including heavy metal, hardcore, jazz, hip hop and ambient. Candiria have often dubbed their sound "urban fusion".- History :...
and
TexturesTextures is a metal band from the Netherlands, formed in 2001. Textures' lineup revolves around founding members Jochem Jacobs, Stef Broks, Bart Hennephof, and bassist Remko Tielemans who joined in 2007...
. Much
minimalistMinimalism describes movements in various forms of art and design, especially visual art and music, where the work is set out to expose the essence, essentials or identity of a subject through eliminating all non-essential forms, features or concepts...
and
totalistIn music, totalism is a term for a style of art music that arose in the 1980s and 1990s as a developing response to minimalism—parallel to postminimalism, but generally among a slightly younger generation, born in the 1950s....
music makes extensive use of polyrhythms.
Henry CowellHenry Cowell was an American composer, music theorist, pianist, teacher, publisher, and impresario. His contribution to the world of music was summed up by Virgil Thomson, writing in the early 1950s:...
and
Conlon NancarrowConlon Nancarrow was a United States-born composer who lived and worked in Mexico for most of his life. He became a Mexican citizen in 1955.Nancarrow is best remembered for the pieces he wrote for the player piano...
created music with yet more complex polytempo and using irrational numbers like
pi' is a mathematical constant that is the ratio of any circle's circumference to its diameter. is approximately equal to 3.14. Many formulae in mathematics, science, and engineering involve , which makes it one of the most important mathematical constants...
:
eThe mathematical constant ' is the unique real number such that the value of the derivative of the function at the point is equal to 1. The function so defined is called the exponential function, and its inverse is the natural logarithm, or logarithm to base...
.
King CrimsonKing Crimson are a rock band founded in London, England in 1969. Often categorised as a foundational progressive rock group, the band have incorporated diverse influences and instrumentation during their history...
used polyrhythms extensively in their 1981 album
Discipline. Above all
Bill BrufordWilliam Scott "Bill" Bruford is an English drummer, percussionist, composer, producer, and record label owner. He was the original drummer for the progressive rock group Yes, from 1968-1972. Bruford has performed for numerous popular acts since the early 1970s, including a stint as touring...
used polyrhythmic drumming throughout his career.
The band
QueenQueen are a British rock band formed in London in 1971, originally consisting of Freddie Mercury , Brian May , John Deacon , and Roger Taylor...
used polyrhythm in their 1974 song "The March of the Black Queen" with 8/8 and 12/8 time signatures.
http://queen.musichall.cz/index_en.php?s=sa&d=rhythm
Nine Inch NailsNine Inch Nails is an American industrial rock project, founded in 1988 by Trent Reznor in Cleveland, Ohio. As its main producer, singer, songwriter, and instrumentalist, Reznor is the only official member of Nine Inch Nails and remains solely responsible for its direction...
front man
Trent ReznorMichael Trent Reznor is an American multi-instrumentalist, composer, record producer, and leader of industrial rock band Nine Inch Nails. Reznor is also a member of How to Destroy Angels alongside his wife, Mariqueen Maandig, and Atticus Ross. He was previously associated with bands Option 30,...
uses polyrhythm frequently. One notable appearance is in the song "La Mer" from the album
The FragileIn terms of narrative, virtually no references are made to the aspects depicted in The Downward Spiral. Like The Downward Spiral, The Fragile is a concept album, but, as a double album, is nearly twice the length of its predecessor. Reznor's vocals, for the most part, are much more melodic and...
. The piano holds a 3/4 riff while the drums and bass back it with a standard 4/4 signature.
Talking HeadsTalking Heads were an American New Wave and avant-garde band formed in 1975 in New York City and active until 1991. The band comprised David Byrne, Chris Frantz, Tina Weymouth and Jerry Harrison...
'
Remain in LightRemain in Light is the fourth studio album by American New Wave band Talking Heads, released on 8 October 1980 on Sire Records. It was recorded at locations in the Bahamas and the United States between July and August 1980 and was produced by the quartet's long-time collaborator...
used dense polyrhythms throughout the album, most notably on the song "The Great Curve".
MegadethMegadeth is an American heavy metal band from Los Angeles, California which was formed in 1983 by guitarist/vocalist Dave Mustaine, bassist Dave Ellefson and guitarist Greg Handevidt, following Mustaine's expulsion from Metallica. The band has since released 13 studio albums, three live albums, two...
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 LifeformsCarbon Based Lifeforms is a psychedelic ambient music group made up of Johannes Hedberg and Daniel Segerstad , in Gothenburg, Sweden...
have a song named "
Polyrytmi",
FinnishFinnish is the language spoken by the majority of the population in Finland Primarily for use by restaurant menus and by ethnic Finns outside Finland. It is one of the two official languages of Finland and an official minority language in Sweden. In Sweden, both standard Finnish and Meänkieli, a...
for polyrhythm, on their album
InterloperInterloper is the third studio album by Swedish ambient duo Carbon Based Lifeforms, released in 2010.-Track listing:Interloper starts at track 24, indicating it is a continuation of World of Sleepers-External links:* official website.*...
. This song indeed does use polyrhythms in its melody.
http://www.youtube.com/watch?v=9eyg3QydFhE
The
Britney SpearsBritney Jean Spears is an American recording artist and entertainer. Born in McComb, Mississippi, and raised in Kentwood, Louisiana, Spears began performing as a child, landing acting roles in stage productions and television shows. She signed with Jive Records in 1997 and released her debut album...
single
Till the World Ends"Till the World Ends" is a song by American recording artist Britney Spears, released as the second single from her seventh studio album, Femme Fatale. It was written and produced by Dr. Luke and Max Martin, with additional writing by Kesha and Alexander Kronlund, and additional production by...
(released March 2011) uses a 4:3 cross-rhythm in its hook.
Examples
The following is an example of a 3 against 2 polyrhythm, given in
time unit box systemTime Unit Box System is a simple system for notating events that happen over a period of time. This system is mostly used for notating rhythms in music. The notation consists of one or more rows of boxes; each box represents a fixed unit of time...
(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 against 2 polyrhythm
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2-beat rhythm |
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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"Carol of the Bells" is the common English language title of a Christmas carol of Ukrainian origin, which has in recent years grown in popularity, particularly in English-speaking countries. The work was originally a choral miniature composition by the Ukrainian composer Mykola Leontovych based on...
".
Similar phrases for the 4 against 3 polyrhythm are "pass the golden butter" or "pass the goddamn butter" and "what atrocious weather"; The 4 against 3 polyrhythm is shown below.
4 against 3 polyrhythm
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3-beat rhythm |
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As can be seen from above, the counting for polyrhythms is determined by the
lowest common multipleIn arithmetic and number theory, the least common multiple of two integers a and b, usually denoted by LCM, is the smallest positive integer that is a multiple of both a and b...
, 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 musiciansThe origins of Indian classical music can be found in the Vedas, which are the oldest scriptures in the Hindu tradition. Indian classical music has also been significantly influenced by, or syncretised with, Indian folk music and Persian music. The Samaveda, one of the four Vedas, describes music...
, can intuitively play high polyrhythms such as 7 against 8.
Polyrhythms are quite common in late
Romantic MusicRomantic music or music in the Romantic Period is a musicological and artistic term referring to a particular period, theory, compositional practice, and canon in Western music history, from 1810 to 1900....
and
20th century classical music20th century classical music was without a dominant style and highly diverse.-Introduction:At the turn of the century, music was characteristically late Romantic in style. Composers such as Gustav Mahler and Jean Sibelius were pushing the bounds of Post-Romantic Symphonic writing...
. 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 MinorThe Piano Concerto in A minor, Op. 16, composed by Edvard Grieg in 1868, was the only concerto Grieg completed. It is one of his most popular works and among the most popular of all piano concerti.-Structure :The concerto is in three movements:...
; 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. 2The Piano Concerto No. 2 in C minor, Op. 18, is a concerto for piano and orchestra composed by Sergei Rachmaninoff between the autumn of 1900 and April 1901. The second and third movements were first performed with the composer as soloist on 2 December 1900...
. 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
glissandoIn music, a glissando is a glide from one pitch to another. It is an Italianized musical term derived from the French glisser, to glide. In some contexts it is distinguished from the continuous portamento...
', fits 52 notes into the space of one
measureIn musical notation, a bar is a segment of time defined by a given number of beats of a given duration. Typically, a piece consists of several bars of the same length, and in modern musical notation the number of beats in each bar is specified at the beginning of the score by the top number of a...
, 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 GriffesCharles Tomlinson Griffes was an American composer for piano, chamber ensembles and for voice.-Musical career:...
’
The White Peacock.
See also
- Ewe music
Ewe music is the music of the Ewe people of West Africa. Instrumentation is primarily percussive and rhythmically the music features great metrical complexity. Its highest form is in dance music including a drum orchestra, but there are also work, play, and other songs. Despite his title Ewe music...
- Beat (acoustics)
In acoustics, a beat is an interference between two sounds of slightly different frequencies, perceived as periodic variations in volume whose rate is the difference between the two frequencies....
- another example of the same effect (mathematically), but with two continuous waves rather than a hit of the instrument only at every peak and trough of either wave.
- Hemiola
In modern musical parlance, a hemiola is a metrical pattern in which two bars in simple triple time are articulated as if they were three bars in simple duple time...
Further reading
- Peter Magadini (2001). Polyrhythms: The Musicians Guide. ISBN 0-634-03283-6. Polyrhythm reference book.
- Peter Magadini (1993). Polyrhythms For The Drumset. ISBN 0-89724-821-X. Study in polymetric independence for drummers.
External links