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.
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 Musical 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 on F!
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.
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