The following writeup provides more detailed information on what a canon is -- in the musical sense. The canon is most often found in classical music, but it appears in other forms as well.
Definition:
A musical passage in which the melody (or theme) is repeated by one or more voices at a different interval of pitch and/or time. It is the strictest form of counterpoint -- both the rhythm and content must be duplicated. Canons involve the concept of contrapuntal inversion -- two melodic themes playing simultaneously with either or both of the voices singing the bass part for the other.
There are many names given for the two voices of a canon: "proposta and risposta", "dux and comes", "antecedens and consequens", and most simply "leader and follower".
Requirements:
Strictly defined, a canon must contain the following elements:
- At least two "voices" -- one of which must follow the other. (The only exceptions allowed are the Crab Canon and the Proportional Canon).
- The second voice must be either an exact replica of the first voice or a contrapuntal derivation of the first voice.
- The second voice must be "mechanically" generated from the first. It is not just similar it must be an exact replica or an isomorphism.
If a canon follows all of the above rules it is considered "strict". A "canon" which does not closely follow these rules is said to be "free".
Canonical types:
- Parallel canon:
- Unison canon:
In this form the follower is an exact copy of the leader -- maintaining both its pitch and rhythm. The only
difference is that follower appears sometime after the leader. Usually this happens somewhere between the 1/2 measure and the fourth measure, but it can appear much later if the composer so desires.
The trailing voice comes in after two measures are completed in this example using Row, Row, Row Your Boat,:
leader : row row row your boat | gently down the stream | merrily merrily
follower : row row row
leader : merrily | life is but a dream |
follower : your boat | gently down the stream | merrily merrily
leader :
follower : merrily | life is but a dream
Some other well-known examples of this type: Frere Jaques, Three Blind Mice, Var. 3 of the Goldberg Variations (canone all' Unisuono ), and Pachelbel Canon. These can also be classified as circular or perpetual canons. The short vocal canons are usually called "rounds".
- Octaval canon:
The "canon at the octave" is just like the unison canon except the follower is one octave above or below the leader. Var. 24 of the Goldberg Variations (canone alla Ottava) is an example of this form.
- Canons at other intervals:
Parallel canons can also have their followers appearing at other intervals besides unison and at the octave. The follower has a different pitch that may or may not be in the same key as the leader. A complete transpositon into a new key is possible or it may be adjusted up or down a fourth or fifth (or any other amount though these are most common).
- Inverted canon:
Also known as a "canon in contrary motion" or an "anti-line canon", the inverted canon features its follower playing a top-to-bottom inversion of the leader. The follower is flipped over the horizontal and usually moved up or down in pitch to play in harmony and retain its key. For example: if the leader moves up a third then the follower moves down a third. An example of this is Bach's "Canon 3. a 2 per Motum contrarium" in Musical Offering.
- Mirror canon:
This is a special sub-type of inverted canon. Here the follower is a top-to-bottom mirror image of the leader. It is constructed so that the follower replicates the precise quality of the leader's interval without adjusting the pitch. This form is one of the most difficult for a composer. Arnold Schoenberg has numerous examples of this form (most have "Spiegelkanon", German for mirror canon, in the title). J.S. Bach is also known for exploiting this form in both the Fourteen Canons on the First Eight Notes of the Goldberg Ground (an appendix to the Goldberg Variations) and in "Canon 9. Canon a 2 Quaerendo invenietis " in his Musical Offering.
- Crab canon:
Also known as a "Retrograde canon" or "Reverse canon", the Crab canon features a follower that is a forwards-to-backwards translation of the leader. It is most unusual because the two voices begin and end at the same time -- making the terms "leader" and "follower" a bit of a misnomer. The most famous example of this is Bach's Canon 1. a 2 cancrizans contained in Musical Offering.
- Proportional canon:
These also are called "Mensuration canons". In this form the two voices may start at the same, but are not required to do so. They come in two types:
- Canon in augmentation:
Also called an "expansed canon", this form has the follower playing at a rhythm slower than the leader. Typically the 2nd voice is played at exactly 1/2 the pace as the 1st voice. Check out Alexei Stanchinsky's Two-part Canon in augmentation in E Flat Minor.
- Canon in diminution:
Also called a "reduced canon", this form has the follower playing at a rhythm faster than the leader. Typically the 2nd voice is played at exactly 2 or 3 times the pace as the 1st voice. You'll find an example of this in Bach's "Canon 14. Canon a 4 per Augmentationem et Diminutionem" in the Goldberg Ground works.
- Spiral canon:
A form of "perpetual canon", this form is disinguished in that the end of the piece is in a different pitch from the beginning. There are two types of spiral canons:
- Modulating spiral canon:
If the new pitch attained at the end is also in a new key then we have a modulating spiral. When the piece is repeated successively it will either endlessly rise or endlessly lower its key. Bach's "Canon 5. a 2 per Tonus" is a famous example of this form.
- Modal spiral canon:
In this form the end key will stay the same only its degree will change. When the piece is repeated successively it will either endlessly rise or endlessly lower its pitch -- but will continue in the same key throughout.
- Accompanied canon:
This is a canon that has one or more voices of free counterpoint accompanying the canonical voices. The counterpoint is usually chosen in the bass clef so that the canonical voices are free from having to provide the bass tones for each other.
- Double canon:
Sometimes called a "canon of 4 in 2", this form has two leaders and two followers. Check out the fourth canon, "Canon Duplex a 4", in Bach's Goldberg Ground works.
- Triple canon:
This extremely rare form features three leaders and three followers. Sometimes it's called a "canon of 6 in 3". An example of this one is found in the thirteenth canon, "Triplex canon", in Bach's Goldberg Ground works.
- Perpetual canon:
Almost every canon is created so that when each voice ends it can repeat itself at the beginning seamlessly. This allows the musicians to arbitrarily extend the total length of the canon. These can also be called circular canons and in the case of vocal works they are called rounds.
Concluding thoughts
The above styles of canons can be combined with each other to form hundreds of different kinds of canons. A single canon can be described as "perpetual", "spiral", and "reverse" (or nearly any other combination). The more a canon deviates from the simpler and strict forms -- the more it becomes free. When this freedom is taken to the extreme the canon can become unrecognizable as such and may even become more closely related to a fugue.
I was first "turned on" to the canon form -- and specifically the Bach canons - by Douglas Hofstadter in his book Godel, Escher, Bach: An Eternal Golden Braid. I -- being more mathematically inclined (rather than musically) -- was very grateful to discover the canon form as it makes listening to classical music more interesting.
Am I missing anything here? Is any of the above information just plain wrong? If so, send me a /msg and let me know so I can fix it.