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- Interval_cycle abstract "In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the notes met on the way). In other words, interval cycles "unfold a single recurrent interval in a series that closes with a return to the initial pitch class". See: wikt:cycle.Interval cycles are notated by George Perle using the letter "C" (for cycle), with an interval class integer to distinguish the interval. Thus the diminished seventh chord would be C3 and the augmented triad would be C4. A superscript may be added to distinguish between transpositions, using 0–11 to indicate the lowest pitch class in the cycle. "These interval cycles play a fundamental role in the harmonic organization of post-diatonic music and can easily be identified by naming the cycle.".Here are interval cycles C1, C2, C3, C4 and C6:Interval cycles C1–C4 and C6Interval cycles assume the use of equal temperament and may not work in other systems such as just intonation. For example, if the C4 interval cycle used justly-tuned major thirds it would fall flat of an octave return by an interval known as the diesis. Put another way, a major third above G♯ is B♯, which is only enharmonically the same as C in systems such as equal temperament, in which the diesis has been tempered out.Interval cycles are symmetrical and thus non-diatonic. However, a seven-pitch segment of C7 will produce the diatonic major scale:7-note segment of C7This is known also known as a generated collection.A minimum of three pitches are needed to represent an interval cycle.Cyclic tonal progressions in the works of Romantic composers such as Gustav Mahler and Richard Wagner form a link with the cyclic pitch successions in the atonal music of Modernists such as Béla Bartók, Alexander Scriabin, Edgard Varèse, and the Second Viennese School (Arnold Schoenberg, Alban Berg, and Anton Webern). At the same time, these progressions signal the end of tonality.Interval cycles are also important in jazz, such as in Coltrane changes."Similarly," to any pair of transpositionally related sets being reducible to two transpositionally related representations of the chromatic scale, "the pitch-class relations between any pair of inversionally related sets is reducible to the pitch-class relations between two inversionally related representations of the semitonal scale." Thus an interval cycle or pair of cycles may be reducible to a representation of the chromatic scale.As such, interval cycles may be differentiated as ascending or descending, with, "the ascending form of the semitonal scale [called] a 'P cycle' and the descending form [called] an 'I cycle'," while, "inversionally related dyads [are called] 'P/I' dyads." P/I dyads will always share a sum of complementation. Cyclic sets are those, "sets whose alternate elements unfold complementary cycles of a single interval," that is an ascending and descending cycle:In 1920 Berg discovered/created a "master array" of all twelve interval cycles: Berg's Master Array of Interval CyclesCycles P 0 11 10 9 8 7 6 5 4 3 2 1 0 P I I 0 1 2 3 4 5 6 7 8 9 10 11 0 _______________________________________ 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 011 1 | 0 11 10 9 8 7 6 5 4 3 2 1 010 2 | 0 10 8 6 4 2 0 10 8 6 4 2 0 9 3 | 0 9 6 3 0 9 6 3 0 9 6 3 0 8 4 | 0 8 4 0 8 4 0 8 4 0 8 4 0 7 5 | 0 7 2 9 4 11 6 1 8 3 10 5 0 6 6 | 0 6 0 6 0 6 0 6 0 6 0 6 0 5 7 | 0 5 10 3 8 1 6 11 4 9 2 7 0 4 8 | 0 4 8 0 4 8 0 4 8 0 4 8 0 3 9 | 0 3 6 9 0 3 6 9 0 3 6 9 0 2 10 | 0 2 4 6 8 10 0 2 4 6 8 10 0 1 11 | 0 1 2 3 4 5 6 7 8 9 10 11 0 0 0 | 0 0 0 0 0 0 0 0 0 0 0 0 0".
- Interval_cycle thumbnail Interval_cycles_C1-C4_and_C6.PNG?width=300.
- Interval_cycle wikiPageExternalLink Cycles.pdf.
- Interval_cycle wikiPageID "692139".
- Interval_cycle wikiPageLength "5881".
- Interval_cycle wikiPageOutDegree "53".
- Interval_cycle wikiPageRevisionID "653664388".
- Interval_cycle wikiPageWikiLink Alban_Berg.
- Interval_cycle wikiPageWikiLink Alexander_Scriabin.
- Interval_cycle wikiPageWikiLink Anton_Webern.
- Interval_cycle wikiPageWikiLink Arnold_Schoenberg.
- Interval_cycle wikiPageWikiLink Array_(music).
- Interval_cycle wikiPageWikiLink Atonality.
- Interval_cycle wikiPageWikiLink Augmented_triad.
- Interval_cycle wikiPageWikiLink Béla_Bartók.
- Interval_cycle wikiPageWikiLink Category:Intervals_(music).
- Interval_cycle wikiPageWikiLink Category:Musical_symmetry.
- Interval_cycle wikiPageWikiLink Chord_progression.
- Interval_cycle wikiPageWikiLink Chromatic_scale.
- Interval_cycle wikiPageWikiLink Coltrane_changes.
- Interval_cycle wikiPageWikiLink Complement_(music).
- Interval_cycle wikiPageWikiLink Cyclic_set.
- Interval_cycle wikiPageWikiLink Diatonic.
- Interval_cycle wikiPageWikiLink Diatonic_and_chromatic.
- Interval_cycle wikiPageWikiLink Diatonic_major_scale.
- Interval_cycle wikiPageWikiLink Diatonic_scale.
- Interval_cycle wikiPageWikiLink Diesis.
- Interval_cycle wikiPageWikiLink Diminished_seventh_chord.
- Interval_cycle wikiPageWikiLink Edgard_Varèse.
- Interval_cycle wikiPageWikiLink Equal-interval_chord.
- Interval_cycle wikiPageWikiLink Equal_temperament.
- Interval_cycle wikiPageWikiLink Generated_collection.
- Interval_cycle wikiPageWikiLink George_Perle.
- Interval_cycle wikiPageWikiLink Gustav_Mahler.
- Interval_cycle wikiPageWikiLink Harmonic.
- Interval_cycle wikiPageWikiLink Identity_(music).
- Interval_cycle wikiPageWikiLink Interval_(music).
- Interval_cycle wikiPageWikiLink Interval_class.
- Interval_cycle wikiPageWikiLink Interval_vector.
- Interval_cycle wikiPageWikiLink Jazz.
- Interval_cycle wikiPageWikiLink Just_intonation.
- Interval_cycle wikiPageWikiLink Major_third.
- Interval_cycle wikiPageWikiLink Mixed-interval_chord.
- Interval_cycle wikiPageWikiLink Music.
- Interval_cycle wikiPageWikiLink Musical_note.
- Interval_cycle wikiPageWikiLink Pitch_(music).
- Interval_cycle wikiPageWikiLink Pitch_class.
- Interval_cycle wikiPageWikiLink Post-diatonic_music.
- Interval_cycle wikiPageWikiLink Richard_Wagner.
- Interval_cycle wikiPageWikiLink Second_Viennese_School.
- Interval_cycle wikiPageWikiLink Set_(music).
- Interval_cycle wikiPageWikiLink Simultaneity_(music).
- Interval_cycle wikiPageWikiLink Simultaneity_succession.
- Interval_cycle wikiPageWikiLink Sum_of_complementation.
- Interval_cycle wikiPageWikiLink Symmetrical.
- Interval_cycle wikiPageWikiLink Symmetry.
- Interval_cycle wikiPageWikiLink Tonality.
- Interval_cycle wikiPageWikiLink Tone_row.
- Interval_cycle wikiPageWikiLink Transposition_(music).
- Interval_cycle wikiPageWikiLink Wikt:cycle.
- Interval_cycle wikiPageWikiLink File:7-note_segment_of_C5.svg.
- Interval_cycle wikiPageWikiLink File:Bergs_Lyric_Suite_cyclic_set.png.
- Interval_cycle wikiPageWikiLink File:Interval_cycles_C1-C4_and_C6.PNG.
- Interval_cycle wikiPageWikiLink File:Twelve-tone_interval_cycles.png.
- Interval_cycle wikiPageWikiLinkText "C7".
- Interval_cycle wikiPageWikiLinkText "Interval Cycles".
- Interval_cycle wikiPageWikiLinkText "Interval cycle".
- Interval_cycle wikiPageWikiLinkText "chain".
- Interval_cycle wikiPageWikiLinkText "cycles".
- Interval_cycle wikiPageWikiLinkText "interval cycle".
- Interval_cycle wikiPageWikiLinkText "interval-7 cycle".
- Interval_cycle hasPhotoCollection Interval_cycle.
- Interval_cycle wikiPageUsesTemplate Template:Music.
- Interval_cycle wikiPageUsesTemplate Template:Reflist.
- Interval_cycle subject Category:Intervals_(music).
- Interval_cycle subject Category:Musical_symmetry.
- Interval_cycle hypernym Collection.
- Interval_cycle type Book.
- Interval_cycle comment "In music, an interval cycle is a collection of pitch classes created from a sequence of the same interval class. In other words a collection of pitches by starting with a certain note and going up by a certain interval until the original note is reached (e.g. starting from C, going up by 3 semitones repeatedly until eventually C is again reached - the cycle is the collection of all the notes met on the way).".
- Interval_cycle label "Interval cycle".
- Interval_cycle sameAs Isointervallakkord.
- Interval_cycle sameAs Intervallsyklus.
- Interval_cycle sameAs m.0336p7.
- Interval_cycle sameAs Q1674430.
- Interval_cycle sameAs Q1674430.
- Interval_cycle wasDerivedFrom Interval_cycle?oldid=653664388.
- Interval_cycle depiction Interval_cycles_C1-C4_and_C6.PNG.
- Interval_cycle isPrimaryTopicOf Interval_cycle.