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Topic: Transpositional equivalency

	Transposition (music) - Wikipedia, the free encyclopedia
		In music transposition is moving a note or collection of notes (or pitches) up or down in pitch by a constant interval.
		It is similar to enharmonic equivalency and octave equivalency.
		Transpositional equivalency is generally supposed by most music theory in that chords which may be transposed onto one another share something in common.
	en.wikipedia.org /wiki/Transpositional_equivalency (385 words)

	equivalence relation - Article and Reference from OnPedia.com
		In mathematics, an equivalence relation on a set X is a binary relation on X that is reflexive, symmetric and transitive, i.e., if the relation is written as ~ it holds for all a, b and c in X that
		Every equivalence relation on X defines a partition of X into subsets called equivalence classes: all elements equivalent to each other are put into one class.
		Consider for instance the square X = 0,1x0,1 and the equivalence relation on X generated by the requirements (a,0) ~ (a,1) for all a in 0,1 and (0,b) ~ (1,b) for all b in 0,1.
	www.onpedia.com /encyclopedia/equivalence-relation (784 words)

	CONK! Encyclopedia: Musical_set_theory (Site not responding. Last check: 2007-10-22)
		Transposition is moving a set up or down in pitch by a constant interval.
		Multiplication is multiplying the pitch class numbers of a set, the most useful multipliers are 1, 5, 7, 11, as multiplication by 1 is the same, multiplication by 11 is inversion, multiplication of the chromatic scale by 5 produces the circle of fourths and multiplication by 7 produces the circle of fifths.
		Transpositions, or transpositions with inversion, are examples of permutation groups.
	www.conk.com /search/encyclopedia.cgi?q=Musical_set_theory (1416 words)

	equivalence class - Article and Reference from OnPedia.com
		The homotopy class of a continuous map f is the equivalence class of all maps homotopic to f.
		In natural language processing, an equivalence class is a set of all references to a single person, place, thing, or event, either real or conceptual.
		Because of the properties of an equivalence relation it holds that a is in a" title="a">a and that any two equivalence classes are either equal or disjoint.
	www.onpedia.com /encyclopedia/equivalence-class (729 words)

	Equivalence class -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		This equivalence relation is known as the (The choicest or most essential or most vital part of some idea or experience) kernel of f.
		Because of the properties of an equivalence relation it holds that a is in [a] and that any two equivalence classes are either equal or (Click link for more info and facts about disjoint) disjoint.
		It follows that the set of all equivalence classes of X forms a (A vertical structure that divides or separates (as a wall divides one room from another)) partition of X: every element of X belongs to one and only one equivalence class.
	www.absoluteastronomy.com /encyclopedia/e/eq/equivalence_class.htm (956 words)

	Equivalence relation -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-10-22)
		Every equivalence relation on X defines a (A vertical structure that divides or separates (as a wall divides one room from another)) partition of X into subsets called (Click link for more info and facts about equivalence class) equivalence classes: all elements equivalent to each other are put into one class.
		The equivalence classes of this relation are the right (Click link for more info and facts about coset) cosets of H in G.
		If an equivalence relation ~ on X is given, then the set of all its equivalence classes is the (Click link for more info and facts about quotient set) quotient set of X by ~ and is denoted by X/~.
	www.absoluteastronomy.com /encyclopedia/e/eq/equivalence_relation.htm (1103 words)

	Inversion (music) - Wikipedia, the free encyclopedia
		Inversional equivalency is the concept that intervals, chords, and other sets of pitches are the same when inverted.
		It is similar to enharmonic equivalency and octave equivalency and even transpositional equivalency.
		Inversional equivalency is used little in tonal theory, though it is assumed a set which may be inverted onto another are remotely in common.
	www.wikipedia.org /wiki/Inversional_equivalency (1408 words)

	Transposition (Site not responding. Last check: 2007-10-22)
		In data transmission, a transmission defect in which, during one character period, one or more signal elements are changed from one significant condition to the other, and an equal number of elements are changed in the opposite sense.
		In cryptography, a transposition is an elementary cryptographic operation somewhat related to the mathematical permutations.
		In genetics, a transposition is a mutation in which a chromosomal segment is transferred to a new position on the same or another chromosome.
	www.sciencedaily.com /encyclopedia/transposition (303 words)

	Equivalence relation - Wikipedia, the free encyclopedia
		The relation "has the same image under a function" on the elements of the domain of the function.
		Since every equivalence relation can be identified with a partition and vice versa, the number of equivalence relations on a set X of n elements is given by the nth Bell number, B
		In music see octave equivalency, transpositional equivalency, inversional equivalency, enharmonic equivalency, rotational equivalency.
	www.wikipedia.com /wiki/equivalence+relation (870 words)

	Read about Octave at WorldVillage Encyclopedia. Research Octave and learn about Octave here! (Site not responding. Last check: 2007-10-22)
		equivalency, and is closely related to the concept of harmonics.
		Thus all C#s, or all 1s (if C=0), in any octave are part of the same pitch class.
		Octave equivalency is a part of most musics, but is far from universal in "primitive" and
	encyclopedia.worldvillage.com /s/b/Octave (455 words)

	CONK! Encyclopedia: Octave (Site not responding. Last check: 2007-10-22)
		For this reason, notes an octave apart are given the same note name in the Western system of music notationâ”the name of a note an octave above A is also A. This is called octave equivalency, and is closely related to the concept of harmonics.
		This is similar to enharmonic equivalency, and less so transpositional equivalency and, less still, inversional equivalency, the latter two of which are generally used only in musical set theory or atonal theory.
		As well as being used to describe the relationship between two notes, the word is also used when speaking of a range of notes that fall between a pair an octave apart.
	www.conk.com /search/encyclopedia.cgi?q=Octave (564 words)

	Inversional equivalency (Site not responding. Last check: 2007-10-22)
		Inversional equivalency is the concept that intervals, chords, and other sets of pitchesare the same when inverted.
		It is similar to enharmonicequivalency and octave equivalency and even transpositional equivalency.
		Inversional equivalencyis used little in tonal theory, though it is assumed a set which may be inverted ontoanother are remotely in common.
	www.therfcc.org /inversional-equivalency-89030.html (1060 words)

	Inversion (music) (Site not responding. Last check: 2007-10-22)
		Inversional equivalency is the concept that intervalss and chordss are the same when inverted.
		It is similar to enharmonic equivalency and octave equivalency and even transpositional equivalency but unlike these is used almost exclusively only in musical set theory.
		When applied to melodies, the inversion of a given melody is the melody turned upside-down - so if the original melody has a rising major third (see interval), the inverted melody has a falling major third.
	encyclopedia.jigyasa.in /wikipedia/i/in/inversion__music_.html (668 words)

	Equivalence relation
		2 Examples of relations that are not equivalences
		The relation "has a common factor with" between natural numbers is not an equivalence relation, because although it is reflexive and symmetric, it is not transitive (2 and 6 have a common factor, and 6 and 3 have a common factor, but 2 and 3 do not have a common factor).
		In music see octave equivalency, transpositional equivalency, inversional equivalency, enharmonic equivalency, rotationalal equivalency.
	pedia.newsfilter.co.uk /wikipedia/e/eq/equivalence_relation.html (825 words)

	Musical set theory (Site not responding. Last check: 2007-10-22)
		Musical set theory may, however, be considered as an unrelated field from mathematical set theory that, at the most, adapted some techniques from mathematical set theory for its own uses.
		In addition to octave and enharmonic equivalency assumed in twelve tone theory, set theory also makes use of inversionalal and transpositional equivalency.
		However, many theorists question or do not use inversional equivalency while Solomon simply adds a distinction to the end of the Forte prime form number of any sets which would be considered inversionally equivalent in his own Solomon Prime form number.
	encyclopedia.jigyasa.in /wikipedia/m/mu/musical_set_theory.html (345 words)

	Lanthionine antibiotic compositions and method - US Patent 6521596 (Site not responding. Last check: 2007-10-22)
		Biologically functional equivalent peptides are thus defined herein as those peptides in which certain, not most or all, of the amino acids may be substituted.
		While discussion has focused on functionally equivalent polypeptides arising from amino acid changes, it will be appreciated that these changes may be effected by alteration of the encoding DNA; taking into consideration also that the genetic code is degenerate and that two or more codons may code for the same amino acid.
		Such sequences may arise as a consequence of codon redundancy and functional equivalency which are known to occur naturally within nucleic acid sequences and the proteins thus encoded.
	www.patentstorm.us /patents/6521596.html (18798 words)

	Equivalence class (Site not responding. Last check: 2007-10-22)
		Any function f : X → Y defines an equivalence relation on X by x ~ y iff f(x) = f(y).
		The equivalence classes are known as right cosets of H in G; one of them is H itself.
		They all have the same number of elements (or cardinality in the case of an infinite H).
	www.tocatch.info /en/Quotient_set.htm (747 words)

	MTO 4.2: Alpern, Review, Webern and the Lyric Impulse
		A note-for-note equivalency relationship unfolding progressively between two sets is ultimately derailed by the last two notes of the piece in a dramatic crescendo.
		Moreover, this is succeeded by another transpositional entrance down another whole step of a third pentachord , whose first four notes transpose those of the first pentachord exactly from its beginning, again with the same intervals <-5 1+3>.
		In light of this conventional transpositional scheme, Shreffler's contention that lyrical Webern was rebelling against Schoenberg's logically ordered retrogrades and inversions when he abandoned this sketch seems to attack a straw man.
	societymusictheory.org /mto/issues/mto.98.4.2/mto.98.4.2.alpern.html (6682 words)

	Books by David Lewin - Advances in Industrial and Labor Relations - 0892327154 where can i download audio books (Site not responding. Last check: 2007-10-22)
		In addition to octave and enharmonic equivalency assumed in twelve tone theory and equal tempered tonal theory, set theory also makes use of inversional and transpositional equivalency.
		I type).A list of all sets which are in the same transpositional type as a given set may be found by transposing the original set by all intervals.
		For odd cardinality sets the middle number is a 1/2 index and the center of inversional symmetry.Transpositional symmetrical sets in normal form may be partitioned into segments which under transposition map onto each other cyclically, so that the last segment maps onto the first.
	www.bookchaptersummary.com /204534_david-lewin_0892327154advancesinindustrialandlaborrelationswherecanidownloadaudiobooks.html (1461 words)

	Transposition (music) - Encyclopedia, History, Geography and Biography (Site not responding. Last check: 2007-10-22)
		Transposition (music) - Encyclopedia, History, Geography and Biography
		This page was last modified 04:18, 19 Jun 2005.
		This encyclopedia, history, geography and biography article about Transposition (music) contains research on
	www.arikah.net /encyclopedia/Transpositional_equivalency (238 words)

	Articles - Tonality (Site not responding. Last check: 2007-10-22)
		The majority of tonal music assumes that notes spaced over several octaves are perceived the same way as if they were played in one octave or octave equivalency.
		This is generally held to imply that a note which has different places in a chord will be heard differently, and that therefore there is not enharmonic equivalency.
		In tonal music chords which are moved to different keys, or played with different root notes are not perceived as being the same, and thus transpositional equivalency and far less still inversional equivalency are not generally held to apply.
	www.mafox.com /articles/Tonality (6655 words)

	The Aural Perception of Pitch-Class Set Relations: A Computer-Assisted Investigation (Site not responding. Last check: 2007-10-22)
		The perception test was designed to measure how recognition of set equivalency may be affected by the perceptual ability of the listener, the set types used and the particular set manipulation involved in the equivalency relationship.
		The test paradigm consisted of the presentation of an original set followed by three comparison sets, one of which was transpositionally or inversionally equivalent to the original, the other two being non-equivalent lures in an Rp, R1 or R2 similarity relation with the original.
		Statistical tests of subject-response data showed that: subjects with absolute-pitch recognition performed with more accuracy; ordered transformations were more recognizable than reordered transformations; transpositional equivalencies were more discernable than inversional equivalencies; octave displacement disguised set equivalency; and non-equivalent sets with similarity through contour or successive interval invariance were easily confused with equivalent sets.
	www.musiccog.ohio-state.edu /Gibson/millar.abstract.html (323 words)

	eLibrary Project : Inversion (music) (Site not responding. Last check: 2007-10-22)
		An inverted chord (music),chord is a chord which has a note other than its Root (chord),root note in the bass note.
		"Inversional equivalency" is the concept that interval (music),intervals, chord (music),chords, and other sets of pitches are the same when inverted.
		In musical set theory inversion may be usefully thought of as the compound operation ''transpositional inversion'', which is the same sense of inversion as in the Inversion (music)#Inverted melodies,Inverted melodies section above, with transposition carried out after inversion.
	elibraryproject.com /info/inversion_%28music%29.html (1263 words)

	Lanthionine antibiotic compositions and methods - Patent 5650320 (Site not responding. Last check: 2007-10-22)
		Initial attempts to identify the gene(s) responsible for mutacin expression employed transpositional mutagenesis using transposon Tn916 as the mutagen (Caufield, et at., 1990B).
		It is thus contemplated by the inventors that various changes may be made in the sequence of mutacin proteins or peptides (or underlying DNA) without appreciable loss of their biological utility or activity.
		It is understood that an amino acid can be substituted for another having a similar hydrophilicity value and still obtain a biologically equivalent, and in particular, an immunologically equivalent protein.
	www.freepatentsonline.com /5650320.html (18203 words)

	What is Equivalence relation? : Abaara fun facts and uncommon knowledge (Site not responding. Last check: 2007-10-22)
		a R b is never true) is not an equivalence relation, because although it is
		topological space and ~ is an equivalence relation on X, then we can turn the quotient set X/~ into a topological space in a natural manner.
		In music see octave equivalency, transpositional equivalency, inversional equivalency,
	www.abaara.com /pac/Equivalence_relation (761 words)

	transpositional - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "transpositional" is defined.
		Transpositional : Online Plain Text English Dictionary [home, info]
		Phrases that include transpositional: transpositional equivalency, transpositional puns
	www.onelook.com /?w=transpositional&ls=a (227 words)

	Musical set theory (Site not responding. Last check: 2007-10-22)
		Thus the trichord, in normal form, is in the same transpositional type as +1=, +2=,,,,,,,,, and.
		All of the above are in the transpositional type
		is equivalent under transposition and/or inversion with twenty four rather than twelve sets, the twelve above and their inversions.
	www.worldhistory.com /wiki/M/Musical-set-theory.htm (1441 words)

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