Origin and Definition of the word "Canon"
"Canon" comes from the Greek word for
rule or law. Musically, it designates the strictest form of counterpoint
in which one voice is bound to imitate the rhythm, and interval content
of another voice.
Requirements of a Canon
To qualify as a canon three conditions
must be met:
Canons are based, in theory, upon the
principle of contrapuntal inversion...two melodic lines that can be performed
simultaneously with either line functioning as the bass.
The 2nd voice must be an exact repetition
or a contrapuntal derivation of the 1st.
The 2nd voice must enter later than
the 1st (cancrizans and proportional canon excepted)
The 2nd voice may not deviate from
the 1st voice or its contrapuntal variations. Thus, the 2nd voice is thought
to be strictly generated by the 1st. The two voices of a canon have been
called dux/comes, antecedens/consequens, or proposta/ risposta;
but this study uses the terms "leader" and "follower."
If all of the above conditions are
met, the canon is said to be "strict." If liberties are taken with one
or more of the above conditions, the canon is said to be "free." Canons
of the 18th and 20th centuries tend to be strict, while canons of the 19th
century may be free.
Categories of Canonic Imitation
The second voice of a canon may imitate
the first voice exactly, at a different pitch level, in contrary motion,
with change of rhythmic proportions, backward, or any combination thereof.
Canon at the Unison or Octave
In a unison canon the follower
performs precisely the same melody as the leader. As the name implies,
canon at the octave involves repetition of the leader an octave higher
or lower. Var. 3 and Var. 24 of the Goldberg Variations are at the
unison and octave respectively. If the end of the canon returns smoothly
to the beginning it might be called a round, circular canon, or perpetual
canon like Canon 7 of the Musical Offering and Bach's Canon a
2 Perpetuus (BWV 1075).
Canon at Intervals Other than the
Octave or Unison
Many canons are contrived so that
the follower begins on a pitch other than the starting pitch of the leader.
The canons of the Goldberg Variations, for example, are ordered
systematically so that each successive canon employs a larger interval
between leader and follower. The follower may be a tonal imitation of the
leader, that is, it may alter the interval qualities somewhat so as to
stay in the same key as the leader, or it may be an exact transposition
to a new key. Var. 18 of the Goldberg Variations is a canon at the
sixth, but the interval may be a major or minor sixth depending upon the
scale degrees that are involved. By contrast, the follower of the Fuga
Canonica in Epidiapente from the Musical Offering is a strict
transposition of the leader up a perfect fifth (each note of the follower
reposing a perfect fifth above its counterpart in the leader). A third
type of interval canon is exemplified in the second of the Canonic Variations
on Vom Himmel hoch, where Bach inflects the pitches of the follower
quite freely in order that the canon might conform to the tonality of the
firmus which it accompanies.
Retrograde Canon (Cancrizans,
or "crab" canon)
One of the more exotic forms, retrograde
canon involves the playing of a melody forward and backward at the same
time. It is the custom, with canons of this sort, for each player to read
the music once from left to right (forward) and then to return from right
to left (backward). Thus, retrograde canons are sometimes called "crab"
or cancrizans (after the sideways manner of that creature). Because
both parts begin simultaneously, the terms "leader" and "follower" hardly
apply to crab canons, examples of which include: the Cancrizans
from the Musical Offering, and the First and second canons from
the Fourteen on the Goldberg Ground.
Canon in Contrary Motion
When the canon leader and follower
progress by the same melodic intervals, but move in the opposite direction,
the canon is said to be in contrary motion. In the context of canons, the
term "inverted canon" is synonymous with "canon in contrary motion." Canons
in contrary motion exemplify the technique of "melodic inversion," and
should not be confused with contrapuntal inversion (also known as "double
counterpoint") in which two contrapuntal lines exchange registers...the
low becoming the high and visa versa. The fourth canon of Die Kunst
employs both techniques: its follower is in contrary motion to its leader,
and its second half involves an exchange of registers (double counterpoint)
between leader and follower. Of the Bach's canons extant, many involve
contrary motion, including the following: the Trias Harmonica, Canon
Concordia Discors, most of the Fourteen Canons on the Goldberg Ground,
Goldberg #12, Goldberg #15, Vom Himmel hoch #3, and Musical Offering
No. 3. Notice that canons in contrary motion are normally constructed
so that if the leader begins on the tonic pitch the follower will begin
on the dominant, and visa versa.
Ordinarily, canons in contrary
motion freely inflect interval qualities in order to stay within the key.
Composers with exceptional skill have constructed a rigorous sub-category,
called "mirror" canon, in which followers mimic the precise quality of
intervals stated by leaders (albeit in the opposite direction). As the
technique is difficult, mirror canons are quite rare. The rule of qualitative
correspondence between intervals implies that mirror canons invoke more
than the usual number of chromatic pitches as No. 6, No. 8, and No. 11
from the Fourteen on the Goldberg Ground, Canon perpetuus and Canon
a 2 Quaerendo invenietis from the Musical Offering demonstrate.
More commonly termed "canon in
augmentation or diminution," proportional canons re-articulate the rhythm
of the leader at a ratio other than one to one. Thus, the follower might
progress at half, twice, or three times, the speed of the leader. Voices
in proportional canon may start at the same time or at different times.
Bach's proportional canons include: the fourth canon of the Musical
Offering the final canon of the Variations on Vom Himmel hoch,
the fourth canon from the Art of Fugue, and, Bach's tour de forcein
this genre, the final canon of the 14 on the Goldberg Ground.
Whereas most canons are repeatable,
when a spiral canon repeats it does so at some other pitch. If the new
pitch is the same scale degree (in a new key), the canon is a modulating
spiral, like Bach's canon a 2 per tonus of the Musical Offering.
If the new pitch is a different scale degree (in the same key), the canon
is a modal spiral. This study contains no examples of modal spiral, but
the four-voice canon Bach composed for Walther puts each of the voices
into a different mode with an overall effect of Dorian.
Music that contains canonic voices
to which have been added one or more voices in free counterpoint is said
to be "accompanied." In most of Bach's accompanied canons this added voice
is the bass. Obviously, when a bass part is added the requirement that
the upper canonic voices be able to function as bass no longer applies.
This liberates the composer to involve the canonic voices in counterpoint
that might not otherwise have been possible. With the exception of the
last (Var. 27), all of the canons of the Goldberg Variations are
accompanied. The added voice may represent a pre-existing melody, such
as the "royal theme" in the second canon of the Musical Offering,
or the canonic voices themselves may be cantus firmi. All of the
canonic preludes of the Orgelbuchlein,Clavier-Ubung III, most of
the Canonic Variations on Vom Himmel hoch, and five of the canons
from the Fourteen on the Goldberg Ground fall into this latter category.
Double and Triple Canon
A canon that has two leaders and
two followers is a double canon...see the fifth canon of the Fourteen on
the Goldberg Ground. Double canons are sometimes referred to as "canon
four in two." In the thirteenth canon of that cycle Bach managed even to
construct a triplex canon, or "canon six in three."
Combining More than One Technique
After listening to the canons of
this study the casual listener might come to the conclusion that they are
not difficult to compose. Nothing could be further from the truth! Even
the simplest types present challenges beyond the abilities of most musicians.
Yet Bach imposed upon himself not only the strictures of contrary motion,
augmentation, and retrograde motion, but in many instances the simultaneous
adherence to more than one canonic rule! Thus, the third canon of the Musical
Offering is an accompanied canon in contrary motion as are the sixth,
seventh, and eighth canons from the Fourteen on the Goldberg Ground. The
eighth canon of the Musical Offering is an accompanied mirror, while
the eleventh canon of the Fourteen on the Goldberg ground is an accompanied
double mirror. Perhaps the most difficult combinations of Bach's repertory
are his three canons in augmentation and contrary motion: No. 14 from the
cycle on the Goldberg ground, No. 4 from the Art of Fugue, and No.
4 from the Musical Offering.
Before 1600 polyphonic music was
normally written in parts, not score. This meant that a musician could
see but one line of music and not the accompanying voices. As a consequence
it was customary in the writing of canons from this era to notate only
the canon leader, with some rule whereby the follower would be generated
from it: a second starting point, another interval or a time proportion.
Many of Josquin's chansons, for example, contain a vocal line intended
to be sung as two--in canon. Today we call this type of notation "cryptic,"
meaning that it is concise not that the composer was wanting to be secretive.
There does exist, however, a genre
of canons where the composer engages in deliberate obfuscation. Many of
Bach's canons are of this type. This study, for example, contains instances
where he hints at the canon by means of a monogram, symbol, or other cryptic
device. When the solution is not obvious the work is said to be a "riddle"
or "enigmatic" canon. J. S. Bach encrypted the cancrizans from the
Offering for example, by placing a backward clef at its conclusion.
He used the same technique in the 1st and 2nd canons on the Goldberg Ground.
Bach encrypted canons in contrary
motion by inverting clefs (see canons four, and nine of the Musical
Offering). Because inverting a C-clef effects no apparent change, contrary
motion is signified by the inversion of key signatures or by the placement
of accidentals on "wrong" lines and spaces. The third and fourth canons
from the Fourteen on the Goldberg Ground, for example, contain C-clefs
with sharps in the key signature that appear "incorrectly" on the pitch
G. Only after the clefs have been inverted do the sharps appear correctly
Canons in which the follower begins
at a pitch other than that of the leader (e.g. numbers five and six from
the Musical Offering) are indicated by the imposition of two or
more clefs upon the staff. Bach's canon for Walther contains four such
clefs, while his canon for Hudemann contains no fewer than eight (four
inverted with different key signatures).
Finally, if the musical symbolism
is not enough, the composer might write clues in prose. The fourth and
fifth canons of the Musical Offering are accompanied by Latin riddles
indicating the nature of the canonic technique, while the Canon Fa Mi
et Mi Fa contains a dedicatory acrostic spelling the composer's name.
Written by Tim Smith, Professor
of Music Theory
Northern Arizona University