music Music is generally defined as the art of arranging sound to create some combination of form, harmony, melody, rhythm or otherwise expressive content. Exact definitions of music vary considerably around the world, though it is an aspect ...

, a prolation canon (also called a mensuration canon or proportional canon) is a type of

canon Canon or Canons may refer to: Arts and entertainment * Canon (fiction), the conceptual material accepted as official in a fictional universe by its fan base * Literary canon, an accepted body of works considered as high culture ** Western ca ...

, a musical composition wherein the main

melody A melody (from Greek language, Greek μελῳδία, ''melōidía'', "singing, chanting"), also tune, voice or line, is a Linearity#Music, linear succession of musical tones that the listener perceives as a single entity. In its most liter ...

is accompanied by one or more imitations of that melody in other voices. Not only do the voices sing or play the same melody, they do so at different speeds (or ''prolations'', a mensuration term that dates to the

medieval In the history of Europe, the Middle Ages or medieval period lasted approximately from the late 5th to the late 15th centuries, similar to the Post-classical, post-classical period of World history (field), global history. It began with t ...

and

Renaissance The Renaissance ( , ) , from , with the same meanings. is a period in European history marking the transition from the Middle Ages to modernity and covering the 15th and 16th centuries, characterized by an effort to revive and surpass ideas ...

eras). Accompanying voices may enter either simultaneously or successively. If voices extend the rhythmic values of the leader (for example, by doubling all note values), a procedure known as augmentation, the resulting canon can be called an augmentation canon or canon by augmentation (''canon per augmentationem'') or sloth canon (recalling the slow movement of the

sloth Sloths are a group of Neotropical xenarthran mammals constituting the suborder Folivora, including the extant arboreal tree sloths and extinct terrestrial ground sloths. Noted for their slowness of movement, tree sloths spend most of their li ...

). Conversely, if they reduce the note values in

diminution In Western music and music theory, diminution (from Medieval Latin ''diminutio'', alteration of Latin ''deminutio'', decrease) has four distinct meanings. Diminution may be a form of embellishment in which a long note is divided into a series of ...

, it can be called a diminution canon or canon by diminution (''canon per diminutionem'').

Examples

Prolation canons are among the most difficult canons to write, and are relatively rare in the repertory, though they are most common in the early Renaissance and from the 20th century to the present. Examples of prolation canons from the Renaissance include ''Le Ray Au Soleyl'' by

Johannes Ciconia Johannes Ciconia ( – between 10 June and 13 July 1412) was an important Flemish composer and music theorist of trecento music during the late Medieval era. He was born in Liège, but worked most of his adult life in Italy, particularly i ...

(late 14th century); the entire ''

Missa prolationum The ''Missa prolationum'' is a musical setting of the Ordinary of the Mass by Johannes Ockeghem, dating from the second half of the 15th century. Based on freely written material probably composed by Ockeghem himself, and consisting entirely of ...

'' by

Johannes Ockeghem Johannes Ockeghem ( – 6 February 1497) was a Franco-Flemish composer and singer of early Renaissance music. Ockeghem was the most influential European composer in the period between Guillaume Du Fay and Josquin des Prez, and he was—with his ...

(mid-15th century), in which each separate section of the mass explores a different prolation (or different gap between entries and relative speed of each voice); the

Agnus Dei is the Latin name under which the " Lamb of God" is honoured within the Catholic Mass and other Christian liturgies descending from the Latin liturgical tradition. It is the name given to a specific prayer that occurs in these liturgies, and ...

from the ''

Missa L'homme armé super voces musicales The ''Missa L'homme armé super voces musicales'' is the first of two settings of the Ordinary of the Mass by Josquin des Prez using the famous '' L'homme armé'' tune as their cantus firmus source material (for the other, presumed later, setting ...

'' by

Josquin des Prez Josquin Lebloitte dit des Prez ( – 27 August 1521) was a composer of High Renaissance music, who is variously described as French or Franco-Flemish. Considered one of the greatest composers of the Renaissance, he was a central figure of the ...

(late 15th century); and the

from the ''

Missa L'homme armé Over 40 settings of the Ordinary of the Mass using the tune '' L'homme armé'' survive from the period between 1450 and the end of the 17th century, making the tune the most popular single source from the period on which to base an imitation mass. ...

'' by

Pierre de la Rue Pierre de la Rue ( – 20 November 1518) was a Franco-Flemish composer and singer of the Renaissance. His name also appears as Piersson or variants of Pierchon and his toponymic, when present, as various forms of de Platea, de Robore, or de Vico ...

(early 16th century). Prolationcanonjosquin

In this example, the first 12 bars of the Agnus Dei II of the earlier of the two masses Josquin wrote based on the '' L'homme armé'' tune, each voice sings the same music, but at different speeds. The top voice is barred in 3/4 meter for clarity. The slowest voice is the one in the middle. The lowest voice sings the same music at twice the speed of the slowest, and the highest voice sings the same music at three times the speed of the slowest. In the original score, only one part is given: a notation over the single line of music indicates the three prolations to be used, and a second notation over the line indicates where each voice should end if sung correctly.

Johann Sebastian Bach Johann Sebastian Bach (28 July 1750) was a German composer and musician of the late Baroque period. He is known for his orchestral music such as the '' Brandenburg Concertos''; instrumental compositions such as the Cello Suites; keyboard w ...

is known for his ''Canon a 4 per Augmentationem et Diminutionem'', the last in a set of 14 canons written as an appendix to the ''

Goldberg Variations The ''Goldberg Variations'', BWV 988, is a musical composition for keyboard by Johann Sebastian Bach, consisting of an aria and a set of 30 variations. First published in 1741, it is named after Johann Gottlieb Goldberg, who may also have ...

''. In the 20th century, one such canon is the ''

Cantus in Memoriam Benjamin Britten ''Cantus in Memoriam Benjamin Britten'' () is a short canon in A minor, written in 1977 by the Estonian composer Arvo Pärt, for string orchestra and bell. The work is an early example of Pärt's tintinnabuli style, which he based on his react ...

'' by

Arvo Pärt Arvo Pärt (; born 11 September 1935) is an Estonian composer of contemporary classical music. Since the late 1970s, Pärt has worked in a minimalist style that employs tintinnabuli, a compositional technique he invented. Pärt's music is in pa ...

(1976). Additionally,

Larry Polansky Larry Polansky (born 1954) is a composer, guitarist, mandolinist, and professor emeritus at Dartmouth College and the University of California, Santa Cruz. He is a founding member and co-director of Frog Peak Music (a composers' collective) ...

has written numerous four-voice prolation canons whose melodies are permutations of a limited number of elements, and

Mark Alburger Mark Alburger (born April 2, 1957 in Upper Darby, Pennsylvania) is a San Francisco Bay area composer and conductor. He is the founder and music director of the San Francisco Composers Chamber Orchestra, as well as the music director of Goat ...

, in ''Immortality'' from ''San Rafael News'', directly maps a new melody into the framework of the aforementioned Josquin. A particularly striking example of prolation canon occurs twice in the opening movement of

Shostakovich Dmitri Dmitriyevich Shostakovich, , group=n (9 August 1975) was a Soviet-era Russian composer and pianist who became internationally known after the premiere of his First Symphony in 1926 and was regarded throughout his life as a major compo ...

's Symphony No. 15 (1971), first in the strings
Rehearsal Figure 27
and later in the woodwind a
Rehearsal Figure 47
A more recent example of a prolation canon in contemporary music is ''rindenmotette'' (2011) by Austrian composer Klaus Lang.

References

* * * * {{cite book, title=The Notation of Polyphonic Music 900-1600, first=Willi, last=Apel, location=Cambridge, Massachusetts, publisher=The Medieval Academy of America, year=1953, lccn=61-12067 , oclc=616117, url=https://archive.org/details/notationofpolyph00apel/page/180/mode/2up?q=%22mensuration+canon%22 Polyphonic form