Crab canon¶
A crab canon sounds a melodic line together with its own temporal reverse, so a single sequence must work as simultaneous counterpoint in both directions.
Core Idea¶
A crab canon aligns a melodic line with itself played backward in time. Both directions sound simultaneously, so the composer has to make the resulting pairs work as counterpoint. It is narrower than a piece that simply plays a reversed second half later. Bach's Canon a 2 cancrizans, BWV 1079/4, is notated as one line with a clue at the end for backward reading; the Netherlands Bach Society performs the forward and reverse lines together.[^ref-a6b6998fcfc1]
Scope of Application¶
This is a device of notated polyphony. Machaut's Ma fin est mon commencement supplies a richer three-voice case: its two upper voices reverse one another while the lower voice has its own symmetry. Original manuscript witnesses are cataloged by DIAMM; the voice-by-voice account here follows a Colby music instructor's analysis, not an independent transcription.[ref-96617cfb49fc][ref-d63e6f101c40]
Clarity¶
If a line is A–B–C–D–E, its reversed partner is E–D–C–B–A. In a crab canon they start together from opposite ends, pairing A with E, B with D, and so forth. Those letters illustrate the relation, not a historical score. In Bach's actual example, an end clef cues the reverse reading of the same notated line.[^ref-a6b6998fcfc1]
Manages Complexity¶
One line and a reversal rule specify two voices, compressing notation but constraining composition: changing one event affects a paired event elsewhere in the piece. Exact reversal gives strong symmetry at the cost of freedom to repair a local interval independently. A merely mechanical reversal may satisfy the order rule without becoming effective music.[^ref-a6b6998fcfc1]
Abstract Reasoning¶
The core can be written as a second voice whose event at position i equals the first voice's event at mirrored position n+1−i. What makes it a Canon is concurrent performance and intentional contrapuntal fit. If the reverse is played only afterward, the structure becomes a successive palindrome; if the second voice is unrelated, it is no longer a crab canon.
Knowledge Transfer¶
The idea helps performers decode compact score cues and analysts find reversible voice pairs inside larger textures. The label should not be stretched to every kind of symmetry in literature or art. The musical entry depends on sounded, simultaneous voices and is not presented as a universal cross-domain prime.[ref-a6b6998fcfc1][ref-d63e6f101c40]
[^ref-a6b6998fcfc1]: Netherlands Bach Society, “Canon a 2 Cancrizans,” BWV 1079/4, performance and work note. [^ref-96617cfb49fc]: Digital Image Archive of Medieval Music, Machaut manuscript witness record. [^ref-d63e6f101c40]: Colby College, Machaut listening assignment IV.
Relationships to Other Abstractions¶
Current abstraction Crab canon Domain-specific
Parents (1) — more general patterns this builds on
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Crab canon is a kind of Musical Structure Domain-specific
The simultaneous retrograde voice relation is an organized musical structure.
Hierarchy path (1) — routes to 1 parentless root
- Crab canon → Musical Structure
Neighborhood in Abstraction Space¶
Crab canon sits in a sparse region of the domain-specific corpus (78th percentile for distinctiveness): few abstractions share its structure, so a faithful description tends to retrieve it precisely.
Family — Musical Form & Rhythmic Devices (13 abstractions)
Nearest neighbors
- Counterpoint — 0.83
- Musical Interval — 0.83
- Ostinato — 0.83
- Chiasmus — 0.83
- Pedal Point — 0.82
Computed from structural-signature embeddings · 2026-10-08