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ways) and thus contrasted with equivalence and similarity (equivalent in one or more ways but not all). For example, the C major scale, G major scale, and the major scale in all keys, are not identical but share transpositional equivalence in that the size of the intervals between scale steps is
171:. "It is not surprising that music theorists have different concepts of equivalence ..." "Indeed, an informal notion of equivalence has always been part of music theory and analysis. Pitch class set theory, however, has adhered to formal definitions of equivalence." Traditionally,
287:). The major third and the minor sixth are not identical but share inversional equivalence (an inverted M3 is a m6, an inverted m6 is a M3). A melody with the notes G A B C is not identical to a melody with the notes C B A G, but they share retrograde equivalence.
202:
A definition of equivalence between two twelve-tone series that
Schuijer describes as informal despite its air of mathematical precision, and that shows its writer considered equivalence and equality as synonymous:
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which are based on transpositional equivalency; similarity within difference; unity within variety/variety within unity).
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speaks of the 'equality,' not the 'equivalence,' of sets." However, equality may be considered
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Analyzing Atonal Music: Pitch-Class Set Theory and Its
Contexts
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A perfect octave between two C's; equivalent but not identical
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will be considered equivalent if and only if, for any p
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247:
The
Function of Set Structure in the Twelve-Tone System
237:. (= denotes numeral equality in the ordinary sense).
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275:identical while pitches are not (C major has F
97:are enharmonic equivalents, both the same as A
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229:of the second set, for all is and js , if i=i
116:Enharmonically equivalent key signatures of B
690:List of dodecaphonic and serial compositions
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254:Forte (1963, p. 76) similarly uses
128:major, each followed by its respective
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187:may or may not be considered (
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719:. You can help Knowledge by
614:All-interval twelve-tone row
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317:Similarity relation (music)
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185:transpositional equivalency
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67:are enharmonic equivalents
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16:Not to be confused with
264:mathematical set theory
619:All-trichord hexachord
567:Second Viennese School
376:Schuijer (2008), p.89.
367:Schuijer (2008), p.87.
358:Schuijer (2008), p.86.
297:Enharmonic equivalency
252:
215:of the first set and p
197:common practice period
195:are techniques of the
159:between properties of
42:Enharmonic equivalence
413:Twelve-tone technique
205:
562:Josef Matthias Hauer
527:Retrograde inversion
644:Formula composition
281:while G major has F
771:Music theory stubs
766:Musical set theory
312:Set theory (music)
307:Invariance (music)
207:Two sets , P and P
175:is assumed, while
173:octave equivalency
20:in mathematics or
728:
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649:Modernism (music)
577:Arnold Schoenberg
347:978-1-58046-270-9
337:Schuijer (2008).
145:equivalence class
18:Equivalence class
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582:Anton Webern
504:Permutations
424:Fundamentals
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654:Punctualism
639:Equivalence
193:modulations
177:inversional
157:equivalence
55:The notes F
760:Categories
669:Time point
664:Set theory
572:Alban Berg
517:Retrograde
456:Invariance
441:Derivation
323:References
256:equivalent
245:, (1992).
233:, then j=j
169:derivation
624:Atonality
544:composers
522:Inversion
512:Prime row
478:Aggregate
461:Partition
446:Hexachord
417:serialism
268:identical
260:identical
189:sequences
659:Semitone
473:Tone row
341:, p.85.
291:See also
284:♯
278:♮
258:to mean
240:—
149:equality
125:♭
119:♮
100:♮
64:♭
58:♯
542:Notable
345:
183:, and
147:is an
711:This
674:Trope
155:) or
132:chord
130:tonic
122:and C
89:and B
61:and G
717:stub
596:more
483:List
415:and
343:ISBN
191:and
161:sets
599:...
593:...
272:all
213:i,j
139:In
762::
330:^
224:,j
179:,
143:,
748:e
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405:e
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349:.
235:′
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220:i
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153:=
151:(
81:G
24:.
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