More than a Game Bach may have composed canons for the same reason that we solve crossword puzzles; they were entertainment...a game. Perhaps he composed canons because he found in them a challenge of the first order. Or Bach may have written canons in order to stimulate his muse; composers often generate new ideas by employing canonic techniques. There is reason to suspect, however, that the Baroque taste for canon was more than a game, challenge, or method for generating ideas.
Window into the laws of music Bach and his contemporaries were of the notion that music was a science..."sounding mathematics" in Mizler's words...therefore reducible to theorem and law. Bach's concurrence with the notion was demonstrated by his membership in Mizler's Society for Musical Sciences...joined in 1747 while composing the Musical Offering...for which he not only submitted the thirteenth canon of the Fourteen on the Goldberg Ground but also composed the Canonic Variations on Vom Himmel hoch. If Bach believed that music was a science, he may have conceived of canon as a window through which it might be possible to glimpse its laws. Given as we are to understand the eighteenth-century compositional ideal of elaboratio...the development of ideas from a single theme (inventio)...Bach's fascination with canon was more than entertainment.
Mystery of Musical Creation There remains a third possible explanation why Bach and his contemporaries practiced the art of writing canons. The technique may have stood for them as a symbol of all that was NOT understood...that which was transcendent, therefore symbolic of themselves as creators and the processes of musical creation. Thus, while Bach may have composed canons in an effort to understand these processes, he could just as well have composed them as an expression of the very mystery of musical creation itself. We know by their enigmatical notations that Baroque composers viewed canon as something to be figured out, if not mediated by that select few (namely, composers) who understood it.
Genitum non factum The theological implications of the canon, while speculative to be sure, invite contemplation no less. Just as a well-composed leader had the potential to animate itself in multifarious followers, so, too, according to Christian cosmogony, the Creator animates all things, including music. And just as the canon follower was not created, but begotten (so to speak), it is conceivable that the process of canonic generation represented, to the Lutheran way of thinking, the second person of the Trinity: genitum non factum...per quem omnia facta sunt ("begotten, not created...by whom all things were created").
It is revealing that when Bach set the foregoing words to music in the Creed of his Mass in B Minor (interesting YouTube), he utilized canonic processes. While not technically a canon, the movement is very canon-like, but with pitch and time intervals continuously mutating. These mutations bring to mind the Trinitarian doctrine...three in one and one in three...in much the same manner as the third canon of the Variations on Vom Himmel hoch portrays heaven and earth by its mutating consonant and dissonant intervals separating leader and follower. Underlying both movements is the Christian doctrine of the dual nature of Christ incarnate, one with God, yet fully human. As sign of this duality, Bach does not allow the canonic followers to engage in unthinking mimicry but gives them independence. Yet, in its independence of time and pitch interval, the follower (Christ) is audibly generated by the leader (the Father), and always doing the Father's will.
About the Nature of Meaning In "Tonal Allegory in the Vocal Music of J. S. Bach," Chafe suggests that Bach's use of the term Symbolum in association with at least one of his canons suggests a metaphoric dimension "permitting us to take the canons as statements about the nature of meaning and the relationship between art and theology." He writes: "Artists of the baroque period had means of expressing basic relationships between art and transcendent meaning." One means was the poetic epigram wherein the author used antithesis, conceit and paradox to "instruct and familiarize the reader with basic concepts of faith in highly condensed form" (p. 14). Also called paradoxa, a typical epigram included juxtapositions of passages such as "God wills all men should be saved" with "Few are chosen" (I Timothy 2:4 and Matthew 22:14).
Chafe likens the allegorical canons of Bach's oeuvre with Lutheran paradoxa noting that they, too, are rooted in antithesis (p. 15). Bach's use of inversion, contrary motion, retrograde, major/minor and sharp/flat contrasts represented a microcosm of musical devices. But Bach's canons are more than compressed tonal materials. With enigmatical notations such as mi contra fa, concordia discors, cross/crown, and beginning/ending, Bach associates his canons with a peculiarly Lutheran dialectic in which antithesis (what Augustine called "antinomy") is a symbol for the cross of Christ. Thus Bach's canons may have stood for the affirmation of Lutheran precept as much, or more, than commentary on Baroque art.
In the Final Analysis We may never know why Bach wrote canons, nor is this necessary. Beauty in any form has reason enough to exist. But to continue to wonder at their creation can only add mystery to beauty, making the canons of J. S. Bach the most beautiful of all!