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A Dictionary of Music and Musicians/Cancrizans

CANCRIZANS. This is a name given to canons by retrogression, on account of their crab-like motion—from the Latin word cancer, a crab. The German term is krebsweis. An example (from A. Andre's 'Lehrbuch der Tonsetzkunst') will best explain their construction.

{ \override Score.Rest #'style = #'classical \time 4/4 << \relative c'' { c2 d4 e | f8 g f e d4 c | b c d8 e f g | f4 e d2 | r4 g, e8 c d4 | e8 d e f e4 d | c b c8 d e d | c4 b c r \bar "||" }
\new Staff { \relative c' { r4 c b c | d8 e d c b4 c | d e f8 e d e | d4 c8 e g4 r | d'2 e4 f | g8 f e d c4 b | c d e8 f g f | e4 d c2 | } } >> }

Sometimes a canon is both cancrizans and by contrary motion—'Retrograde-inverse,' of which we give an example from Fétis's 'Traite du Contrepoint et de la Fugue.'

{ \time 4/2 \key f \major << \relative a' { r\breve | a1 g | a2 g c a | g1 c | r g | f2 a bes c | bes1 a | e\breve }
\new Staff { \clef alto \key f \major \relative c' { c\breve | f2 c bes g | f g a f' | e1 c | e r | r2 c bes a | bes g f f' | g\breve } }
\new Staff { \clef alto \key f \major \relative g' { g\breve | f2 f, g bes | a bes c r | r1 e | c e | f2 a g f | g bes c f, | c'\breve } }
\new Staff { \clef bass \key f \major \relative e { e\breve | a1 bes | c2 bes a f | g1 r | c g | a2 c g a | g1 a | r\breve } } >> }


The book should be turned upside down to show the retrograde and inverse structure.