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Topic: Retrograde inversion

	Canon: Anatomy of
		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.
		Because inverting a C-clef effects no apparent change, contrary motion is signified by the inversion of key signatures or by the placement of accidentals on "wrong" lines and spaces.
	www2.nau.edu /~tas3/canonanatomy.html (1902 words)

	Twelve-tone technique
		P can be used starting on any one of the twelve notes of the chromatic scale - so long as the intervals are the same, the rows are equivalent.
		The inversion is the prime series with the intervals inverted (so that a rising minor third becomes a falling minor third):
		A simple case is the ascending chromatic scale, the retrograde inversion of which is identical to the prime form, and the retrograde of which is identical to the inversion (thus, only 24 forms of this tone row are available).
	www.ebroadcast.com.au /lookup/encyclopedia/tw/Twelve-tone_music.html (694 words)

	What Is "The Matrix"?
		So in the case of inversional equivalence, the equivalence will be assumed for the purposes of identifying pc sets by their equivalence classes, but it may often be more useful to distinguish between a sonority and its inversion.
		Because there is a one-to-one correspondence between the prime forms and the retrograde forms that are their backwards-renditions, the retrograde forms are labelled with an R and the number of the pc that ends the row form (R3, etc.).
		Although a composer's main concern with using retrograde material is the question of whether the listener will recognize that two melodies are from the same source when one is presented backwards, this concern seems not to have bothered composers who work with series.
	www.robertkelleyphd.com /12-tone.htm (3502 words)

	Lesson 1 for "Form & Analysis"
		The second operation, called INVERSION, involves reading intervals of PRIME in the same order but moving them in the opposite direction (or the same pitches can be produced by moving the INVERSION of the original interval in the SAME direction).
		Consider, for example, the first interval of Webern's row: G ascending a M3 to B. The inversion could be produced in two ways: (1) G descending a M3 to Eb, or (2) G ascending a m6 to Eb.
		Observe that inversions of trichord (a) relocate the smaller interval (which had been at the top) to the bottom of the texture.
	jan.ucc.nau.edu /~tas3/mus303/operations.html (944 words)

	Channel4.com - SlashMusic - Retrograde Inversion (Site not responding. Last check: 2007-11-04)
		Retrograde Inversion play an aggressive mixture of experimental, funk-infused hard rock, with material ranging from the ethereal strummings of 'Lost at Sea', through the chaotic darkness of 'Wake Up (Its a Mindset)', right out to the apocalyptic riffage of 'Cut Loose'.
		After a series of live dates since formation, Retrograde Inversion completed their first recorded release 'The Funk EP' in late 2004 and started promoting it at venues across Surrey and Hampshire, in an effort to garner greater interest in what they had to offer.
		Throughout the coming months Retrograde Inversion will be taking itself around the UK, with gigs in Liverpool, Manchester, Leeds and London in the pipeline, as well as a slot at Guilfest Festival 2006 with acts such as Billy Idol and The Stranglers.
	www.channel4.com /music/myband/retrogradeinversion (242 words)

	Twelve-Tone Composition
		The retrograde of P(7) is called R(7) and is (2 6 5 1 4 0 9 8 10 11 3 7).
		The most difficult to understand transformation is the inversion (I).
		We have seen that transposition can be combined with both retrograde and inversion.
	www.geocities.com /al6an6erg/serial.html (1085 words)

	Humdrum Toolkit Command Reference -- reihe
		For prime and inversion forms, the numerical parameter indicates the pitch-class value for the first "note" of the output form.
		In addition to the traditional set-transformations of transposition, inversion, retrograde, and retrograde-inversion, reihe also provides for rotation -- where the set elements are cyclically shifted by a specified number of positions.
		By default, the reihe command assumes modulo 12 arithmetic for prime, inversion, retrograde, and retrograde-inversion transformations.
	www.music-cog.ohio-state.edu /Humdrum/commands/reihe.html (725 words)

	Retrograde & Inversion, Serial Music Lesson (Site not responding. Last check: 2007-11-04)
		Retrograde is simply the statement of a row in reverse order.
		Inversion of a row is determined by finding the complement of a pitch class.
		The inversion of P0 is I0 and given by:
	www.wsu.edu /~dpalmen/mathlessons/html/serialmusic/retrograde.html (53 words)

	Permutation (music) - Wikipedia, the free encyclopedia
		The permutations resulting from applying the inversion or retrograde operations are categorized as the prime form's inversions and retrogrades, respectively.
		Likewise, applying both inversion and retrograde to a prime form produces its retrograde-inversions, which are considered a distinct type of permutation.
		If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upside down), the next three are retrograde (backwards), and the last three are its inversion (upside down).
	en.wikipedia.org /wiki/Permutation_(music) (275 words)

	Sonic Glossary: Twelve-Tone Composition
		The fourth transformation is a combination of the last two, retrogression and inversion.
		Using these four types of transformations (transposition, retrograde, inversion, retrograde inversion), 47 variants may be derived from the original series.
		To derive related series, a series is typically subjected to four types of transformation: transposition, retrograde, inversion, and retrograde inversion.
	www.columbia.edu /ccnmtl/draft/paul/sonic/ttc.html (1025 words)

	MUS 312 Form & Analysis, Study Guide M
		In such a set the pattern is transposed, inverted, retrograded, or inverted and retrograded to "generate" the remainder of the set.
		The pattern 6-5 within the row is reversed later as 5-6, and it is also part of a larger pattern that reverses itself: 6-5-3-5-6.
		Such a pattern may indicate that a segment of the row is its own retrograde or retrograde inversion.
	spider.georgetowncollege.edu /music/burnette/Mus312/312m.htm (2888 words)

	the dorian mode, topology ... and stravinsky (Site not responding. Last check: 2007-11-04)
		From here there would appear to be endless possibilities, such as the retrograde of the Inverted-Retrograde, which you would expect to return you to the Inversion, but does not quite...
		This row has the same step-sequence as the original Inversion but starting on the last note of the Prime - which in this example means the that the new sequence is the same as the Inversion, but transposed 3 semitones.
		This means you can apply an Inversion and all the new notes are still within the scale (i.e.
	members.aol.com /cacophonyoflight/musictheory3.html (566 words)

	John Greschak - An Open Letter to JS Bach on Visual-Spatial Music
		You might also have a retrograde inversion whereby the subject is inverted and played backwards.
		By using retrograde or inversion, one generates a mirror image of a given subject.
		I believe that when a person who possesses a strong ability for spatial reasoning listens to music that employs transformations such as retrograde and inversion, they use this ability to recognize that the various transformed versions of a given subject are related.
	www.greschak.com /letters/olbachvs.htm (1620 words)

	[No title]
		The retrograde is relatively tricker to identify, although it's simpler in theory.
		¥ ¥ ¥ ¥ Bb F# E C The inverse retrograde is, naturally, the inverse of the retrograde,-- or the retrograde of the inverse,-- both are the same at different transposition levels.
		The inverse retrograde is actually, counter-intuitive as it may seem, sometimes more easily identified than the inverse or the retrograde themselves.
	home.earthlink.net /~tagutcow/line.txt (1301 words)

	Rotation, Stravinsky's Variations - J. Nagel
		As the monodic section used rotationally-related row-forms beginning or ending on pitch-class 2 (D), which is the first note of the original row, the first six measures of Section VI use row-forms based on pitch-class 5 (F), which is the last note of the original row.
		The second constant in all three 12-part polyphonic sections is the use of row-forms that either begin with pitch-class 2 or end with pitch-class 5 (the first and last notes of the original row).
		All told, 6 Primes (from squares 7,8,9,10,11,0), 6 Retrogrades (from squares 7,8,9,10,11,0), 13 Inversions (from squares 0,0,0,1,2,3,4,5,7,8,9,10,11), and 12 Retrograde Inversions (from squares 0,0,1,2,3,4,5,7,8,9,10,11) are used within the passage.
	www.jomarpress.com /nagel/articles/StravinskyVariations.html (4341 words)

	Set Theory Glossary
		In first inversion the chord structure cycles to 354 (E G C E), and in second inversion it is 543 (G C E G).
		abbreviation for inversion; e.g., Io is the inversion of a row form at zero transposition, having the same initial pc as Po.
		To retrograde a theme it is turned around a time axis.
	solomonsmusic.net /setgloss.htm (3865 words)

	International Clarinet Association - ClarinetFest Archives (Site not responding. Last check: 2007-11-04)
		A 12-tone row is a pattern containing all 12 notes of the chromatic scale, and is used as the foundation for both melody and harmony.
		During the compositional process the original row, called the prime row, may undergo various changes, including transposition, inversion (upside down), retrograde (backwards), and retrograde inversion (backwards and upside down).
		Prime rows are read left to right, inverted rows are read from top to bottom, retrograde rows are read from right to left, and retrograde inversion rows are read from bottom to top.
	www.clarinet.org /fests/2000/Gibson.asp (1831 words)

	LISP Workshop for Musicians #6
		The function retrograde tests if the list-of-notes is empty (line 1), if it's not it appends (line 2) the last element of the list-of-notes in the front of the retrograde of the list-of-notes without its last element (butlast, line 3).
		When list-of-notes is empty retrograde returns an empty list (NIL, line 1) where it will append all the previous values coming from the other layers.
		The output format is a list containing lists with all the transpositions in the order: (original inversion retrograde retrograde-inversion).
	ccrma.stanford.edu /CCRMA/Courses/LispWorkshop/Lisp-06.html (889 words)

	George Tremblay Biography
		He embarked on a thirty year search for a logical expansion of the twelve tone series that would free it from inversion, retrograde inversion, and transposition.
		In this cycle, the retrograde is created by logic and order rather than as a device.
		In this expanded cycle, there is no inversion, no retrograde inversion, and no transposition.
	www.composerjohnbeal.com /Tremblay.html (421 words)

	Stockhausen's New Morphology of Musical Time, Serialism: C. Koenigsberg December 1991
		Variations of the initial row are obtained by the combinatorial permutations called "inversion", "retrograde", and "retrograde inversion".
		But once the basic row and its variations are established, the twelve-tone system of composition requires the composer to use the pitch classes in the order (with limited variations) given by these rules.
		In his Concerto for Nine Instruments of 1934, for example, all the pitch material is derived only from the three-note series B-Bb-D and its three mirror forms (retrograde, inversion, retrograde inversion).
	www.music.princeton.edu /~ckk/smmt/serialism.3.html (4966 words)

	Babbitt (Site not responding. Last check: 2007-11-04)
		Some hexachords have structures such that they can be transformed into themselves or their complement by the standard transformations of transposition, inversion, and retrograde inversion.
		This particular hexachord is an all-combinatorial hexachord since there are both inversional and transpositional ways of replicating either the hexachord or its complement.
		Note that the Inversion beginning on Eb (read down on the matrix) is combinatorial with Prime form beginning on D. The Prime on D is combinatorial with RI G# (read up on the matrix).
	www.sinc.sunysb.edu /Class/mus352/notes/babbitt.htm (343 words)

	tremblay2
		Unlike inversion, retrograde is not affected by the scale and thus can be used on any instrument that accepts the roll backwards and upside down.
		Retrograding a MIDI file is easy with a sequencer that offers that function, like Cakewalk.
		Retrograde music is a kind of palindrome -- a sentence that can be read backwards -- as in: "Madam, I'm Adam", or in the "Satanic" messages on Rock records.
	mmd.foxtail.com /Sounds/Sankyo20/tremblay2.html (587 words)

	Sounding Stone Twelve-Tone Row Calculator (Site not responding. Last check: 2007-11-04)
		In this case, the calculator uses the prime, inverted, retrograde and retrograde inverted ordering of the trichord to derive a unique twelve pitch series.
		The results are presented in a matrix presenting all the transpositions of the prime form read from left to right and retrograde form read from right to left.
		Inversion (5): {C, Ab, A} In this example, each of the trichords belongs to {0, 1, 4}.
	www.soundingstone.net /cgi-bin/rowgen.cgi (263 words)

	12 tone music (Site not responding. Last check: 2007-11-04)
		The retrograde of P0 is called R0 and it is 2 6 5 1 4 0 9 8 10 11 3 7.
		All the inversions can be transposed or, if you prefer, all the transposed 'P' rows can be inverted.
		The inversions can also be used backwards, in Retrograde to give Retrograde Inversions.
	www.duckmusic.free-online.co.uk /hatton/serial/partone.htm (1353 words)

	[No title]
		In general, the reason why RI is favored to IR is that, retrograde (of prime) is already represented on the matrix (right to left), so there is no need to write a seperate retrograde, although this is not the case with inversion.
		retrograde inversion is an ancient musical technique, and outside of an atonal/serial context, it's possible to come out with different results if you do the two operations in a different order, depending on the constraints in play..." It is precisely these two different results that I am most interested in.
		In context of strict counterpoint students are taught to take as the pitch axis for inversion the 2nd step in Major and the 4th in minor, lest a forbidden tritone succession comes out in the result of inversion.
	www.societymusictheory.org:16080 /pipermail/smt-talk/2003-June.txt (16421 words)

	Crayola Creativity Central
		Then play the inversion of the first phrase: F, E, D, F, F, E, D, F, C, B-flat, A, C, B-flat, A. Ask students if they can figure out how the two melodies are different and the same.
		Have one group sing the original melodic phrase (ask one child to be the leader) while the second group sings the inversion (with you as leader).
		Tell students which is the original row, and ask them to identify the retrograde and the inversion.
	www.crayola.com /educators/dreammakers/add.cfm?page=2 (825 words)

	Tone row
		A twelve tone or serial composition will take one or more tone rows as its basis plus their transformations (inversion, retrograde, retrograde inversion; see twelve-tone technique for details).
		If the first three notes are regarded as the "original" cell, then the next three are its retrograde inversion (backwards and upsidedown), the next three are retrograde (backwards) and the last three are its inversion (upsidedown).
		The tone row of many of other Webern's late works are similarly intricate.
	www.ebroadcast.com.au /lookup/encyclopedia/to/Tone_row.html (266 words)

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		All songs, lyrics and pictures © Retrograde Inversion.
	www.purevolume.com /retrogradeinversion (106 words)

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	www.myspace.com /retrogradeinversion (2024 words)

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