Polyrhythm () 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.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 polyrhythmic because its three section suggests a different meter from the pulse of the entire pattern.Novotney, Eugene D. (1998: 265). , Urbana, Illinois: University of Illinois.
In western art music In 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 ( and ):
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."Swafford, J. (1997) Johannes Brahms, a Biography. London, Macmillan.
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." "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.
Hemiola Concerning 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 time, but with a curiously persistent cross-rhythm that does its best to persuade us that it is really in ."Walker, Ernest (1905: 79) The Music of the Masters; Beethoven. New York: Brentano's Union Square.
Polyrhythm, not polymeter The illusion of simultaneous and , suggests polymeter: triple meter combined with compound duple meter.
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 hemiola The 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.
Cross-rhythm Cross-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.” Kennedy, M. and Bourne, J. (eds) (2007) The Concise Oxford Dictionary of Music, Oxford University Press. 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. ”Da Fonseca-Wollheim, C. (2018), "Does Brahms’s Obsession With Rhythmic Instability Explain His Music’s Magic?" New York Times, 19 October.
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 interval ratios are found in the harmonic series. These are called harmonic polyrhythms.
Sub-Saharan African music traditions
Comparing European and Sub-Saharan African meter 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 generating principle In 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.
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 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. 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.
Adaptive instruments Sub-Saharan instruments are constructed in a variety of ways to generate polyrhythmic melodies. Some instruments organize the pitches in a uniquely divided alternate array, not in the straight linear bass 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.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.The Gravikord web site : http://www.gravikord.com/instrument.html#gravikord