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Topic: Crab canon

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	AllRefer.com - canon, in music (Music: Theory, Forms, And Instruments) - Encyclopedia (Site not responding. Last check: 2007-10-08)
		canon, in music, a type of counterpoint employing the strictest form of imitation.
		Another form of canon is the circle canon, or round, e.g., Sumer Is Icumen In.
		mensuration canons were frequently written, in which the voices sing the same melodic pattern in different, but proportional, note values, i.e., to be sung at different speeds.
	reference.allrefer.com /encyclopedia/C/canon-mus.html (282 words)

	Canon (music) - Wikipedia, the free encyclopedia
		In a crab canon, also known as cancrizans, the follower accompanies the leader backward (in retrograde).
		Many such canons were composed during the Renaissance, particularly in the late 15th and early 16th centuries; Johannes Ockeghem wrote an entire mass (the Missa Prolationum) in which each section is a mensuration canon, and all at different speeds and entry intervals.
		Such a canon is often called a round or rota (Sumer is icumen in) is one example of a piece designated rota.
	en.wikipedia.org /wiki/Canon_(music) (873 words)

	Canon: Anatomy of
		Canons are based, in theory, upon the principle of contrapuntal inversion...two melodic lines that can be performed simultaneously with either line functioning as the bass.
		A third type of interval canon is exemplified in the second of the Canonic Variations on Vom Himmel hoch, where Bach inflects the pitches of the follower quite freely in order that the canon might conform to the tonality of the cantus firmus which it accompanies.
		In the context of canons, the term "inverted canon" is synonymous with "canon in contrary motion." Canons in contrary motion exemplify the technique of "melodic inversion," and should not be confused with contrapuntal inversion (also known as "double counterpoint") in which two contrapuntal lines exchange registers...the low becoming the high and visa versa.
	jan.ucc.nau.edu /~tas3/canonanatomy.html (1902 words)

	Canon
		A canon in one sense is a rule adopted by a Council of the Catholic or Eastern Orthodox churches.
		The criteria for deciding whether a particular work of fiction is considered to be canonical for a particular setting or not varies, sometimes being dictated by a particular authority (often a copyright or trademark holder) and sometimes being decided by informal consensus among those who care.
		Types of canon include the crab canon, in which one voice is reversed in time and pitch, and the sloth canon, in which one voice sings faster than another.
	usapedia.com /c/canon.html (535 words)

	Counterpoint
		The particular contrapuntal interplay in a canon is imitative.
		The earliest known canon, in fact, is a famous popular round from the late 13th century called Sumer Is I-Cumen In.
		To describe a canon as "four in one at the third" simply says that there are four voices singing one tune pitched an interval of a third apart.
	www-personal.umich.edu /~msmiller/counterpoint.html (884 words)

	MUS 311 Counterpoint, Study Guide H
		Canons at the unison, 2nd and 3rd may cause the undesirable crossing of voices.
		Such canons are still considered "strict," as long as the basic pitches, apart from the accidentals, conform to the leader.
		Canons at the 12th are somewhat common; canons at intervals larger than a 12th are rare.
	spider.georgetowncollege.edu /music/burnette/Mus311/311h.htm (454 words)

	Anatomy of a canon
		Canons of the 18th and 20th centuries tend to be strict, while canons of the 19th century may be free.
		In the context of canons, the term inverted canon is synonymous with canon in contrary motion.
		Canons in contrary motion exemplify the technique of melodic inversion, and should not be confused with contrapuntal inversion (also known as double counterpoint) in which two contrapuntal lines exchange registers...the low becoming the high and visa versa.
	www.kunstderfuge.com /theory/smith/canon.htm (2802 words)

	Crab canon - Wikipedia, the free encyclopedia
		A crab canon is an arrangement of two things 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.
		The use of the term in non-musical contexts was popularized by Douglas Hofstadter in Gödel, Escher, Bach.
	www.wikipedia.org /wiki/Crab_canon (84 words)

	[No title]
		Bach's marginal notes to the fourth and fifth canons are to be interpreted as decoratively allegorical - in the fourth at the augmentation "Notulis crescentibus crescat Fortuna Regis" ("May the King's fortunes increase with the increasing note-values") and in the fifth "Ascendenteque Modulatione ascendat Gloria Regis" ("May the King's fame rise as these modulations rise").
		Canon: A canon is a composition in which at least two voices are identical in certain aspects such as melodic line and rhythmic structure, one voice following another.
		Mirror Canon: A canon in which an entire section of music is inverted, as opposed to individual voices being inverted.
	www.tdch.org /musicaloffering.html (926 words)

	Sonic Glossary: Canon
		Canon has been obsolete at no time since its inception in the 13th century; countless examples can be found in polyphonic music written between then and the present day.
		The construction of a canon requires the establishment of a pitch interval, which determines the vertical distance between the lines, and a time interval, which marks the temporal distance (the "delay") between the original line and its second presentation.
		The construction of a canon requires the establishment of a pitch interval, which determines the vertical distance between the lines, and a time interval, which marks the temporal distance between the original and the restatement.
	www.columbia.edu /ccnmtl/draft/kristen/sonic/canon.html (1016 words)

	Math 3500 Questions on Hofstadter from Oct 10 (Site not responding. Last check: 2007-10-08)
		Canon by intervallic Augmentation, the processor of meaning – the parallel to the human mind, one might suppose – is a jukebox.
		The dialogue itself is in the form of a crab canon, which means that the first half of the dialogue is identical to the last half (except for a midsection that is not repeated), but in the opposite order.
		There is even a further “crab” reference in the middle section of the dialogue where a crab makes reference to its genes and an accompanying diagram (Figure 43) shows a section of “crab DNA” wherein the matching bases are aligned in a sequence in which the bottom line is the reverse of the top line.
	www.yorku.ca /bwall/math3500/0304/hofstadter2.htm (3992 words)

	Mathematical Labyrinths - Gödel, Escher, Bach (Site not responding. Last check: 2007-10-08)
		In order for a theme to work as a canon theme, each of its notes must be able to serve in a dual [or triple, or quadruple] role; it must firstly be part of a melody, and secondly it must be part of a harmonization of the same melody.
		When there are three canonical voices for instance, each note of the theme must act in two distinct harmonic ways as well as melodically.
		A canon which uses this trick is affectionately known as a crab canon, because of the peculiarities of crab locomtion.
	www.geocities.com /g0del_escher_bach/geb.html (1811 words)

	Oct 17, Question 1 (Site not responding. Last check: 2007-10-08)
		In the dialogue (Crab Canon) preceding chapter VI, the form describe here is the structure of the dialogue where the last half is self-reference of the first half but in the opposite order.
		The middle section is where the Crab speaks (this dialogue is after all called ‘Crab Canon’, so it is only suitable and fair that a Crab exists in it!).
		Since there is no step for the Crab’s words to be mirrored (odd number of lines), then this is the only part where the dialogue is not of any particular form.
	www.yorku.ca /bwall/math3500/responses/oct17q1.htm (1875 words)

	Crab canon -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-08)
		A crab canon is an arrangement of two things that are complementary and backward, similar to a (A word or phrase that reads the same backward as forward) palindrome.
		Originally it is a musical term for a kind of (A contrapuntal piece of music in which a melody in one part is imitated exactly in other parts) canon in which one line is reversed in time from the other (e.g.
		The use of the term in non-musical contexts was popularized by (Click link for more info and facts about Douglas Hofstadter) Douglas Hofstadter.
	www.absoluteastronomy.com /encyclopedia/c/cr/crab_canon.htm (101 words)

	CONTEXT (Site not responding. Last check: 2007-10-08)
		This type of canon is also knows as a crab canon.
		Important feature of any canon structure is that the main theme is fully recoverable from any of the "copies".
		A fugue is like a canon, in that it is usually based on one theme which gets played in different voices and different keys, but the notion is much less rigid.
	people.interaction-ivrea.it /n.sopieva/8.html (158 words)

	[No title]
		But speaking of taste, I finally saw that Crab Canon by your favorite artist, M.C. Escher, in a gallery the other day, and I fully appreciate the beauty and ingenuity with which he made one single theme mesh with itself going both backwards and forwards.
		Were it in my nature, I would crab up a storm, but in the time-honored tradition of my species, I backed off.
		But speaking of taste, I finally heard that Crab Canon by your favorite composer, J.S. Bach, in a concert the other day, and I fully appreciate the beauty and ingenuity with which he made one single theme mesh with itself going both backwards and forwards.
	www.evl.uic.edu /swami/crabcanon (608 words)

	crab canon (Site not responding. Last check: 2007-10-08)
		This is one small section of it, a dialog that echoes the Crab Canon of JS Bach.
		But speaking of taste, I finally saw that Crab Canon by your favorite artist, M. Escher, in a gallery the other day, and I fully appreciate the beauty and ingenuity with which he made one single theme mesh with itself going both backwards and forwards.
		That reminds me — I've always wondered, "Which came first — the Crab, or the Gene?" That is to say, "Which came last — the Gene or the Crab?" I'm always turning things round and round, you know.
	www.barryland.com /canon.html (594 words)

	About the music (Site not responding. Last check: 2007-10-08)
		What you should hear is a three-part polyphonic harpsichord piece consisting of three canons using the same theme - a theme beginning with four notes based in pitch and duration on the letters Glia Society in a fairly trivial way - in three different manners.
		A "crab" canon follows between the two upper voices; that is, the middle voice plays the theme while the top voice plays it backwards.
		Finally the first canon is repeated, but backwards and an octave higer (lower for the bottom voice).
	paulcooijmans.lunarpages.com /aboutmusic.html (237 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		Their destination is The Crab House, a popular restaurant offering the freshest fruits of the sea.
		My companion began with broiled savory Maryland crab cakes ($15.95) that were succulent and contained large lumps of crabmeat.
		Next came garlic crabs (large bowl, $14.50; jumbo bowl, $18.50) and the crème de la crème of the crab canon, the sweet-flavored Dungeness ($15.95).
	www.pbol.com /pbillustrated/gourmet/6-96.html (709 words)

	Re: serialism and the crab
		It is the custom, with > canons of this sort, for each player to read the music once from left to > right (forward) and then to return from right to left (backward).
		Thus, > retrograde canons are sometimes called "crab" or cancrizans (after the > sideways manner of that creature).
		I've always assumed that you might be able to do something fancy (at least non-tonally maybe) by having a crab canon by diminution where one part is half as long as the other, played twice against the "backwards" original.
	www.talkaboutthemusic.com /group/rec.music.compose/messages/132309.html (280 words)

	SOB(Switched-On Bach)-like MIDIs
		This Escher crab drawing was adopted from http://bach.ece.jhu.edu/~tim/pictures/.
		WzLittleFugue.mid (in 4 voices) The original was this MIDI file at later.
		tf-crabcan2.mid Crab Canon (palindromic) The original was this MIDI file at later.
	www.geocities.com /SOBlikeMIDIs (431 words)

	Read about Crab canon at WorldVillage Encyclopedia. Research Crab canon and learn about Crab canon here! (Site not responding. Last check: 2007-10-08)
		Research Crab canon and learn about Crab canon here!
		A crab canon is an arrangement of two things that are complementary and backward, similar to a
		canon in which one line is reversed in time from the other (e.g.
	encyclopedia.worldvillage.com /s/b/Crab_canon (95 words)

	Reviews -- The Bach Sinfonia (Site not responding. Last check: 2007-10-08)
		Perhaps the funniest thing about the "Crab" Canon that opened the Bach Sinfonia's ingenious "What's in a Joke?" program Saturday night at the Washington Conservatory was the attachment of Mozart's name to it.
		Dialogue for two violins (Levy and concertmaster Elizabeth Field) was a prominent element, together with many other funny little touches, in Haydn's Symphony No. 67, and it was easy to imagine that Mestrino might have been one of the soloists in its first performance, not long after the "Crab" Canon was composed.
		Abraham had constructed, conducted and commented on a program that was itself a sort of musical joke, almost a crab canon.
	www.bachsinfonia.org /reviews_011016.shtml (294 words)

	Crab Canon Encyclopedia Article, Definition, History, Biography (Site not responding. Last check: 2007-10-08)
		Looking For crab canon - Find crab canon and more at Lycos Search.
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	www.karr.net /encyclopedia/Crab_canon (252 words)

	Encyclopedia: Palindrome
		See also crab canon, in classical music: a canon in which one line of the melody is reversed in time and pitch from the other.
		The dialogue "Crab Canon" in Douglas Hofstadter's GÃ¶del, Escher, Bach is nearly a palindrome-by-lines.
		The second half of the dialog is, with some very minor changes, the same lines as the beginning, in reverse order, spoken by the opposite characters (i.e., lines spoken by Achilles in the first half are spoken by the Tortoise in the second, and vice versa).
	www.nationmaster.com /encyclopedia/Palindrome (8867 words)

	Math Night Module: Mathematics of Music
		The Crab Canon music is printed on two lines: it needs to be cut apart and taped together so that it extends across one line.
		The Crab Canon: There's a version of the Crab Canon written out in two parts.
		The Canons and Fugues of J. Bach by Timothy Smith
	orion.math.iastate.edu /mathnight/activities/modules/music/aboutmod.shtml (812 words)

	[No title] (Site not responding. Last check: 2007-10-08)
		in terms of formal trickery and level-play" in GEB is the Crab Canon.
		Complications of canons occur when the "copies" of the theme are varied in time, pitch, speed etc.
		A crab canon is one where the theme is played backwards in time!
	www.evl.uic.edu /swami/geb.html (345 words)

	CSCI 221
		Johann Sebastian Bach (1685-1750) explored the connection between mathematics and music by creating a variety of compositions that are especially pleasing to those with a mathematical inclination.
		His fugues and canons are particularly mathematical in nature.
		For example, a sheet of music with his "Crab Canon" on it can literally be turned upside down and remain unchanged.
	www.cs.cofc.edu /~manaris/spring05/cs221/hmwk2.html (669 words)

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