Mensuration canon

Canon (music)

In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration (e.g. quarter rest, one measure, etc.). The initial melody is called the leader, while the imitative melody is called the follower which is played in a different voice. The follower must be created from the leader by being either an exact replication of the rhythms and intervals of the leader, or a transformation such as those listed in "Types of canon" (below). Canons where all parts sing identical music and which repeat are called rounds, such as "Row, Row, Row Your Boat" and "Frère Jacques".

Accompanied canon is a canon accompanied by one or more additional independent parts which do not take part in imitating the melody.


The Old French canon, which meant 'learned', was taken from the Greek kanon for a rule or law, which eventually came to mean 'an accepted rule' in English, and the term was first used for the rule that describes how the voices relate to each other. Not until the sixteenth century was canon used to describe the musical form. The earliest known canons are the rounds (or rondellus) in England from the thirteenth century; the best known is Sumer Is Icumen In. In the fourteenth century many canons were written in Italy under the name caccia, and occasionally French chansons of that period used canon technique. During the period of the Franco-Flemish School (1430-1550), canon as a contrapuntal art form received its greatest development, while the Roman School gave it its most complete application. In the later periods the canon played a less important role (as entertainment), with a few notable exceptions like Bach's The Musical Offering. Arnold Schoenberg revived the interest in canon with his twelve-tone technique.

Types of canon

The most rigid and ingenious forms of canon are not strictly concerned with pattern but also with content. Canons are classified by various traits: the number of voices, the interval at which each successive voice is transposed in relation to the preceding voice, whether voices are inverse, retrograde, or retrograde-inverse; the temporal distance between each voice, whether the intervals of the second voice are exactly those of the original or if they are adjusted to fit the diatonic scale, and the tempo of successive voices. However, canons may use more than one of the above methods.

How voices in a canon are named

Although, for clarity, this article uses leader and follower(s) to denote the leading voice in a canon and those that imitate it, musicological literature also uses the traditional Latin terms Dux and Comes for "leader" and "follower", respectively. The terms "Proposta" for the leader, and "Riposta" for the follower, are also common terms.

Number of voices

A canon of two voices may be called a canon in two, similarly a canon of x voices would be called a canon in x. This terminology may be used in combination with a similar terminology for the interval between each voice, different from the terminology in the following paragraph.

Another standard designation is "Canon: Two in One", which means two voices in one canon. "Canon: Four in Two" means four voices with two simultaneous canons. While "Canon: Six in Three" means six voices with three simultaneous canons, and so on.


A simple canon (also known as a round) imitates the leader perfectly at the octave or unison. Well-known canons of this type include the famous children's song Row, Row, Row Your Boat and Frère Jacques.


An interval canon imitates the leader at any interval other than the octave or unison (e.g. canon at the second, fifth, seventh, etc.). If the follower imitates the precise interval quality of the leader, then it is called an exact canon; if the follower imitates the interval number (but not the quality), it is called a diatonic canon.

Contrapuntal derivations

The follower may be a contrapuntal derivation of the leader.


An inverted canon (also called canon in contrary motion) moves the follower in contrary motion to the leader. Where the leader would go down a fifth, the follower goes up, and vice versa. A sub-order of canon in contrary motion, "mirror," maintains the precise quality of each interval.


In a crab canon, also known as cancrizans, the follower accompanies the leader backward (in retrograde). A canon that is retrograde and inverse is called a Table Canon. A Table Canon would be placed on a table with a musician on either side, both reading the same line of music in opposite directions.

Mensuration and tempo canons

In a mensuration canon (also known as a prolation canon, or a proportional canon), the follower imitates the leader by some rhythmic proportion. The follower may double the rhythmic values of the leader (augmentation or sloth canon) or it may cut the rhythmic proportions in half (diminution canon). Phasing involves the application of modulating rhythmic proportions according to a sliding scale. The cancrizans, and often the mensuration canon, take exception to the rule that the follower must start later than the leader.

Technically, mensuration canons are among the most difficult to write. Many such canons were composed during the Renaissance, particularly in the late fifteenth and early sixteenth centuries; Johannes Ockeghem wrote an entire mass (the Missa Prolationum) in which each section is a mensuration canon, and all at different speeds and entry intervals. In the twentieth century, Conlon Nancarrow composed complex tempo or mensural canons, mostly for the player piano as they are extremely difficult to play; they have also influenced many younger composers. Larry Polansky has an album of mensuration canons, Four-Voice Canons.

Other types of canon

The most familiar of the canons might be the perpetual/infinite canon (in Latin: canon perpetuus) or round. As (each voice of) the canon arrives at its end it can begin again, in a Perpetuum mobile fashion; e.g. "Three Blind Mice". Such a canon is often called a round or rota. Sumer is icumen in is one example of a piece designated rota.

Additional types include the spiral canon, accompanied canon, and double or triple canon.

Puzzle canon

A Puzzle canon can be any of the above types, but only one voice is notated, and it is up to the performer to find out which rule applies to the canon. Often some kind of riddle is given as a hint. Machaut's rondeau Ma fin est mon commencement et mon commencement est ma fin (My end is my beginning and my beginning is my end) is a crab canon with a third voice which is a musical palindrome. In the Agnus Dei movement of Dufay's mass L'homme armé is this rule noted: Cancer eat plenis et redeat medius ('Let the crab proceed full and return half'). This means that the cantus firmus must be sung first in full note values (and retrograde, since it is a crab), then in halved values and retrograde (that is, normal motion, since it is a crab).

Mirror canon

In a Mirror Canon (or canon by contrary motion), the subsequent voice imitates the initial voice in inversion. They are not very common, though examples of mirror canons can be traced to Bach, Mozart (e.g., the trio from Serenade for Wind Octet in C, K. 388), Webern, and other composers.

Table Canon

A Table Canon is a retrograde and inverse Canon meant to be placed on a table in between two musicians who both read the same line of music in opposite directions. Seeing that both parts are included in each single line, a second line is not needed. Bach wrote a few table canons. Table canons are novelty musical works and have never had much popularity with the general public.

Elaborate use of canon technique

  • Josquin Desprez, Missa L'homme armé super voces musicales, Agnus Dei 2: One voice write with the words 'ex una voce tres' (three voice parts out of one), a mensuration canon in three voices in different tempos.
  • Josquin Desprez, Missa L'homme armé sexti toni, Agnus Dei 2: two simultaneous canons in the four upper voices, and at the same time a crab canon in the two lower voices.

Contemporary canons

The most popular canons heard today are from the Baroque period, such as Johann Pachelbel's Canon in D (Pachelbel's Canon), in which a canon between the three upper voices are accompanied by a repeating bass melody or ground, or every third variation in Bach's Goldberg Variations. The third movement of Gustav Mahler's First Symphony starts with an accompanied simple canon based on Frère Jacques, albeit in D Minor. Jean Sibelius's Sixth Symphony contains many hidden canons: for instance, a 3-in-1 in the strings in which each part is thickened to a third; a 4-in-2; a canon by diminution; and a canon with augmentations at two different speeds. What may be George Rochberg's best known work, his String Quartet No. 6, includes a set of variations on the Pachelbel Canon in D. Henryk Górecki's Third Symphony begins with an extensive eight voice canon in the strings. Steve Reich uses a process he calls phasing which is a canon with variable distance between the voices.



  • Canonic Studies: A New Technique in Composition. Bernhard Ziehn; edited and introduced by Ronald Stevenson. Publisher: New York : Crescendo Pub., 1977. ISBN 0-87597-106-7.
  • Lamla, Michael: Kanonkünste im barocken Italien, insbesondere in Rom, Berlin 2003, ISBN 3-89825-556-5.
  • Katelijne Schiltz and Bonnie J. Blackburne (eds.), Canons and Canonic Techniques, 14th-16th Centuries: Theory, Practice, and Reception History. Proceedings of the International Conference Leuven, 4-5 October 2005, Leuven, 2007.

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