The term polytempo or polytempic is used to describe

music Music is generally defined as the The arts, art of arranging sound to create some combination of Musical form, form, harmony, melody, rhythm or otherwise Musical expression, expressive content. Exact definition of music, definitions of mu ...

in which two or more tempi occur simultaneously. In the Western world, the practice of polytempic music has its roots in the music theory of

Henry Cowell Henry Dixon Cowell (; March 11, 1897 – December 10, 1965) was an American composer, writer, pianist, publisher and teacher. Marchioni, Tonimarie (2012)"Henry Cowell: A Life Stranger Than Fiction" ''The Juilliard Journal''. Retrieved 19 June 20 ...

, and the early practices of Charles Ives. Later on, composer

Elliott Carter Elliott Cook Carter Jr. (December 11, 1908 – November 5, 2012) was an American modernism (music), modernist composer. One of the most respected composers of the second half of the 20th century, he combined elements of European modernism a ...

, in the fifties, began polymetric experiments in his

string quartet The term string quartet can refer to either a type of musical composition or a group of four people who play them. Many composers from the mid-18th century onwards wrote string quartets. The associated musical ensemble consists of two violinist ...

s that inevitably amounted to polytempic behavior by nature of several competing lines at different surface speeds. At around the same time, composer

Henry Brant Henry Dreyfuss Brant (September 15, 1913 – April 26, 2008) was a Canadian-born American composer. An expert orchestrator with a flair for experimentation, many of Brant's works featured spatialization techniques. Biography Brant was born i ...

expanded on Ives's ''

The Unanswered Question ''The Unanswered Question'' is a musical work by American composer Charles Ives. Originally paired with '' Central Park in the Dark'' as ''Two Contemplations'' in 1908, ''The Unanswered Question'' was revised by Ives in 1930–1935. As with ma ...

'' to create a spatial music in which entire ensembles, separated by vast distances, play in distinct simultaneous tempi. Some types of

African drumming Sub-Saharan African music is characterised by a "strong rhythmic interest" that exhibits common characteristics in all regions of this vast territory, so that Arthur Morris Jones (1889–1980) has described the many local approaches as constit ...

exhibit this phenomenon. Today's composers are employing polytempi as a compositional strategy to create total and complete independence of line in

polyphonic Polyphony ( ) is a type of musical texture consisting of two or more simultaneous lines of independent melody, as opposed to a musical texture with just one voice, monophony, or a texture with one dominant melodic voice accompanied by chords, h ...

music. Composers such as

Conlon Nancarrow Samuel Conlon Nancarrow (; October 27, 1912 – August 10, 1997) was an American- Mexican composer who lived and worked in Mexico for most of his life. Nancarrow is best remembered for his ''Studies for Player Piano'', being one of the firs ...

David A. Jaffe David Aaron Jaffe (born April 29, 1955) is an American composer who has written over ninety works for orchestra, chorus, chamber ensembles, and electronics. He is best known for his use of technology as an electronic-music or computer-music c ...

, Evgeni Kostitsyn,

Kyle Gann Kyle Eugene Gann (born November 21, 1955, in Dallas, Texas) is an American professor of music, critic, analyst, and composer who has worked primarily in the New York City area. As a music critic for ''The Village Voice'' (from 1986 to 2005) and ...

, Kenneth Jonsson, John Arrigo-Nelson,

Brian Ferneyhough Brian John Peter Ferneyhough (; born 16 January 1943) is an English composer. Ferneyhough is typically considered the central figure of the New Complexity movement. Ferneyhough has taught composition at the Hochschule für Musik Freiburg and ...

Karlheinz Stockhausen Karlheinz Stockhausen (; 22 August 1928 – 5 December 2007) was a German composer, widely acknowledged by critics as one of the most important but also controversial composers of the 20th and early 21st centuries. He is known for his groundb ...

Frank Zappa Frank Vincent Zappa (December 21, 1940 – December 4, 1993) was an American musician, composer, and bandleader. His work is characterized by nonconformity, free-form improvisation, sound experiments, musical virtuosity and satire of A ...

, and Peter Thoegersen have used various methods in achieving polytempic effects in their music. Polytempic music also harkens to the rhythmic practices of some Renaissance and medieval composers (see

hemiola In music, hemiola (also hemiolia) is the ratio 3:2. The equivalent Latin term is sesquialtera. In rhythm, ''hemiola'' refers to three beats of equal value in the time normally occupied by two beats. In pitch, ''hemiola'' refers to the interval of ...

Multitemporal music

Multitemporal music is composed using sound streams that have different internal tempi or

pulse In medicine, a pulse represents the tactile arterial palpation of the cardiac cycle (heartbeat) by trained fingertips. The pulse may be palpated in any place that allows an artery to be compressed near the surface of the body, such as at the ...

speed, for example one part at 115 bpm and at 105 bpm at the same time. Multitemporal music was first heard in US-Mexican composer

's work, discovered by Hungarian

György Ligeti György Sándor Ligeti (; ; 28 May 1923 – 12 June 2006) was a Hungarian-Austrian composer of contemporary classical music. He has been described as "one of the most important avant-garde composers in the latter half of the twentieth century" ...

,{{Explanation needed, reason=The word "discovered" implies that Ligeti was the first person to find it., date=March 2018 who undertook the task of bringing Nancarrow's music to the fore. To overcome the limits posed by a human performer in playing a multitemporal score Nancarrow used two modified

player-pianos A player piano (also known as a pianola) is a self-playing piano containing a pneumatic or electro-mechanical mechanism, that operates the piano action via programmed music recorded on perforated paper or metallic rolls, with more modern i ...

, punching the rolls by hand. One of the few recordings of this composer's work is found in Wergo's " Studies for Player Piano" series. The idea was then proposed by

Iannis Xenakis Giannis Klearchou Xenakis (also spelled for professional purposes as Yannis or Iannis Xenakis; el, Γιάννης "Ιωάννης" Κλέαρχου Ξενάκης, ; 29 May 1922 – 4 February 2001) was a Romanian-born Greek-French avant-garde ...

in the early seventies and more recently by Italian born composer Valerio Camporini Faggioni Valerio Camporini F., ''Multitemporal Designs,'' (Line)
/ref> using synthetic and software devices. A similar technique, with the tempi similar to each other is rhythm phasing – a technique introduced by

Steve Reich Stephen Michael Reich ( ; born October 3, 1936) is an American composer known for his contribution to the development of minimal music in the mid to late 1960s. Reich's work is marked by its use of repetitive figures, slow harmonic rhythm, ...

and used especially in

minimalist In visual arts, music and other media, minimalism is an art movement that began in post–World War II in Western art, most strongly with American visual arts in the 1960s and early 1970s. Prominent artists associated with minimalism include Do ...

and

post-minimalist Postminimalism is an art term coined (as post-minimalism) by Robert Pincus-Witten in 1971Chilvers, Ian and Glaves-Smith, John, ''A Dictionary of Modern and Contemporary Art'', second edition (Oxford and New York: Oxford University Press, 2009), p. ...

music.

References

Rhythm and meter

Multitemporal music

See also

References