Crab canon
Encyclopedia
A crab canon—also known by the Latin form of the name, canon cancrizans—is an arrangement of two musical lines that are complementary and backward, similar to a palindrome
. Originally it is a musical term for a kind of canon
in which one line is reversed in time from the other (e.g. FABACEAE <=> EAECABAF). A famous example is found in J. S. Bach's The Musical Offering
, which also contains a canon ("Quaerendo invenietis") combining retrogression
with inversion
, i.e., the music is turned upside down by one player, which is a table canon
. The use of the term in non-musical contexts was popularized by Douglas Hofstadter
in Gödel, Escher, Bach
.
Palindrome
A palindrome is a word, phrase, number, or other sequence of units that can be read the same way in either direction, with general allowances for adjustments to punctuation and word dividers....
. Originally it is a musical term for a kind of canon
Canon (music)
In music, a canon is a contrapuntal composition that employs a melody with one or more imitations of the melody played after a given duration . The initial melody is called the leader , while the imitative melody, which is played in a different voice, is called the follower...
in which one line is reversed in time from the other (e.g. FABACEAE <=> EAECABAF). A famous example is found in J. S. Bach's The Musical Offering
The Musical Offering
The Musical Offering , BWV 1079, is a collection of canons and fugues and other pieces of music by Johann Sebastian Bach, all based on a single musical theme given to him by Frederick II of Prussia , to whom they are dedicated...
, which also contains a canon ("Quaerendo invenietis") combining retrogression
Retrograde (music)
A musical line which is the reverse of a previously or simultaneously stated line is said to be its retrograde or cancrizans. An exact retrograde includes both the pitches and rhythms in reverse. An even more exact retrograde reverses the physical contour of the notes themselves, though this is...
with inversion
Inversion (music)
In music theory, the word inversion has several meanings. There are inverted chords, inverted melodies, inverted intervals, and inverted voices...
, i.e., the music is turned upside down by one player, which is a table canon
Table Canon
A Table canon is a retrograde and inverse canon meant to be placed on a table in between two musicians, who both read the same line of music in opposite directions. As both parts are included in each single line, a second line is not needed. Bach's The Musical Offering contains a table canon....
. The use of the term in non-musical contexts was popularized by Douglas Hofstadter
Douglas Hofstadter
Douglas Richard Hofstadter is an American academic whose research focuses on consciousness, analogy-making, artistic creation, literary translation, and discovery in mathematics and physics...
in Gödel, Escher, Bach
Gödel, Escher, Bach
Gödel, Escher, Bach: An Eternal Golden Braid is a book by Douglas Hofstadter, described by his publishing company as "a metaphorical fugue on minds and machines in the spirit of Lewis Carroll"....
.